Efficient and Flexible Deformation Representation for Data-Driven Surface Modeling

Abstract

Effectively characterizing the behavior of deformable objects has wide applicability but remains challenging. We present a new rotation-invariant deformation representation and a novel reconstruction algorithm to accurately reconstruct the positions and local rotations simultaneously. Meshes can be very efficiently reconstructed from our representation by matrix predecomposition, while, at the same time, hard or soft constraints can be flexibly specified with only positions of handles needed. Our approach is thus particularly suitable for constrained deformations guided by examples, providing significant benefits over state-of-the-art methods. Based on this, we further propose novel data-driven approaches to mesh deformation and non-rigid registration of deformable objects. Both problems are formulated consistently as finding an optimized model in the shape space that satisfies boundary constraints, either specified by the user, or according to the scan. By effectively exploiting the knowledge in the shape space, our method produces realistic deformation results in real-time and produces high quality registrations from a template model to a single noisy scan captured using a low-quality depth camera, outperforming state-of-the-art methods.

Articulated‐Motion‐Aware Sparse Localized Decomposition

“…Gao et al . [GLL*16] introduced a new rotation invariant deformation representation called rotation‐invariant mesh difference (RIMD) representation and applied PCA to such representation for data‐driven deformation and registration.…”

Principal Geodesic Analysis in the Space of Discrete Shells

“…Fröhlich and Botsch [FB11] additionally introduce a bending term, expressing deformations in terms of changes to geometric quantities (triangle edge lengths and the dihedral angle between adjacent triangles). Gao et al [GLL*16] introduce a rotation‐invariant mesh difference representation in which plausible deformations often form a near linear subspace. The deformations produced by all of these approaches will not in general be realisable by a connected triangle mesh.…”

“…. We compare against [FB12] with 60 dimensions retained, the data‐driven approach of [GLL*16] using all training shapes and the Shell PCA model [ZHRS15]. Using only 20 dimensions, our model generalises almost as well as [GLL*16] and outperforms the other two models substantially.…”

“…Leave‐one‐out evaluation of generalisation error on the SCAPE data set compared to [GLL*16] (using all shapes), [FB12] (60 dimensions) and [ZHRS15]…”

“…[SZGP05], [FB11] and [GLL*16] are data‐driven and use the same set of training shapes as we use to build our model. These provide more natural results but [SZGP05] and [FB11] produce significant distortions and self‐intersections while even the state of the art [GLL*16] loses details, causes the arms to thin and the back to curve and deforms the head. Our result preserves details and retains plausible arms and head and a straight back.…”