[Paper Review] Geometric Transformer for Fast and Robust Point Cloud Registration

Zheng Qin, Hao Yu+4 more|arXiv (Cornell University)|Feb 14, 2022

3D Shape Modeling and Analysis21 citations

TL;DR

GeoTransformer learns transformation-invariant geometric features using pairwise distances and triplet-wise angles to robustly match superpoints, enabling RANSAC-free, fast point cloud registration with high inlier ratio and recall.

ABSTRACT

We study the problem of extracting accurate correspondences for point cloud registration. Recent keypoint-free methods bypass the detection of repeatable keypoints which is difficult in low-overlap scenarios, showing great potential in registration. They seek correspondences over downsampled superpoints, which are then propagated to dense points. Superpoints are matched based on whether their neighboring patches overlap. Such sparse and loose matching requires contextual features capturing the geometric structure of the point clouds. We propose Geometric Transformer to learn geometric feature for robust superpoint matching. It encodes pair-wise distances and triplet-wise angles, making it robust in low-overlap cases and invariant to rigid transformation. The simplistic design attains surprisingly high matching accuracy such that no RANSAC is required in the estimation of alignment transformation, leading to $100$ times acceleration. Our method improves the inlier ratio by $17{\sim}30$ percentage points and the registration recall by over $7$ points on the challenging 3DLoMatch benchmark. Our code and models are available at https://github.com/qinzheng93/GeoTransformer.

Motivation & Objective

• Address the challenge of accurate correspondences in point cloud registration, especially under low-overlap conditions.
• Develop a keypoint-free matching approach that relies on robust superpoint correspondences.
• Learn transformation-invariant geometric representations to improve matching reliability and registration accuracy.

Proposed method

• Propose Geometric Transformer (GeoTransformer) that encodes pairwise distances and triplet-wise angles for superpoints.
• Implement geometric self-attention to capture intra-point-cloud geometry with a transformation-invariant structure embedding.
• Use a cross-attention module to model inter-point-cloud consistency and derive hybrid features for robust matching.
• Compute superpoint correspondences via global feature correlation and an overlap-aware circle loss to emphasize high-overlap patches.
• Refine to dense point correspondences with an optimal transport layer and mutual top-k selection.
• Perform RANSAC-free local-to-global registration (LGR) using weighted SVD on local candidates and global inlier counting to select the final transform.

Experimental results

Research questions

• RQ1 Can a geometry-aware transformer learn transformation-invariant features for robust superpoint matching in low-overlap scenarios?
• RQ2 Does a keypoint-free, RANSAC-free registration pipeline achieve competitive accuracy and speed on indoor and outdoor benchmarks?
• RQ3 How does an overlap-aware loss influence convergence and matching quality for patch-level correspondences?
• RQ4 To what extent can dense point correspondences be recovered from reliable superpoint matches without traditional robust estimators?

Key findings

• GeoTransformer significantly improves inlier ratio for superpoint (patch) correspondences in low-overlap cases.
• Dense point correspondences achieve high accuracy due to high-quality superpoint matches from GeoTransformer.
• The method enables RANSAC-free registration with substantially reduced computation time (e.g., up to 100x faster than RANSAC) in experiments.
• On 3DLoMatch, inlier ratio and registration recall improve by substantial margins compared to baselines (e.g., 17–30 pp inlier ratio, >7 pp RR).
• Without RANSAC, GeoTransformer with weighted SVD attains competitive registration recall close to RANSAC-based methods on challenging datasets.