Monocular obstacle detection using reciprocal-polar rectification

Our obstacle detection method is applicable to deliberative translation motion of a mobile robot and, in such motion, the epipole of each image of an image pair is coincident and termed the focus of expansion (FOE). We present an accurate method for computing the FOE and then we use this to apply a novel rectification to each image, called a reciprocal-polar (RP) rectification. When robot translation is parallel to the ground, as with a mobile robot, ground plane image motion in RP-space is a pure shift along an RP image scan line and hence can be recovered by a process of 1D correlation, even over large image displacements and without the need for corner matches. Furthermore, we show that the magnitude of these shifts follows a sinusoidal form along the second (orientation) dimension of the RP image. This gives the main result that ground plane motion over RP image space forms a 3D sinusoidal manifold. Simultaneous ground plane pixel grouping and recovery of the ground plane motion thus amounts to finding the FOE and then robustly fitting a 3D sinusoid to shifts of maximum correlation in RP space. The phase of the recovered sinusoid corresponds to the orientation of the vanishing line of the ground plane and the amplitude is related to the magnitude of the robot/camera translation. Recovered FOE, vanishing line and sinusoid amplitude fully define the ground plane motion (homography) across a pair of images and thus obstacles and ground plane can be segmented without any explicit knowledge of either camera parameters or camera motion.

[1]  S. Shankar Sastry,et al.  Two-View Segmentation of Dynamic Scenes from the Multibody Fundamental Matrix , 2002 .

[2]  Andrew Blake,et al.  Surface Orientation and Time to Contact from Image Divergence and Deformation , 1992, ECCV.

[3]  Zezhi Chen,et al.  From an uncalibrated image sequence of a building to virtual reality modeling language (VRML) , 2002 .

[4]  Carlos Sagues,et al.  Navigation from Uncalibrated Monocular Vision , 1998 .

[5]  Bernhard P. Wrobel,et al.  Multiple View Geometry in Computer Vision , 2001 .

[6]  Ian D. Reid,et al.  Single View Metrology , 2000, International Journal of Computer Vision.

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

[8]  Giulio Sandini,et al.  Divergent stereo in autonomous navigation: From bees to robots , 1995, International Journal of Computer Vision.

[9]  Christopher G. Harris,et al.  A Combined Corner and Edge Detector , 1988, Alvey Vision Conference.

[10]  Kenneth Levenberg A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES , 1944 .

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

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

[13]  Reinhard Koch,et al.  A simple and efficient rectification method for general motion , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[14]  Martin Herman,et al.  Real-time obstacle avoidance using central flow divergence and peripheral flow , 2017, Proceedings of IEEE International Conference on Computer Vision.

[15]  R. Chellappa Introduction of New Editor-in-Chief , 2005 .

[16]  Long Quan,et al.  Match Propagation for Image-Based Modeling and Rendering , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  Peter F. Sturm,et al.  Camera Calibration and 3D Reconstruction from Single Images Using Parallelepipeds , 2001, ICCV.

[18]  Olivier D. Faugeras,et al.  The geometry of multiple images - the laws that govern the formation of multiple images of a scene and some of their applications , 2001 .

[19]  Jean Ponce,et al.  Computer Vision: A Modern Approach , 2002 .

[20]  Hiroshi Hattori,et al.  A practical stereo scheme for obstacle detection in automotive use , 2004, Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004..

[21]  Nick Pears,et al.  Visual navigation using planar homographies , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[22]  Stephen M. Smith,et al.  SUSAN—A New Approach to Low Level Image Processing , 1997, International Journal of Computer Vision.

[23]  Long Quan,et al.  A quasi-dense approach to surface reconstruction from uncalibrated images , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[24]  John Clarke,et al.  Applications of Sequence Geometry to Visual Motion , 1997 .

[25]  Olivier Faugeras,et al.  Motion and Structure from Motion in a piecewise Planar Environment , 1988, Int. J. Pattern Recognit. Artif. Intell..

[26]  Andrew Blake,et al.  Quantitative planar region detection , 2004, International Journal of Computer Vision.

[27]  D. Marquardt An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[28]  Zezhi Chen,et al.  Image dense matching based on region growth with adaptive window , 2002, Pattern Recognit. Lett..

[29]  Nick Pears,et al.  Ground plane segmentation from multiple visual cues , 2002, Other Conferences.

[30]  Thomas S. Huang,et al.  Estimating three-dimensional motion parameters of a rigid planar patch , 1981 .

[31]  George Wolberg,et al.  Robust image registration using log-polar transform , 2000, Proceedings 2000 International Conference on Image Processing (Cat. No.00CH37101).