MorphModes: Non-rigid Registration via Adaptive Skinning Eigenmodes

TL;DR

This work tackles non-rigid registration by moving from closest-point-based NRICP to a volumetric SDF-matching framework. It constrains deformations with an adaptive Skinning Eigenmode subspace derived from the cotangent Laplacian, enabling a global-to-local, energy-efficient optimization without relying on regularizers. The key contributions are the SDF energy formulation, the spectral subspace construction, and the adaptive scheme that progressively incorporates higher-frequency modes to avoid degeneracies. Experiments across pose transfer, cross-category, and high-deformation scenarios demonstrate improved robustness and accuracy over NRICP, even with poor initial alignments or meshes of limited quality, highlighting a practical shift toward volumetric, geometry-aware registration.

Abstract

Non-rigid registration is a crucial task with applications in medical imaging, industrial robotics, computer vision, and entertainment. Standard approaches accomplish this task using variations on the Non-Rigid Iterative Closest Point (NRICP) algorithms, which are prone to local minima and sensitive to initial conditions. We instead formulate the non-rigid registration problem as a Signed Distance Function (SDF) matching optimization problem, which provides richer shape information compared to traditional ICP methods. To avoid degenerate solutions, we propose to use a smooth Skinning Eigenmode subspace to parameterize the optimization problem. Finally, we propose an adaptive subspace optimization scheme to allow the resolution of localized deformations within the optimization. The result is a non-rigid registration algorithm that is more robust than NRICP, without the parameter sensitivity present in other SDF-matching approaches.

Figures (14)

• Figure 1: Didactic illustration of the shrinkage occurring throughout non-rigid ICP iterations leading to incorrect registration.
• Figure 2: An example showing limb shrinkage occurring with ICP-based registration. Directly using NRICP leads to extreme shape collapse. Aligning the two meshes first using RICP, followed by NRICP leads to a better result, but with the back right leg of the hippo collapsing onto the belly. Our method leads to the correct registration.
• Figure 3: A didactic illustration of the null space problem in the SDF matching objective, which shows that twisting and collapsing the source surface onto itself leads to the same SDF as the true solution, so long as other parts of the source shape stretch to the target shape to compensate.
• Figure 4: A small affine subspace can align the source and target shape globally, but cannot capture localized deformations. A higher dimensional subspace allows for localized deformations, but exhibits null-space degeneracy. Our adaptive subspace scheme gradually refines the subspace, allowing for both global and localized deformations, while avoiding the null-space degeneracy.
• Figure 5: We visualize the first 7 skinning eigenmodes. As they increase in number the skinning eigenmodes describe higher frequency motion, enabling for more localized deformation to occur.