kNN-Res: Residual Neural Network with kNN-Graph Coherence for Point Cloud Registration

In this paper, we present a method based on a residual neural network for point set registration that preserves the topological structure of the target point set. Similar to coherent point drift (CPD), the registration (alignment) problem is viewed as the movement of data points sampled from a target distribution along a regularized displacement vector field. Although the coherence constraint in CPD is stated in terms of local motion coherence, the proposed regularization relies on a global smoothness constraint as a proxy for preserving local topology. This makes CPD less flexible when the deformation is locally rigid but globally non-rigid as in the case of multiple objects and articulate pose registration. A kNN-graph coherence cost and geometric-aware statistical distances are proposed to mitigate these issues. To create an end-to-end trainable pipeline, a simple Jacobian-based cost is introduced as a proxy for the intrinsically discrete kNN-graph cost. We present a theoretical justification for our Jacobian-based cost showing that it is sufficient for the preservation of the kNN-graph of the transformed point set. Further, to tackle the registration of high-dimensional point sets, a constant time stochastic approximation of the kNN-graph coherence cost is introduced. The proposed method is illustrated on several 2-dimensional examples and tested on high-dimensional flow cytometry datasets where the task is to align two distributions of cells whilst preserving the kNN-graph in order to preserve the biological signal of the transformed data .