High-Pass Quantization for Mesh Encoding

EUROGRAPHICS/ACM SIGGRAPH Symposium on Geometry Processing 2003
Olga Sorkine-Hornung, Daniel Cohen-Or, Sivan Toledo
ACM Transactions on Graphics 24(4), 2005

High-Pass Quantization for Mesh Encoding

The delta-coordinates quantization to 5 bits/coordinate (left) introduces low-frequency errors to the geometry, whereas Cartesian coordinates quantization to 11 bits/coordinate (right) introduces noticeable high-frequency errors. The upper rows shows the quantized model and the bottom figures use color to visualize corresponding quantization errors.


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 "delta-coordinates". We show that the high-frequency quantization errors in the delta-coordinates are transformed into low-frequency errors when the quantized delta-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 delta-coordinates.applications.


low-frequency errors are less noticeable

The human perception seems to be more sensitive to normals/lighting errors.

Can you see a difference between these two horses?

Horse unquantized Horse 1 anchor

original model

delta-quantization (8 b/c, 1 anchor)

There is a big difference in terms of geometric RMS error, but small "smoothness" or "normals" error.

Horses animation

some results

Max-Planck original model Max-Planck delta-quantization Max-Planck Cartesian quantization

Max Planck - original mesh

Entropy: 7.6252

Cartesian quantization
Entropy: 7.6481

Horse original model Horse delta-quantization Horse Cartesian quantization

Horse - original model

Entropy: 10.3095

Cartesian quantization
Entropy: 10.3131

Fandisk original Fandisk delta-quantization Fandisk Cartesian quantization

Fandisk - original model

Entropy: 6.6912

Cartesian quantization
Entropy: 7.1767


We would like to thank Tali Irony for helping us with the implementation. The Max-Planck and Fandisk models are courtesy of Christian Roessl and Jens Vorsatz of Max-Planck-Institut fuer Informatik. This work was supported in part by grants from the Israel Science Foundation (founded by the Israel Academy of Sciences and Humanities), by the Israeli Ministry of Science, by an IBM Faculty Partnership Award, by the German Israel Foundation (GIF) and by the EU research project "Multiresolution in Geometric Modelling (MINGLE)" under grant HPRN-CT-1999-00117.