KR20000028583A - 3-D mesh coding/decoding method and apparatus for error resilience and incremental rendering - Google Patents

Abstract

PURPOSE: A method for incrementally coding/decoding of a three-dimensional mesh information is provided to reduce the charge of a network and the transmitting time by re-transmitting the part generated an error or by restoring the rest restoring data being independently with the erred part through the error is generated during transmitting. CONSTITUTION: A coding method contains steps of: sectioning a polygonal three-dimensional mesh(MO) to more than one connected components; generating an information of apex graph and an information of triangle tree/triangle data for each connected component; and coding the information of apex graph and the information of triangle tree/triangle data composing the connected components for each connected component with a form of a basic mesh(MOBL) having a form to be independently decoded. The three-dimensional mesh data (100) is coded with a coder(101) equipped a coder of connectivity(102), a coder of geometry(103) and a coder of photometry(112) by dividing to the connectivity, the geometry and the photometry. The information compressed in the coder of connectivity(102), the coder of geometry(103) and the coder of photometry(112) is replaced to a bit stream(111) compressed with an entropy coder(104).

Description

Coding / Decoding Method of Progressive Three-Dimensional Mesh Information with Loss Elasticity {3-D mesh coding / decoding method and apparatus for error resilience and incremental rendering}

The present invention is an error resilience and progressive data recovery for three-dimensional mesh data used in the Moving Pictures Expert Group-4 (MPEG4) -Synthetic and Natural Hybrid Coding (SNHC) field and the Virtual Reality Modeling Language (VRML). The present invention relates to a method and apparatus for encoding and decoding to have an incremental build-up characteristic.

In the transmission of three-dimensional objects made of a three-dimensional mesh, not only efficient encoding of mesh data but also progressive restoration or lossy elastic restoration of transmitted data are recognized as important requirements. In progressive restoration, if data is lost due to an error on the line during transmission, partial restoration may be possible even with only data that has already been transmitted, thereby minimizing the amount of mesh data to be retransmitted. In loss-elastic restoration, irrespective of whether or not an error occurs in a specific unit data transmitted, the restoration can be independently performed for each transmitted unit data, thereby increasing data restoration efficiency and reducing user's waiting time. As a strong feature against such a line error, it is a technology that can be effectively used in future wireless communication or low data rate communication. The present invention relates to a method for encoding / decoding three-dimensional mesh data consisting of connectivity, geometry, and image information to impart progressive encoding of three-dimensional mesh data and elasticity to data loss. will be.

Conventional encoding of three-dimensional mesh data is sequentially encoded on all of the mesh data, and thus, it is impossible to restore only some data before receiving the entire bit stream when transmitting the encoded data. In addition, there was an inefficiency in that the entire data must be retransmitted even if a small part of data is lost due to an error in the line generated during transmission. An example is the encoding scheme proposed by IBM, which is currently employed in MPEG-4 SNHC three-dimensional mesh coding (ISO / IEC JTC1 / SC29 / WG11 MPEG98 / W2301, "MPEG-4". SNHC Verification Model 9.0).

MPEG-SNHC designs a mesh coding / decoding method based on VRML. In VRML, meshes are described in a node type called IndexedFaceSet. One of the main techniques for coding mesh data is IBM's Topological Surgery technique. This technique assumes a given mesh is topologically identical to a sphere and then forms a binary spanning triangle spanning graph by cutting the mesh along a given cutting-edge. In this case, the cutting edge defined for cutting the mesh is a form of connecting vertices with vertices, and is given in a tree structure having a loop. This is called the vertex spanning graph. Therefore, if these two trees are encoded / decoded, the original mesh can be reproduced without loss.

In MPEG-SNHC, there may be multiple IndexedFaceSets in one VRML file, but basically, compression is performed based on only one IndexedFaceSet. However, one IndexedFaceSet can consist of several meshes. That is, if an edge connecting an arbitrary vertex and another arbitrary vertex is a set of polygons existing in a circle mesh as a connected component, an IndexedFaceSet allows a plurality of connected components to be configured.

In general, for fast processing of graphics, the modeling unit is a triangle, and it is preferable that the triangles are connected to each other in the form of strips or fans, rather than randomly constructed. In addition, the compression rate is better that the symbol is repeatedly represented. In terms of this compression and graphics processing, IBM makes the mesh as one long triangle strip as possible.

1A-1F illustrate a Topological Surgery technology process that cuts and produces a triangle spanning graph from IBM along a vertex spanning graph. 1A and 1D show a method of cutting a mesh along a cutting-edge defined by a thick line, FIG. 1B shows the overall shape of the cutting-edge, and FIG. 1E shows FIG. 1B 1c is a vertex spanning graph formed by connecting vertices that are cutting reference points, and FIG. 1f defines a strip that is a set of connected triangles by cutting a mesh along a vertex spanning graph. A triangular spanning graph is shown. In addition, if a triangular spanning graph is generated in the same manner as in FIGS. 1A to 1F, the length of a run in one direction of the two runs that branch in the triangular spanning graph is generally equal to a run in the other direction. It can be expressed considerably shorter than the length of run).

2A to 2D show examples of applying a topological surgery technique to an actual mesh. The vertex spanning graph, on the other hand, can be split from one branch to several branches. FIG. 3 shows that a vertex run returns to the position of one of the previous vertices, i.e. a vertex spanning with a loop. An example of the graph is shown. In addition, one mesh may be composed of a plurality of connected components, and in reality, a pair of vertex spanning graphs as shown in FIG. 1C and triangle spanning graphs as shown in FIG. 1F is generated per component constituting the mesh. In general, one IndexedFaceSet consists of several connected components, so coding one IndexedFaceSet yields a pair of triangle spanning and vertex spanning graphs.

The method of restoring the data encoded by the Topological Surgery technique consists of the following procedures.

1. Create a bounding loop using the vertex spanning graph.

2. The third vertex of a triangular triangle in the triangle spanning graph is called a Y-vertex. The triangle vertex is calculated using a bitstream of the triangle spanning graph and has a series of connected triangles and polygons in the form of strips. Construct a set. At this time, a triangle or a polygon is generated by using a triangle marching bit pattern of the triangle spanning graph.

3. Using mesh information of tree structure composed through the process of 1 and 2, the mesh is reconstructed according to the topological structure.

IBM uses lossless compression of vertex spanning graphs and triangle spanning graphs using entropy arithmetic coding. However, in order to recreate the original structure in IBM's method, all bitstreams have to enter the decoder, which has the following disadvantages.

1. In order to decode the mesh data, the entire bitstream must be received. However, if an error occurs during transmission, there is an inefficiency of retransmitting the entire bitstream.

2. If the amount of data is large compared to the bandwidth, the transmission time is long and the user's waiting time is long. In order to reduce the waiting time of the user, it is necessary to partially restore and render the mesh by using the previously transmitted data. However, in the conventional technology, the number of triangles that can be restored is smaller than the amount of transmitted bits in the structure of the bit stream.

In order to overcome the disadvantages of the existing technology, the following points should be solved.

1. The mesh data should be divided into efficient unit sizes in consideration of the bandwidth of the transmission path and the characteristics of the decoder, and the elasticity of loss should be provided so that the decoder can reconstruct and render the bitstream of this unit size.

2. It should provide a progressive encoding / decoding method to allow partial restoration and rendering even with some data currently received.

In order to provide the above two functions on the basic structure of the existing IBM method, the performance depends on the method of processing the bounding loop and Y-vertex as shown in FIG. In FIG. 1F, the points corresponding to the numbers 10, 14 and 18 are Y-vertexes. This Y-vertex can be calculated only if at least one run of the two triangular runs has been processed. In other words, triangles located within a triangle run can use the marching bit pattern and the bounding loop to determine the indices of the triangle's three vertices, the Y-vertexes of the third vertex of the branching triangle, which are all of the at least one of the other two runs that follow. Determination can only be made when the bitstream is input. Therefore, the triangle after the branch triangle cannot be restored and rendered until all subsequent bitstreams are input. The existing IBM method assumes that all bitstreams are received by the decoder, so this problem is not considered. However, in order to encode / decode them in a progressive manner, such a problem must be solved.

The present invention was devised to solve the above problems, and even if an error occurs during transmission, the network burden and transmission time can be reduced by retransmitting only the error part or restoring the restoring data independently of the error part. It is possible to minimize the increase in the amount of bits generated by relying the error recovery function on the network layer, and to gradually recover the three-dimensional mesh using some connection information, geometry information, and characteristic information transmitted. It is an object of the present invention to provide a progressive encoding / decoding method of three-dimensional mesh information.

1A to 1F illustrate a method of generating a vertex spanning graph and a triangle spanning graph for an example of a triangle mesh.

2A to 2D show an example of application of the topological surge technique.

3 shows an example of a vertex spanning graph with a loop.

4 illustrates a method of constructing a bounding loop in a topological surgeon.

5A and 5B show examples of polygon meshes and their dual graphs, respectively.

6 conceptually illustrates a conventional three-dimensional mesh information encoding scheme.

7 conceptually illustrates hierarchical three-dimensional mesh information representation.

8A and 8B illustrate three-dimensional mesh information (MO) and basic mesh information (MOBL), respectively.

9 conceptually illustrates a relationship between a triangular tree / triangle data pair and a bounding loop index.

10A to 10C conceptually illustrate coding using directional information.

11A and 11B compare encoding sequences according to the presence or absence of directional information.

12A-12I illustrate a method of dividing a fixed structure.

13A and 13B conceptually illustrate data partitioning.

14A to 14D illustrate a variable structure dividing method.

15A to 15D illustrate the division by the variable structure division method.

16 illustrates data partitioning on the main stem.

17 illustrates a data partitioning method using tt_mean.

18A to 18C illustrate a method of configuring a virtual connection component.

19 illustrates triangular meshing of a polygonal mesh.

20A-20E illustrate the segmentation and associated syntax in a polygon mesh.

21 illustrates a method of indexing a bounding loop and a method of coding header information of a partition accordingly.

22 illustrates data partitioning including a bounding loop.

23A and 23B illustrate bounding loop index definition methods.

24A to 24E illustrate a method of encoding geometric information.

25A and 25B illustrate a grammar structure for geometric information, color information, normal information, and texture coordinate information.

26 conceptually illustrates a geometric coding method.

In order to achieve the above object, an embodiment of a method for encoding a polygonal three-dimensional mesh to recover gradually and lossy elasticity according to the present invention is to (a) fragment the polygonal three-dimensional mesh (MO) into one or more connected components step; (b) generating vertex graph information and triangle tree / triangle data information for each connection component; And (c) encoding the vertex graph information and the triangle tree / triangle data information constituting the connected component according to the format of the basic mesh (MOBL) having a format that can be independently decoded for each connected component. It is characterized by.

In order to achieve the above object, another embodiment of a method for encoding a polygonal three-dimensional mesh in accordance with the present invention to recover progressively and losslessly elasticity is to (a) fragment the polygonal three-dimensional mesh (MO) into one or more connected components step; (b) generating vertex graph information and triangle tree / triangle data information for each connection component; And (c) encoding the vertex graph information and the triangle tree / triangle data information constituting the connected component with respect to the format of the basic mesh (MOBL) having a fixed bitstream format so that each connected component can be independently decoded. Characterized in that it comprises a step.

In order to achieve the above object, another embodiment of a method for encoding a polygonal three-dimensional mesh so that the progressive angle three-dimensional mesh can be resiliently restored (a) a polygonal three-dimensional mesh (MO) to one or more connectivity Fragmenting into those; (b) generating vertex graph information and triangle tree / triangle data information for each connection component; And (c) for each connection component, a base mesh (MOBL) having a bitstream format that is variable according to the characteristics of the information so that vertex graph information and triangle tree / triangle data information constituting the connection component can be independently decoded. And encoding according to a format.

In order to achieve the above object, another embodiment of a method for encoding a polygonal three-dimensional mesh in accordance with the present invention to recover progressively and elastically elastic (a) fragment the polygonal three-dimensional mesh (MO) into one or more connected components Doing; (b) generating vertex graph information and triangle tree / triangle data information for each connection component; (c) encoding, for each connection component, the vertex graph information constituting the connection component; And (d) constructing and encoding virtual connection components by adding virtual bit pairs to data partitions obtained by dividing the triangular tree / triangle data information.

In order to achieve the above object, when encoding the triangular three-dimensional mesh in accordance with the present invention to recover gradually and lossy elasticity, an embodiment of a method for packetizing by dividing the triangular three-dimensional mesh into data partitions (a) Calculating a total bit generation amount in the triangle by sequentially visiting the triangles included in the triangle tree; (b) accumulating the total bit generation amount of the triangle calculated in step (a); And (c) if the value accumulated in step (b) is smaller than the packet size multiplied by the packet allowance, repeats step (a) or less for the next visited triangle included in the triangle tree, and if it is not small, And dividing the triangular tree / triangle data information up to the visited triangle into data partitions.

In order to achieve the above object, one embodiment of a method of lossless elastically decoding a polygonal three-dimensional mesh (a) dividing the input bitstream by a basic mesh (MOBL) unit; (b) determining a partition type of the basic mesh (MOBL); (c) if vertex graph information is included in the basic mesh (MOBL), generating a bounding loop table by decoding the vertex graph information; (d) generating tridimensional meshes by decoding the triangular tree / triangle data information when the basic mesh (MOBL) includes triangular tree / triangle data information; And (e) generating a three-dimensional mesh by repeating steps (a) to (d).

In order to achieve the above object, another embodiment of a method of lossless elastically decoding a polygonal three-dimensional mesh includes the steps of: (a) dividing the input bitstream by a basic mesh (MOBL); (b) determining a partition type of the basic mesh (MOBL); (c) if vertex graph information is included in the basic mesh (MOBL), generating a bounding loop table by decoding the vertex graph information; (d) generating triangular three-dimensional meshes by decoding the triangular tree / triangle data information in units of connected components if the triangular tree / triangle data information is included in the basic mesh (MOBL); And (e) repeating step (a) or less if the connected component in step (d) is a virtual connected component, otherwise completing the generation of a triangular three-dimensional mesh.

Polygonal Mesh-Polygonal Mesh does not affect the coordinates of the vertices in 3D space (geometry), the relationship between each face and the vertices that make up it (connection information), and the geometry of the mesh, but how it will look. Note is defined by color, normal, and texture coordinate information (image information).

Faces A face is a set of vertex indices, and a corner is a pair of (faces, vertices). When the vertices that make up a face are a set of different vertex indices, they are called "simple faces".

Edges-Pairs of vertex indices are called edges. If an edge in a polygon mesh appears on only one side, it is defined as a "boundary edge". If the same edge appears on several faces, this edge is defined as "singular". An edge that appears only on two adjacent faces is defined as "internal". "boundary edge" and "internal edge" are called "regular".

Dual graph A graph that defines a point inside each side of a mesh and connects the previously defined points through the inner edge between the faces is called a "dual graph." FIG. 5A illustrates a polygon mesh, and FIG. 5B illustrates a dual graph of the polygon mesh graph shown in FIG. 5A.

Connected Component The edges of a dual graph of a polygonal three-dimensional mesh can define the unique part of the faces of the polygonal three-dimensional mesh as one or more separate sets of faces. Here, if two faces share one edge, they belong to the same set. In this case, each set is defined as a connection component of the polygonal three-dimensional mesh.

VRML-Virtual Reality Modeling Language, a graphics standard format designed to describe and transfer virtual space over the Internet.

MPEG-Moving Picture Expert Group, an international standardization activity designed to standardize the compression format for the transmission of various media such as video.

Mesh-An object composed of multiple polygons.

Node-Vertex Spanning The smallest unit of description used in a vertex, or VRML, in a spanning graph.

Topological Surgery-A method for mesh coding by IBM that cuts a mesh along a given path to make the mesh into a triangular strip.

Vertex Spanning Graph-A path to cut a mesh in Topological Surgery.

Triangular Spanning Graph-A triangular strip that appears along a vertex spanning graph in Topological Surgery, a binary tree structure.

Vlast-The upper vertex run can branch to multiple branches, indicating whether it is the last branch of that branch of the current run. 1 if the end of the branch, otherwise 0.

Vleaf-Indicates whether the end of the current vrun ends with a leaf or branch node. If it ends with a leaf, it is assigned a value of 1, or 0.

Vrun-Checks if the vertex run has only one next node.

Vlength-The length of the vertex run.

Loopstart Some of the vertex runs occur when the leaf meets another vertex run, indicating the beginning of such a case.

Loopend-A vertex If the leaf of a run forms a loop, it represents that end point.

Loopmap-shows the correlation between loopstart and loopend. A set of indices that associate the edges from loopend to loopstart.

Trun-A set of contiguous triangles whose ends consist of leaf triangles or branching triangles.

Tleaf-Indicates whether the triangle run ends with a leaf triangle or a branching triangle. If the triangle is a leaf triangle, the value is 1;

Tmarching-Describes the forward aspect of a triangle. A strip has an edge of 1 on the right boundary and an edge on the left boundary of 0.

Polygonedge-indicates whether the current edge is the given model in the original mesh model, or whether the edge has been inserted to represent a polygon as a set of triangles. 1 if the edge is originally given, 0 otherwise.

Triangulated-Indicates the presence of polygons in the mesh. 0 if present, 1 otherwise.

Nvertices-indicates the number of vertices

Nloops-It shows the number of loops.

Nvedges-Shows the size of the vrun

Nvleaves-Shows the number of leaves in the vertex spanning graph.

Bitspernvedges-Number of bits used for nvedges.

Simple-If the vertex spanning graph has a loop, 0 is assigned, otherwise 1 is assigned.

Nloops-The number 1 in loopstart and loopend.

Ntriangles-Displays the number of triangles in the triangle spanning graph.

Ntbranches-triangles Displays the number of triangles that branch on the spanning graph.

Nmarchingtrans, nmarchingkeepleft-Statistical model for compression of tmarching.

Npolytrans, nkeeppoly-Statistical model for compressing polygon edges.

The compression method of three-dimensional mesh data used in the conventional MPEG is as shown in FIG.

Referring to FIG. 6, the three-dimensional mesh data 100 is divided into connection information, geometry information, and image information, and includes an encoder 101 having a connection information encoder 102, a geometry information encoder 103, and an image information encoder 112, respectively. Is encoded by In this case, the information 105 about the vertex structure is transferred from the connection information encoder 102 to the geometry information encoder 103. The information compressed by the connection information encoder 102, the geometry information encoder 103, and the image information encoder 112 is replaced by the bitstream 111 compressed by the entropy encoder 104.

The compressed bitstream 111 is input to the decoder 112 again. That is, the compressed bitstream 111 is divided into connection information, geometry information, and image information via an entropy decoder 106, and these pieces of information are respectively connected information decoder 107, geometry information decoder 108, and image information. Decoded by the decoder 113, respectively. As in the encoder 101, the information 109 for the vertex structure is transferred from the connection information decoder 107 to the geometry information decoder 108. The reconstructed three-dimensional mesh 110 may be configured by using the decoded connection information, the geometric information, and the image information.

According to Figure 6, the three-dimensional mesh is transmitted in the form of a compressed bitstream in a communication line or the like. However, since the compression method of the three-dimensional mesh data used in the conventional MPEG as shown in Figure 6 uses the entropy encoder 104, it can be said that it is vulnerable to transmission errors generated in the communication line. Therefore, in the present invention, a technique capable of gradually reconstructing the three-dimensional mesh using transmission information, previously transmitted connection information, location information, and other information is shown.

First, in order to process a progressive three-dimensional mesh, the present invention proposes a new mesh structure as shown in FIG. As shown in FIG. 7, the three-dimensional mesh (MO) may be configured as a mesh object layer (MOL) in which information of the mesh is classified into several levels. In this case, each MOL includes one or more basic meshes (Mesh Object Base Layer: MOBL). One MOBL includes connection information, geometry information, and image information necessary for its restoration. That is, MO is defined in units of three-dimensional mesh objects to be encoded, classified into various stages according to various image quality and functional aspects of these mesh information, and each classified stage is defined as a staged mesh (MOL). In addition, when a three-dimensional mesh object is composed of a plurality of independent mesh information (that is, connection components) having no interconnection by using a topology geometric method, the meshes are independent according to the size of data to be encoded or other characteristics. The basic mesh defines what is integrated or divided information.

8A and 8B show examples of MO and MOBL.

In order to more efficiently recover / render mesh information in such a new mesh structure, an index determination method of bounding loops considering Y-vertices is required. In order to restore one triangular mesh, as shown in FIG. 9, partitions of triangular tree / triangle data (tt / td pair) are given indices of bounding loops for right boundary and left boundary starting points. . In FIG. 9, m is a right starting index, n is a left starting index, and an arrow is a sequence of coded triangles, and the boundary located on the right side of the triangular strip with respect to the advancing direction. The right boundary, the left boundary of the left boundary, and the triangles painted in gray represent branching triangles. The following additional information is needed to determine the index of the bounding loop for each triangle of the tt / td pair.

● for triangles before branching triangles

In the case of triangles before the branching triangle as shown in Fig. 9, the indices of the bounding loop increase by 1 on the left boundary and by 1 on the right boundary, so that the three vertices of the triangle can be restored immediately when marching bits are decoded. Do.

● For divergent triangles

In FIG. 9, the triangular triangle consists of three vertices b [m-3], b [m-10], and b [n + 2]. However, if triangular information of the right branch in the branching triangle, that is, information indicating the number of triangles is not input, the index m-10, which is the index in the bounding loop of the Y-vertex, which is the third vertex of the branching triangle, is not known. Therefore, in order to determine the index of the Y-vertex, there must be information that can know the number of triangles of at least one branch. To know the total number of triangles in one branch, we need to know the information about the triangle run in the tt / td pair. Assuming that the number of triangles in the right branch is p in FIG. 9, the number of vertices used by Equation 1 can be determined. have.

For example, in FIG. 9, using the fact that the index of the bounding loop of the Y-vertex, the third vertex of the branching triangle, is the index of the vertex on the right boundary is m-3 and the number of triangles in the branch is six,

It can be determined that the index of the Y-vertex = (m-3)-(6 + 2-1) = m-3-7 = m-10.

For triangles in branches branching from a branching triangle

If the index of the Y-vertex is provided, the triangles can be restored and rendered in the same way as the triangles before the divergence triangle. However, if the Y-vertex of the divergence triangle is not determined, the index of the vertex of the triangle is obtained. Can't decide This is because the indices of the vertices located above the left boundary cannot be determined for the above reason unless the Y-vertex having the right branch as shown in FIG. 9 is solved.

As described above, a method for solving the Y-vertex problem occurring in the branch triangle to provide more efficient incremental reconstruction and rendering is presented in Section 1 below.

In addition, in the present invention, in order to divide the mesh data in consideration of the bandwidth of the transmission path or the characteristics of the decoder in order to provide resilience to the loss, it can be processed in two ways, fixed structure partitioning and variable structure partitioning, respectively. In Section 2, we present a method for restoring and rendering the generated data independently of each other. Here, the fixed structure partitioning is a method in which all the divided data has the same structure, and the variable structure partitioning is appropriately combined by information such as a vertex graph, a triangle tree, and triangle data in consideration of coding efficiency and packetization. It is a method configured to have a structure.

Section 1. Progressive Coding Method Considering Y-Vertex

In the conventional topological surgery method, the coding order is fixed only in a specific direction for the entire tt / td pair. In order to encode only the progressive rendering performance in this method, information such as index values of all Y-vertexes generated in the mesh data and the total number of Y-vertices may be included in the bitstream and transmitted to the decoder. However, this method is very undesirable in terms of coding efficiency. Therefore, there is a need for a more efficient encoding method for Y-vertexes that can satisfy these two aspects, namely progressive rendering effects and coding efficiency.

In the topological surgery method, there is a problem that the larger the difference in the length between the dependent trees and the larger the mesh data, the more the Y- vertex can be effectively determined and the progressive rendering effect due to the polygonal restoration cannot be expected. Therefore, if there is a difference in length between dependent trees, that is, two branched branches do not have the same size, it is more efficient to encode the shorter dependent tree first in terms of Y-vertex determination and rendering. Here, when the mesh data is obtained using the topological surgery technique illustrated in FIGS. 2A to 2D, the number of triangles of one branch is generally smaller than the number of triangles of the other branch. According to such a characteristic, the present invention provides a method for individually determining coding order based on branch triangles by providing orientation information according to the size of a dependent tree. That is, if the directional information consisting of 1 bit is 1, it is the same as the encoding sequence first determined, so that the right side is visited first, and if the value is 0, the left side is visited first and encoded. Therefore, it can be expected to improve the progressive decoding and rendering effect by passing the directional information to the decoder in this way. In addition, the directional information can classify an arbitrary mesh tree into a main tree and a subordinate tree, thereby providing a function of more efficiently partitioning data while maintaining connectivity information based on this characteristic.

10A to 10C show an example of an encoding method using directional information determined by the above method. In FIG. 10A, the light gray triangle is a branching triangle that has directional information while present in the main tree, the line inside the binary mesh tree is the main stem of the binary mesh tree having the dependent tree, and the line outside the binary mesh tree is The order of encoding in the dependent tree, that is, the direction in which the decoder maps the index of the bounding loop. Here, the direction of mapping the index of the bounding loop is determined in the same direction as the directional information (for example, clockwise if 0 and counterclockwise if 1), as defined in FIG. 10A, and is defined differently for each subtree. Can be. Alternatively, the directions for mapping the indices of the bounding loops may be defined in all clockwise or all counterclockwise directions regardless of the directional information. On the other hand, when the number of triangles in the dependent tree to be restored is t, the Y-vertex value has a difference in the following formula depending on the directional information.

● If the right branch is encoded first (orientation value is 1)

If the index in the bounding loop of the vertex on the right boundary of the branch triangle is p, then the Y-vertex is Position of Y-vertex = p-t-1

● If the left branch is encoded first (orientation value is 0)

If the index in the bounding loop of the vertex on the left boundary of the branch triangle is p, then the Y-vertex is Y-vertex position = p + t + 1

In FIG. 10B and FIG. 10C, tr denotes a triangular run, tl denotes tleaf, to denotes orientation information, and tm denotes marching, and FIG. 10B illustrates a directionality in the triangular tree among the components of the tt / td pair information. FIG. 10C shows a configuration diagram of a bitstream in which orientation information is disposed in triangular data among components of tt / td pair information. The difference between FIG. 10B and FIG. 10C is that FIG. 10B has the advantage of simplicity of implementation, and FIG. 10C shows that the delay time is short because the information of one triangle is restored, so that the delay time is short and that the memory usage in the decoder design is FIG. 10B. Compared to the lower cost is less expensive.

FIG. 11A illustrates a conventional topological surgery coding sequence, and FIG. 11B illustrates an example of applying a coding order determination method according to sizes of two branches in a diverging triangle, and illustrates the meaning of directional information. will be. The method of determining directional information in data segmentation is presented in Section 2.

Section 2. Progressive Coding Method Considering Elasticity for Loss

When data loss occurs due to an error in a bitstream generated by a data transmission path or an encoder, an effective method for dealing with this is needed from the decoder side. Accordingly, the data to be encoded is divided into meaningful units (that is, partitions or basic meshes), and the data is divided, and the data is transmitted in a processing unit having a predetermined size (hereinafter, weakly referred to as a packet). In other words, a packet is defined to have a certain length as a bundle of bits arranged in a particular format. If a long length of data is to be transmitted on a transmission path, congestion may occur in a transmission path in which a plurality of users exist, so that a limited transmission path may be shared by a plurality of users by binding a transmission unit to a certain length. On the other hand, if a packet bundles a bit string obtained as a result of encoding to be transmitted at a predetermined length, a partition refers to a partition of original information (mesh) to be encoded in an appropriate unit. In the partitioning process, when recovering at the receiving side, consider to effectively cope with errors on the transmission path. In other words, if the entire mesh is divided into meaningful parts, even if the coded bitstream cannot be completely restored at the receiver, including errors on the transmission path, only the partition containing the error will be damaged and other errors will not be included. Partitions can be restored completely. Here, the meaningful parts mean that each part has a meaning that is related to each other when the animal picture is divided into, for example, an arm, a leg, a torso, and the like. In the partitioning process, the size is not fixed as in the packet. However, the present invention provides various partitioning methods so that the receiver can effectively restore data even when an error is included in the received data.

By dividing the data to be encoded into partitions as described above, the following effects can be expected.

Reduce network load and decryption latency by retransmitting only lost data units.

Ensures independence between the divided data units,

☞ It is possible to restore and render the mesh with only the remaining data without loss of data without retransmitting the lost data, eliminating the decoding delay time caused by the loss.

☞ Receives and renders the currently received data sequentially even when the entire mesh data is not received.

Compared to the coding method that does not guarantee mutual independence between data units, the mesh reconstruction capability is better in case of no retransmission of lost data. In addition, even in the case of retransmission, transmission efficiency (decoding wait time) is improved.

2.1 Partitioning of Fixed Structures

12A to 12I show a data partitioning scheme with a fixed structure. sc is a start code indicating a start position of a partition in a packetized mesh bitstream, and id is an identifier of a partition. In one embodiment of the encoding grammar according to the present invention, 3D_MOBL_start_code and mobl_id are represented. vg_id is an indicator used to designate the corresponding vertex graph when restoring each tt / td pair partition when grouping vertex graph information from mesh data composed of several connection components. In one embodiment of the encoding grammar according to the present invention, it is represented by codap_vg_id. vi is a indicator indicating a bounding index (bounding_index) value of the root triangle of a partition partitioned as a visiting index, and has left_index and right_index information as shown in FIG. 4, which is one of encoding syntaxes according to the present invention. In the embodiment, these are represented by codap_left_idx and codap_right_idx, respectively. bp is an indicator indicating boundary_prediction and determines a method of encoding geometry, color, normal, and texture coordination information. In other words, if bp is 1, it means a method of allowing overlapping with respect to the previously encoded vertex, and if it is 0, it means a method of encoding a vertex without overlapping. bp is represented by codap_bdry_pred in one embodiment of the encoding grammar according to the present invention. lbl is an indicator that is generated to allow the decoder to calculate the Y-vertex index of the branch triangle with the current partition information only when the current partition ends in the branch triangle. Indicates the size. lbl is represented as codap_branch_len in one embodiment of the encoding grammar according to the present invention. vg denotes a vertex graph, tt denotes a triangle tree in triangle tree / triangle data, and td denotes triangle data in triangle tree / triangle data. In addition, lvg is a 1-bit indicator defined to indicate whether there is a connection component to be restored in one partition, and is defined as 0 if there is a vg to be restored next, or 1 if not. ltg is a 1-bit indicator indicating whether there is a connection component to be restored or whether there is a dependent tree in a partition. If ltg is 0, it indicates that there is a case. The fixed structure dividing method is a method of uniformly encoding the entire mesh data in any one form according to an application field among the bitstream forms defined in FIGS. 12A to 12I.

In terms of structure, FIG. 12A illustrates a method of processing all mesh data according to an encoding order to configure one partition. FIG. 12B illustrates a method of configuring the entire mesh data in one partition as shown in FIG. 12A and separating the vertex graph data and the tt / td pair. 12C illustrates a method of configuring a partition with a minimum unit of one connection component. FIG. 12D illustrates a method of collecting a plurality of vertex graphs constituting mesh data into one partition, and collecting a corresponding tt / td pair into one partition. FIG. 12E illustrates a method of collecting a plurality of vertex graphs into one partition and splitting the tt / td pair into a plurality of partitions in consideration of the size of the partition. FIG. 12F illustrates a method of configuring a vertex graph and a tt / td pair separately as shown in FIG. 12D, and configuring them as separate partitions for each connection component unit. FIG. 12G illustrates a method of constructing a plurality of vertex graphs constituting a mesh object into separate partitions, and then dividing all corresponding tt / td pairs into a plurality of partitions in consideration of the size of the partition. . FIG. 12H illustrates a method of encoding all components by first partitioning a vertex graph constituting each connection component and partitioning a corresponding tt / td pair. 12I illustrates a method of first partitioning vertex graph data into one partition in each connection component and partitioning the corresponding tt / td pair by considering the partition size.

In terms of functionality, each method of FIGS. 12A-12I is discussed. First, the method illustrated in FIGS. 12A and 12B is used when loss elasticity is not provided or is not limited to transmission line or decoder performance. FIG. 12A is more effective in processing cost and rendering efficiency than FIG. 12B. Retransmission costs incurred in the event of data loss are higher. 12C, 12D, 12F, and 12H are independent of each partition, but have a disadvantage in that they are difficult to fit in packets of a specific size unit. That is, in the case of transmitting a packet having a specific size, when the partition size is smaller than the packet size, dummy information corresponding to the difference amount should be added. In the opposite case, the packetization cannot be performed, and a separate processing method and additional information on this should be provided by the decoder. Therefore, there is a problem in that the overall coding efficiency is lowered, and the complexity and cost increase. 12E, 12G, and 12I, the vertex graph data providing the connectivity information of the mesh is processed like the above method, but tt / td provides a configuration of triangles (polygons) in the mesh. Pairs can be divided and processed according to partition size while ensuring mutual independence. The partitions of the tt / td pair are appended with vg_id, vi and bp information. Here, vg_id is a designator that designates a vertex graph corresponding to the tt / td pair to be restored, and is used when the vertex graph is combined and processed as shown in FIGS. 12D to 12G. vi is a specifier that specifies the left_index and right_index values at the start triangle of each partition when the tt / td pair is divided into multiple partitions, so that the current packet is independent of the previous packet even if the previous partition cannot be restored due to loss. This information is provided to enable restoration. In addition, bp is a 1-bit indicator that defines a method of encoding position, color, normal, and texture coordinate information about vertices, and is defined for each partition of the tt / td pair. Also, in the method shown in Figs. 12E, 12G and 12I, lbl is configured to be selectively used only when the partition is finished in the branch triangle. As shown in FIGS. 12A to 12D, 12F, and 12H, when a tt / td pair can be encoded in a connection component unit, bp is set to 1 and restored in such a manner as to allow duplication. 12E, 12G, and 12I, when the tt / td pair constituting any one connection component is divided into several pieces, a bp indicator is defined and restored for each partition.

ltg is encoded in an optional manner. That is, if the information of the current partition is the end of any branch of the tt / td pair, it is encoded as 1, otherwise it is encoded as 0. This is determined by using a visiting index and the following formula is used.

right_index-left_index-1 = number of triangles in current partition

If the above Equation 2 is satisfied, the end of the branch means ltg is encoded as 1.

The method of data partitioning to provide such a structure is as follows.

1. Segmentation of data by connected component units

As in the case of Figures 12C and 12H, this method is simple to implement and efficient unless there is a difference in size between the connecting components. However, if the data size of the connected component is not uniform and the difference is large, the size of the data partition is not constant and additional bits are generated for this, thereby lowering the coding efficiency. On the other hand, when the data size of the connection component itself is large, not only the coding efficiency is lowered, but also the packet size can not be packetized to a predetermined size. Therefore, this method can be limitedly applied only when the performance of the transmission line or the decoder is not limited. 12A, 12B, 12D, and 12F also have the above problems.

2. A method of segmenting data by combining smaller connected components

In the mesh including a large number of small connection components, applying the first method is not an appropriate method in terms of coding efficiency. Therefore, as in the case of FIGS. 12A and 12B, it is preferable to collect small connection components until they satisfy a partition size of a predetermined size and process them in one partition unit. In this method, an identifier (vg_id) for defining a tt / td pair corresponding to a specific vertex graph must be provided in the header information of the partition.

3. Data segmentation of large connected components

In case of using the above method 1, it is only possible to encode a connection component larger than the packet size in a limited environment. Accordingly, the present invention proposes a more general encoding method capable of dividing a single connection component having a large size to satisfy both the flexibility of the partition size and the mutual independence of partitions. 12E, 12G and 12I show a method of encoding and dividing only a tt / td pair into a plurality of partitions again in an arbitrarily large connection component. 12E shows a modified form in FIG. 12D, FIG. 12G in FIG. 12F, and FIG. 12I in FIG. 12H. On the other hand, Figure 12e and 12g has the disadvantage that the cost is increased because the decoder must store all the information about the entire vertex graph, as in Figures 12d and 12f, Figure 12i is for the connection size of the small size in terms of coding efficiency It has the disadvantage of being burdensome.

In addition, in this method, a specifier (vg_id) for defining a tt / td pair corresponding to a specific vertex graph, a specifier (vi) for specifying a boundary loop index of the start triangle of a partition, and geometry, color, normal, and texture coordinate information. There is a burden that indicator (bp) information indicating how to encode the data is defined in addition to the partition header information. However, this method is a more general partitioning method that can easily protect mesh data from loss independently from each other, and also reduce coding loss due to partitioning.

In addition, FIG. 13A illustrates an example of the structure of the bitstream when the tt / td pair is divided, and the vertical dotted line indicates the divided position, and shows a correlation between the triangle tree and the triangle data. 13B illustrates an example of performing data partitioning by applying the above methods. In FIG. 13B, the id information is omitted for convenience, but is defined after the start code. Hereinafter, vg is a vertex graph, tt / td is triangle tree / triangle data, and cc is abbreviated as a connected component. In FIG. 13B, n is the number of connected components and n` is the number of components when the connected components are reconfigured according to size. Reconstruction method

1.Resynthesis of Linked Components (Step 201)

Smaller connected components are combined to fall within the size range of the data partition. In FIG. 13B, CC ₁ and CC ₂ are combined to form CC ′ ₁ . On the other hand, those larger in size compared to the data partition size are divided internally into smaller virtual components. In the example of FIG. 13B, CC ₃ is divided into several CC ′ ₂ ,..., CC ′ _k .

2. Creating vg and tt / td Pairs (Step 202)

Create a pair of vg and tt / td for each reconstituted component.

3. Integration of vg and tt / td pairs (step 203)

Integrate the vg and tt / td pairs generated in step 202 separately.

4. Partitioning of vg Information (Step 204)

The vg information integrated in step 203 is divided into data of appropriate size.

5. Partitioning of tt / td Pair Information (Step 205)

The tt / td pair information generated in step 203 is divided into meaningful units of appropriate size.

Since the fixed structure partitioning method requires all of the decoders capable of supporting the structure for each of the schemes listed in FIGS. 12A to 12I, it is unreasonable in terms of complexity and cost in terms of actual system configuration. Accordingly, the present invention proposes a variable structure partitioning method so that only one decoder can adaptively decode all of the above-listed bitstreams.

2.2 Variable Structure Partitioning Method

In the variable structure partitioning method, pt (partition type) information that is not provided by the fixed structure partitioning method, that is, information designating the partitioned type of the current partition is added, and thus, a total of four structures are illustrated in FIGS. 14A to 14D. Classified as Pt defined in the present invention is defined according to sc value, and the relationship between sc and pt value is shown in Table 1.

Bit value Contents 0000 0000 0011 0001 It contains one or several vg's, and this vg data is used in one or several other data partitions. 0000 0000 0011 0011 Only the tt / td information is included. When restoring the information, the header includes the vg_id corresponding to the tt / td pair to the arbitrary vg, vi (visiting index) and bp (boundary prediction), which are starting points of the triangle stream. 0000 0000 0011 0100 vg, tt, and td form one data partition, and vg is used by one or more data partitions.

Variable structure partitioning is a method to consider cost and complexity, which considers the following.

Start code cannot be applied selectively. That is, the decoder decodes without knowing in which mode the type of the current bitstream is encoded. Accordingly, when a start code is selectively provided by an encoder according to an encoding mode, only a limited bitstream may be restored, and in some cases, various types of decoders should be provided. This results in increased cost and complexity. As a result, the variable grammar system should be excluded in order to decode regardless of the encoding condition of the encoder.

▶ When encoding only one specific type, unnecessary information is provided according to the characteristics of the mesh or the characteristics of the decoder, thereby lowering the encoding efficiency.

14A to 14D illustrate four grammar modules capable of supporting a variable structure. FIG. 14C has a grammar that adaptively provides vg_id and ltg, as defined in FIGS. 12A-12I. That is, when only one vg is configured in the grammar of FIG. 14B, since the correspondence relationship between the vg and the tt / td pair is known during the restoration, vg_id does not need to be provided. ltg is provided only to indicate when the split tt / td pair corresponds to the end of the branch of the entire tt / td pair. The discriminant for this is shown in Equation 2. FIG. 14A shows a structure in which pt = 0 and constituting a partition with any number of connected components. 14B shows a structure in which pt = 1 and a partition is constituted by any number of vgs only. Fig. 14C shows a structure in which only tt / td pairs corresponding to one connection component are partitioned, with pt = 2. Fig. 14D shows a structure in which pt = 3 and partitions of vg and tt / td pairs corresponding to one connection component. Therefore, such a combination of grammar structures may support all types of grammar structures except for FIG. 12B. That is, in the case of FIG. 12A, pt = 0 may be implemented, and in FIG. 12I, pt = 1 and pt = 2 may be implemented. Therefore, in the present invention, in consideration of encoding efficiency, the connection components that are relatively smaller than the packet size are encoded by collecting several connection components in one partition by using pt = 0, and in the case of the connection components that are relatively large compared to the packet size. For coding, use pt = 1 and pt = 2 or pt = 2 and pt = 3. In addition, when considering a transmission path or a decoder capability aspect, various types of grammars may be provided in various combinations.

15A to 15D show an example of applying a structure division method. In FIG. 15A, since cc1 to cc3 are small meshes, pt = 0 or pt = 3 is defined and processed for each connection component. Since cc4 is a large mesh, we divide the tt / td pair into multiples and treat them as a combination of pt = 3 and pt = 2. In addition, in case of cc4, as shown in FIG. 15B, the combination of pt = 1 and pt = 2 may also be processed. In addition, as shown in FIG. 15C, in order to improve coding efficiency, the mesh data may be transformed into another combination structure. FIG. 15C illustrates a case where the mesh data of cc1 to cc3 is defined as pt = 0. Also, the mesh data of cc1 to cc3 is defined as a combination of FIG. 15C and FIG. 15A or a combination of FIG. 15C and FIG. 15B to represent the entire mesh data. It is possible. However, in order to provide the structure of FIG. 15C, a condition for determining the last connection component is required. In the conventional method, a 1-bit indicator called last_cc is used to determine the last connected component, where 1 means the last connected component. Therefore, in the present invention, it is possible to determine whether there is a connection component to be restored using the ltg indicator having a function similar to last_cc and the pt information in sc as follows.

if (ltg == 1) {

if (pt == 0) {

if (next-2_bytes () == sc) The currently restored cc is the last cc in the partition;

else cc currently restored is the last partition to be restored;

} else The currently restored cc is the last cc in the partition;

} else Currently restored cc is not the last cc in the partition;

next_2_bytes () is a function that reads only 2 bytes of the bitstream in advance from the decoder. 15D shows an embodiment using pt = 0,1,2. As can be seen from the above example, the variable structure partitioning method has an excellent adaptability to an encoding environment and is an improved method than the fixed structure partitioning method in terms of coding efficiency and cost.

2.3 Data partitioning method of tt / td pair

For the splitting of the tt / td pair, the present invention is based on splitting data at a position (= main stem) after all triangular information of a diverging triangle first appearing at the end of the previous partition. 16 shows this example. The splitting of tt / td pairs in the main stem is because, as discussed in Section 1, it is impossible to restore and render the triangle after the corresponding branch triangle unless the index of the Y-vertex is determined. However, this method may be inefficient depending on the traversing order originally established and the actual tt / td pair type. That is, if the left (right) branch coding is the priority, if the left branch of the branching branch of the tt / td pair is very large, it will still exceed the packet size, and determining the index of the Y-vertex after the branch triangle There is a burden to wait until a lot of information is processed, that is, information about the number of triangles on the other side.

Therefore, the present invention proposes three methods for a method of efficiently partitioning mesh data. In the present invention, one or more partitions may be included in the packet. However, this section describes the assumption that only one partition is included in one packet.

The first method is to divide and set a packet allowance (= t_rate) for a packet size (= target) of reference numeral 300 as shown in FIG. 17. The average bit generation amount of tt to be encoded in units of connection components (= tt_mean is obtained and actual data partitioning is performed within a range that satisfies a preset packet allowance (= t_rate). In FIG. 17, tt_mean of reference numeral 300 is an average bit amount of tt calculated for each connection component, td_bits _i of reference number 320 is a bit generation amount of remaining information except for vg and tt information when the i th triangle is encoded, and Cur_bits of 320 is the sum of the bit generation amounts (tt_mean + td_bits _i ) generated from the first triangle to the i-th triangle of the packet. Therefore, if the total bit generation amount (cur_bits) up to the i th satisfies the allowed packet size (= t_rate * target) (330), data is coded by performing partition (340), otherwise The encoding of the triangle is performed (350). By repeating this process until all the meshes are encoded, partitioning or packetization is performed.

The point to consider here is how to determine the division in the branch triangle on the main stem. That is, under the assumption that the basic partition position is defined only on the main stem to take into account the Y-vertex problem, the subtree may be encoded by including a dependent tree in an arbitrary direction to be encoded after the branch triangle, that is, a direction determined according to the directional information. Should be decided. In order to determine this, the present invention uses a method of encoding the dependent tree to be encoded in advance. In other words, when encoding is performed in advance, if the packet size is satisfied in the dependent tree, it violates the basic condition of splitting in the main stem, so that the split is performed on the previous branch triangle as shown in FIG. If the packet size is smaller than this packet size, the dependent tree is included in the packet in the form as shown in FIG.

The second method does not reach the packet allowance, but if the next triangle to be encoded is a branched triangle, and the sum of the amount of bits expected to occur in the branching dependent tree and the amount of bits generated in the current partition exceeds the packet size, splitting is performed. Do it. This will be described in detail as follows.

1. Stores the number of encoded bits (cur_bit) in the first partition of each connection component.

2. If the target bit has not been reached, but the next triangle is a branching triangle, the size (nst) of the dependent tree in the next triangle is obtained.

3. Find the number of vertices (cur_ng) of triangles encoded from the current partition to the present.

4. If cur_ng + nst + 2> ng, split. Perform the split as follows.

(1) If the amount of bit prediction to occur in the dependent tree is larger than the packet size, the partition is divided up to the next branch triangle. That is, if nst + 2> ng, the partition is divided to include the next branch triangle as shown in FIG.

(2) Otherwise, divide at the current triangle.

The third method does not set the packet allowance, always encodes one packet unit of the next mesh to be encoded in advance, calculates the total number of triangles when the packet size is satisfied, and then uses the number information of the triangles to determine the actual packet. A method of constructing a bitstream of a unit. In this method, the same method of determining whether to include dependent trees considered in the above method is applied.

On the other hand, there are two additional considerations when partitioning mesh data in the above way. The first is the problem of delay time during decoding based on the Y-vertex calculation, and the second is the problem of independence between the divided data. In the present invention, the first problem is minimized by the method of setting the virtual connection components as in Section 2.4. The second problem is the orientation information, the bounding loop index (= vi) information, and the triangle (= solve by defining polygon edge information in packet unit.

2.4 Y-Vertex Processing Method Using Virtual Connected Components

Two methods are used to handle the Y-vertex while maintaining mutual independence between the partitioned data of the tt / td pair. The simplest method is to send the split data length and Y-vertex information to the decoder. The other method is to define the divided data as a virtual connection component according to the characteristics of the tt / td pair. According to the first method, since the total mesh length and the length of the divided mesh can be known when decoding, the mesh structure to be reconstructed can be estimated, and the Y-vertex information can also be known, so that progressive rendering can be performed. However, there is a disadvantage that the coding efficiency is lowered due to these additional information.

The second method is to define a virtual connected component. The tt / td pair consisting of binary trees defines the connected component by the number of branches and leaves as shown in Equation 3. Defining a virtual bit to satisfy 3 allows a virtual connected component to be configured. At this time, the starting position of the partition is always configured to occur only in the run of the main tree of the binary tree. This is a condition for facilitating the processing of the Y-vertex. For example, when the partition is separated from the main stem, the problem of the Y-vertexes listed above is provided, and additional information for the Y-vertex processing is provided. You will either have to restore or render on a partition-by-partition basis.

There are two ways to define virtual bits.

When a partition ends in a run or leaf

In order to satisfy Equation 3, one virtual bit pair of (1,1) is added to (trun, tleaf).

2. If the partition ends at a branch

In order to satisfy Equation 3, two virtual bit pairs of (1, 1) are added to (trun, tleaf).

In addition, when the branch ends on a branch and processes per vertex geometry, color, normal, and texture coord information, the branch triangle is the last triangle. This information is not encoded. This is because the branch triangle can be restored by the Y-vertex index determined by the index information of the triangle immediately before the branch of the current partition and the root triangle of the partition to be encoded next. However, if a loss occurs in a partition to be encoded next, a branch triangle appearing at the end of the current partition cannot be restored. The above problem can be solved by including the total size information lbl of any one dependent tree derived from both branches of the triangular triangle in the tt / td pair information and transmitting it to the decoder. This is because the lbl value can be used to compute the Y-vertex index of the triangular triangle without the partition information to be restored next. On the other hand, when encoding per face or per corner, encoding is performed in all cases because it is not dependent on the Y-vertex index. 18A to 18C are conceptual views constituting a virtual connection component. FIG. 18A shows the virtual bit when the partition ends in a leaf, FIG. 18B shows the partition ending in the run, and FIG. 18C shows the virtual bit when the partition ends in a branch, and the virtual bit indicates It is defined to form a virtual triangle.

On the other hand, if the division in the form of the leaf triangle (leaf triangle) immediately after the branching triangle in Figure 18a, the same tree structure as in the case of Figure 18c. In this case, since the decoders cannot distinguish the shapes of FIGS. 18A and 18C, the encoder does not divide at the leaf triangle immediately after the branching triangle except for the end of the tree branch. It should not be. In this way, the decoding unit can decode all the triangles without any other information for distinguishing the shapes of Figs. 18A and 18C.

Therefore, there is a problem that packetization cannot be made when the dependent tree is large under the basic condition of splitting only on the main stem. When the virtual connection component is configured as in the above method, the dependent tree is divided into several independent virtual connection components. It can be configured as, the additional advantage arises that packetization is possible in all cases.

In addition, when a virtual connection component is configured and encoded in this manner, a method of determining a virtual bit in a decoder is as follows.

1. Determine whether virtual bits exist in runs and leaves

If the expression 4 is satisfied, the virtual bit exists, otherwise it does not exist. If the last to third triangles among the encoded triangles as shown in FIGS. 18A and 18B are not branch triangles and satisfy Equation 4, it is determined that only a pair of (1,1) virtual information is generated in (trun, tleaf). The td data is not decoded for the triangle.

2. Determining the presence of virtual bits in branches

When splitting is performed in the branching triangle as shown in FIG. 18C, two virtual leaf triangles are added. Therefore, if the third triangle at the end of the data is a branch triangle and satisfies Equation 4, since there are two pairs of virtual bit information (trun, tleaf) in (1,1), the last two leaf triangles (leaf) triangle), td data is not decoded.

2.5 Partitioning Data in Polygon Meshes

In topological surgery, polygon information is first reconstructed into triangles in order to code mesh information composed of polygons. 19 shows this example, where the solid line represents the actual edge of the circular polygonal mesh, and the dotted line represents the virtual edge added to divide the polygon into triangles. A virtual edge is added to divide the polygon into triangles. In order to restore the original polygon from the decoder, information for removing the virtual edge must be transmitted. This information is called polygon edge information. When one piece of polygon edge information is sent per triangle, 1 indicates a real edge and 0 indicates a virtual edge.

In the conventional method, polygon edge information is generated by the number of all triangles except the first triangle after meshing polygons included in the mesh. Here, since the encoder sets the first triangle to the actual edge, the decoder assumes that the polygon edge information of the first triangle is 1 and restores it.

However, when data must be partitioned for partitioning inside a polygon, not a triangle, as shown in FIG. 20B, there is a problem in that the mesh information cannot be restored under the existing method. In addition, this restricts the segmentation of the mesh data to satisfy the packet size, which also acts as a factor of lowering the coding efficiency.

Therefore, when a partition is started on a virtual edge, polygon edge information defined in the partition must be defined for the first triangle of the partition to eliminate the above limitations and disadvantages. In FIG. 20, tt denotes triangular run information, tm denotes marching information, pe denotes polygon edge information, subscript denotes tm and pe in the same order corresponding to tt, and n denotes the number of triangles. Means. FIG. 20D is a grammar for dividing a polygonal mesh only on an actual edge, and FIG. 20C corresponds, and FIG. 20E is a grammar for dividing a polygonal mesh on a virtual edge, and corresponds to the case of FIG. 20B.

Accordingly, the present invention provides a grammar that is based on partitioning at an actual edge, but may be restored even when partitioned inside a polygon in some cases. Accordingly, processing of polygon edges in each partition can be defined by using partition type information pt or triangulated and polygon_edge information as follows.

1. Processing method according to partitioned type information pt of partition

(1) In the case of the 0th partition type (pt = 0), the first polygon edge value is not coded.

(2) The first polygon edge value is coded only when the second partition type (pt = 2) and one or more polygons exist in the mesh in one partition (triangulated = 0).

2. Processing method based on triangulated and polygon_edge information

(1) When partitioning on an actual edge, the first polygon edge value in the partition is not coded.

(2) If partitioning is allowed on the virtual edge, code the first polygon edge value in the partition.

Here, the determination of the actual edge and the virtual edge in any polygon is defined according to the following conditional expression.

if (triangulated == 1) real edge

else if (polygon_edge == 0) virtual edge

else real edge

Therefore, in the decoder, when triangulated is 0, the first polygon edge value (polygon_edge) is unconditionally restored, and if the value is 0, the first polygon edge value is designated, and the 1 is designated as the second polygon edge value.

The triangulated information indicates 0 if one or more polygons exist in a mesh in a partition, and 1 otherwise, so that 1-bit information is configured in units of partitions.

2.6 Data Segmentation Method According to Orientation

The necessity and definition method of directional information defined in Section 1 apply equally to data segmentation. However, the additional consideration here is that in case of using virtual connected component as in Section 2.4, since the partition can be split in the dependent tree, the mesh of the current partition to be restored is main when the previous partition is not restored. You can't tell if it's connected to a branch or to a sub branch. Accordingly, a calculation error of the bounding loop index may be caused, and a problem may occur that restoration and rendering are not performed.

Therefore, in the present invention, the directional information can be independently restored and rendered in the virtual connected component by defining all of the directional information in the virtual connected component in the same manner as the method of defining the connected component of the actual mesh.

2.7 Data segmentation method with bounding loop information (vi)

In the bounding loop information, index values of the geometric information of the actual vertices are mapped. Therefore, if the index of the bounding loop is known, the actual coordinate values of the vertices of the triangle may be mapped. Therefore, if there is no retransmission of the lost partition, as shown in FIG. 9, the next partitions to be restored cannot know the bounding loop index information for the triangle at the start position of the partition and thus cannot be restored. To avoid this inefficiency, each partition must be restored and rendered independently. To do this, you must specify the starting position on the bounding loop where the first triangle in each partition begins.

In the process of restoring the mesh in the decoder, vg stores the vertices of the triangles to be restored in a table called a bounding loop. At this time, the index value of the vertex of each triangle is stored in the table by increasing or decreasing the index value of the vertex of the triangle at the start position as shown in FIG. Therefore, if only the index of the bounding loop of the first triangle vertex of the partition can be determined, the vertex of the remaining triangle to be restored next can be determined by increasing or decreasing by 1 from the bounding loop index of the first triangle vertex.

Accordingly, in the present invention, only the bounding loop indexes of the vertices of the first triangle of the partition can be designated for each corresponding partition, thereby ensuring the independence of each partition. In addition, vi defined in the present invention is composed of two index information, left index (left index) and right index (right index) as shown in FIG. The bitstream configuration for this is illustrated in FIG. 22. In FIG. 22, L (left index) denotes an index in a bounding loop of a first vertex on a left boundary of a triangular strip, and R (right index) denotes an index in a bounding loop of a first vertex on a right boundary.

On the other hand, when the bitstream is received or restored only in sequential order through a storage medium such as a compact disc (CD), the index of the bounding loop exists between the sizes of the bounding loop starting from 0 for each connection component (CC). The index value given to the header of the partition can also be defined as a value in between. This is possible because the bounding loop and the tt / td pair information are exactly one-to-one correspondence and are always coded in the order of tt followed by the tt / td pair. However, depending on the characteristics of the transmission medium, the transmission order and the reception order may be different due to the transmission delay, or the bitstream may be lost at all. In this case, since the vg information corresponding to the tt / td pair cannot be guaranteed to be received or restored only in the sequential order, it is necessary to specify the index value in another way only in this case. 21 shows a relationship between a bounding loop and a tt / td pair when the polygon mesh has several connection components. Here, the first column shows the case where the bounding loop is independently indexed by the connected components, and the second column shows the case where the indexing of the current bounding loop is continuously increased to the last value of the previous bounding loop. 23A and 23B show differences between methods of specifying index information for these two cases. For example, when the size of the bounding loop of the first connected component is n1 and the size of the bounding loop of the second connected component is n2, the index values for the partition of the second connected component are indexed in two ways as shown in FIGS. 23A and 23B. Given in the header. FIG. 23A shows header information of partitions when bounding loop indexing is performed for each connection component, and FIG. 23B shows header information of partitions when bounding loop indexing is performed over the entire mesh.

2.8 Data segmentation method considering geometric information

Up to now, the present invention has been described based mainly on the connection information of the data partition model. Here, we describe a method for ensuring mutual independence between partitions of geometric information and improving encoding efficiency. When dividing the data, if the vertex of each triangle is in contact with the vertex of the triangle included in the previous partition, information about whether or not the geometry is already encoded. This is defined by the visited indicator, where visited is 1 if it is already encoded and 0 if it is not. In general, the geometry used for both the previous partition and the current partition appears at the boundary of both partitions. When encoding the current partition, all the geometry located at the boundary of the previous partition is defined as visited = 2. In consideration of this point, the following encoding method is possible.

1. As shown in FIG. 24A, in the current partition, only the geometry information not visited in the previous partition is encoded.

2. As shown in FIG. 24B, the information coded in another partition is encoded repeatedly in the current partition, so that the geometric information can be restored only by the current partition independently of the previous partition.

3. A method of overlapping encoding only on important geometric information appearing in connection with a plurality of geometric information newly appearing in the current partition among geometric information already encoded in another partition as shown in FIG. 24C.

4. As shown in FIG. 24D, the geometric information duplicated in the previous partition and the current partition is generally displayed continuously at one boundary of the triangular strip, so that half of the duplicated data is sampled in the previous partition and the remaining half is duplicated in the previous partition. How to encode in the current partition.

In FIGS. 24A to 24D, gray circles represent previously visited geometry information, black circles represent geocoded overlapping codes in the previous partition and the current partition, white circles represent geometric information that have not been visited yet, and solid black solid lines indicate partition boundaries. It is shown.

Each of these methods has the following advantages and disadvantages.

▶ Method 1 is easy to implement and has good coding efficiency. However, the accuracy of accuracy is lowered because the surrounding geometric information to be predicted is relatively smaller than other methods.

▶ Method 2 is easy to implement and can refer to all surrounding geometric information, so the accuracy is relatively high, but it is the lowest in coding efficiency by overlapping coding.

▶ Method 3 maintains the compression rate and loses geometric information, but it is difficult to implement and complexity is increased because the characteristics of the connection information around the boundary must be known in advance.

Method 4 can compensate for the disadvantages of Method 2, but there is a delay in rendering. This is because methods 1, 2, and 3 can be immediately restored and rendered on their own, but method 4 can interpolate the omitted values using the surrounding geometry or render them only when the next partition is restored. to be.

On the other hand, the first and second methods can be adaptively applied to each partition when partitioning the actual data. In other words, the partition having the start and end positions of data partitioning on the main stem in consideration of encoding efficiency and partition independence can be known exactly from the previously encoded partitions. Partitions in the dependent tree with the end position can be partitioned using method 2 because the visited information is not known when the previous partition is lost and cannot be restored. In the present invention, the above-described information on the geometric encoding method is provided to the header information of each partition. When only the above methods 1 and 2 are adaptively applied, 0 is used by using a 1-bit boundary prediction indicator. If it is 1, the method 2 indicates that the geometric information is encoded partition. 24E shows the grammar of the structure in which the boundary prediction indicator is included in the header information.

2.9 Predictive Coding Method of Location Information

The prediction coding method of the mesh predicts the position information (= d) of any one vertex by using the position information of three vertices (a, b, c) of adjacent triangles, which are already encoded, and predicts the predicted value. An object of the present invention is to improve the coding efficiency by encoding a difference between a value and an actual value. Such a prediction method may be defined as in Equation 5.

On the other hand, such a method of predicting the location information should be different depending on the boundary prediction (boundary predicition) value. This is because independent reconstruction of partition units cannot be guaranteed for all methods because the use of three vertices of adjacent triangles used for prediction depends on the method of boundary predicition. Therefore, in the present invention, when the boundary predicition value is 1, that is, when duplication is allowed, the prediction encoding method is applied in the same manner as the conventional method using only visited information of neighboring vertices, and when 0, that is, When duplication is not allowed and predictive encoding is to be performed using only location information in its own partition, a method of performing predictive encoding as shown in Equation (6) is proposed.

if (a, b, c not available both) d '= 0

else if (only one of a, b, c is available) d '= t

else if (only two of a, b, c are available) {

if (if the distance of each of the two vertices is 1 for d) d '= (t1 + t2) / 2

else if (only one vertex (= t1) distance is 1 for d) d '= t1

else d '= t2

} else d '= f (a, b, c)

Here, t means any one vertex available among three vertices a, b, and c, and t1 and t2 mean two vertices available among a, b, and c.

2.10 Bitstream Configuration and Processing Method of Geometric and Image Information

The method of encoding image information such as geometric information, color information, normal information, and texture coordinates is as follows. First, as shown in FIG. 25A, when a single marching bit of a triangle appears, the associated characteristic information is encoded. When the decoder restores one of the marching bit and polygon edge information, the triangle can be rendered immediately. There is a characteristic. The other method is a method of encoding all characteristic information appearing in one data partition separately by information characteristic as shown in FIG. 25B. A flowchart for encoding actual image information under such a grammar is shown in FIG. Referring to FIG. 26, as the geometry encoding method, the schemes illustrated in FIGS. 24A and 24B are mixed, and the scheme using the grammar system of FIG. 25A is illustrated.

1. Determine a boundary prediction method (step 401). That is, it is determined whether to encode using the method of FIG. 24A or the method of FIG. 24B.

2. Encode the root triangle (the triangle that first appears in the partition) (step 402).

3. Root geometric information is encoded (step 403).

4. Move to the next triangle (step 405).

5. For each vertex of the triangle, it is determined whether it has been visited in the previous partition (step 407). If not, it is determined whether it is encoded in the current partition (step 409), and if not, it is encoded (step 410). .

6. If the vertex is coded in the previous partition or the boundary prediction value is 1 (step 408), it is determined whether the value has already been coded in the current partition (step 409), and if not, the code is encoded (410). step).

7. Repeat the above steps 4 to 6 until the last triangle is encoded.

27 is an overall flowchart of dividing and encoding a polygonal three-dimensional model into partition units.

Hereinafter, an embodiment of an encoding grammar for implementing progressive three-dimensional mesh information and elasticity for loss will be described below.

The compressed bitstream for a three-dimensional mesh is composed of a header data block with global information followed by a series of connected component data blocks associated with one connected component of the three-dimensional mesh.

3D Mesh Header CC Data # 1 … CC Data #nCC

If the 3D mesh is encoded in the error resilient mode, the concatenated component data blocks are grouped or divided into partitions.

Partition # 1 Partition # 2 … Partition #nPT

Each connected component data block consists of three records: a vertex graph record, a triangle tree record, and a triangle data record.

The triangular tree record has the structure of a triangular spanning graph that links all the triangles of the corresponding connected component forming a simple polygon. Polygonal meshes are represented as triangles in the bit stream, which also contain the information needed to reproduce the original face. A vertex graph record contains the information needed to sew pairs of boundary edges of a simple polygon to reproduce the original connection information in the previously decoded connection component as well as the current connection component. The linking information is divided into global information (per linking component) and local information (per triangle). Global information is stored in vertex graphs and triangle tree records. Local information is stored in triangle data records. Triangle data is ordered based on triangular units, the order of the triangles being determined by the traverse of the triangle tree.

The data for a given triangle consists of:

marching pattern td_orientation polygon_edge coord Normal color texCoord

The marching patterns, td_orientation and polygon_edge, constitute triangular connection information. The other fields contain vertex coordinates and optionally information for reproducing normal, color and texture coordinate (texCoord) information.

▶ 3D_Mesh_Object

3D_MO_start_code: This is the only code of length 16 used for synchronization purposes. The value of this code is always '0000 0000 0010 0000'.

▶ 3D_Mesh_Object_Layer

3D_MOL_start_code: This is the only code of length 16 used for synchronization purposes. The value of this code is always '0000 0000 0011 0000'.

mol_id: This 8-bit unsigned integer represents the unique identifier for the mesh object layer (MOL). A value of 0 represents a base layer, and a value greater than 0 represents a refinement layer. The first 3D_Mesh_Object_Layer after the 3D_Mesh_Object_Header must be mol_id = 0, and subsequent 3D_Mesh_Object_Layers with the same 3D_Mesh_Object must have mol_id> 0.

cgd_n_vertices is the number of vertices at the current resolution of the 3D mesh. Used to reduce calculations.

cgd_n_triangles is the number of triangles at the current resolution of the three-dimensional mesh. Used to reduce calculations.

cgd_n_edges is the number of edges at the current resolution of the three-dimensional mesh. Used to reduce calculations.

▶ 3D_Mesh_Object_Base_Layer

3D_MOBL_start_code: This is the only code of length 16 used for synchronization purposes. It is also used to indicate three different types of partitions used for error resilience.

mobl_id: This 8-bit unsigned integer represents the unique identifier for the mesh object component.

one_bit: This boolean value is always true.

last_component: This boolean value indicates whether there are more connected components to decode. If last_component is true, the last component is decoded. Otherwise, there are more components to decode. This field is arithmetically encoded.

codap_last_vg: This boolean value indicates whether the current vg is the last vg in the partition. If there are more vg to be decrypted in the partition, it is false.

codap_vg_id: This unsigned integer indicates the vertex graph identifier that tt / td pair should use. The length of this value, log_vgid_len, is the value obtained by logging the vg_number of the vg decoded in the previous partition_type_1. If there is only one vg in the previous partition_type_1, codap_vg_id is not encoded.

codap_left_bloop_idx: This unsigned integer represents the left starting index in the bounding loop table for the triangular strip to be played in the partition. The length of this value, log_bloop_len, is a value obtained by logging the size of the bounding loop table.

codap_right_bloop_idx: This unsigned integer indicates the right starting index in the bounding loop table for the triangular strip to be played in the partition. The length of this value, log_bloop_len, is a value obtained by logging the size of the bounding loop table.

codap_bdry_pred: This boolean flag indicates how to predict the geometry and image information common to two or more partitions. If codap_bdry_pred is '1', all common information is predicted in the current partition, otherwise common information is predicted in only one partition.

▶ 3D_Mesh_Object_Header

ccw: This boolean value indicates whether the vertex order of the faces to be decoded is also in the order of the system direction.

convex: This boolean value indicates whether the model is convex.

solid: This boolean value indicates whether the model is solid.

creaseAngle: This 6-bit unsigned integer indicates whether it is a crease angle.

Coord_header

coord_binding This 2-bit unsigned integer represents the union of the vertex coordinates for the three-dimensional mesh. The only acceptable value is '01'.

coord_bbox: This boolean value indicates whether a bounding box is provided for geometry. If no bounding box is provided, the default is used.

coord_xmin, coord_ymin, coord_zmin These floating point values represent the lower left corner of the bounding box where the geometry is placed.

coord_size: This floating point value indicates the size of the bounding box.

coord_quant: This 5-bit unsigned integer represents the quantization step for the geometry.

coord_pred_type This 2-bit unsigned integer represents the type of prediction used to reconstruct the vertex coordinates of the mesh.

coord_nlambda: This 2-bit unsigned integer represents the number of ancestors used to predict the geometry. The allowable values for coord_nlambda are 3. Table 46 shows the allowable values as a function of coord_pred_type.

coord_lambda: This unsigned integer represents the weight given to ancestors for prediction. The number of bits used in this field is equal to coord_quant + 3.

Normal_header

normal_binding: This 2-bit unsigned integer represents the combination of normals to the three-dimensional mesh. Acceptable values are described in Table 47.

normal_bbox: This boolean value should always be false ('0').

normal_quant: This 5-bit unsigned integer represents the quantization step used for normal.

normal_pred_type: This 2-bit unsigned integer indicates how normal values are predicted.

normal_nlambda: This 2-bit unsigned integer represents the number of ancestors used to predict normals. Acceptable values for normal_nlambda are 1, 2, 3. Table 50 shows the allowable values as a function of normal_pred_type.

normal_lambda: This unsigned integer represents the weight given to ancestors for prediction. The number of bits used in this field is equal to normal_quant + 3.

▶ color_header

color_binding: This 2-bit unsigned integer represents the combination of colors for the three-dimensional mesh. Acceptable values are described in Table 51.

color_bbox: This boolean value indicates whether a bounding box is given for the colors.

color_xmin, color_ymin, color_zmin: These floating point values represent the position of the lower left corner of the bounding box in RGB space.

color_size: This floating point value indicates the size of the color bounding box.

color_quant: This 5-bit unsigned integer represents the quantization step used for color.

color_pred_type: This 2-bit unsigned integer indicates how colors are predicted.

color_nlambda: This 2-bit unsigned integer represents the number of ancestors used to predict the colors. Acceptable values for color_nlambda are 1, 2, 3. Table 54 shows the allowable values as a function of color_pred_type.

color_lambda: This unsigned integer represents the weight given to ancestors for prediction. The number of bits used in this field is equal to color_quant + 3.

▶ texCoord_header

texCoord_binding This 2-bit unsigned integer represents the combination of textures for a three-dimensional mesh. Acceptable values are described in Table 55.

texCoord_bbox This boolean value indicates whether a bounding box is given for the textures.

texCoord_xmin, texCoord_ymin, texCoord_zmin: These floating point values indicate the position of the lower left corner of the bounding box in two-dimensional space.

texCoord_size This floating point value represents the size of the texture bounding box.

texCoord_quant: This 5-bit unsigned integer represents the quantization step used for the texture.

texCoord_pred_type This 2-bit unsigned integer indicates how the color is predicted.

texCoord_nlambda: This 2-bit unsigned integer represents the number of ancestors used to predict the textures. Acceptable values for texCoord_nlambda are 1, 2, 3. Table 58 shows the allowable values as a function of texCoord_pred_type.

texCoord_lambda: This unsigned integer represents the weight given to ancestors for prediction. The number of bits used in this field is equal to texCoord_quant + 3.

▶ Cgd_header

cgd_n_proj_surface_spheres is the number of projected surface spheres. Typically, this number is equal to one.

cgd_x_coord_center_point is the x-coordinate of the center point (typically, the center of gravity of the object) of the projected surface sphere.

cgd_y_coord_center_point is the y-coordinate of the center point (typically, the center of gravity of the object) of the projected surface sphere.

cgd_z_coord_center_point is the z coordinate of the center point (typically, the center of gravity of the object) of the projected surface sphere.

cgd_normalized_screen_distance_factor indicates where the virtual screen is located compared to the radius of the projected surface sphere. The distance between the center point of the projected surface sphere and the virtual screen is equal to Radius / (Normalized_Screen_Distance_Factor + 1). cgd_radius is described for each projected surface sphere, but cgd_normalized_screen_distance_factor is described only once.

cgd_radius is the radius of the projected surface sphere.

cgd_min_proj_surface is the minimum projected surface value for the corresponding projected surface sphere. This value is often (but not necessarily) the same as one of the cgd_proj_surface values.

cgd_n_proj_points is the number of points on the projected surface sphere to which the ejected surface is to be transmitted. For all other points, the ejected surface is determined by linear interpolation. cgd_n_proj_points are typically small for the first projected surface sphere (eg, 20) and very small for additional projected surface spheres (eg, 3).

cgd_sphere_point_coord is the index of the point position within the octahedron.

cgd_proj_surface is the ejected surface within the point described by cgd_sphere_point_coord.

Vertex graph

vg_simple: This boolean value specifies whether the current vertex graph is simple. The simple vertex graph does not contain any loops. This field is arithmetically encoded.

vg_last: This boolean flag indicates whether the current run is the last run starting from the current branching vertex. This field is not encoded when the first run of each branching vertex, i.e. the skip_last variable is true. If the value of vg_last is not encoded for the current vertex run, it is assumed to be false. This field is arithmetic coded.

vg_forward_run: This Boolean flag indicates whether the current run is a new run. If it is not a new run, it must be a traversed run that represents a loop in the graph. This field is arithmetic coded.

vg_loop_index: This unsigned integer represents the index of the run to which the current loop is connected. Its unary representation is arithmetic coded. If the variable openloops is equal to vg_loop_index, the trailing '1' in that single expression is deleted.

vg_run_length This unsigned integer represents the length of the current vertex run. Its single representation is arithmetic coded.

vg_leaf This boolean flag indicates whether the last vertex of the current run is a leaf vertex. If it is not a lip vertex, it is a branching vertex. This field is arithmetic coded.

vg_loop This boolean flag indicates whether the lip of the current run represents a loop and is connected to the branching vertex of the graph. This field is arithmetic coded.

Triangle_tree

branch_position The variable of this integer is used to store the last branch position in the triangle tree.

tt_run_length This unsigned integer represents the length of the current triangular run. Its single representation is arithmetic coded.

tt_leaf This boolean flag indicates whether the last triangle of the current run is a leaf triangle. If it is not a lip triangle, it is a branching triangle. This field is arithmetic coded.

triangulated: This Boolean value indicates whether the current connected component contains triangles only. This field is arithmetic coded.

marching_triangle: This Boolean value is determined by the triangle's position in the triangle tree. If the triangle is a leaf or branch, marching_triangle = 0, otherwise marching_triangle = 1.

marching_pattern This Boolean flag indicates the marching pattern of the edges inside a triangle run. 0 represents a march from the left and 1 represents a march from the right. This field is arithmetic coded.

polygon_edge: This Boolean flag indicates whether the base of the current triangle is an edge that should be retained when playing a 3D mesh object. If the base of the current triangle is not maintained, it is discarded. This field is arithmetic coded.

codap_branch_len: This unsigned integer represents the total size of the subtree on one branch of the branch triangle to compute the Y-vertex index value of the branch triangle to be recreated in the partition. The length of this value is the logarithm of the size of the bounding loop table.

▶ triangle

td_orientation: This one bit flag tells the decoder the order of visit of the tt / td pair in the branch. This field is arithmetic coded.

visited: This variable indicates whether the current vertex has been visited.

no_ancestors: This Boolean variable is true if no ancestors are currently used to predict the vertices.

coord_bit: This boolean indicates the value of the geometry bit. This field is arithmetic coded.

coord_heading_bit: This boolean indicates the value of the heading geometry bit. This field is arithmetic coded.

coord_sign_bit: This Boolean value indicates the sign of the geometry sample. This field is arithmetic encoded.

coord_trailing_bit: This Boolean value indicates the value of the trailing geometry bit. This field is arithmetic encoded.

normal_bit: This Boolean value indicates the value of a normal bit. This field is arithmetic encoded.

normal_heading_bit: This Boolean value indicates the value of the heading normal bit. This field is arithmetic encoded.

normal_sign_bit: This Boolean value indicates the sign of a normal sample. This field is arithmetic encoded.

normal_trailing_bit: This Boolean value indicates the value of the trailing normal bit. This field is arithmetic encoded.

color_bit: This boolean indicates the value of the color bit. This field is arithmetic encoded.

color_heading_bit: This Boolean value indicates the value of the heading color bit. This field is arithmetic encoded.

color_sign_bit: This Boolean value indicates the sign of a color sample. This field is arithmetic encoded.

color_trailing_bit: This Boolean value indicates the value of the trailing color bit. This field is arithmetic encoded.

texCoord_bit: This Boolean value indicates the value of the texture bit. This field is arithmetic encoded.

texCoord_heading_bit: This Boolean value indicates the value of the heading texture bit. This field is arithmetic encoded.

texCoord_sign_bit: This Boolean value indicates the sign of a texture sample. This field is arithmetic encoded.

texCoord_trailing_bit: This Boolean value indicates the value of the trailing texture bit. This field is arithmetic encoded.

▶ 3DMeshObject_Refinement_Layer

3D_MORL_start_code: This is the only code of length 16 used for synchronization purposes. The value of this code is always '0000 0000 0011 0010'.

morl_id: This 8-bit unsigned integer is the unique identifier for the forest partition component.

connectivity_update: This 2-byte variable indicates whether the partitioning operation is the result of refinement of the mesh's connectivity information.

pre_smoothing: This boolean indicates whether the current forest splitting operation uses a pre-smoothing step to predict the vertex positions as a whole.

post_smoothing: This Boolean value indicates whether the current forest splitting operation uses a post-smoothing step to remove the quantization artifact.

stuffing_bit: This boolean is always true.

other_update: This boolean indicates whether the feature related to facets and corners that follow ganging of vertex coordinates and not incident to any tree in the forest is followed in the bitstream.

Pre_smoothing parameters

pre_smoothing_n: This integer value indicates the number of iterations of the pre-smoothing filter.

pre_smoothing_lambda: This floating point value is the first parameter of the pre-smoothing filter.

pre_smoothing_mu: This floating point value is the second parameter of the pre-smoothing filter.

Post_smoothing parameters

post_smoothing_n: This integer value represents the number of iterations of the post-smoothing filter.

post_smoothing_lambda: This floating point value is the first parameter of the post-smoothing filter.

post_smoothing_mu: This floating point value is the second parameter of the post-smoothing filter.

Fs_pre_update

pfs_forest_edge: This boolean indicates that the edge should be added to the forest created so far.

Smoothing_constraints

smooth_with_sharp_edges: This Boolean value indicates whether the data is included in the bitstream indicating smoothing discontinuity edges. If smooth_with_sharp_edges == 0, no edge is marked as a smoothing discontinuity edge. If smoothing discontinuity edges are indicated, pre-smoothing filters and post-smoothing filters take them into account.

smooth_with_fixed_vertices: This boolean indicates whether data that is not moving during the smoothing process is included in the bitstream. If smooth_with_fixed_vertices == 0, no vertices are allowed to move. If fixed vertices are marked, pre-smoothing filters and post-smoothing filters take them into account.

smooth_sharp_edge: This Boolean value indicates whether the corresponding edge is marked as a smoothing discontinuity edge.

smooth_fixed_vertex: This Boolean value indicates whether the corresponding vertex is a fixed vertex or not.

According to the present invention, even if an error occurs during transmission, the network burden and transmission time can be reduced by retransmitting only the portion where the error occurs, and the three-dimensional mesh is gradually restored using the connection information, the geometric information, and the characteristic information of the transmitted part. can do.

Claims (83)

In the method for encoding the polygon three-dimensional mesh to be gradually restored, (a) fragmenting a polygonal three-dimensional mesh (MO) into one or more connecting components; (b) generating vertex graph information and triangle tree / triangle data information for each connection component; And (c) encoding the vertex graph information and the triangle tree / triangle data information constituting the connected component according to the format of the basic mesh (MOBL) having a format that can be independently decoded for each connected component. A method of encoding polygonal three-dimensional mesh information, characterized in that. The method of claim 1, wherein step (a) A method of encoding polygonal three-dimensional mesh information, comprising: classifying a polygonal three-dimensional mesh (MO) into a plurality of stepped meshes (MOL) and fragmenting the polygonal three-dimensional mesh classified into each stepped mesh (MOL) into one or more connected components. . The method of claim 1, wherein in step (c) When the triangle tree / triangle data information constituting one connection component is so large that it does not fit in the format of the basic mesh (MOBL), the triangle tree / triangle data information is divided into data partitions having a format that can be independently decoded. Split and encode according to the format of the basic mesh (MOBL), and when the information constituting the plurality of connected components is adapted to the format of the basic mesh (MOBL), the information constituting the plurality of connected components is combined into one data partition A method of encoding polygonal three-dimensional mesh information, characterized by encoding according to the format of a basic mesh (MOBL). The basic mesh of claim 1, wherein the triangular tree / triangle data information is encoded. Where a branched triangle located in the main tree of the triangular tree is provided with a 1-bit directional indicator (td_orientation), the coding order of the subordinate trees following the branched triangle is determined by the direction indicated on the directional indicator. A method of encoding polygonal three-dimensional mesh information. The method of claim 4, wherein the orientation indicator (td_orientation) is The method of encoding polygonal three-dimensional mesh information, characterized in that determined by the size information of the subtrees from the branched triangle. The visit order of triangles in said dependent trees A method for encoding polygonal three-dimensional mesh information, characterized by the same direction for all dependent trees. The visit order of triangles in said dependent trees And encoding the three-dimensional mesh information according to the value of the directional indicator (td_orientation). The basic mesh encoded by the triangle tree / triangle data information comprises: Polygonal three-dimensional mesh information comprising the total size information (codap_branch_len) of the subordinate tree located on any one branch of the branched triangle located in the main stem of the triangle tree, and the index of the Y-vertex is determined by the total size information. Encoding method. In a method for encoding a polygonal three-dimensional mesh so that it can be recovered progressively and elastically, (a) fragmenting a polygonal three-dimensional mesh (MO) into one or more connecting components; (b) generating vertex graph information and triangle tree / triangle data information for each connection component; And (c) encoding vertex graph information and triangle tree / triangle data information constituting the connected component according to the format of the basic mesh (MOBL) having a fixed bitstream format so that each connected component can be independently decoded. Polygon three-dimensional mesh information encoding method comprising a. The method of claim 9, wherein step (c) The method of encoding polygonal three-dimensional mesh information, characterized in that all the connected components constituting the polygonal three-dimensional mesh arranged in the order of vertex graph information, triangle tree / triangle data information in one data partition. The method of claim 9, wherein step (c) Vertex graph information corresponding to all connection components constituting the polygonal three-dimensional mesh is arranged first, and then triangular tree / triangle data information corresponding to all connection components is arranged later to form one data partition for encoding. Method of encoding polygonal three-dimensional mesh information. The method of claim 9, wherein step (c) A method for encoding polygonal three-dimensional mesh information, characterized in that for each connection component, information constituting the connection component is encoded by forming an independent data partition. The method of claim 9, wherein step (c) Vertex graph information corresponding to all connection components of the polygon mesh is configured into one data partition, and triangle tree / triangle data information corresponding to all connection components is configured into another data partition and encoded. A method of encoding polygonal three-dimensional mesh information. The method of claim 9, wherein step (c) The vertex graph information corresponding to all the connected components of the polygon mesh is composed of one data partition, and the triangle tree / triangle data information corresponding to each connected component is composed of independent data partitions. In comparison, triangular tree / triangular data information of a connected component having a large size is divided and encoded into a plurality of data partitions that can be independently decoded. The method of claim 9, wherein step (c) And a plurality of independent data partitions for each vertex graph information and triangle tree / triangle data information constituting each connection component. The method of claim 9, wherein step (c) Vertex graph information corresponding to each connected component is composed of independent data partitions and encoded first, and triangle tree / triangle data information corresponding to each connected component is composed of independent data partitions, but is larger than the size of a transmission packet. The triangular tree / triangular data information of a component is composed of a plurality of divided data partitions that can be independently decoded and encoded later. The method of claim 9, wherein step (c) A method of encoding polygonal three-dimensional mesh information, comprising: independent data partitions for vertex graph information corresponding to each connected component, and independent data partitions for triangle tree / triangle data information, and encoding for each connected component. The method of claim 9, wherein step (c) It consists of independent data partitions for each vertex graph information corresponding to each connected component, and consists of independent data partitions for each triangle tree / triangle data information, but triangle tree / triangle data information of large connection components is independently compared to the size of the transmission packet A method of encoding polygonal three-dimensional mesh information, characterized by comprising data partitions divided into decodable forms and encoding by connection components. In a method for encoding a polygonal three-dimensional mesh so that it can be recovered progressively and elastically, (a) fragmenting a polygonal three-dimensional mesh (MO) into one or more connecting components; (b) generating vertex graph information and triangle tree / triangle data information for each connection component; And (c) For each connected component, a format of a basic mesh (MOBL) having a bitstream format that varies according to the characteristics of the information so that vertex graph information and triangle tree / triangle data information constituting the connected component can be independently decoded. And encoding according to the polygon three-dimensional mesh information. The method of claim 19, wherein step (c) And encoding a bitstream structure using some bits in the start code of the data partition as a partition type. The method of claim 20, wherein the partition type And a zero partition type (partition_type_0) for collecting and encoding information corresponding to one or more connected components into one data partition and encoding the same. The method of claim 21, wherein the 0th partition type is encoded in the basic mesh (MOBL) And a bit (last_component) for indicating whether there is further connection component to be encoded after each connection component is encoded. The method of claim 20, wherein the partition type And a first partition type (partition_type_1) for collecting and encoding vertex graph information corresponding to one or more connected components into one data partition. 24. The method of claim 23, wherein the first partition type is encoded in the basic mesh (MOBL) And a bit (codap_last_vg) for indicating whether there is further vertex graph information to be encoded after the vertex graph information corresponding to each connection component is encoded. The method of claim 20, wherein the partition type And a second partition type (partition_type_2) for dividing triangle tree / triangle data information into data partitions and encoding the same. 27. The method of claim 25, wherein the second partition type is encoded in the basic mesh (MOBL) And an identifier (codap_vg_id) of a vertex graph corresponding to the triangular tree / triangle data information. The method of claim 26, And when there is only one vertex graph to which the triangle tree / triangle data information can refer, the identifier of the vertex graph is not encoded. 27. The method of claim 25, wherein the second partition type is encoded in the basic mesh (MOBL) And a start index (codap_left_bloop_idx, codap_right_bloop_idx) in the bounding loop table for the triangle strip to be reproduced. 27. The method of claim 25, wherein the second partition type is encoded in the basic mesh (MOBL) And a boundary prediction indicator (codap_bdry_pred) indicating how to predict geometric and image information common to two or more data partitions. The method of claim 20, wherein the partition type And a third partition type (partition_type_3) for configuring and connecting one connection component into one data partition. In a method of packetizing a triangular three-dimensional mesh by dividing the triangular three-dimensional mesh into data partitions when encoding the triangular three-dimensional mesh to be incrementally and elastically reconstructed, (a) calculating the total bit generation amount in the triangle by sequentially visiting the triangles included in the triangle tree; (b) accumulating the total bit generation amount of the triangle calculated in step (a); And (c) If the value accumulated in step (b) is smaller than the packet size multiplied by the packet allowance value, repeat step (a) or less for the next visited triangle included in the triangle tree, and if not smaller, And dividing the triangular tree / triangle data information up to the visited triangle into data partitions and packetizing them. The method of claim 31, wherein when the visited triangle in step (a) is a branched triangle, (d) If the sum of the bit generation amounts of all triangles included in the dependent tree determined according to the coding order to the value accumulated in step (b) is smaller than the packet size multiplied by the packet allowance, Repeating step a) and, if not smaller, dividing the triangular tree / triangle data information up to the branched triangle into data partitions and packetizing the polygonal triangular mesh into data partitions. Way. The method of claim 31, wherein when the visited triangle in step (a) is a branched triangle, (d) when the sum of the bit generation amount estimated by the size of the dependent tree determined according to the encoding order is accumulated in the step (b) is smaller than the packet size multiplied by the packet allowance, (a) The method of claim 1, further comprising: dividing the triangular tree / triangle data information up to the branched triangle into data partitions and packetizing the data into polygons. In a method for encoding a polygonal three-dimensional mesh so that it can be recovered progressively and elastically, (a) fragmenting a polygonal three-dimensional mesh (MO) into one or more connecting components; (b) generating vertex graph information and triangle tree / triangle data information for each connection component; (c) encoding, for each connection component, the vertex graph information constituting the connection component; And and (d) configuring and encoding virtual connection components by adding virtual bit pairs to data partitions obtained by dividing the triangular tree / triangle data information. 35. The method of claim 34, wherein the dividing in step (d) A method for encoding polygonal three-dimensional mesh information, characterized in that it is made only on the main stem of a triangular tree. 36. The method of claim 35, wherein the dividing in step (d) A method of encoding polygonal three-dimensional mesh information, comprising a virtual connection component by adding a pair of (1,1) to a (trun, tleaf) pair when the run is made from a run or leaf of a triangular tree. 36. The method of claim 35, wherein the dividing in step (d) A method of encoding polygonal three-dimensional mesh information, wherein the virtual connection component is formed by adding two pairs of (1,1) to a (trun, tleaf) pair when the triangle is a branched triangle of a tree. The method of claim 34, And reconstructing the polygonal three-dimensional mesh into a triangular three-dimensional mesh before step (a). The method of claim 38, wherein the division of step (d) A method of encoding polygonal three-dimensional mesh information, wherein the polygon edge information (pe) of the first triangle included in the data partition of the triangular tree / triangle data is not encoded. The method of claim 38, wherein the division of step (d) Polygon edge information (pe) of the first triangle included in the zero partition type of the triangular tree / triangle data, which is formed at the real edge and the virtual edge of the polygon mesh, is encoded without encoding the remaining partition types. A method of encoding polygonal three-dimensional mesh information. 35. The polygonal three-dimensional mesh of claim 34, further comprising a 1-bit orientation indicator (td_orientation) for the branching triangle located on the main stem among all the branching triangles existing in the data partition composed of the virtual connection component. Method of encoding information. 35. The header of a data partition in which the triangular tree / triangle data information is divided. And a start index (codap_left_bloop_idx, codap_right_bloop_idx) in a bounding loop table so that the data can be restored independently of a previously restored data partition. 43. The method of claim 42 wherein the starting index is The first left and right indices mapped in the boundary loop corresponding to the start vertices of the triangles that are successively restored in the boundary loop table corresponding to the triangle tree / triangle data information. A method of encoding three-dimensional mesh information, characterized in that it is given within a range of two. 43. The method of claim 42 wherein the starting index is The first left and right indices mapped in the boundary loop corresponding to the start vertices of triangles which are successively restored in the boundary loop table corresponding to the triangle tree / triangle data information are defined and the index of the boundary loop is determined by considering the entire mesh. A method of encoding three-dimensional mesh information. 35. The header of a data partition in which the triangular tree / triangle data information is divided. And an identifier (codap_vg_id) of a vertex graph corresponding to the triangular tree / triangle data information. The header of the data partition of claim 34, wherein the triangle tree / triangle data information is divided into: A method of encoding polygonal three-dimensional mesh information, comprising: a boundary prediction indicator (codap_bdry_pred) indicating how to predict geometric and image information common to two or more data partitions. The method of claim 46, When the beginning and the end of the data partition are located on the main stem of the triangle tree, only the one data partition includes geometry and image information common to the data partition and the previously encoded data partition. If the end is located in the dependent tree, it is determined whether the geometric information and the image information which are common to the data partition and the previously encoded data partition are included. The encoding method of the polygonal three-dimensional mesh information, characterized in that included in only one data partition. The method of claim 34, A method of encoding polygonal three-dimensional mesh information, wherein the triangle data information included in the triangle tree / triangle data information is arranged for each triangle forming a corresponding triangle tree. The method of claim 34, The triangular data information included in the triangular tree / triangle data information is arranged in order of marching information of all triangles constituting the corresponding triangular tree, geometric information of all triangles, and image information of all triangles. Encoding Method. In the method of progressively and losslessly decoding a polygonal three-dimensional mesh, (a) dividing the input bitstream into units of a basic mesh (MOBL); (b) determining a partition type of the basic mesh (MOBL); (c) if vertex graph information is included in the basic mesh (MOBL), generating a bounding loop table by decoding the vertex graph information; (d) generating tridimensional meshes by decoding the triangular tree / triangle data information when the basic mesh (MOBL) includes triangular tree / triangle data information; And (e) generating a three-dimensional mesh by repeating the steps (a) to (d). 51. The method of claim 50, wherein step (a) If the input bitstream is divided into polygonal three-dimensional mesh (MO) units, the type of the meshes included in the polygonal three-dimensional mesh (MOL) is determined, and the decoding is a stepped mesh (MOL), the bitstream in the stepped mesh Method of decoding polygonal three-dimensional mesh information, characterized in that divided into the base mesh (MOBL) unit. 51. The method of claim 50, wherein when the triangle tree / triangle data information is decoded in the step (d), The decoding method of polygonal three-dimensional mesh information, characterized in that when decoding a branched triangle located on the main stem of the triangle tree, the decoding order of the subordinate trees following the branched triangle is determined by the direction indicated in the direction indicator (td_orientation). 53. The method of claim 52, wherein the visit order of triangles in the dependent trees is Method for decoding polygonal three-dimensional mesh information, characterized in that the same direction for all the dependent tree. 53. The method of claim 52, wherein the visit order of triangles in the dependent trees is And decoding the polygonal three-dimensional mesh information according to the value of the directional indicator (td_orientation). The method of claim 52, wherein step (b) And a partition type is determined according to a start code value of the data partition. 56. The method of claim 55, wherein the partition type And a zero partition type (partition_type_0) for collecting and encoding information corresponding to one or more connected components into one data partition and encoding the same. 57. The method of claim 56, wherein when decoding the basic mesh (MOBL) of the zero partition type, A method for decoding polygonal three-dimensional mesh information, characterized by determining whether there is further connection component to be decoded by a predetermined bit (last_component) located after each connection component. 55. The method of claim 54, wherein the partition type And a first partition type (partition_type_1) for collecting and encoding vertex graph information corresponding to one or more connected components into one data partition. 59. The method of claim 58, wherein when decoding the basic mesh of the first partition type, And determining whether there is further vertex graph information to be decoded by a predetermined bit (codap_last_vg) located after the vertex graph information corresponding to each connection component. 56. The method of claim 55, wherein the partition type And a second partition type (partition_type_2) for dividing triangle tree / triangle data information into data partitions and encoding the same. 61. The method of claim 60, wherein when decoding the basic mesh of the second partition type, And identifying corresponding vertex graph information by an identifier (codap_vg_id) of a vertex graph located before the triangle tree / triangle data information. 61. The method of claim 60, wherein when decoding the basic mesh of the second partition type, If the vertex graph information corresponding to the triangle tree / triangle data information can be uniquely identified, it is determined that the identifier (codap_vg_id) of the vertex graph is not located before the triangle tree / triangle data information. Method of decoding mesh information. 61. The method of claim 60, wherein when decoding the basic mesh of the second partition type, And decoding independently of a previous data partition by a start index (codap_left_bloop_idx, codap_right_bloop_idx) in a boundary loop table located in front of the triangle tree / triangle data information. 61. The method of claim 60, wherein when decoding the basic mesh of the second partition type, A method of decoding polygonal three-dimensional mesh information, comprising determining how to predict geometric and image information common to a data partition previously decoded by a boundary prediction indicator (codap_bdry_pred) located in front of the triangle tree / triangle data information. . 56. The method of claim 55, wherein the partition type And a third partition type (partition_type_3) comprising one connection component as one data partition. 51. The method of claim 50, wherein when decoding the triangle tree / triangle data information in the step (d), Polygonal three-dimensional mesh information, characterized in that the Y-vertex index of the branched triangle is determined by the total size information (codap_branch_len) of the dependent tree located on any one branch when decoding the branched triangle located in the main stem of the triangle tree. Decryption method. In the method of progressively and losslessly decoding a polygonal three-dimensional mesh, (a) dividing the input bitstream into units of a basic mesh (MOBL); (b) determining a partition type of the basic mesh (MOBL); (c) if vertex graph information is included in the basic mesh (MOBL), generating a bounding loop table by decoding the vertex graph information; (d) generating triangular three-dimensional meshes by decoding the triangular tree / triangle data information in units of connected components if the triangular tree / triangle data information is included in the basic mesh (MOBL); And (e) repeating step (a) or less if the connected component in step (d) is a virtual connected component; otherwise, completing the generation of the triangular three-dimensional mesh; Decryption method. 68. The method of claim 67, wherein in step (d), the basic mesh (MOBL) including the triangular tree / triangle data information is included. A start method (codap_left_bloop_idx, codap_right_bloop_idx) in a bounding loop table for restoring independently of a previously restored base mesh (MOBL) is provided. 69. The method of claim 68, wherein the starting index is The first left and right indexes mapped in the boundary loop corresponding to the start vertices of triangles that are successively restored in the boundary loop table corresponding to the triangle tree / triangle data information are determined, and the index of the boundary loop is the index of the component's vertices. A method of decoding three-dimensional mesh information, characterized in that it is given within a range of adding two to the number. 69. The method of claim 68, wherein the starting index is The first left and right indexes mapped in the boundary loop corresponding to the start vertices of triangles that are successively restored in the boundary loop table corresponding to the triangular tree / triangle data information are determined. A method of decoding three-dimensional mesh information, characterized in that determined. The method of claim 68, wherein in step (d), If (codap_right_bloop_idx-codap_left_bloop_idx-1) is larger than the total number of triangles generated when only triangular tree information of the basic mesh (MOBL) is restored, the connection component is determined as a virtual connection component. Decryption method. 72. The method of claim 71, wherein if the last to third triangles of the triangles decoded in the step (d) are branching triangles, it is determined that two pairs of virtual triangles exist in the pair (trun, tleaf); tleaf) It is determined that two pairs of virtual triangles exist in the pair, and the decoding method of the polygonal three-dimensional mesh information, characterized in that for the virtual triangle do not decode the triangle data information. The method of claim 67, And reconstructing the triangular three-dimensional mesh into a polygonal three-dimensional mesh. 74. The method of claim 73, Partitioning in the encoding process is performed only on the actual edge of the polygon mesh, and polygonal three-dimensional, characterized in that the polygon edge of the first triangle included in the basic mesh (MOBL) of the triangle tree / triangle data is determined as the actual edge without decoding Method of decoding mesh information. 74. The method of claim 73, Partitioning in the encoding process is also performed inside the polygon mesh, and the polygon edge of the first triangle included in the first basic mesh of the triangle tree / triangle data is determined as a real edge without decoding. Decryption method. The method of claim 67, For every branch triangle existing in the basic mesh composed of the virtual connected components, when decoding the branch triangle, the decoding order of the dependent trees following the branch triangle is determined by the direction indicated in the direction indicator (td_orientation). A method of decoding polygonal three-dimensional mesh information. 68. The method of claim 67, wherein in step (d), the basic mesh (MOBL) including the triangular tree / triangle data information is included. A boundary prediction indicator (codap_bdry_pred) is provided to indicate how to predict geometric and image information common to two or more basic meshes. 78. The method of claim 77, wherein the boundary prediction indicator (codap_bdry_pred) is 0, A method of decoding polygonal three-dimensional mesh information, characterized in that all geometric information and image information common to the currently decoded basic mesh and the previously decoded basic mesh are not included in the currently decoded basic mesh. 79. The method of claim 78, When decoding the geometric information (d) using the predicted value (d ') and the encoded value (e) predicted by the ancestors (a, b, c) visited in the previous data partition, none of the necessary ancestors are decoded. If no value is available, the prediction value is set to zero, and if only one value is available, the value is set to the prediction value. If only two values are available and both of them have a node distance of 1 from the current vertex, With the arithmetic mean as the predicted value, if only two values are available and the node distance from the current vertex of the two values is 1, the value is assumed as the predicted value, and if all three values are available, the predicted value is determined by a predetermined prediction method. A method for decoding polygonal three-dimensional mesh information, characterized in that for determining. The method of claim 77, wherein the boundary prediction indicator (codap_bdry_pred) is 1, A method of decoding polygonal three-dimensional mesh information, characterized in that all geometric information and image information common to the base mesh currently decoded and the previously decoded base mesh are included in the base mesh currently decoded. 82. The method of claim 80, When the geometric information d is decoded using the predicted value d 'predicted by the visited ancestors a, b and c and the encoded value e, no vertices are visited in the previous data partition. A method for decoding polygonal three-dimensional mesh information, characterized in that it is assumed that the prediction value is determined by a predetermined prediction method. The method of claim 67, And the triangle data information included in the triangle tree / triangle data information is decoded in order of marching information, geometry information, and image information for each triangle constituting the corresponding triangle tree. The method of claim 67, The triangular data information included in the triangular tree / triangle data information is decoded in order of marching information of all triangles constituting the corresponding triangular tree, geometric information of all triangles, and image information of all triangles. Decryption method.