Amir Vaxman (Computer Science, Technion)
Studying the behavior of the heat diffusion process on a manifold
is emerging as an important tool for analyzing the geometry of the manifold.
Unfortunately, the high complexity of the computation of the heat kernel -
the key to the diffusion process - limits this type of analysis to 3D models
of modest resolution. We show how to use the unique properties of the heat
kernel of a discrete two dimensional manifold to overcome these limitations.
Combining a multi-resolution approach with a novel approximation method for
the heat kernel at short times results in an efficient and robust algorithm
for computing the heat kernels of detailed models. We show experimentally
that our method can achieve good approximations in a fraction of the time
required by traditional algorithms. Finally, we demonstrate how these heat
kernels can be used to improve a diffusion-based feature extraction
Joint work with Mirela Ben Chen (Stanford University) and Craig Gotsman"