Shape Compression using Spherical Geometry Images

Question

1. What contributions have the authors mentioned in the paper "Shape compression using spherical geometry images" ?

2. What future works have the authors mentioned in the paper "Shape compression using spherical geometry images" ?

3. What is the limitation of the spherical parametrization approach?

4. What is the way to compress the geometry of irregular meshes?

Accepted Answer

The authors recently introduced an algorithm for spherical parametrization and remeshing, which allows resampling of a genus-zero surface onto a regular 2D grid, a spherical geometry image.. In this paper, the authors detail two wavelet-based approaches for shape compression using spherical geometry images, and provide comparisons with previous compression schemes.

Accepted Answer

One area of future work is to attempt to reduce these rippling effects by modifying the parametrization process.. One possibility would be to encode a separate bit-plane indicating which subset of samples lie in the “ holes ” of the remeshed model.. The accuracy of remesh representations can be improved by refitting to the original model as an optimization ( e. g. [ 23 ] ).

Accepted Answer

For shapes containing many extremities, the parametrization onto the sphere suffers from distortion, and these distortions give rise to rippling effects under lossy reconstruction.

Accepted Answer

Since shape compression is generally lossy, resampling the geometry onto a new mesh (with different connectivity) is quite reasonable.

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To compute a local frame for each “odd” sample, the authors first obtain vectors corresponding to the row and column directions of the grid.

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In the remeshing approach of Attene et al. [5], an irregular-mesh compression algorithm resamples geometry as it traverses the mesh, by incrementally wrapping the mesh with isosceles triangles.

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Standard tricks used in signal processing to extend an image beyond its borders include replicating the boundary samples or reflecting the image across its boundaries.

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These include progressive meshes [14], progressive forest split compression [27], and the valence-driven simplification approach of Alliez and Desbrun [2].

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The globally smooth parametrization of Khodakovsky et al. [18] reduces the entropy of these tangential components by constructing a remesh that is parametrically smooth across patch boundaries.

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The many compression techniques can be categorized into two broad approaches: irregular mesh compression and remeshing compression, depending on whether or not they preserve the original mesh connectivity.

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if the map is one-to-one prior to inserting a new vertex, it can be shown that the new vertex’s neighborhood is always non-empty, and thus new vertices can always be inserted into the parametrization while maintaining a bijection.

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It is advantageous to enforce consistency at all the resolution levels, rather than just once at the end, in order to avoid “step functions” from appearing in the result.

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The samples of the octahedron are then associated with the grid locations of a square geometry image by cutting four edges of the octahedron meeting at a vertex, and unfolding the four faces incident to the vertex like flaps.

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The drawback of basing the prediction model on a local neighborhood is that it cannot capture the low-frequency features of the model.

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this spectral analysis is costly and unstable, and therefore becomes practical only when performed piecewise on a partitioned model.

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The mesh-based spherical wavelet scheme seems more natural for coding geome-try, and provides good reconstruction of sharp detail at very low bit budgets.

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Compressing the geometry of irregular meshes is difficult because the irregular sampling does not admit traditional multiresolution wavelet hierarchies.

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One possibility would be to encode a separate bit-plane indicating which subset of samples lie in the “holes” of the remeshed model.

Accepted Answer

The reason is that the spherical wavelet kernels have more localized support than the particular image wavelets that the authors used, and therefore adapt more quickly to the fine detail.

Accepted Answer

they help the prediction for the samples near the boundaries, since the image signal appears smooth not only in the interior of the image but also near its borders (see Fig. 6).

Shape Compression using Spherical Geometry Images

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Most frequently asked questions

1. What contributions have the authors mentioned in the paper "Shape compression using spherical geometry images" ?

2. What future works have the authors mentioned in the paper "Shape compression using spherical geometry images" ?

3. What is the limitation of the spherical parametrization approach?

4. What is the way to compress the geometry of irregular meshes?

5. How do the authors compute the local frame for each odd sample?

6. What is the remeshing approach of Attene et al.?

7. What is the way to extend an image beyond its borders?

8. What are some of the schemes that support progressive representations of irregular meshes?

9. How does the remeshing of a triangle mesh work?

10. What are the two broad approaches to compression of geometry?

11. How can the authors show that a new vertex is always non-empty?

12. Why is it advantageous to enforce the constraints at all the resolution levels?

13. How do the authors map the octahedron to the square?

14. What is the drawback of basing the prediction model on a local neighborhood?

15. What is the disadvantage of spectral analysis?

16. What is the way to code a spherical wavelet?

17. What is the problem with irregular meshes?

18. What is the possibility of encoding a bit-plane?

19. Why do the graphs show the spherical wavelets?

20. What are the constraints that help the prediction of the 3D model?

Figures

Citations

Mesh parameterization: theory and practice

Mesh Parameterization Methods and Their Applications

Technologies for 3D mesh compression: A survey

3D Mesh Compression: Survey, Comparisons, and Emerging Trends

Compression of point-based 3D models by shape-adaptive wavelet coding of multi-height fields

References

Image coding using wavelet transform

Progressive meshes

Multiresolution analysis of arbitrary meshes

Geometry images

Spherical wavelets: efficiently representing functions on the sphere

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Spherical parametrization and remeshing

Progressive meshes

Spectral compression of mesh geometry

Triangle mesh compression