Extraction of quadrics from noisy point-clouds using a sensor noise model

Fitting optimum quadrics on segmented noisy range-image is a challenging task. The algebraic least-squares fit usually considered in the literature is biased, although it is fast to compute. We extend our previous work in planar patch extraction using a detailed sensor noise model to the extraction of quadrics. First, the fast least-squares method is modified to detect degeneracy automatically and it is used to aid segmentation. The final segmented quadric patch is then refined using a numerical maximum likelihood approach which employs the sensor range error model. Experimental results for artificial data and two different 3D sensors are provided to show the feasibility of our approach.

[1]  N. Shrikhande,et al.  Quadric surface fitting for sparse range data , 1991, Conference Proceedings 1991 IEEE International Conference on Systems, Man, and Cybernetics.

[2]  Alireza Bab-Hadiashar,et al.  Range image segmentation using surface selection criterion , 2006, IEEE Transactions on Image Processing.

[3]  P. Besl.  Surfaces in early range image understanding , 1986 .

[4]  Andreas Birk,et al.  Uncertainty analysis for optimum plane extraction from noisy 3D range-sensor point-clouds , 2010, Intell. Serv. Robotics.

[5]  Jouni Kuha.  Measurement Error in Quadratic Regression Models , 1999 .

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

[7]  Alonzo Kelly,et al.  Experimental Characterization of Commercial Flash Ladar Devices , 2005 .

[8]  M. Hebert,et al.  The Representation, Recognition, and Locating of 3-D Objects , 1986 .

[9]  Andrew W. Fitzgibbon,et al.  Extracting surface patches from complete range descriptions , 1997, Proceedings. International Conference on Recent Advances in 3-D Digital Imaging and Modeling (Cat. No.97TB100134).

[10]  Andreas Birk,et al.  Fast plane detection and polygonalization in noisy 3D range images , 2008, 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[11]  Alireza Bab-Hadiashar,et al.  A comparative study of model selection criteria for computer vision applications , 2008, Image Vis. Comput..

[12]  Andreas Birk,et al.  Online three‐dimensional SLAM by registration of large planar surface segments and closed‐form pose‐graph relaxation , 2010, J. Field Robotics.

[13]  Ivan Bricault,et al.  From Volume Medical Images to Quadratic Surface Patches , 1997, Comput. Vis. Image Underst..

[14]  Andrew W. Fitzgibbon,et al.  High-level model acquisition from range images , 1997, Comput. Aided Des..

[15]  Sylvain Petitjean,et al.  A survey of methods for recovering quadrics in triangle meshes , 2002, CSUR.

[16]  Moonhong Baeg,et al.  Pose estimation of quadratic surface using surface fitting technique , 1995, Proceedings 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human Robot Interaction and Cooperative Robots.

[17]  Gabriel Taubin,et al.  Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation , 1991, IEEE Trans. Pattern Anal. Mach. Intell..