Heat Diffusion Over Weighted Manifolds: A New Descriptor for Textured 3D Non-Rigid Shapes

Mostafa Abdelrahman, Aly Farag, David Swanson, Moumen T. El-Melegy; Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2015, pp. 187-195

This paper propose an approach for modeling textured 3D non-rigid models based on Weighted Heat Kernel Signature(W-HKS). As a first contribution, we show how to include photometric information as a weight over the shape manifold, we also propose a novel formulation for heat diffusion over weighted manifolds. As a second contribution we present a new discretization method for the proposed equation using finite element approximation. Finally, the weighted heat kernel signature is used as a shape descriptor. The proposed descriptor encodes both the photometric, and geometric information based on the solution of one equation. We also propose a new method to introduce the scale invariance for the weighted heat kernel signature. The performance is tested on two benchmark datasets. The results have indeed confirmed the high performance of the proposed approach on the textured shape retrieval problem, and show that the proposed method is useful in coping with different challenges of shape analysis where pure geometric and pure photometric methods fail.