SDFReg: Learning Signed Distance Functions for Point Cloud Registration

TL;DR

SDFReg reframes point cloud registration as aligning a source cloud to a neural implicit surface representing the target, using a signed distance function $f_c$ to measure Dist$(\mathbf{R}\mathbf{p}_i+\mathbf{t}, f_c)$ and solving for the rigid transform $\,\hat{\\Theta} \\in SE(3)$ with Levenberg–Marquardt. The framework learns the target SDF with a neural network $\\Phi(\\mathbf{x} \\\mid \\\mathbf{Q})$ via a self-supervised GenSDF loss and an Eikonal regularizer, and adopts a coarse-to-fine strategy that iteratively refines both the SDF and the registration using query points drawn from the evolving source. This correspondence-free approach demonstrates strong robustness to noise, partial visibility, and density changes, achieving superior results on ModelNet40 and 3DMatch compared with several state-of-the-art methods. Overall, SDFReg offers a practical, implicit-surface-based solution for reliable 3D registration in real-world, imperfect data scenarios.

Abstract

Learning-based point cloud registration methods can handle clean point clouds well, while it is still challenging to generalize to noisy, partial, and density-varying point clouds. To this end, we propose a novel point cloud registration framework for these imperfect point clouds. By introducing a neural implicit representation, we replace the problem of rigid registration between point clouds with a registration problem between the point cloud and the neural implicit function. We then propose to alternately optimize the implicit function and the registration between the implicit function and point cloud. In this way, point cloud registration can be performed in a coarse-to-fine manner. By fully capitalizing on the capabilities of the neural implicit function without computing point correspondences, our method showcases remarkable robustness in the face of challenges such as noise, incompleteness, and density changes of point clouds.

Figures (5)

• Figure 1: Our method makes full use of a signed distance function (SDF) for point cloud registration: (a) Initial position of source (yellow) and target (blue) point sets; (b) Then the target set is represented by an SDF; (c) The registration result of the source set and the SDF is obtained; (d) The output point cloud registration results of the target set (blue) and the transformed source set (yellow).
• Figure 2: The structure of our framework consists of encoder and decoder parts. First, the encoder extracts the features $z$ for the target input point cloud. The encoder section only needs to be done once. Then the coordinates of the source point cloud and the feature $z$ are concatenated and input to the decoder. Furthermore, the distance between the source point and the implicit surface $f_c$ will be decoded as the value of SDF on the source point, $\operatorname{Dist}\left(\mathbf{RP}+\mathbf{t}, f_{c}\right)=\operatorname{SDF}\left(\mathbf{RP}+\mathbf{t}\right)$. Meanwhile, the $\mathbf{J}$ is the Jacobian matrix of $\operatorname{Dist}\left(\mathbf{RP}+\mathbf{t}, f_{c}\right)$ with respect to transformation parameters $\mathbf{\xi}$. Since the distance error is in the non-linear least squares form, it can be optimized by the Levenberg-Marquardt algorithm to estimate transformation increment $\mathbf{\Delta\xi}$ and iteratively update the transformation parameters $\mathbf{\Delta\Theta}$.
• Figure 3: Qualitative evaluation on Gaussian noise point clouds.
• Figure 4: Qualitative evaluation on partial point clouds.
• Figure 5: Qualitative evaluation on density changes.