JP3009651B1 - Method for compressing and restoring three-dimensional data - Google Patents

Abstract

An object of the present invention is to compress and decompress unstructured data such as three-dimensional shape data and texture data. An unstructured data of a position coordinate and an attribute value is divided into a set of structured data in which an adjacent relation is expressed by a rectangular lattice. The structured data represented as a two-dimensional array is folded at the boundary between the data and the background to maintain continuity, and is subjected to decomposition having a symmetric weight coefficient, subband decomposition using a synthesis filter, or wavelet transform. The original data is restored from the bitmap mask representing the domain of the data and the transform coefficients in the domain.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for compressing and restoring three-dimensional shape data and texture data.

[0002]

2. Description of the Related Art An object in a three-dimensional space is represented by a set of three-dimensional coordinates of points on the surface and ancillary data such as a texture on each point. Conventionally, as a method of reducing the amount of data, a method of obtaining the curvature of each sample point, thinning out the sample points in a flat area having a small curvature, reducing the total number of data points, and reducing the data amount has been adopted.

[0003]

[Problems to be solved by the invention] Three-dimensional computer
Data used for graphics is represented by a set of coordinates of a point in a three-dimensional space and data attached to the point as a basic element. On the other hand, images and videos captured by digital cameras and videos are sampled at grid points that are equally spaced vertically and horizontally on the imaging surface, and the scanning order is determined. It is represented as a collection of data. Such data is referred to as structured data. Significant data compression is realized by standard image and video encoding means such as JPEG and MPEG. In standard image and video coding methods,
Although a method of decomposing image data into two-dimensional frequency components is used as a basic technique, conventional frequency decomposition means cannot be applied to unstructured data such as three-dimensional shape data and texture as it is.

[0004]

According to the present invention, there is provided a method for compressing three-dimensional data, a method for restoring the data, and a program for executing each method on a computer. The storage medium mainly has the following configuration.

That is, an object existing in a three-dimensional space is represented by a set of points including three-dimensional coordinate values of a sequence of points on the surface thereof and attribute values representing a texture or the like at a position indicated by the coordinate values. A method of compressing the three-dimensional data obtained is to obtain a triangular patch representation of the three-dimensional coordinate values of the object surface, and to decompose the adjacent relation of the triangular patches into a set of triangular patches that can be structured by a quadrangular lattice. Step, the quadrilateral lattice structured by each set of the triangular patches and the two-dimensional array are associated, and 1 is assigned to the array element associated with the vertex of the triangular patch,
A step of giving 0 to uncorresponding ones and creating a bitmap mask, and according to the bitmap mask,
An encoding step of encoding the position and attribute value of the point corresponding to each point after converting the data domain into the two-dimensional array data in which the bitmap mask is equal to 1 for each component.

In the data structuring step, the three-dimensional coordinate values of the sample points on the object surface are converted into a triangular patch representation using the Delaunay method or the like, and adjacent triangles are tracked and one-to-one with a part of a quadrangular lattice. A corresponding stripe region is extracted, and a stripe that can correspond to a part of the square lattice is extended from both sides of the stripe, and a curved surface that can correspond one-to-one with a part of the square lattice is extracted. After removing the extracted triangles, the same processing is repeated, and all sample points are decomposed into a set of curved surfaces that can be associated with a rectangular grid. A two-dimensional array indicating whether or not the sample points are associated with the rectangular grid is used as a bitmap mask. If a sample point is associated with each element, 1 is given, and if there is no association, 0 is given.

[0007]

A method for restoring compressed data of a point including three-dimensional coordinate values of an object existing in a three-dimensional space and attribute values representing a texture or the like at a position indicated by the coordinate values is provided. A bitmap mask restoring step of restoring a bitmap mask having an element associated with each point based on the coordinate values of the three-dimensional coordinates and attributes of the point corresponding to each point according to the bitmap mask A restoring step of restoring values and the restored three-dimensional coordinates
The same position as before encoding based on the target value and bitmap mask
Plays a triangular patch that has a connection between coordinates and attribute values
And

[0009]

The computer-readable storage medium creates a bitmap mask representing connectivity in four directions, up, down, left, and right, on the surface of the object based on the three-dimensional coordinate values of the object existing in the three-dimensional space. A data structuring step of converting the connectivity of the three-dimensional coordinates and attribute values into structured data represented by the bitmap mask, and representing the position, texture, and the like of the point corresponding to each point according to the bitmap mask A program for causing a computer to execute an encoding step of encoding the attribute value.

A computer-readable storage medium stores three-dimensional coordinate values of sample points on an object surface in Delaunay.
It converts to a triangular patch expression using the method, etc., traces adjacent triangles, extracts a stripe region corresponding one-to-one with a part of a square grid, and can correspond to a part of a square grid from both sides of the stripe The stripe is extended, and a curved surface that can correspond one-to-one with a part of the square lattice is extracted. After removing the extracted triangles, the same processing is repeated, and all sample points are decomposed into a set of curved surfaces that can be associated with a rectangular grid. A two-dimensional array indicating whether or not a sample point is associated with a rectangular lattice is used as a bitmap mask, and 1 is assigned when a sample point is associated with each element, and 0 is assigned when there is no association. Is stored in the computer.

[0012]

[0013]

[0014]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS (Embodiment) A method for compressing and restoring three-dimensional shape data which is unstructured data according to the present invention, and a program for causing a computer to execute the method are stored. The storage medium will be described in detail with reference to the drawings.

<Three-dimensional image information> In computer graphics, an image of an object existing in a three-dimensional space can be freely generated by changing a light source and a viewpoint. In order to describe the shape and optical characteristics of an object, three-dimensional position coordinate values (x, y, z) of a group of points representing the shape of the surface of the object
And attribute values, such as a texture composed of color information (r, g, b) on each point and a direction vector (nx, ny, 1) of a normal line, are required.

If sample points are densely taken on the surface of the object, the information of coordinate values and attribute values becomes enormous. Therefore, the sampling density is reduced in a region where the attribute values such as the shape and the texture are small, and in a region where the fluctuation is large. The data amount is reduced by increasing the sampling density.

FIG. 1A is a three-dimensional representation of a human face using a wire frame, and the intersections of short straight lines indicate data sample points. To reduce the amount of data,
A method of obtaining the curvature of the surface at each sample point and deleting a sample point having a small curvature is employed, and FIG. 6B shows this example.

To represent the face shape, a set of three-dimensional coordinates (x, y, z) of the sample points is required. To display the face texture etc., the color information (r, g, b) ) Is also required. Although these data are shown in FIG. 2, the data is a collection of data for each sample point, and is meaningless unstructured data in the order in which the sample points are arranged.

<Formation of Triangle Patch> In order to represent point information as area information, a triangle area connecting points from a set of points as shown in FIG. Patch "). The space defined by the three points is a region having a high correlation as an attribute value. The formation of the triangular patch follows the flowchart of FIG. Here, according to the Delaunay method, which is a mathematically known method, a triangular patch is formed under a constraint condition that minimizes the angle formed by each side. The mathematical means for forming a triangular patch is described above.
The method is not limited to the Delaunay method, but is also possible by other mathematical means. In the present embodiment, the angle is used as a reference, but the area or the total number of formed triangular patches may be used as the constraint condition.

In the flowchart of FIG. 4, step S301 extracts position information from unstructured data describing image information of a three-dimensional object. In step S302, three adjacent points are connected based on the extracted position information. Of the angles formed by the three points connected in step S303, the calculation is repeatedly performed so that the largest angle is minimized. When searching for a combination with another point (S303-No), the process returns to step S302, and a combination with another point is similarly determined. When the angle between the sides satisfies the condition (S303-Yes), the formation of the triangular patch is completed (S304).

<Generation of Structured Data Using Square Grid>
The previously determined individual triangles are integrated into a set of triangles whose adjacency of sample points can be structured by a square grid. Generation of structured data will be described with reference to FIG.

As shown in FIG. 5A, starting from an arbitrary triangle, a left-right walk is continued to the end, and a stripe region is extracted. Here, the end means reaching the boundary of the object or hitting a triangle that has already been traced. Next, as shown in FIG. 5B, the start side of the stripe is associated with the position (io, jo) of the rectangular lattice. io and jo are integers indicating positions on the square lattice.

The following vertices on the left side along the stripe axis are (io + 1, jo), (io +
1, jo + 1),... The vertices along the right side of the stripe axis are (io, jo + 1), (io
+1, jo + 1), (io + 2, jo + 1),.

As shown in FIG. 6A, for each side on the left side of the stripe, a triangle adjacent to the side is traced to the end by walking left-right. The left vertex of the newly obtained stripe is a grid point of (io, jo-1), (io, jo-2),..., And the right vertex is (io, jo-1), (io, jo). jo-2), ...
Is associated with. Then, a stripe is extracted from the next side along the axis of the initial stripe, and newly extracted vertices are (io + 1, jo-1), (io + 1, jo-2),.・
However, only when the vertices are not yet corresponded to these grid positions or the already-existed vertices are equal to the newly extracted vertices, the left-right walk is advanced to extend the stripe. . The extracted right vertex is (io
+2, jo-1), (io + 2, jo-2),... The same processing is continued up to the leading end of the initial stripe.

As shown in FIGS. 6 (c) and 6 (d), the same processing is performed on the right side of the initial stripe, and the vertices of the newly extracted stripe are associated with the square lattice.

Grid position (i, j) to which the vertex is associated
Is the maximum value of imax, the minimum value in the j direction, and the maximum value is jmi
Assuming that n, jmax and io = 0, jo = -jmin, the coordinate values and attribute values of the extracted vertices are ｛x (i, j), y (i,
j), z (i, j)}, {r (i, j), g (i, j), b (i, j)}, i
= 0,1, ... imax, j = 0,1, ..., jmax-jmin,
It becomes structured data in which the adjacency is defined by the square grid.

As shown in FIG. 7, after removing the previously extracted stripe group from the triangular patch, the process of extracting a new stripe group is repeated. Thereby, the triangle patch data can be represented as a set of some structured coordinate values and attribute values.

<Generation of Bitmap Mask> The coordinate values and attribute values structured by the rectangular grid are represented as a two-dimensional array by ｛x (i, j), y (i, j), z (i, j). }, ｛R (i, j),
g (i, j), b (i, j)}, but the domain of the array element is not generally rectangular as shown in FIG. 8A, but has an arbitrary shape. The shape of this domain is the same as the coordinate value and the attribute value, and a shape represented by a two-dimensional array having 1 or 0 elements is called a bitmap mask.

As shown in FIG. 8 (b), the bitmap mask is a two-dimensional array having the same size as the structured data, and the value of the element to which the data is associated is set to 1. The value of the missing element is created as 0.

<Subband division, wavelet transformation>
In consideration of the domain of the data indicated by the bitmap mask (FIG. 8B), compression of the data amount is performed by applying subband division or wavelet transform to the structured data of coordinate values and attribute values. The processing to be performed will be described.

For the structured data, the sub-band division forms a band-pass filter (sub-band) for dividing the frequency band into two in the horizontal direction and the vertical direction in a tree shape. On the other hand, in the wavelet transform, a tree structure is used in which only the lower subband is recursively divided.

FIG. 9 shows a general filter bank configuration for two-dimensional wavelet transform in which frequency division is performed once each in the horizontal and vertical directions. When the vertical frequency division is completed, four different frequency components (LL, LH,
HL, HH).

FIG. 10A shows the configuration of a filter bank in the case where 2: 1 downsampling is performed three times on original data. The decomposition of the frequency components is shown in FIG.
The multi-resolution expression is as shown in FIG. FIG. 10A shows the configuration of a filter that performs frequency component decomposition three times, but it goes without saying that the effect of the present invention does not depend on the frequency of frequency component decomposition.

In the three-dimensional data compression apparatus 1500 shown in FIG. 19, the multi-resolution decomposition means 152 performs this processing.
Here, the components from HH1 to HL3 excluding the LL3 component are signals subjected to wavelet transform, and are called wavelet transform coefficients.

<Folding> When sub-band division or wavelet transformation is performed on an object area (element value = 1) and background area (element value = 0) defined by a bitmap mask, the former division is performed. The band contains large coefficient components,
The latter contains many coefficients close to 0, and discontinuities occur at the boundaries. If the conversion is performed without considering the discontinuity, large energy may appear at the boundary of the output of the high-pass filter due to the influence of the low-frequency component. Further, in order to reproduce data, a conversion coefficient of the background area is also required, which is larger than the number of elements in the target area. In order to solve such a problem, for the discontinuous boundary part, the array element of the object area is folded pointwise symmetrically in the horizontal or vertical direction around the boundary array, and the virtual An array element is generated in order to eliminate the influence of discontinuity at the boundary portion during wavelet transformation. Further, two filters (low-pass (LPF), high-pass
(HPF)), it is possible to obtain a low frequency output and a high frequency output symmetrical with respect to the boundary.

FIG. 12 is a view for explaining the folding at the boundary. Here, a case where an analysis / synthesis filter having an odd tap length is used is shown. FIG. 12A shows an example of structured data, in which processing is performed for each data connection region. In the analysis process in the horizontal direction, point symmetrical folding is performed on the connected area ABCDE with the elements A and E at both ends as centers. This processing is shown in FIG. 12B. The low-pass and high-pass filter outputs having point-symmetric weighting coefficients also have point-symmetric values with respect to points A and E. From the downsampled value in the output target area, the output downsampled value can be obtained by performing point-symmetrical folding.

Therefore, the data to be stored and transmitted is only the downsampled value in the object area, which is the same as the number of data in the object area. Even when an even tap length filter is used, the same folding as the filter symmetry may be performed at both ends of the connection region.

By performing the same processing on all the connected areas, a transform coefficient divided into two in the horizontal direction is obtained. By performing the same process on the two components in the vertical direction, the components are decomposed into four components LL, LH, HL, and HH.

FIG. 13A shows the multi-resolution-decomposed structured data when the horizontal and vertical analysis processes are repeated three times for the lowest frequency component LL. FIG. 1 shows an octave-divided bitmap mask obtained when the downsampling of this analysis process is performed on the bitmap mask.
This is shown in FIG. If this bitmap mask and the conversion coefficient of the coordinate value and attribute value corresponding to the element when scanning the bitmap mask are encoded, stored and transmitted, the structured data of the coordinate value and attribute value can be reproduced from these data. .

<Encoding> The details of the conversion process to the bit string by the variable length code in FIG. 14 will be described with reference to FIG. Since the sub-band division or the wavelet-transformed multi-resolution expression (wavelet transform coefficient) generally has redundancy in each frequency component, the redundancy is removed by the zero tree method (S1103). The zero tree method is shown in FIG.
This is a known method of compressing information using the positional correlation that the frequency components before and after the decomposition are similar in position in the tree structure of the decomposition filter as described above. Variable-length coded bits are generated for the zero tree symbol sequence obtained as a result (S1104). The wavelet transform coefficient of the position and attribute value from which the redundancy has been removed and the bit sequence of the bitmap mask are transmitted or stored as data necessary for decoding (restoration) (S1105).

<Decoding (Decompression) of Compressed Information> FIG.
Is a flowchart for restoring compressed information. FIG. 20 is a block diagram showing the configuration of the three-dimensional data restoration device 1600.

In step S1601, compressed bit sequence data of variable length code is received and read. This data is data received from the transmission / storage means 155 (FIG. 19) of the three-dimensional data compression device 1500. Data reception and reading are performed by the three-dimensional data restoration device 16 of FIG.
At 00, the receiving / reading means 161 performs the processing.

The bitmap mask is decoded from the received and read data (S1602), zero-tree decoding is performed from the bit sequence of the variable length code, and the multiresolution data sequence is synthesized (S1603). This processing is performed by the zero tree decoding means 163 and the multi-resolution data memory 164.
Is executed by reference.

The information on the position and attribute value subjected to the subband synthesis or the inverse wavelet transform is stored in a decoded bitmap mask (refer to the bitmap mask memory 165).
Is decoded into a data sequence as shown in FIG. At this time, based on the bitmap mask, the boundary area is determined at the edge of the target object area (second determination processing), and the decomposed data is folded (second folding processing), and subband synthesis or Wavelet inverse transformation. The second return processing is performed by the return data processing unit 166b of the three-dimensional data restoration device 1600. In the second folding process, as shown in FIG. 17, the same process as the folding process at the edge at the time of compression (first folding process) is performed on the upsampled transform coefficients.

FIG. 18 shows a basic configuration of a filter bank for performing synthesis / inverse conversion. FIG. 10A is a diagram in which a root input image is decomposed by a filter bank having a tree structure, and data is reproduced by performing synthesis / inverse conversion processing from the end of the tree structure toward the root. The synthesis filter is created by the synthesis filter processing unit 166d of the image decoding device 1600, and the upsampling unit 166c of the image decoding device 1600 processes the synthesis (upsampling) of the low-frequency and high-frequency components.

Returning to FIG. 16, a triangular patch representation or unstructured data is obtained from the coordinate value and attribute value structured data synthesized from the multi-resolution data, and displayed and stored (S1605).

[0048]

Another object of the present invention is to supply a storage medium storing program codes of software for realizing the functions of the above-described embodiments to a system or an apparatus, and to provide a computer (or CPU) of the system or apparatus. And MPU) read and execute the program code stored in the storage medium.

In this case, the program code itself read from the storage medium realizes the functions of the above-described embodiment, and the storage medium storing the program code constitutes the present invention.

As a storage medium for supplying the program code, for example, a floppy disk, hard disk, optical disk, magneto-optical disk, CD-ROM, CD
-R, a magnetic tape, a nonvolatile memory card, a ROM, or the like can be used.

When the computer executes the readout program code, not only the functions of the above-described embodiment are realized, but also the OS (Operating System) running on the computer based on the instruction of the program code. ) May perform some or all of the actual processing, and the processing may realize the functions of the above-described embodiments.

Further, after the program code read from the storage medium is written into a memory provided in a function expansion board inserted into the computer or a function expansion unit connected to the computer, based on the instructions of the program code, It goes without saying that the CPU included in the function expansion board or the function expansion unit performs part or all of the actual processing, and the processing realizes the functions of the above-described embodiments.

When the present invention is applied to the storage medium, the storage medium stores program codes corresponding to the above-described flowcharts. Each module shown will be stored in a storage medium. That is, at least the “input module 1701”, the “data structuring module 1702”, and the “multi-resolution decomposition module 170”
3 "" Zero tree symbol generation module 1704 "
“Variable length code generation module 1705”, “Transmission / storage module 1706”, “Reception / readout module 170”
7, "variable length decoding module 1708", "zero tree decoding module 1709", "data synthesis module 17"
10 "" 3D display data generation module 1711 "
What is necessary is just to store the program code of each module of the “display module 1712” in the storage medium.

[0054]

According to the present invention, several sets of unstructured data represented as a set of points including a position coordinate of a three-dimensional image and an attribute value representing a texture or the like at the position can be expressed by a rectangular lattice. And a structured two-dimensional array of position coordinates and attribute values of each set is obtained, and it is possible to decompose the data into multi-resolution components that maintain continuity at the boundary of the data domain.

The domain of the data is represented by a bitmap mask, and the original data can be reproduced from a bit sequence in which the transform coefficients and the bitmap mask only in the domain are greatly compressed using a variable length code.

For a boundary portion that is discontinuous between the object region and the background region, continuous repetitive data is generated by point-symmetrical folding around the boundary, and frequency decomposition (decoding) is performed by a filter having a symmetric weighting coefficient. By doing so, it becomes possible to perform subband division (synthesis) or wavelet transformation (inverse transformation) excluding the influence of the background region.

By performing the second loopback processing based on the bitmap mask and inversely converting the position and the attribute value, the structured data of the position and the attribute value can be decoded.

[0058]

[Brief description of the drawings]

FIG. 1A is a diagram in which densely sampled data is three-dimensionally displayed by a wire frame, and FIG. 1B is a diagram in which data obtained by thinning out sample points at places where the surface curvature is small is three-dimensionally displayed. is there.

FIG. 2 is a diagram illustrating unstructured data of position coordinates and attribute values.

FIG. 3 is a diagram illustrating a set of points in a three-dimensional space and a triangular patch expression.

FIG. 4 is a flowchart for generating a triangular patch from unstructured data.

FIG. 5 is a diagram illustrating a process of extracting an initial stripe from a triangular patch representation.

FIG. 6 is a diagram illustrating a process of associating a triangular patch with a rectangular grid.

FIG. 7 is a flow chart for integrating a triangular patch representation into a set of structurable data by a square grid.

FIG. 8 is a diagram illustrating a process of structuring data and generating a bitmap mask.

FIG. 9 is a diagram showing a configuration of a basic filter bank for subband division or wavelet transform.

FIG. 10 is a diagram illustrating a filter configuration of wavelet transform and divided frequency band components.

FIG. 11 is a diagram illustrating an analysis / synthesis filter having a weight coefficient symmetric with respect to the center.

FIG. 12 is a diagram for explaining the return of connected areas and band division processing.

FIG. 13 is a diagram illustrating multi-resolution decomposition of structured data and division processing of a bitmap mask.

FIG. 14 is a flowchart illustrating a compression process.

FIG. 15 is a flowchart for encoding structured data.

FIG. 16 is a flowchart illustrating a reproduction process.

FIG. 17 is a diagram illustrating the conversion coefficient wrapping processing in the reproduction processing.

FIG. 18 is a diagram showing the configuration of a basic filter bank for subband synthesis or inverse wavelet transform.

FIG. 19 is a diagram illustrating a configuration of a three-dimensional data compression device.

FIG. 20 is a diagram illustrating a configuration of a three-dimensional data restoration device.

FIG. 21 is a diagram showing a memory map of a storage medium.

[Explanation of symbols]

 1500 Three-dimensional data compression device 150 Input means 151 Data structuring means 152 Multi-resolution decomposition means 153 Zero tree symbol generation means 154 Variable length code generation means 155 Transmission / storage means 156 Shape data memory 157 Attribute value data memory 1600 3D Data restoration device 161 Receiving / reading means 162 Variable length code decoding means 163 Zero tree decoding means 164 Memory for multi-resolution data 165 Memory for bitmap mask 166 Data synthesizing means 167 Three-dimensional display data generating means 168 Display means

──────────────────────────────────────────────────続 き Continued on the front page (58) Fields surveyed (Int. Cl. ⁷ , DB name) G06T 15/00 G06T 17/00-17/40 H04N 7/30

Claims (5)

(57) [Claims] 1. An object present in a three-dimensional space is represented by a set of points including three-dimensional coordinate values of a sequence of points on the surface thereof and attribute values representing a texture or the like at a position indicated by the coordinate values. A triangular patch representation of the three-dimensional coordinate values of the object surface, and decomposing the adjacent relation of the triangular patches into a set of triangular patches that can be structured by the quadrangular lattice. A structuring step, in which a quadrangular lattice structured by each set of the triangular patches is associated with a two-dimensional array, and 1 is assigned to an array element associated with a vertex of the triangular patch, and 0 and creating a bitmap mask; and, according to the bitmap mask, the data domain for each component is used to determine the position and attribute value of the point corresponding to each point. After the mask is a two-dimensional array data that matches the first region, a method for compressing three-dimensional data, characterized in that it comprises a coding step of coding, the. 2. The step of structuring with a rectangular grid, starting from an arbitrary triangular patch, continuing left-right walking to the end, and matching the vertices of the extracted stripes with two adjacent straight lines of the rectangular grid; For each side on the left side along the axis of the extracted stripe, trace the triangle adjacent to the side to the end by the left-right walking, and associate the vertices of the extracted stripe with a square lattice. Performing the same processing on each side on the right side of the extracted stripe; and removing the extracted triangular patch, and then repeating the processing from stripe extraction on all sample points. 2. The method according to claim 1, further comprising: dividing the set of vertices into a set of vertices having adjacent relations associated with each other in the rectangular grid. 3. The method according to claim 1, wherein the encoding step determines a boundary between the target area and the background area from the bitmap mask.
And a point symmetrical folding in a horizontal direction or a vertical direction centering on the boundary portion based on the determination, and information of the position and the attribute value of the object area is copied to the corresponding background area. Folding step, frequency decomposition is performed using a filter having a symmetric weight coefficient for the object area and the copied area, and the obtained value in the object area is vertically or horizontally similar to the above. A frequency decomposition step of performing aliasing and frequency decomposition to obtain a multi-resolution representation in the object area; a zero tree symbol generation step of generating an encoded symbol by removing redundancy from the frequency-decomposed data; 2. A variable-length encoding step of generating a variable-length encoded bit sequence based on an encoded symbol. How to. 4. The method according to claim 3, wherein the frequency decomposition uses subband division or wavelet transform.
A method for compressing the described three-dimensional data. 5. A method for restoring compressed data of a point including three-dimensional coordinate values of an object existing in a three-dimensional space and attribute values representing a texture or the like at a position indicated by the coordinate values, A bitmap mask restoring step of restoring a bitmap mask having an element associated with each point based on the coordinate values of each point; three-dimensional coordinate values of the point corresponding to each point according to the bitmap mask And a restoration step of restoring the attribute values and the restored three-dimensional coordinate values and the bitmap mask.
Has the same connection relationship between position coordinates and attribute values as before encoding.
Reproducing a triangular patch to be reproduced .