[Paper Review] You Only Hypothesize Once: Point Cloud Registration with Rotation-equivariant Descriptors

Haiping Wang, Yuan Liu+2 more|arXiv (Cornell University)|Sep 1, 2021

3D Shape Modeling and AnalysisEngineering60 references19 citations

TL;DR

This paper proposes YOHO, a point cloud registration framework that uses rotation-equivariant and rotation-invariant descriptors to enable accurate and efficient registration with minimal RANSAC iterations. By leveraging group-equivariant deep learning on the icosahedral group, YOHO estimates rotation from a single matched pair, drastically reducing the search space and achieving state-of-the-art performance on 3DMatch, 3DLoMatch, ETH, and WHU-TLS datasets with under 400 RANSAC iterations.

ABSTRACT

In this paper, we propose a novel local descriptor-based framework, called You Only Hypothesize Once (YOHO), for the registration of two unaligned point clouds. In contrast to most existing local descriptors which rely on a fragile local reference frame to gain rotation invariance, the proposed descriptor achieves the rotation invariance by recent technologies of group equivariant feature learning, which brings more robustness to point density and noise. Meanwhile, the descriptor in YOHO also has a rotation equivariant part, which enables us to estimate the registration from just one correspondence hypothesis. Such property reduces the searching space for feasible transformations, thus greatly improves both the accuracy and the efficiency of YOHO. Extensive experiments show that YOHO achieves superior performances with much fewer needed RANSAC iterations on four widely-used datasets, the 3DMatch/3DLoMatch datasets, the ETH dataset and the WHU-TLS dataset. More details are shown in our project page: https://hpwang-whu.github.io/YOHO/.

Motivation & Objective

• To address the challenge of robust point cloud registration under noise, density variation, and partial overlaps.
• To overcome the limitations of existing local descriptors that rely on fragile local reference frames (LRFs) for rotation invariance.
• To exploit rotation-equivariant features to estimate global transformation from a single correspondence pair, reducing RANSAC search space.
• To achieve state-of-the-art registration accuracy with significantly fewer RANSAC iterations than baseline methods.

Proposed method

• The proposed YOHO-Desc descriptor is constructed using group-equivariant convolutional networks on the icosahedral group, enabling inherent rotation equivariance.
• Rotation invariance is achieved by pooling features over the icosahedral group, making the descriptor robust to input rotation.
• The rotation-equivariant part of the descriptor allows estimating the relative rotation between two corresponding local patches from a single matched pair.
• A single matched pair is used to compute a candidate transformation (rotation + translation), which is then validated via RANSAC with a drastically reduced hypothesis space.
• Feature extraction is performed on 60 rotated versions of each local patch to capture equivariant representations, followed by pooling for invariance.
• The framework uses a single feature extraction per point cloud fragment, enabling reuse across all pairwise alignments and improving computational efficiency.

Experimental results

Research questions

• RQ1 Can a rotation-equivariant descriptor enable accurate registration with only one correspondence hypothesis, reducing RANSAC iterations?
• RQ2 How does the proposed descriptor perform under high noise and significant point density variations compared to LRF-based methods?
• RQ3 To what extent does the use of group-equivariant features improve robustness and accuracy in point cloud registration?
• RQ4 Can the framework achieve state-of-the-art performance with significantly fewer RANSAC iterations than existing methods?

Key findings

• YOHO achieves superior registration accuracy on 3DMatch, 3DLoMatch, ETH, and WHU-TLS datasets with less than 400 RANSAC iterations.
• YOHO-C and YOHO-O both find the correct transformation in under 400 iterations, while baseline methods only achieve a small portion of correct transformations within 500 iterations.
• On the 3DLoMatch dataset with low inlier ratios (<0.1), YOHO-O maintains high success probability due to its reliance on a single matched pair, unlike baseline methods that require triplets.
• Despite longer feature extraction time due to 60 forward passes, YOHO’s total registration time is the shortest on 3DMatch and 3DLoMatch due to efficient RANSAC and feature reuse.
• YOHO demonstrates robustness to noise and density variation, outperforming LRF-based methods that are sensitive to such distortions.
• The method fails on planar-overlap regions due to ambiguous rotation estimation, indicating a limitation in flat surface scenarios.