三维激光扫描仪与全向摄像头的外部校准方法

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"Extrinsic Calibration of a 3D Laser Scanner and an Omnidirectional Camera" 这篇论文主要探讨了如何对外部校准一个三维激光扫描仪（3D Laser Scanner）和一个全向摄像机（Omnidirectional Camera）系统。精确的外部校准对于计算机视觉和机器人领域中的多种先进算法至关重要，因为它可以实现相机图像与3D点云之间的精确配准。这种配准能力能够提升目标检测、场景理解、定位导航等任务的性能。论文首先介绍了利用RANSAC（Random Sample Consensus）算法来计算从激光扫描数据中提取的平面方程。RANSAC是一种迭代算法，常用于估计模型参数，同时剔除异常值，它在此处被用来确定扫描数据中的平面特征。接下来，通过计算方位角，可以得知激光雷达（LIDAR）扫描到的障碍物相对于激光雷达的位置，这有助于进一步理解环境的三维结构。为了校准激光雷达，论文采用了一个包含多个视图的平面棋盘格图案。至少需要3个不同的观察角度，以便获取足够的数据来确定两者之间的几何关系。通过这些观察，可以计算出平面的法线和位于平面上的3D点。接着，使用这些数据来最小化实际距离与由激光雷达测量的距离之间的误差，从而优化校准过程。在传统的2D激光测距仪和单摄像头的校准方法基础上，论文扩展了这种方法，以适应3D激光扫描仪和全向摄像机系统。全向摄像机的特点是拥有广泛的视野，能捕捉到周围环境的360度全景，这在机器人和自动驾驶等领域有广泛应用。与2D激光雷达不同，3D激光扫描仪可以提供更丰富的三维信息，但其校准过程也更为复杂。论文的贡献在于提出了一种有效的校准框架，不仅适用于静态环境，还可以应用于动态环境中，如移动机器人或自动驾驶车辆。这样的系统能够在不断变化的环境中提供准确的感知信息，对于实时的导航和避障任务尤其重要。这篇论文提供了3D激光扫描仪和全向摄像机联合校准的理论和实践指导，对于那些需要精确融合不同传感器数据的系统设计者来说，是一份宝贵的参考资料。通过这种方法，可以提高系统的整体性能，并推动计算机视觉和机器人技术的发展。

Extrinsic Calibration of a 3D Laser Scanner

and an Omnidirectional Camera

Gaurav Pandey

∗

James McBride

∗∗

Silvio Savarese

∗

Ryan Eustice

∗

University of Michigan, Ann Arbor, MI 48109 USA

(e-mail: pgaurav,eustice,silvio@umich.edu)

∗∗

Ford Motor Company Research and Innovation Center, Dearborn,

MI 48124 USA (e-mail: jmcbride@ford.com)

Abstract: We propose an approach for external calibration of a 3D laser scanner with an

omnidirectional camera system. The utility of an accurate calibration is that it allows for

precise co-registration between the camera imagery and the 3D point cloud. This association

can be used to enhance various state of the art algorithms in computer vision and robotics. The

extrinsic calibration technique used here is similar to the calibration of a 2D laser range ﬁnder

and a single camera as proposed by Zhang (2004), but has been extended to the case where

we have a 3D laser scanner and an omnidirectional camera system. The procedure requires

a planar checkerboard pattern to be observed simultaneously from the laser scanner and the

camera system from a minimum of 3 views. The normal of the planar surface and 3D points

lying on the surface constrain the relative position and orientation of the laser scanner and the

omnidirectional camera system. These constraints can be used to form a non-linear optimization

problem that is solved for the extrinsic calibration parameters and the covariance associated

with the estimated parameters. Results are presented for a real world data set collected by a

vehicle mounted with a 3D laser scanner and an omnidirectional camera system.

Keywords: Sensor Calibration, 3D Laser Scanner, Omnidirectional Camera.

1. INTRODUCTION

One of the basic tasks of mobile robotics is to automat-

ically create a 3D map of the environment. However, to

create realistic 3D maps, we need to acquire visual infor-

mation (e.g. color, texture) from the environment and this

information has to be precisely mapped onto the range

information. To accomplish this task, the camera and 3D

laser range ﬁnder must be extrinsically calibrated, i.e.,

the rigid body transformation between the two reference

systems must be estimated. On platforms where a camera

provides intensity information in the form of an image

and laser supplies depth information in the form of a set

of 3D points, external calibration allows reprojection of

the 3D points from the laser coordinate frame to the 2D

coordinate frame of the image.

Most previous works on extrinsic laser-camera calibration

concern calibration of perspective cameras to 2D laser

scanners (Zhang (2004)). Mei and Rives (2006) have de-

scribed the calibration of a 2D laser range ﬁnder and

an omnidirectional camera. They showed the results for

both visible (laser is observed in camera image also) and

invisible lasers. Unnikrishnan and Hebert (2005) extended

Zhang’s (Zhang (2004)) method to calibrate a 3D laser

scanner with a perspective camera. Recently Aliakbarpour

et al. (2009) have proposed a novel approach for calibration

of a 3D laser scanner and a stereo camera, which uses an

Inertial Measurement Unit (IMU) to decrease the number

This work is supported through a grant from Ford Motor Company

via the Ford-UofM Alliance (Award #N008265).

of points needed for a robust calibration.

In contrast to previous works, here we consider the ex-

trinsic calibration of an omnidirectional camera with a

3D laser range ﬁnder. The problem of extrinsic calibration

of a 3D scanner and an omnidirectional camera was ﬁrst

addressed by Scaramuzza et al. (2007). There, they pro-

posed a technique that requires manual selection of point

correspondences from a scene viewed from the two sensors.

In this work, we describe a method of extrinsic calibration

of an omnidirectional camera and a high resolution 3D

laser scanner (with invisible lasers) that does not require

any explicit point correspondence.

The outline of the paper is as follows: In Section 2.1

we describe a procedure for the automatic reﬁnement

of the intrinsic calibration of the Velodyne laser scanner

range correction. Section 2.2 describes the omnidirectional

camera system used. Section 2.3 describes the proposed

extrinsic laser-camera calibration method and in Section 3

we present some calibration results. In Section 4 we discuss

the implications of the laser-camera mapping presented in

this paper.

2. METHODOLOGY

Extrinsic calibration requires co-observable features in

both camera and laser data, moreover these features

should be easy to extract from both sensor modalities.

In our calibration procedure we employ a checkerboard

pattern mounted on a planar surface, which we will refer

to as the target plane from now onwards. Our selection

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