Deep Point-to-Plane Registration by Efficient Backpropagation for Error Minimizing Function

TL;DR

This paper introduces the first deep learning approach for point-to-plane registration, efficiently computing rigid transformations and their gradients using implicit function theorem, outperforming traditional point-to-point methods especially with noisy data.

Contribution

It proposes a novel deep learning framework for point-to-plane registration that uses analytic gradients via implicit function theorem, enabling efficient training.

Findings

Outperforms point-to-point based methods on noisy and low-quality point clouds.

Efficient backpropagation of rigid transformations using analytic gradients.

Demonstrates robustness and improved accuracy over traditional methods.

Abstract

Traditional algorithms of point set registration minimizing point-to-plane distances often achieve a better estimation of rigid transformation than those minimizing point-to-point distances. Nevertheless, recent deep-learning-based methods minimize the point-to-point distances. In contrast to these methods, this paper proposes the first deep-learning-based approach to point-to-plane registration. A challenging part of this problem is that a typical solution for point-to-plane registration requires an iterative process of accumulating small transformations obtained by minimizing a linearized energy function. The iteration significantly increases the size of the computation graph needed for backpropagation and can slow down both forward and backward network evaluations. To solve this problem, we consider the estimated rigid transformation as a function of input point clouds and derive its analytic gradients using the implicit function theorem. The analytic gradient that we introduce is independent of how the error minimizing function (i.e., the rigid transformation) is obtained, thus allowing us to calculate both the rigid transformation and its gradient efficiently. We implement the proposed point-to-plane registration module over several previous methods that minimize point-to-point distances and demonstrate that the extensions outperform the base methods even with point clouds with noise and low-quality point normals estimated with local point distributions.