High-Pass Quantization for Mesh Encoding (English)

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Any quantization introduces errors. An important question is how to suppress their visual effect. In this paper we present a new quantization method for the geometry of 3D meshes, which enables aggressive quantization without significant loss of visual quality. Conventionally, quantization is applied directly to the 3-space coordinates. This form of quantization introduces high-frequency errors into the model. Since high-frequency errors modify the appearance of the surface, they are highly noticeable, and commonly, this form of quantization must be done conservatively to preserve the precision of the coordinates. Our method first multiplies the coordinates by the Laplacian matrix of the mesh and quantizes the transformed coordinates which we call "d-coordinates". We show that the high-frequency quantization errors in the d-coordinates are transformed into low-frequency errors when the quantized d-coordinates are transformed back into standard Cartesian coordinates. These low-frequency errors in the model are much less noticeable than the high-frequency errors. We call our strategy high-pass quantization, to emphasize the fact that it tends to concentrate the quantization error at the low-frequency end of the spectrum. To allow some control over the shape and magnitude of the low-frequency quantization errors, we extend the Laplacian matrix by adding a number of spatial constraints. This enables us to tailor the quantization process to specific visual requirements, and to strongly quantize the d-coordinates.

Table of contents conference proceedings

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Provably Good Surface Sampling and Approximation
Boissonnat, J-D. / Oudot, S. | 2003
Explicit Surface Remeshing
Surazhsky, Vitaly / Gotsman, Craig | 2003
Domain Decomposition for Multiresolution Analysis
Boier-Martin, Ioana M. | 2003
High-Pass Quantization for Mesh Encoding
Sorkine, Olga / Cohen-Or, Daniel / Toledo, Sivan | 2003
Geometry Compression of Normal Meshes Using Rate-Distortion Algorithms
Lavu, Sridhar / Choi, Hyeokho / Baraniuk, Richard | 2003
Edge-Sharpener: Recovering sharp features in triangulations of non-adaptively re-meshed surfaces
Attene, Marco / Falcidieno, Bianca / Rossignac, Jarek / Spagnuolo, Michela | 2003
A scalable data structure for three-dimensional non-manifold objects
Floriani, Leila De / Hui, Annie | 2003
A concise b-rep data structure for stratified subanalytic objects
Gomes, Abel J.P. | 2003
CLODs: Dual Hierarchies for Multiresolution Collision Detection
Otaduy, Miguel A. / Lin, Ming C. | 2003
Simple Silhouettes for Complex Surfaces
Kirsanov, D. / Sander, P. V. / Gortler, S. J. | 2003
Statistical Point Geometry
Kalaiah, Aravind / Varshney, Amitabh | 2003
Efficient Max-Norm Distance Computation and Reliable Voxelization
Varadhan, Gokul / Krishnan, Shankar / Kim, Young J. / Diggavi, Suhas / Manocha, Dinesh | 2003
Global Conformal Surface Parameterization
Gu, Xianfeng / Yau, Shing-Tung | 2003
Smooth Geometry Images
Losasso, F. / Hoppe, H. / Schaefer, S. / Warren, J. | 2003
Multi-Chart Geometry Images
Sander, P. V. / Wood, Z. J. / Gortler, S. J. / Snyder, J. / Hoppe, H. | 2003
Rotation Invariant Spherical Harmonic Representation of 3D Shape Descriptors
Kazhdan, Michael / Funkhouser, Thomas / Rusinkiewicz, Szymon | 2003
A Geometric Database for Gene Expression Data
Ju, Tao / Warren, Joe / Eichele, Gregor / Thaller, Christina / Chiu, Wah / Carson, James | 2003
Estimating Differential Quantities Using Polynomial Fitting of Osculating Jets
Cazals, F. / Pouget, M. | 2003
Stellar Subdivision Grammars
Velho, Luiz | 2003
Filling Holes in Meshes
Liepa, Peter | 2003
Mesh Forging: Editing of 3D-Meshes Using Implicitly Defined Occluders
Bendels, G. H. / Klein, R. | 2003
A Geometric Convection Approach of 3-D Reconstruction
Chaine, Raphaëlle | 2003
A Geometric-Based Convection Approach of 3-D Reconstruction
Chaine, R. / Eurographics / ACM SIGGRAPH | 2003
Approximating and Intersecting Surfaces from Points
Adamson, Anders / Alexa, Marc | 2003
Approximate Implicitization Via Curve Fitting
Wurm, E. / Jüttler, B. | 2003
3D Reconstruction Using Labeled Image Regions
Ziegler, Remo / Matusik, Wojciech / Pfister, Hanspeter / McMillan, Leonard | 2003