A shape deformation algorithm for constrained multidimensional scaling

Abstract

We present a new Euclidean embedding technique based on volumetric shape registration. Extrinsic representation of the intrinsic geometry of a shape is preferable in various computer graphics applications as it poses only a small degrees of freedom to deal with during processing. A popular Euclidean embedding approach to achieve such a representation is multidimensional scaling (MDS), which, however, distorts the original geometric details drastically. Our method introduces a constraint on the original MDS formulation in order to preserve the initial geometric details while the input shape is pulled towards its MDS pose using the perfectly accurate bijection in between. The regularizer of this registration framework is chosen in such a way that the system supports large deformations yet remains fast. Consequently, we produce a detail-preserving MDS pose in 90s for a 53K-vertex high-resolution mesh on a modest computer. We can also add pairwise point constraints on the deforming shape without any additional cost. Detail-preserving MDS is superior for non-rigid shape retrieval and useful for shape segmentation, as demonstrated.