Optical Flow Computation for Compound Eyes: Variational Analysis of Omni-Directional Views

This paper focuses on variational optical flow computation for spherical images. It is said that some insects recognise the world through optical flow observed by their compound eyes, which observe spherical views. Furthermore, images observed through a catadioptric system with a conic mirror and a fish-eye-lens camera are transformed to images on the sphere. Spherical motion field on the spherical retina has some advantages for the ego-motion estimation of autonomous mobile observer. We provide a framework for motion field analysis on the spherical retina using variational method for image analysis.

[1]  Titus R. Neumann.  Modeling Insect Compound Eyes: Space-Variant Spherical Vision , 2002, Biologically Motivated Computer Vision.

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

[3]  Jean-Michel Morel,et al.  Variational methods in image segmentation , 1995 .

[4]  Todd D. Ringler,et al.  Climate modeling with spherical geodesic grids , 2002, Comput. Sci. Eng..

[5]  J. Aloimonos,et al.  Finding motion parameters from spherical motion fields (or the advantages of having eyes in the back of your head) , 1988, Biological Cybernetics.

[6]  J. Zanker,et al.  Motion vision : computational, neural, and ecological constraints , 2001 .

[7]  R. Franke,et al.  A Survey on Spherical Spline Approximation , 1995 .

[8]  Atsushi Imiya,et al.  Optical Flow Computation of Omni-Directional Images , 2006 .

[9]  Yiannis Aloimonos,et al.  Ambiguity in Structure from Motion: Sphere versus Plane , 1998, International Journal of Computer Vision.

[10]  S. Osher,et al.  Geometric Level Set Methods in Imaging, Vision, and Graphics , 2011, Springer New York.

[11]  Seong-Whan Lee,et al.  Biologically Motivated Computer Vision , 2002, Lecture Notes in Computer Science.

[12]  Pierre Kornprobst,et al.  Mathematical problems in image processing - partial differential equations and the calculus of variations , 2010, Applied mathematical sciences.

[13]  Hans-Hellmut Nagel,et al.  On the Estimation of Optical Flow: Relations between Different Approaches and Some New Results , 1987, Artif. Intell..

[14]  Kostas Daniilidis,et al.  Catadioptric Projective Geometry , 2001, International Journal of Computer Vision.

[15]  Shree K. Nayar,et al.  A Theory of Single-Viewpoint Catadioptric Image Formation , 1999, International Journal of Computer Vision.

[16]  Tomás Svoboda,et al.  Epipolar Geometry for Central Catadioptric Cameras , 2002, International Journal of Computer Vision.

[17]  G. Sapiro,et al.  Geometric partial differential equations and image analysis [Book Reviews] , 2001, IEEE Transactions on Medical Imaging.

[18]  Berthold K. P. Horn,et al.  Determining Optical Flow , 1981, Other Conferences.

[19]  Atsushi Imiya,et al.  Voting method for the detection of subpixel flow field , 2003, Pattern Recognit. Lett..

[20]  John H. E. Clark.  Dynamics of the Atmosphere , 2004 .