kNN-Res: Residual Neural Network with kNN-Graph coherence for point cloud registration (2304.00050v3)

Abstract: 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. The implementation of the proposed approach is available at https://github.com/MuhammadSaeedBatikh/kNN-Res_Demo/ under the MIT license.

• The paper presents kNN-Res, integrating residual neural networks with a kNN-graph coherence constraint to enhance point cloud registration.
• It employs innovative Jacobian-based cost functions and geometric-aware statistical distances to maintain local topology amid complex deformations.
• Experimental results on synthetic and biological datasets show improved alignment accuracy and preserved neighborhood structures compared to CPD.

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

This paper presents a novel method, termed kNN-Res, for aligning point clouds through residual neural networks (ResNets) enhanced by a k-nearest neighbor (kNN) graph coherence constraint. This approach addresses the intricate task of point set registration, specifically focusing on maintaining the topological integrity of the target point set. The authors take inspiration from Coherent Point Drift (CPD), aiming to overcome its limitations in handling complex deformations that are locally rigid but globally non-rigid.

Methodological Innovations

The primary innovation of the kNN-Res method is the incorporation of Jacobian-based cost functions and geometric-aware statistical distances into the registration process. This is motivated by the need for more flexible transformations that preserve local topology and can adapt to intricate global deformations. The regularization term based on global smoothness serves as a proxy for maintaining local coherence, a concept that significantly differentiates this work from traditional CPD, which primarily relies on local constraints.

The concept is further advanced by employing a Jacobian orthogonality loss. This measure, represented as the deviation of the Jacobian matrix's orthogonality from the identity matrix, is pivotal for preserving the kNN-graph structure throughout the registration process. This structured approach ensures the biological signals in high-dimensional data, such as flow cytometry, remain intact post-transformation.

Experimental Validation

The kNN-Res method is comprehensively evaluated across both low-dimensional synthetic datasets and high-dimensional biological datasets, such as those derived from flow cytometry. It demonstrates significant improvements over existing methods, such as CPD and other variants, particularly when handling deformable shapes with complex characteristics. The experimental results highlight the method's proficiency in not only enhancing alignment accuracy but also preserving neighborhood topology, as evidenced by low Hamming losses in kNN graph coherence tests.

Implications and Future Directions

The implications of this research extend into various domains where point cloud registration is crucial, such as computer vision, medical imaging, and bioinformatics. The method addresses the challenges of aligning high-dimensional data while preserving its inherent topological features, making it particularly relevant for biological data integration and enhancement processes.

Looking forward, further refining the regularization techniques could enhance the method's adaptability to even more complex point cloud deformations. Moreover, exploring extensions to accommodate partial matching and local deformations could broaden the applicability of this framework, paving the way for more robust data representation and interpretation in burgeoning multimodal analysis domains. In sum, the kNN-Res framework sets the stage for more nuanced and topologically faithful point cloud registration approaches in future research.