Signed poisson map for shape analysis

Statistical shape analysis is a widely studied topic with applications ranging in biology, anatomy, neuroscience, agriculture, paleontology, etc. In many cases, two sets of shapes are input to the algorithm and the output is a mean shape with a scalar map defined on it indicating the local discrepancy between the two groups. In this work, we propose a new shape analysis algorithm. It is able to handle shapes with arbitrary topology. Specifically, the algorithm constructs a Signed Poisson Map (SPM) by solving two Poisson equations on the volumetric shapes, and statistical analysis is then carried out on the SPMs. The algorithm is tested on both synthetic and real shape data sets.