SAC-COT:基于样本兼容三角形的3D点云定位鲁棒估计方法

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SAC-COT（Sample Consensus by Sampling Compatibility Triangles）是一项针对3D点云注册问题的创新算法，发表在《IEEE Transactions on Geoscience and Remote Sensing》期刊的一篇论文中。该方法在6-DOF（六自由度）姿态估计领域具有显著价值，特别是在处理初始对应关系中可能存在大量噪声或异常值的情况下。传统上，通过特征对应关系进行6-DOF定位是3D registration中的一个常用且稳定的策略，但处理异常数据的挑战仍然存在。 SAC-COT的核心贡献在于提出了一种基于样本的兼容性三角形（Compatibility Triangle, COT）的引导性三点采样方法。不同于传统的对应点表示，COT是一种新的数据结构，它代表了三个相互兼容的点之间的关系，这些点共同构成一个有效的几何约束。首先，作者将对应关系集建模为图，其中节点连接着兼容的对应点对，形成一个图结构。算法的关键步骤包括： 1. 模型构建：利用COT作为节点间的连接，构建一个图，图中边的权重可能反映了对应点之间匹配的可靠性。 2. COT排序与筛选：通过某种排序策略（如基于COT的质量评估或基于图的排序算法），对图中的COT进行优先级排序，确保在处理过程中优先考虑最可靠的匹配。 3. 采样策略：通过采样高质量的COT，形成一个小型的样本集，这有助于减少噪声和异常的影响。采样过程可能涉及到局部搜索、随机抽样或基于置信度的选择。 4. 一致性检验：对采样的COT进行一致性检查，如果它们可以构成一个稳定的三角形系统，那么就可以推断出相对应的6-DOF姿态估计。 5. 迭代优化：基于样本的共识，可能需要多次迭代来逐步改进估计结果，直到达到预设的精度标准或达到收敛。 6. 鲁棒性和效率：SAC-COT的优势在于其简单易实现且有效，能够在保持高精度的同时抵抗大规模的噪声，提高了3D点云注册的鲁棒性和效率。通过SAC-COT，研究者们能够处理初始对应关系中的噪声挑战，从而实现更准确和稳健的3D点云配准，这对于许多应用，如遥感、机器人导航、虚拟现实等领域都具有重要的实际意义。

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

YANG et al.: SAC-COT FOR 3-D POINT CLOUD REGISTRATION 3

method. Section IV presents the deployed experiments to

validate the effectiveness of our method. Finally, Section V

concludes this article and presents future research directions.

II. R

ELATED WORK

This section ﬁrst gives a brief review on 6-DOF pose estima-

tors, geometrics constraints, and deep learning techniques for

3-D registration. Then, since SAC-COT is a guided sampling-

based estimator, existing guided sampling approaches in the

RANSAC family is recapped.

A. 6-DOF Pose Estimators for 3-D Registration

For the problem of estimating a 6-DOF pose from cor-

respondences with outliers in the context of 3-D regis-

tration, RANSAC [15] and its variants remain the main-

stream solution. The classical RANSAC exhibits two main

limitations when faced with heavy outliers: low time efﬁ-

ciency and limited accuracy. To overcome the two limita-

tions, Rusu et al. [10] presented a sample consensus-based

initial alignment (SAC-IA) method, which samples corre-

spondences spread out on the point cloud and leverages the

Huber penalty for hypothesis evaluation. To achieve more

reliable hypothesis evaluation, Yang et al. [7] proposed a point

cloud distance metric to assess pose hypotheses and intro-

duced the optimal sample consensus (OSAC) method. Both

SAC-IA and OSAC are three-point-based sampling methods

that exhibit a theoretical computational complexity of O(n

Some methods that sample fewer correspondences per itera-

tion have also been proposed. For instance, two-point-based

sample consensus with global constraint (2SAC-GC) [21] and

compatibility-guided sample consensus (CG-SAC) [1] addi-

tionally consider the normal information of keypoints during

the sampling process; globally constrained one-point-based

sample consensus (GC1SAC) [17] and one-point RANSAC

(1P-RANSAC) [16] additionally employ the LRF cue and only

sample one correspondence per iteration. Unfortunately, these

RANSAC methods still fail to achieve a good balance in terms

of accuracy, speed, and robustness to common nuisances (as

will be veriﬁed in Section IV).

In addition to RANSAC methods, Guo et al. [20] proposed a

clustering-based method that ﬁrst generates pose hypotheses in

the rotation and translation spaces and then locates the cluster

centers in both spaces; Tombari and Di Stefano [18] and Buch

et al. [19] proposed two voting-based methods that serve pose

hypotheses as voters and perform voting in a Hough space. All

these methods are dependent on the normals or LRFs, which

have been demonstrated to be instable in the presence of noise,

partial overlap, and occlusions [13], [27], [28].

B. Geometric Constraints for 3-D Registration

Point-, plane-, and correspondence-level geometric con-

straints have been proposed to assist 3-D registration. For

point-level constraints, Aiger et al. [29] enforced coplanar

constraints to four-point sets in point clouds to achieve reg-

istration; Drost et al. [30] presented a point pair voting-

based method for 3-D registration, where distance and angle

constraints are employed to describe point pair features. For

plane-level constraints, Xu et al. [31] introduced a voxel-

based four-plane congruent set (V4PCS) method for pair-

wise coarse registration, which ﬁrst extracts the planes for

point clouds and then leverages the plane-based geometric

constraints formed by four planes to achieve registration;

Chen et al. [32] presented a plane-based descriptor using dis-

tance and angle properties derived from planes for 3-D regis-

tration. For correspondence-level geometric constraints, most

of the existing methods focus on pairwise constraints. They

typically include the L

distance constraint [22], [33], normal

deviation angle constraint [21], [34], and LRF constraint [35].

Nonetheless, these pairwise constraints either suffer from

ambiguities or lack robustness to common nuisances. The

readers can refer to a related survey [36] for terrestrial laser

scanner point cloud registration for more details on geometrics

constraints proposed for 3-D registration.

SAC-COT leverages the correspondence-level geometric

constraints for registration, while it proposes a novel triplet

constraint that is validated to be far less ambiguous and more

robust than existing pairwise constraints.

C. Deep Learning for 3-D Registration

In addition to geometric-only methods, a few deep learning-

based point cloud registration methods have been pro-

posed recently. We review some typical examples here.

Aoki et al. [37] proposed the PointNetLK network for 3-D

registration in an iterative manner, where PointNet [38]

was employed for descriptor extraction combined with

a Lucas/Kanade-like optimization algorithm. Wang and

Solomon [39] presented deep closest point (DCP) that incor-

porates a point cloud embedding network, an attention-based

module to approximate combinatorial matching, and a differ-

entiable singular value decomposition (SVD) layer for 6-DOF

pose estimation. PRNet [40], as an extension to DCP, speciﬁ-

cally focuses on partial-to-partial registration, which contains

a keypoint detection module and is able to establish partial

correspondences.

Deep learning techniques have demonstrated a great poten-

tial for 3-D registration, while usually, adequate labeled train-

ing data should be prepared. This may not be feasible in many

practical scenarios, and as such, we still focus geometric-only

methods.

D. Guided Sampling Approaches for RANSAC

As the key novelty of SAC-COT is its sampling method,

we herein review existing guided sampling methods for

RANSAC. In the 2-D domain, guided sampling approaches

preferentially sample correspondences with high conﬁdence

scores [26], [41]. By contrast, guided sampling approaches

for RANSAC in the 3-D domain, as will be discussed in the

following, are more diverse.

For one-point-based sampling methods [16], [17], because

they have a linear time complexity, guided or random sampling

ways generate the same outcome as long as all correspon-

dences have been traversed. However, these one-point-based

sampling methods typically guide the sampling process based

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