New Error Measures for Evaluating Algorithms that Estimate the Motion of a Range Camera

We compare the classical point-based algorithms for the extrinsic calibration of a range camera to the recent plane-based method. This method does not require any feature detection, and appears to perform well using a small number of planes (minimally 3). In order to evaluate the accuracy of the computed rigid motion we propose two new error metrics that get direct access to the ground truth provided by a mechanism with reliable motion control. Furthermore, these error metrics do not depend on an additional hand-eye calibration between the mechanism and the sensor. By means of our objective measures, we demonstrate that the planebased method outperforms the point-based methods that operate on 3-D or 2-D point correspondences. In our experiments we used two types of TOF cameras attached to a robot arm, but our evaluation tool applies to other sensors and moving systems.

[1]  Robert C. Bolles,et al.  Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography , 1981, CACM.

[2]  Urbano Nunes,et al.  Fast and Accurate Calibration of a Kinect Sensor , 2013, 2013 International Conference on 3D Vision.

[3]  Maarten Weyn,et al.  A Survey of Rigid 3D Pointcloud Registration Algorithms , 2014 .

[4]  Wilfried Philips,et al.  Extrinsic Calibration of Camera Networks Using a Sphere , 2015, Sensors.

[5]  Wilfried Philips,et al.  Extrinsic Calibration of Camera Networks Based on Pedestrians , 2016, Sensors.

[6]  Urbano Nunes,et al.  A Minimal Solution for the Extrinsic Calibration of a Camera and a Laser-Rangefinder , 2012, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[7]  Rudi Penne,et al.  An Incremental Procedure for the Lateral Calibration of a Time-of-Flight Camera by One Image of a Flat Surface , 2014, International Journal of Computer Vision.

[8]  Zhengyou Zhang,et al.  A Flexible New Technique for Camera Calibration , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  K. S. Arun,et al.  Least-Squares Fitting of Two 3-D Point Sets , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[10]  Kaare Brandt Petersen,et al.  The Matrix Cookbook , 2006 .

[11]  Paul J. Besl,et al.  A Method for Registration of 3-D Shapes , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  Sebastian Thrun,et al.  Unsupervised Intrinsic Calibration of Depth Sensors via SLAM , 2013, Robotics: Science and Systems.

[13]  Stefan May,et al.  Calibration and registration for precise surface reconstruction with Time-Of-Flight cameras , 2008, Int. J. Intell. Syst. Technol. Appl..

[14]  Helder Araújo,et al.  Investigating new calibration methods without feature detection for TOF cameras , 2015, Image Vis. Comput..

[15]  Robert B. Fisher,et al.  Estimating 3-D rigid body transformations: a comparison of four major algorithms , 1997, Machine Vision and Applications.

[16]  Mili Shah,et al.  An overview of robot-sensor calibration methods for evaluation of perception systems , 2012, PerMIS.

[17]  Jake K. Aggarwal,et al.  Estimation of motion from a pair of range images: A review , 1991, CVGIP Image Underst..

[18]  Radu Horaud,et al.  Time-of-Flight Cameras: Principles, Methods and Applications , 2012 .

[19]  Xianping Huang,et al.  A flexible solution to AX=XB for robot hand-eye calibration , 2010 .

[20]  Andrew Zisserman,et al.  MLESAC: A New Robust Estimator with Application to Estimating Image Geometry , 2000, Comput. Vis. Image Underst..

[21]  Narendra Ahuja,et al.  Motion and Structure From Two Perspective Views: Algorithms, Error Analysis, and Error Estimation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[22]  Javier González,et al.  Extrinsic calibration of a set of 2D laser rangefinders , 2015, 2015 IEEE International Conference on Robotics and Automation (ICRA).

[23]  Rudi Penne,et al.  Planar Segmentation by Time-of-Flight Cameras , 2013, ACIVS.

[24]  Andreas Birk,et al.  Fast Registration Based on Noisy Planes With Unknown Correspondences for 3-D Mapping , 2010, IEEE Transactions on Robotics.

[25]  H. Pottmann,et al.  Computational Line Geometry , 2001 .