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Calculus of nonrigid surfaces for geometry and texture manipulation
Alexander Bronstein1, Michael Bronstein, Ron Kimmel
1Technion, Israel Institute of Technology, Haifa, Israel. bron@cs.technion.ac.il
IEEE Transactions on Visualization and Computer Graphics
|July 12, 2007
Summary
We developed a geometric method to find intrinsic correspondence between 3D nonrigid objects by modeling deformation and minimizing distortion. This enables manipulating object geometry and texture for applications like facial animation and virtual painting.
Area of Science:
- Computer Vision
- Computational Geometry
- 3D Computer Graphics
Background:
- Establishing intrinsic correspondence between nonrigid 3D objects is challenging.
- Deformations in 3D objects require robust mapping techniques.
Purpose of the Study:
- To present a novel geometric framework for automatic intrinsic correspondence detection.
- To enable manipulation of 3D object geometry and texture through a unified approach.
Main Methods:
- Modeling object deformation as near isometries.
- Finding correspondence via minimum-distortion mapping.
- Utilizing a generalization of multidimensional scaling.
Main Results:
- Achieved automatic intrinsic correspondence for 3D nonrigid objects.
- Enabled manipulation of extrinsic geometry and texture as linear space vectors.
- Demonstrated applications in expression-invariant texture mapping, exaggeration, morphing, and virtual painting.
Conclusions:
- The proposed geometric framework offers a powerful tool for 3D object correspondence.
- The method facilitates advanced applications in computer graphics and animation.
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