基于场景角点的2D激光雷达与相机外标定方法

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本文主要探讨了2D激光测距仪（Laser-Range Finder, LRF）与相机的外在标定问题，即如何确定两者在三维空间中的相对位置关系。标题"Extrinsic Calibration of a 2D Laser-Range-finder and a Camera based on Scene Corners"表明研究者们采用了一种新颖的方法，这种方法依赖于人类制造环境中常见的场景角落作为标定特征，而非传统的特定图案如平面或V形图案。通常，机器人设备为了实现更准确的空间感知和导航，会配备2D激光测距仪和摄像头，因为它们能互补彼此的不足。然而，正确融合来自这两种传感器的数据，即完成它们的外在标定，至关重要。作者提出的方法利用场景角落作为标定依据，这使得整个过程无需专门设计的图案，从而简化了操作流程，并加快了标定速度。该方法的核心在于，通过观察场景中的正交三面体——这些在现实环境中广泛存在，研究人员可以同时应用线到平面和点到平面的约束，这相较于仅依赖平面或V形图案的先前方法，提供了更为丰富的配置，进而提高了标定精度。作者通过合成实验和实际应用验证了他们的方法，结果显示，相比于现有的先进技术，这种基于场景角落的外在标定法具有更好的性能表现。具体实施时，首先，系统需要识别并定位场景中的角落点，这些点与激光测距仪和相机的测量数据之间建立了关联。然后，通过线段和面的几何关系，可以构建一系列方程组，用于求解相机和激光测距仪之间的旋转和平移参数。这种方法的优点在于其普适性和鲁棒性，即使在复杂或变化的环境中，也能有效地执行标定任务。此外，由于文中强调了对精度的要求，实验结果应包括详细的误差分析，以及对比不同方法在精度、速度和鲁棒性方面的优势，以便为其他研究者提供有价值的参考。这篇论文提供了一种创新的、实用的2D激光测距仪和相机外在标定方法，对于机器人技术、自动化导航以及环境感知等领域有着重要的理论和实践价值。

Extrinsic Calibration of a 2D Laser-Rangeﬁnder and a Camera based

on Scene Corners

Ruben Gomez-Ojeda, Jesus Briales, Eduardo Fernandez-Moral and Javier Gonzalez-Jimenez

Abstract— Robots are often equipped with 2D laser-

rangeﬁnders (LRFs) and cameras since they complement well

to each other. In order to correctly combine measurements from

both sensors, it is required to know their relative pose, that is, to

solve their extrinsic calibration. In this paper we present a new

approach to such problem which relies on the observations of

orthogonal trihedrons which are profusely found as corners in

human-made scenarios. Thus, the method does not require any

speciﬁc pattern, which turns the calibration process fast and

simpler to perform. The estimated relative pose has proven

to be also very precise since it uses two different types of

constraints, line-to-plane and point-to-plane, as a result of a

richer conﬁguration than previous proposals that relies on plane

or V-shaped patterns. Our approach is validated with synthetic

and real experiments, showing better performance than the

state-of-art methods.

I. INTRODUCTION

The combination of a laser-rangeﬁnder (LRF) and a cam-

era is a common practice in mobile robotics. Some examples

are the acquisition of urban models [1] [2], the detection

of pedestrians [3], or the construction of semantic maps

[4]. In order to effectively exploit measurements from both

type of sensors, a precise estimation of their relative pose,

that is, their extrinsic calibration, is required. This paper

presents a method for such extrinsic calibration which relies

on the observation of three perpendicular planes (orthogonal

trihedron), which can be found in any structured scene, for

instance, buildings. This idea to calibrate the sensors from

the elements of the environment was inspired by our previous

work for RGB-D cameras [5] and LRFs [6]. In a nutshell, the

calibration process is performed by ﬁrst extracting the three

plane normals from the projected junctions of the trihedron,

and then imposing co-planarity between the scanned points

and those planes.

A. Related Work

The most precise and effective strategy to perform the

extrinsic calibration between a camera and a LRF is by

establishing some kind of data association between the sensor

measurements. For that, the intuitive approach is to detect

the laser spot in the image, but this is rarely feasible since

most LRFs employ invisible light beams. Then, the common

The authors are with the Mapir Group of Department of System

Engineering and Automation, University of Málaga, Spain. +E-mail:

{rubengooj|jesusbriales}@gmail.com

This work has been supported by two projects: "GiraffPlus", funded by

EU under contract FP7-ICT-#288173, and "TAROTH: New developments

toward a robot at home", funded by the Spanish Government and the

"European Regional Development Fund ERDF" under contract DPI2011-

25483.

Fig. 1. Observation of a trihedron structure, which is deﬁned by three

orthogonal planes {Π

, Π

} intersecting at three orthogonal lines

, L

}, by a rig formed by a 2D LRF and a camera.

practice is to establish geometric constraints from the asso-

ciation of different 3D features (e.g. points, lines and planes)

observed simultaneously by both sensors. Depending on the

nature of the detected features, two methodologies have been

considered in the literature. The ﬁrst one employs point-to-

line restrictions, establishing correspondences between some

identiﬁable scanned points and line segments in the image.

A typical calibration target for this technique is the V-

shaped pattern proposed by Wasielewski and Strauss [7].

Their approach computes the intersection point of the LRF

scan plane with the V-shaped target, and then minimizes the

distance from the projected point to the line segment detected

in the image. In general, this procedure requires a large

number of observations to have a well-determined problem

and to reduce the error introduced by the mismatch between

the scan point and the observed line. To overcome this

limitation, in [8] the number of point-to-line correspondences

in each observation is increased to three by introducing

virtual end-points, and also the effect of outliers is lowered

down with a Huber weighting function.

A different strategy is the one proposed by Zhang and

Pless [9], which makes use of a planar checkerboard pattern.

Similarly to the camera calibration method in [10], they

ﬁrst estimate the relative pose between the camera and the

pattern in each observation. Then, they impose point-to-

plane restrictions between the laser points and the pattern

plane to obtain a linear solution, which is employed as

initial value in a ﬁnal non-linear optimization process. This

approach has two problems: the initial value may not be a

valid pose, since there is no guarantee that the rotation R ∈

SO(3), and it is often a poor guess which leads to a local

minimum. These disadvantages are addressed in [11], where

the authors reformulate the estimation as a linear Perspective

2015 IEEE International Conference on Robotics and Automation (ICRA)

Washington State Convention Center

Seattle, Washington, May 26-30, 2015

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