A review on egomotion by means of differential epipolar geometry applied to the movement of a mobile robot

The estimation of camera egomotion is an old problem in computer vision. Since the 1980s, manyapproaches based on both the discrete and the di#erential epipolar constraint have been proposed. The discrete case is used mainlyin self-calibrated stereoscopic systems, whereas the di#erential case deals with a single moving camera. This article surveys several methods for 3D motion estimation unifying the mathematics convention which are then adapted to the common case of a mobile robot moving on a plane. Experimental results are given on synthetic data covering more than 0.5 million estimations. These surveyed algorithms have been programmed and are available on the Internet.

[1]  Emanuele Trucco,et al.  Computer and Robot Vision , 1995 .

[2]  Ian D. Reid,et al.  Motion estimation using the differential epipolar equation , 2000, Proceedings 15th International Conference on Pattern Recognition. ICPR-2000.

[3]  Carlo Tomasi,et al.  Good features to track , 1994, 1994 Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[4]  Carlo Tomasi,et al.  Direction of heading from image deformations , 1993, Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[5]  Xavier Armangué,et al.  A comparative review of camera calibrating methods with accuracy evaluation , 2002, Pattern Recognit..

[6]  Carlo Tomasi,et al.  Comparison of approaches to egomotion computation , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[7]  K. Prazdny.  Determining The Instantaneous Direction Of Motion From Optical Flow Generated By A Curvilinearly Moving Observer , 1981, Other Conferences.

[8]  Narendra Ahuja,et al.  Matching Two Perspective Views , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  Olivier D. Faugeras,et al.  Structure and motion from two noisy perspective views , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[10]  Yoshiaki Shirai,et al.  Three-Dimensional Computer Vision , 1987, Symbolic Computation.

[11]  Thomas S. Huang,et al.  Uniqueness and Estimation of Three-Dimensional Motion Parameters of Rigid Objects with Curved Surfaces , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  Paul R. Cohen,et al.  Camera Calibration with Distortion Models and Accuracy Evaluation , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  Allan D. Jepson,et al.  Subspace methods for recovering rigid motion I: Algorithm and implementation , 2004, International Journal of Computer Vision.

[14]  Roland N. Ibbett.  The MU5 instruction pipeline , 1972, Comput. J..

[15]  K. Prazdny,et al.  Determining The Instantaneous Direction Of Motion From Optical Flow Generated By A Curvilinearly Moving Observer , 1981, Other Conferences.

[16]  Richard I. Hartley,et al.  Kruppa's Equations Derived from the Fundamental Matrix , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  Kenichi Kanatani,et al.  3-D interpretation of optical flow by renormalization , 1993, International Journal of Computer Vision.

[18]  Wojciech Chojnacki,et al.  Robust Techniques for the Estimation of Structure from Motion in the Uncalibrated Case , 1998, ECCV.

[19]  Ernest L. Hall,et al.  Measuring Curved Surfaces for Robot Vision , 1982, Computer.

[20]  Allan D. Jepson,et al.  Linear subspace methods for recovering translational direction , 1994 .

[21]  Joaquim Salvi,et al.  A robust-coded pattern projection for dynamic 3D scene measurement , 1998, Pattern Recognit. Lett..

[22]  Xavier Armangué,et al.  Overall view regarding fundamental matrix estimation , 2003, Image Vis. Comput..

[23]  J HeegerDavid,et al.  Subspace methods for recovering rigid motion I , 1992 .

[24]  S. Shankar Sastry,et al.  c ○ 2000 Kluwer Academic Publishers. Manufactured in The Netherlands. Linear Differential Algorithm for Motion Recovery: A Geometric Approach , 2022 .

[25]  Olivier D. Faugeras,et al.  The fundamental matrix: Theory, algorithms, and stability analysis , 2004, International Journal of Computer Vision.

[26]  Carlo Tomasi,et al.  Fast, robust, and consistent camera motion estimation , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[27]  Axel Ruhe,et al.  Algorithms for separable nonlinear least squares problems , 1980 .

[28]  Philip H. S. Torr,et al.  The Development and Comparison of Robust Methods for Estimating the Fundamental Matrix , 1997, International Journal of Computer Vision.

[29]  Kenichi Kanatani,et al.  Unbiased Estimation and Statistical Analysis of 3-D Rigid Motion from Two Views , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[30]  KanadeTakeo,et al.  Shape and motion from image streams under orthography , 1992 .

[31]  Olivier D. Faugeras,et al.  The First Order Expansion of Motion Equations in the Uncalibrated Case , 1996, Comput. Vis. Image Underst..

[32]  Wojciech Chojnacki,et al.  Determining the egomotion of an uncalibrated camera from instantaneous optical flow , 1997 .

[33]  K. Prazdny,et al.  Egomotion and relative depth map from optical flow , 2004, Biological Cybernetics.

[34]  Peter I. Corke,et al.  A tutorial on visual servo control , 1996, IEEE Trans. Robotics Autom..

[35]  Berthold K. P. Horn.  Relative orientation , 1987, International Journal of Computer Vision.

[36]  Linda G. Shapiro,et al.  Computer and Robot Vision , 1991 .

[37]  Peter J. Rousseeuw,et al.  Robust regression and outlier detection , 1987 .

[38]  S. Shankar Sastry,et al.  Motion Recovery from Image Sequences: Discrete Viewpoint vs. Differential Viewpoint , 1998, ECCV.

[39]  Olivier D. Faugeras,et al.  Some Properties of the E Matrix in Two-View Motion Estimation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[40]  Takeo Kanade,et al.  Shape and motion from image streams under orthography: a factorization method , 1992, International Journal of Computer Vision.

[41]  David J. Fleet,et al.  Performance of optical flow techniques , 1994, International Journal of Computer Vision.

[42]  ZhangZhengyou.  Determining the Epipolar Geometry and its Uncertainty , 1998 .

[43]  A. Jepson,et al.  A fast subspace algorithm for recovering rigid motion , 1991, Proceedings of the IEEE Workshop on Visual Motion.

[44]  Xinhua Zhuang,et al.  A simplified linear optic flow-motion algorithm , 1988, Comput. Vis. Graph. Image Process..

[45]  David J. Kriegman,et al.  Structure and Motion from Line Segments in Multiple Images , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[46]  H. C. Longuet-Higgins,et al.  A computer algorithm for reconstructing a scene from two projections , 1981, Nature.

[47]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[48]  Roger Y. Tsai,et al.  A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses , 1987, IEEE J. Robotics Autom..

[49]  Madieng Seck.  Optimal Motion From Image Sequences : A RiemannianViewpoint , 1998 .

[50]  Zhengyou Zhang,et al.  Determining the Epipolar Geometry and its Uncertainty: A Review , 1998, International Journal of Computer Vision.

[51]  B. Ripley,et al.  Pattern Recognition , 1968, Nature.

[52]  Berthold K. P. Horn,et al.  Passive navigation , 1982, Computer Vision Graphics and Image Processing.