NRGA: Gravitational Approach for Non-rigid Point Set Registration

Abstract

This article introduces a new physics-based method for rigid point set alignment called Fast Gravitational Approach (FGA). In FGA, the source and target point sets are interpreted as rigid particle swarms with masses interacting in a globally multiply-linked manner while moving in a simulated gravitational force field. The optimal alignment is obtained by explicit modeling of forces acting on the particles as well as their velocities and displacements with second-order ordinary differential equations of motion. Additional alignment cues (point-based or geometric features, and other boundary conditions) can be integrated into FGA through particle masses. We propose a smooth-particle mass function for point mass initialization, which improves robustness to noise and structural discontinuities. To avoid prohibitive quadratic complexity of all-to-all point interactions, we adapt a Barnes-Hut tree for accelerated force computation and achieve quasilinear computational complexity. We show that the new method class has characteristics not found in previous alignment methods such as efficient handling of partial overlaps, inhomogeneous point sampling densities, and coping with large point clouds with reduced runtime compared to the state of the art. Experiments show that our method performs on par with or outperforms all compared competing non-deep-learning-based and general-purpose techniques (which do not assume the availability of training data and a scene prior) in resolving transformations for LiDAR data and gains state-of-the-art accuracy and speed when coping with different types of data disturbances.

HandVoxNet++: 3D Hand Shape and Pose Estimation using Voxel-Based Neural Networks

“…For this reason, alternatively to DispVoxNet and GCN-MeshReg (Sec. 4.3.1), we propose NRGA++, i.e., a classical physicsbased algorithm for registering the template mesh VT with the reference voxelized hand VS , which is a modified version of NRGA [19]. Our choice falls to NRGA as it preserves local hand mesh topology and is robust to noise present in VS .…”

“…For the endeffectors, e.g., we select half of the vertices present in the segment nearest joint. Apart from that, all steps of NRGA++ are as in the original NRGA (e.g., k-d tree building and calculating the consensus per-point transformations), see [19] for more details. The proposed segment-wise point set alignment strategy leads to a significant improvement in runtime performance of NRGA++.…”

“…To combine the advantages of both representations, we register the estimated hand surface to the estimated voxelized hand shape. In [17], we introduced two different variants of shape registration methods, i.e., CNN-based [18] and NRGA-based [19]. In this article, we propose two additional novel and more accurate registration algorithms, namely GCN-MeshReg and NRGA++.…”

“…In the GCN-MeshReg, we employ graph convolutions to explicitly utilize the topology of the hand shape. The Non-Rigid Gravitational Approach (NRGA) for point set alignment [19] is extended to support segmented hand surface. We call this extended version of the registration method NRGA++.…”

DispVoxNets: Non-Rigid Point Set Alignment with Supervised Learning Proxies

“…Recently, physics-based alignment approaches were discovered [11,15,1,30,19]. Deng et al [11] minimise a distance metric between Schrödinger distance transforms performed on the point sets.…”