Minimal Surfaces for 3D Shape Matching: A Linear Programming Solution

We propose a novel method for computing a spatially dense matching between two 3D shapes. It is based on finding a minimal surface in the high-dimensional space representing the product of two shape surfaces. Computationally, the proposed approach leads to a binary linear program whose relaxed version can be solved efficiently in a globally optimal manner. We consider two cost functions for matching. The first one aims at computing a matching which minimizes a thin-shell energy measuring the physical energy necessary to deform one shape into the other. The second one additionally imposes that corresponding elements on either surface should have a similar local feature descriptor. Experimental results demonstrate that the proposed LP relaxation allows to compute high-quality matchings which reliably put into correspondence articulated 3D shapes.      «

We propose a novel method for computing a spatially dense matching between two 3D shapes. It is based on finding a minimal surface in the high-dimensional space representing the product of two shape surfaces. Computationally, the proposed approach leads to a binary linear program whose relaxed version can be solved efficiently in a globally optimal manner. We consider two cost functions for matching. The first one aims at computing a matching which minimizes a thin-shell energy measuring the phy...     »