Discrete time evolution process descriptor for shape analysis and matching

In shape analysis and matching, it is often important to encode information about the relation between a given point and other points on a shape, namely, its context. To this aim, we propose a theoretically sound and efficient approach for the simulation of a discrete time evolution process that runs through all possible paths between pairs of points on a surface represented as a triangle mesh in the discrete setting. We demonstrate how this construction can be used to efficiently construct a multiscale point descriptor, called the Discrete Time Evolution Process Descriptor, which robustly encodes the structure of neighborhoods of a point across multiple scales. Our work is similar in spirit to the methods based on diffusion geometry, and derived signatures such as the HKS or the WKS, but provides information that is complementary to these descriptors and can be computed without solving an eigenvalue problem. We demonstrate through extensive experimental evaluation that our descriptor can be used to obtain accurate results in shape matching in different scenarios. Our approach outperforms similar methods and is especially robust in the presence of large nonisometric deformations, including missing parts.