GB2336979A

GB2336979A - Triangular mesh decimation method and apparatus

Info

Publication number: GB2336979A
Application number: GB9827012A
Authority: GB
Inventors: Kwang-Sung Shin
Original assignee: Daewoo Electronics Co Ltd
Current assignee: WiniaDaewoo Co Ltd
Priority date: 1998-04-28
Filing date: 1998-12-08
Publication date: 1999-11-03
Also published as: KR100269431B1; GB9827012D0; KR19990081321A

Abstract

A triangular mesh decimation method and apparatus acquires a 3 dimensional image for an object, wherein the 3 dimensional image contains vertices on the surface of the object, each vertex having a depth value representing a distance from a predetermined base plane. The 3 dimensional image is highpass filtered to detect salient vertices and the salient vertices are marked to provide a marked 3 dimensional image, wherein each of the salient vertices has a depth value substantially larger than depth values of its adjacent vertices. A marked triangular mesh corresponding to the marked 3 dimensional image is generated based thereon, with the salient vertices being still marked. Then, non-salient vertices in the marked triangular mesh are decimated, wherein the non-salient vertices are vertices exclusive of the salient vertices.

Description

2336979 TRIANGULAR MESH DECIMATING METHOD AND APPARATUS BY USING A

HIGHPASS FILTER The present invention relates to a method and apparatus for decimating a triangular mesh; and, more particularly, to a method and apparatus for efficiently selecting vertices to be decimated by using a highpass filter to thereby provide an adaptively decimated mesh.

is A polygon is still a popular graphics primitive for computer graphics applications. Consequently, computer rendering of polygons is widely supported by commercial graphics hardware and software. However, because of the linearity of the polygon, thousands to millions of primitives are often required to approximate the details of a complex geometry. Models of such magnitudes are generally not practicable since the rendering speeds and memory requirements are proportional to the number of polygons.

The basic problem lies in the fact that the techniques that generate large polygonal meshes are extremely valuable; and, furthermore, they cannot be easily modified to produce fewer polygons. Hence a general technique for reducing or decimating a mesh composed of a large number of polygons to one containing fewer polygons is necessary. Furthermore, for - 1 the decimation process to be truly effective, it must be able to preserve the topological and shape properties of the original mesh.

"Decimation of Triangle Meshes" by Schroeder et al., Computer Graphics., 26, No-22, pp.65-70, July 1992, describes an algorithm which reduces the number of triangles required to model a physical or abstract object. In the Schroeder technique, multiple passes are made over an existing triangular mesh by using the local geometry and topology to remove vertices that satisfy a distance or an angle criterion. Holes left by the vertices removed are patched by using a local triangulation process.

Referring to Figs. 1A and IB, there are depicted 5 types of vertices, wherein each vertex may be classified into one of the 5 types.

A vertex 110 is a simple vertex surrounded by a complete cycle of triangles, and each edge that passes through the vertex 110 is shared by exactly 2 triangles.

If only a dihedral angle between 2 adjacent triangles is greater than a predetermined angle threshold, then an edge shared by the 2 adjacent triangles is a feature edge. In Fig. 1A, a feature edge 123 is shared by 2 adjacent triangles 121 and 122, and a feature edge 126 is shared by 2 adjacent triangles 124 and 125. A vertex 120 shared by the 2 feature edges 123 and 126 is an interior edge vertex.

If one or three or more feature edges use a vertex, the is vertex is classified a corner vertex. In Fig. 1A, a feature edge 133 is shared by 2 adjacent triangles 131 and 132, a feature edge 135 is shared by 2 adjacent triangles 131 and 134, and a feature edge 138 is shared by 2 adjacent triangles 136 and 137. Thus, a vertex 130 is a corner vertex.

If a vertex is on the boundary of a mesh, i.e., within a semicycle of triangles as shown in a vertex 140 of Fig. IB, the vertex is a boundary vertex.

if a vertex is shared by triangles in a cycle and triangles not in the cycle, like a vertex 150 of Fig. IB, the vertex is a complex vertex. Complex vertices are not to be deleted from a mesh. All other vertices are candidates for deletion.

After the vertices has been classified, it is determined whether or not the triangles forming a cycle can be deleted and replaced by another triangulation exclusive of the original vertex.

Simple vertices employ a distance to a plane criterion, as shown in Fig. 2A. An average plane 210 is constructed by using a predetermined scheme, and a distance 220 from the simple vertex 110 to the average plane 210 is calculated. Or, the distance from the simple vertex 110 to each of 6 triangles which share the simple vertex 110 is calculated and averaged. If either one of the calculated and the averaged distances is smaller than a predetermined distance threshold, the simple vertex 110 may be deleted.

- 3 Boundary and interior edge vertices use a distance to an edge criterion, as shown in Fig. 2B. A straight line connecting 2 vertices creating a. boundary or a feature edge is generated and a distance from a boundary or an interior edge vertex to the straight line is calculated. For an exemplary case of the boundary vertex 140, a straight line 230 connecting 2 vertices creating a boundary is generated and a distance 240 from the boundary vertex 140 to the straight line 230 is calculated. If the distance 240 is smaller than the predetermined distance threshold, the boundary vertex 140 can be deleted.

Corner vertices, which are usually not deleted, are occasionally evaluated by using c-he distance to a plane criterion when a mesh contains areas of relatively small is triangles with large dihedral angles, contributing relatively little to the geometric approximation.

If a vertex is eliminated, a loop created by removing triangles using the vertex from a cycle must be triangulated. Deleting a vertex and its associated triangles creates one loop for the case of a simple or a boundary vertex or 2 loops for the case of an interior edge vertex. Within each loop, triangles that approximate the original cycle as closely as possible must be created.

Each loop to be triangulated is divided into 2 halves.

The division is done along a split line defined from two nonneighboring vertices in the loop. Each new loop is divided 4 - again until only three vertices remain therein. A loop of three vertices forms a triangle that may be added to the mesh.

In Fig. 3, an average plane 310 containing a loop 340, a split line 330 and a split plane 320 which contains the split line 330 and is orthogonal to the average plane 310 are depicted. Typically, each loop may be split in more than one way. In this case, a best split plane must be selected. One of the selection criteria is an aspect ratio. The aspect ratio is defined as the minimum distance of the loop vertices to the split plane, divided by the length of the split line. The best split plane is the one that yields the maximum aspect ratio. Constraining this ratio to be greater than a specified value, e.g., 0.1, produces acceptable meshes. When it fails to produce a successful split, the removed vertex and surrounding triangles should be reinstated.

However, one of the difficulties with the Schroeder technique is that it is relatively slow since the process for selecting vertices to be decimated is time-consuming. Therefore, there has existed a need to develop a mesh data reduction scheme capable of selecting vertices to be decimated more efficiently.

It is, therefore, a primary object of the invention to provide a method and apparatus for efficiently selecting vertices to be decimated by using a highpass filter to thereby - is provide an adaptively decimated mesh.

In accordance with one aspect of the present invention, there is provided a triangular mesh decimation method, comprising the steps of: (a) acquiring a 3 dimensional image of an object, wherein the 3 dimensional image contains vertices, each vertex having a depth value; (b) highpass filtering the 3 dimensional image to detect salient vertices and marking the salient vertices, wherein each of the salient vertices has a depth value substantially larger than at least one of the depth values of its adjacent vertices; (c) generating a marked triangular mesh corresponding to the 3 dimensional image, with the salient vertices being still marked; and (d) decimating non-salient vertices in the marked triangular mesh, wherein the non-salient vertices are vertices exclusive of the salient vertices.

in accordance with another aspect of the present in.,re.-.:ion, there is provided a triangular mesh decimation apparatus, comprising: a block for acquiring a 3 dimensional image for an object, wherein the 3 dimensional image contains ver-t-c:es,. each vertex having a depth value; a block for detecting salient vertices, wherein each of the salient vertices has a depth value substantially larger than at least one of the depth values of its adjacent vertices; a block for marking the detected salient vertices to provide a marked 3 dimensional image; a block for converting the marked 3 dimensional image into a marked triangular mesh, with the - 6 salient vertices being still marked, and a block for decimating non- salient vertices in the marked 3 dimensional image, wherein the non- salient vertices are vertices exclusive of the salient vertices.

is The above and other objects and features of the present invention will become apparent from the following description of preferred embodiments given in conjunction with the accompanying drawings, in which:

Fig. 1A represents a simple vertex, an interior edge vertex, and a corner vertex; Fig. 1B provides a boundary vertex and a complex vertex; Fig. 2A presents a distance to a plane criterion; Fig. 2B shows a distance to an edge criterion; Fig. 3 describes a loop splitting scheme; and Fig. 4 illustrates a triangular mesh decimation apparatus in accordance with a preferred embodiment of the present invention.

Referring to Fig. 4, there is illustrated an adaptive triangular mesh decimating apparatus 400 in accordance with a preferred embodiment of the present invention, wherein the apparatus 400 comprises a 3 dimensional (3D) image acquisition block 410, a highpass filtering block 420, a mesh generation block 430 and a mesh decimation block 440.

The 3D image acquisition block 410 acquires a 3D image of an object by means of, for example, a 3D scanner, wherein the 3D image comprises vertices on the surface of the object, each vertex having a depth value representing a distance from the 3D scanner to the vertex. The acquired 3D image is applied to the highpass filtering block 420.

The highpass filtering block 420 classifies the vertices into two groups, wherein vertices of a first group can be decimated in further processing and vertices of a second group forming sharp edges cannot be decimated. In order to classify the vertices, the highpass filtering block 420 includes a highpass filter for detecting an edge quantity of the 3D image. In general, a highpass filter is used to emphasize edges of an image, wherein pixels in the image have pixel values representing luminance or chrominance values. However, the highpass filter of the present invention performs the same processing on depth values of the vertices instead of pixel values thereof.

The.highpass filter of the present invention calculates differences between a depth value of each vertex and depth values of its adjacent vertices. If one or more calculated differences are greater than a predetermined threshold, the vertex is classified into the second group; and if otherwise, the vertex is classified into the first group. The highpass filtering block 420 marks vertices classified into the second 8 group in the 3D image and provides the marked 3D image to the mesh generation block 430.

The mesh generation block 430 converts the marked 3D image into a marked triangular mesh, with the vertices of the second group is still marked. The marked triangular mesh is provided to the mesh decimation block 440.

The mesh decimation block 440 performs a triangular mesh decimation process on the marked triangular mesh while excluding the marked vertices of the second group from further processing. Remaining vertices in the marked triangular mesh are decimated based on, e.g., a Schroeder's triangular mesh decimation scheme. In detail, each of the remaining vertices is classified into one of 5 kinds of vertices, i.e., a simple vertex, a boundary vertex, an interior edge vertex, a corner vertex and a complex vertex, and an appropriate decimation process is performed based thereon.

Accordingly, in accordance with the present invention, the processing time can be substantially reduced since vertices forming sharp edges are simply detected by using a highpass'filter and only the remaining vertices are further processed for decimating.

While the present invention has been described with respect to certain preferred embodiments only, other modifications and variations may be made without departing from the scope of the present invention as set forth in the following claims.

Claims

Claims:

1. A triangular mesh decimation method, comprising the steps of:

(a) acquiring a 3 dimensional image of an object, wherein the 3 dimensional image contains vertices, each vertex having a depth value; (b) highpass filtering the 3 dimensional image to detect salient vertices and marking the salient vertices, wherein each of the salient vertices has a depth value substantially larger than at least one of the depth values of its adjacent vertices; (c) generating a marked triangular mesh corresponding to the 3 dimensional image, with the salient vertices being still marked; and (d) decimating non-salient vertices in the marked triangular mesh, wherein the non-salient vertices are vertices exclusive of the salient vertices.

2. The method of claim 1, wherein the step (b) includes the steps of:

(bl) calculating differences between the depth value of each vertex and the depth values of its adjacent vertices; (b2) classifying said each vertex into a salient vertex if one or more calculated differences are greater than a predetermined threshold, and classifying said each vertex into a non-salient vertex if otherwise; and (b3) marking the salient vertices.

3. The method of claim 1 or 2, wherein the vertices are on the surface of the object.

4 The method of any of claims 1 to 3, wherein the depth value represents a distance from a predetermined base plane.

5. A triangular mesh decimation apparatus, comprising:

means for acquiring a 3 dimensional image for an object, wherein the 3 dimensional image contains vertices, each vertex having a depth value; means for detecting salient vertices, wherein each of the salient vertices has a depth value substantially larger than at least one of the depth values of its adjacent vertices; means for marking the detected salient vertices to provide a marked 3 dimensional image; means for converting the marked 3 dimensional image into a marked, triangular mesh, with the salient vertices being still marked; and means for decimating non-salient vertices in the marked 3 dimensional image, wherein the non-salient vertices are vertices exclusive of the salient vertices.

6. The apparatus of claim 5, wherein the detecting means 11 includes: means for calculating differences between a depth value of each vertex and the depth values of its adjacent vertices; means for classifying said each vertex into a salient vertex if one or more calculated differences are greater than a predetermined threshold, and classifying said each vertex into a non-salient vertex if otherwise; and means for markinST the salient vertices.

7. The apparatus of claim 5 or 6, wherein the vertices are on the surface of the object.

8. The apparatus of any of claims 5 to 7, wherein the depth value represents a distance from a predetermined base plane.

is 9. A triangular mesh decimation method, substantially as herein described with reference to or as shown in figures 1 to 4 of the accompanying drawings.

19. A triangular mesh decimation method, constructed and arranged substantially as herein described with reference to or as shown in figures 1 to 4 of the accompanying drawings.

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