Abstract:
Understanding shapes is an organic process for us (humans) as this is fundamental to our interaction with the surrounding world. However, it is daunting for the machines. Any shape analysis task, particularly non-rigid shape correspondence is challenging due to the ever-increasing resolution of datasets available. Shape Correspondence refers to finding a mapping among various shape elements. The functional map framework deals with this problem efficiently by not processing the shapes directly but rather specifying an additional structure on each shape and then performing analysis in the spectral domain of the shapes. To determine the domain, the Laplace-Beltrami operator has been utilized generally due to its capability of capturing the global geometry of the shape. However, it tends to smoothen out high-frequency features of shape, which results in failure to capture fine details and sharp features of shape for the analysis. To capture such high-frequency sharp features of the shape, this work proposes to utilize a Hamiltonian operator with gaussian curvature as an intrinsic potential function to identify the domain. Computationally it is defined at no additional cost, keeps global structural information of the shape intact and preserves sharp details of the shape in order to compute a better point-to-point correspondence map between shapes.
