Multiresolution Surfaces and Surface Processing

armadillo head with wireframe
head with a hole
leg with enhanced texture

Multiresolution surfaces are a natural extension of subdivision surfaces; in addition to refining a base control mesh using a fixed subdivision rule, details are added at each refinement step. The resulting mesh is a semiregular mesh, that is, most vertices of the mesh have fixed valence (same as for a regular grid), and only few isolated vertices have a different valence. This representation inherits many attractive features and efficiency of subdivision, while allowing one to represent high resolution surface geometry, either constructed from scratch or obtained using a 3D scanner.

One of the crucial advantages of multiresolution surfaces for representing most common high-resolutiuon surfaces comes from the fact that the connectivity of the mesh need not be explicitly stored, except for few extraordinary vertices, just as pixel adjacencies need not be explicit for an image. In most cases, connectivity of a fine mesh approximating a surface is an artifact of a triangulation process, such as marching cubes, and conversion to a semiregular mesh does not result in the loss of geometric information. Regular structure of multiresolution surfaces considerably reduces memory requirements, improves data coherence and allows one to use much more efficient algorithms.

Multiresolution surfaces are closely related to wavelet-based and overcomplete image representations, and more generally, makes surfaces much more similar to images. This makes it possible to generalize many of the signal processing techniques to handle geometric data, with applications in modification, compression and transmission of surface data (surface processing).

Our research in this area includes several directions:

More information coming soon!



Procedural Shape Synthesis on Subdivision Surfaces
Luiz Velho, Ken Perlin, Lexing Ying, Henning Biermann
Proc. SIBGRAPI 2001.
Sharp features on Multiresolution Subdivision Surfaces
Henning Biermann, Ioana M. Martin, Denis Zorin, Fausto Bernardini
Proc. Pacific Graphics 2001.
Texture and Shape Synthesis on Surfaces
Lexing Ying, Aaron Hertzmann, Henning Biermann, Denis Zorin
Proc. 12th Eurographics Workshop on Rendering, Jun 2001.
Boolean Operations on Free-form Solids
Henning Biermann, Daniel Kristjansson, Denis Zorin
Proc. SIGGRAPH 2001.
Interactive multiresolution mesh editing
D. Zorin, P. Schröder, W. Sweldens
Computer Graphics (SIGGRAPH '97 Proceedings), pp. 256-268.
Subdivision and Multiresolution Surfaces
Denis Zorin
Ph.D. Thesis, Caltech, 1998.