AWEDD: a descriptor simultaneously encoding multiscale extrinsic and intrinsic shape features

We construct a novel descriptor called anisotropic wavelet energy decomposition descriptor (AWEDD) for non-rigid shape analysis, based on anisotropic diffusion geometry. We first extend the Dirichlet energy of the vertex coordinate function to an anisotropic version, then use multiscale anisotropic spectral manifold wavelets to decompose the Dirichlet energy to all vertices and collect local energy at each vertex to form AWEDD. AWEDD simultaneously encodes multiscale extrinsic and intrinsic shape features, which are more informative and robust than purely intrinsic or extrinsic descriptors. And the introduction of anisotropy endows AWEDD with stronger abilities of feature discrimination and intrinsic symmetry identification. Our results demonstrate that AWEDD is more discriminative than current state-of-the-art descriptors. In addition, we show that AWEDD is an excellent choice of the initial inputs for various shape analysis approaches, such as functional map pipelines and deep convolutional architectures.