Point cloud registration

Overview

Registration asks for the rotation and translation that bring one 3D point set onto another 2305.10854 §1. A common pipeline proposes correspondences between the two sets from per-point descriptors, removes the wrong ones, and fits a rigid transform to the rest. Most proposed matches are wrong, so the hard part is the filtering step 2305.10854 §1.

The filter relies on one fact about rigid motion. For two true correspondences, the distance between their points is the same in both sets, up to noise 2305.10854 §3.2. Pairs of matches that agree on this distance can be checked against each other without knowing the transform.

This page currently covers one compiled paper. Other families, such as iterative closest point for refinement from a coarse start, are not yet compared here.

Variants

Maximal-clique filtering, training-free

Each putative match is a node. Two nodes are joined when their distance mismatch is small under a Gaussian score 2305.10854 §3.2 eq. 1-2. The second-order graph keeps an edge only when the two nodes also share compatible neighbours, which makes the graph sparser 2305.10854 §3.2 eq. 3.

The method enumerates maximal cliques, scores each by its summed edge weight, and keeps the heaviest clique that contains each node [arxiv:2305.10854 §3.3 eq. 4]. An SVD fit gives one transform per kept clique 2305.10854 §3.4. The paper is 3D Registration with Maximal Cliques.

With FCGF matches, the authors report 93.72% registration recall on 3DMatch and 59.85% on 3DLoMatch 2305.10854 tab. 1, tab. 2. With FPFH matches they report 84.10% and 40.88% on the same sets 2305.10854 tab. 1, tab. 2.

Boosting a learned matcher

The same back-end can filter matches from a learned model. The authors report 3DMatch recall with 5000 correspondences rising from 92.0 to 95.7 for GeoTransformer, from 85.1 to 91.3 for FCGF, and from 88.6 to 95.3 for SpinNet 2305.10854 tab. 3. These are the authors' own baselines.

Hypothesis scoring

After the cliques give candidate transforms, one must be chosen. The default scores each hypothesis with a mean-absolute-error measure. The paper gives no inlier threshold for it 2305.10854 §3.4. In the authors' FPFH ablation on 3DMatch, ranking by inlier count gives 83.86% recall and the default scoring gives 84.10% 2305.10854 tab. 5.

When to use which

The margins over the strongest baseline are small for FCGF on 3DMatch (0.56 points) and largest for the boosted and FPFH settings [arxiv:2305.10854 tab. 1, tab. 2, tab. 3].

Implementation sketch

The core of the maximal-clique variant. Descriptor matching runs before this step, and the per-clique hypothesis score is left as a black box.

# Maximal-clique registration  [arxiv:2305.10854 §3]
# Input:  src, tgt (N, 3): N putative matches; d_cmp, t_cmp
# Output: rigid transform (R, t)

def register(src, tgt, d_cmp, t_cmp):
    # Pairwise compatibility from distance mismatch  [§3.2 eq. 1-2]
    w1 = first_order_weights(src, tgt, d_cmp, t_cmp)
    # Second-order weights: keep edges with shared neighbours  [§3.2 eq. 3]
    w2 = w1 * (w1 @ w1)
    # Enumerate maximal cliques of at least three nodes  [§3.3]
    cliques = maximal_cliques(w2, min_size=3)
    # Clique weight is its summed edge weight; keep the heaviest per node  [§3.3 eq. 4]
    selected = node_guided_selection(cliques, w2)
    # One SVD fit per selected clique  [§3.4]
    hyps = [svd_fit(src[c], tgt[c]) for c in selected]
    # Return the hypothesis with the best score  [§3.4]
    return max(hyps, key=lambda h: score(h, src, tgt))

The paper's Gaussian kernel uses a width d_cmp tied to the point-cloud resolution, and the threshold t_cmp removes weak edges [arxiv:2305.10854 §3.2 §4.1]. Both need the input's resolution, which the paper leaves to an external reference 2305.10854 §4.1.

Contradictions

• Compatibility threshold. The paper gives 0.99, rising to 0.999 above 5000 matches 2305.10854 §4.1. The authors' C++ code uses 0.999 for FCGF and 0.995 for FPFH on 3DMatch whatever the match count 2305.10854 Paper vs code.
• Kernel form. The paper gives one Gaussian kernel 2305.10854 §3.2 eq. 2. The authors' Python demos use a linear kernel with a 0.1 m width, and the C++ KITTI path uses a linear kernel with width 0.6 2305.10854 Paper vs code.
• Refinement. The paper's text describes no post-refinement. The C++ code runs up to 20 MAE-based refinement steps 2305.10854 Paper vs code.
• Clique size. The paper uses a minimum of three 2305.10854 §4.1. The code call uses three, but its comment says four for 3DMatch 2305.10854 Paper vs code.
• Timing at 5000 matches. The two timing tables give 3265.42 ms and 3259.38 ms. The paper does not explain the gap 2305.10854 tab. 8, tab. 12.

Papers

• 3D Registration with Maximal Cliques: training-free maximal-clique filtering of correspondences with SVD fitting per clique; the same back-end can boost learned matchers.