3D Mesh Unfolding via Semidefinite Programming

Abstract

Mesh unfolding is a powerful pre-processing tool for many tasks such as non-rigid shape matching and retrieval. Shapes with articulated parts may exist large variants in pose, which brings difficulties to those tasks. With mesh unfolding, shapes in different poses can be transformed into similar canonical forms, which facilitates the subsequent applications. In this paper, we propose an automatic mesh unfolding algorithm based on semidefinite programming. The basic idea is to maximize the total variance of the vertex set for a given 3D mesh, while preserving the details by minimizing locally linear reconstruction errors. By optimizing a specifically-designed objective function, vertices tend to move against each other as far as possible, which leads to the unfolding operation. Compared to other Multi-Dimensional Scaling (MDS) based unfolding approaches, our method preserves significantly more details and requires no geodesic distance calculation. We demonstrate the advantages of our algorithm by performing 3D shape matching and retrieval in two publicly available datasets. Experimental results validate the effectiveness of our method both in visual judgment and quantitative comparison.