A Feature-Preserved Canonical Form for Non-rigid 3D Meshes

Measuring the dissimilarity between non-rigid objects is a challenging problem in 3D shape retrieval. One potential solution is to construct the models' 3D canonical forms (i.e., isometry-invariant representations in 3D Euclidean space) on which any rigid shape matching algorithm can be applied. However, existing methods, which are typically based on embedding procedures, result in greatly distorted canonical forms, and thus could not provide satisfactory performance to distinguish non-rigid models. In this paper, we present a feature-preserved canonical form for non-rigid 3D meshes. The basic idea is to naturally deform original models against corresponding initial canonical forms calculated by Multidimensional Scaling (MDS). Specifically, objects are first segmented into near-rigid subparts, and then, through properly-designed rotations and translations, original subparts are transformed into poses that correspond well with their positions and directions on MDS canonical forms. Final results are obtained by solving some nonlinear minimization problems for optimal alignments and smoothing boundaries between subparts. Experiments on a widely utilized non-rigid 3D shape benchmark not only verify the advantages of our algorithm against existing approaches, but also demonstrate that, with the help of the proposed canonical form, we can obtain significantly better retrieval accuracy compared to the state-of-the-art.