Approximately Isometric Shape Correspondence by Matching Pointwise Spectral Features and Global Geodesic Structures

Abstract

A practical method for finding correspondences between nonrigid isometric shapes is presented. It utilizes both pointwise surface descriptors, and metric structures defined on the shapes to perform the matching task, which is formulated as a quadratic minimization problem. Further, the paper explores the correspondence ambiguity problem arising when matching intrinsically symmetric shapes using only intrinsic surface properties. It is shown that when using isometry invariant surface descriptors based on eigendecomposition of the Laplace-Beltrami operator, it is possible to construct distinctive sets of surface descriptors for different possible correspondences. When used in a proper minimization problem, those descriptors allow us to explore number of possible correspondences between two given shapes.

Robust Nonrigid Registration by Convex Optimization

“…Many approaches guide the registration by computing local shape descriptors [11,29,32,34,33]. While this strategy has been successful for rigid matching [1], its application to nonrigid registration is complicated by the requirement that the descriptors themselves be invariant to deformations.…”

“…A number of nonrigid registration pipelines reformulate the objective as an integer quadratic program, which can then be approximately solved using integer programming techniques or by relaxation [11,31,32,34,47]. These formulations commonly suffer from extremely high computational complexity, which restricts their applicability to a small number of feature points [11,31,47].…”

“…These formulations commonly suffer from extremely high computational complexity, which restricts their applicability to a small number of feature points [11,31,47]. In particular, Wang et al [47] use an integer quadratic programming formulation and optimize it using the dual decomposition algorithm of Torresani et al [44].…”

Automatic posing of a meshed human model using point clouds

“…More serious is the problem posed by the symmetry present in the human body. Although spectral matchings are good in factoring out the isometric deformations [27,25], they sometimes provide wrong correspondences in presence of human body symmetries. For example, the left foot extremity in one model may match to that of the right foot in another model leading to catastrophic result when such a coarse matching is attempted to be extended to the whole body.…”

“…For example, the left foot extremity in one model may match to that of the right foot in another model leading to catastrophic result when such a coarse matching is attempted to be extended to the whole body. Taking the cue from [27], we try all possible matchings between only a very few extremities and settle on the one that provides the best overall matching in a spectral embedding.…”