Geodesic squared exponential kernel for non-rigid shape registration

TL;DR

This paper introduces a geodesic squared exponential kernel for Gaussian Process Morphable Models to improve non-rigid 3D shape registration, especially around holes and curved regions, and enhances robustness to outliers.

Contribution

It proposes a novel geodesic-based kernel for GPMMs and a modified loss function for non-rigid ICP, improving registration accuracy and robustness.

Findings

Geodesic kernel outperforms state-of-the-art kernels on face registration.

Optimized hyperparameters improve registration accuracy.

Modified loss function increases robustness to outliers.

Abstract

This work addresses the problem of non-rigid registration of 3D scans, which is at the core of shape modeling techniques. Firstly, we propose a new kernel based on geodesic distances for the Gaussian Process Morphable Models (GPMMs) framework. The use of geodesic distances into the kernel makes it more adapted to the topological and geometric characteristics of the surface and leads to more realistic deformations around holes and curved areas. Since the kernel possesses hyperparameters we have optimized them for the task of face registration on the FaceWarehouse dataset. We show that the Geodesic squared exponential kernel performs significantly better than state of the art kernels for the task of face registration on all the 20 expressions of the FaceWarehouse dataset. Secondly, we propose a modification of the loss function used in the non-rigid ICP registration algorithm, that allows to weight the correspondences according to the confidence given to them. As a use case, we show that we can make the registration more robust to outliers in the 3D scans, such as non-skin parts.