高效算法：结构化点云中的3D配准与全局定位旋转估计

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本文主要探讨了"在结构化点云中进行3D配准和全局定位的高效旋转估计"这一关键问题。随着三维扫描技术的发展，对结构化环境中的点云数据进行精确的3D配准和全局定位变得越来越重要，尤其是在自动驾驶、无人机导航和虚拟现实等领域。针对这一挑战，研究人员提出了一种高效的旋转估计算法。该算法的核心思想是充分利用结构化场景中点云的几何特性。结构化环境，如建筑物、桥梁或城市规划，通常具有明显的特征点和重复的几何模式，这为算法设计提供了稳定的信息基础。通过与传统的迭代closest point (ICP)方法不同，该算法专注于挖掘这些结构信息，减少对小范围重叠区域的依赖，从而提高了配准的精度和鲁棒性。论文的创新之处在于它采用了一种新颖的角度，即方向角的计算，来估计旋转矩阵。方向角反映了点云中特征元素的方向关系，这在处理大规模点云和非线性变形时尤为有效。算法的设计旨在处理小规模的重叠区域，避免了常见的局部最优解问题，从而实现全局优化。文章经过了严格的审稿过程，自2016年6月23日初次提交至2017年9月9日接受，最终于2017年9月20日在线发表在《图像与视觉计算》（Image and Vision Computing）期刊上。关键词包括“结构化点云”、“小规模重叠”、“3D配准”、“全局定位”以及“ICP”算法。总结来说，这篇研究论文提供了一个重要的解决方案，通过高效旋转估计，显著改善了在复杂结构化环境中对点云进行3D配准和全局定位的精度和效率。这对于提高基于点云的自动化应用性能具有深远的影响，并可能推动相关领域的技术进步。

54 Y. Ma et al. / Image and Vision Computing 67 (2017) 52–66

angles can reﬂect the rotation between two point clouds. Based on

this observation, a direction angle is ﬁrst deﬁned and the statistics

information of the direction angles is used to obtain the rotation

matrix.

To perform 3D registration, our registration algorithm is decom-

posed into two parts: rotation estimation and translation estimation.

For rotation estimation, a novel estimation algorithm is proposed

using the direction angle histograms. For translation estimation, the

centers of the rotated point clouds are aligned using a variant of ICP.

Speciﬁcally, we only conduct translation estimation without consid-

ering the rotation. Since the rotation angles are precisely estimated,

we can obtain an accurate translation estimation after a few itera-

tions (10 in our case). The proposed rotation estimation algorithm

does not require any initial alignment, and can be implemented eﬃ-

ciently as it does not have to generate point correspondences. A set

of experiments have been conducted on indoor point clouds. Exper-

imental results show that the proposed algorithm outperforms the

ICP algorithm [15,25], the Coherent Point Drift (CPD) algorithm [18],

the Accelerated Coherent Point Drift (ACPD) algorithm [17] and the

algorithm proposed in [26] on point clouds with small overlaps.

Moreover, the proposed rotation estimation algorithm is used to

address the global localization problem in 3D maps. For translation

estimation, we use the projection information of each point cloud.

The point cloud is projected onto the coordinate plane and the trans-

lation vector is then extracted by template matching between the

two corresponding projection images. Experiments have been con-

ducted on indoor point clouds. Experimental results show that the

proposed algorithm achieves a high localization accuracy.

The rest of this paper is organized as follows. Section 2 reviews

existing work on point cloud registration. Section 3 deﬁnes our

problem. Section 4 introduces our direction angle distribution based

rotation estimation algorithm. Section 5 presents the comparative

experimental results and analyses in point clouds registration and

global localization. Section 6 concludes this paper.

2. Related work

2.1. 3D point cloud registration

Despite of the recent research progress, 3D point cloud reg-

istration remains a challenging task. The task of 3D point cloud

registration is to estimate the rotation and translation parameters to

align the 3D point clouds acquired from different viewpoints. Many

existing 3D registration algorithms consider the rotation and trans-

lation estimation task as an iterative optimization problem. The ICP

algorithm [15] and its variants [16,25,27-33] have been frequently

used to perform 3D point cloud registration. ICP is one of the earli-

est point cloud registration techniques, it uses a least square method

to achieve optimal matching between two point clouds. At each

step, the algorithm estimates the rotation and translation param-

eters by minimizing the Euclidean distance between correspond-

ing points. Subsequently, many ICP variants have been proposed.

Granger and Pennec [31] formulated the registration problem as

a general Maximum-Likelihood (ML) estimation of the transforma-

tion and proposed an improved ICP using Expectation-Maximization

(EM) principles, namely EM-ICP. To improve the computational eﬃ-

ciency of EM-ICP, Tamaki et al. [32] implemented the EM-ICP using

CUDA and achieved a faster performance than the CPU based imple-

mentation. Chen and Medioni [30] used a more robust point-to-plane

distance to replace the point-to-point distance in the original ICP.

This variant improves the robustness and applicability of ICP. Segal et

al. [27] developed a probabilistic version of ICP, namely Generalized-

ICP (GICP). GICP also uses point-to-plane distance to generate point

correspondences, and assigns a weight to each pairs of corresponding

points in the objective function using their surface normals. Seraﬁn

and Grisetti [29] used normal features to obtain more accurate point

correspondences, resulting in an improved registration accuracy for

large-scale point clouds. The classical ICP algorithm and its variants

require an accurate initial alignment and a large percent of overlaps.

Moreover, only a local optima can be achieved by these algorithms.

Besides, several registration algorithms [17–20] consider a point

cloud as a probabilistic model (e.g., GMM [19]). Evangelidis et al. [20]

proposed a generative model based on multiple GMMs for joint reg-

istration of multiple point clouds. Myronenko et al. [18] proposed

a Coherent Point Drift (CPD) algorithm to achieve high registration

accuracy by maximizing the likelihood between the two GMMs

of point clouds. The original CPD algorithm is time-consuming.

Myronenko and Song [18] then proposed a Fast Gauss Transform

based CPD (FGT-CPD) algorithm. To achieve a robust and faster reg-

istration, Lu et al.

[17] proposed

an Accelerated Coherent Point Drift

(ACPD) algorithm. Experimental results show that the computational

complexity of these probabilistic algorithms is very high, especially

for large-scale point clouds.

Generally, the ICP variants and the probabilistic algorithms are

prone to local optima. Yang et al. [28] proposed a Global Opti-

mal ICP (GO-ICP) algorithm for point cloud registration. The GO-ICP

algorithm combines the traditional ICP with a branch-and-bound

(bnb) scheme to perform rotation estimation. It achieves a global

accurate registration in a small-scale scene. Recently, several algo-

rithms have been proposed to estimate the rotation and translation

parameters [26,34-37]. Generally, these algorithms are able to obtain

global optima at the cost of high computational complexity. A simi-

lar technique is used to estimate the rotation between two 3D point

clouds in [34,35,37]. First, keypoints are extracted from the given

point clouds, followed by the generation of keypoint matches. The

keypoint matches [35,37] or the original points [34] can then be

used to solve the point correspondence problem. The point corre-

spondence searching process in [34,35,37] is slow, which requires

at least three correct keypoint matches to guarantee reliable fea-

ture correspondence. As a major component in these algorithms,

keypoint extraction and matching is computationally expensive. Fur-

thermore, it is challenging for keypoint extraction algorithms to

work in textureless environments. Makadia et al. [26] used the ori-

entation histogram in spherical coordinates to estimate the rotation.

Once a rough rotation and translation estimation is completed, ICP

is performed to achieve ﬁne alignment. Similar to [26], the global

direction information of the normal vectors of all points is used for

rotation estimation and a variant of ICP is used for translation esti-

mation in this paper. Different from [26], we deﬁne a measure named

direction angle and use the peaks of the direction angle histograms

to obtain the rotation angles. No Fourier transform or Inverse Fourier

transform (which is the key step in [26]) is needed in our algorithm.

For automatic 3D point cloud registration in structural environ-

ments, the proposed algorithm is simple but effective. No keypoint

or local feature extraction is required by our algorithm. Furthermore,

our algorithm is more robust to outliers.

2.2. Global localization

Real-time localization forms the basis for outdoor and indoor

navigation [38–41]. It can be used for many applications including

robotics, and unmanned vehicles. The task of global localization is to

estimate its position without any initial knowledge about its loca-

tion. It also requires the platform (e.g., a vehicle or robot) to be able

to relocate itself if its position is lost.

Indoor robot localization is an extensively investigated topic in

the area of global localization. A large number of approaches have

been proposed for mobile robot global localization using RGB/RGB-

D cameras. Global navigation is usually achieved by matching a

local map to the global map using global or local features extracted

from the maps. Schiele and Crowley [38] proposed a Hough trans-

form based localization algorithm. It uses Hough transform to extract

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