On the Advantages of Polar and Log-Polar Mapping for Direct Estimation of Time-To-Impact from Optical Flow

The application of an anthropomorphic retina-like visual sensor and the advantages of polar and log-polar mapping for visual navigation are investigated. It is demonstrated that the motion equations that relate the egomotion and/or the motion of the objects in the scene to the optical flow are considerably simplified if the velocity is represented in a polar or log-polar coordinate system, as opposed to a Cartesian representation. The analysis is conducted for tracking egomotion but is then generalized to arbitrary sensor and object motion. The main result stems from the abundance of equations that can be written directly that relate the polar or log-polar optical flow with the time to impact. Experiments performed on images acquired from real scenes are presented. >

[1]  Giulio Sandini,et al.  Motor and spatial aspects in artificial vision , 1988 .

[2]  Giulio Sandini,et al.  3D object reconstruction using stereo and motion , 1989, IEEE Trans. Syst. Man Cybern..

[3]  Giulio Sandini,et al.  A Foveated Retina-Like Sensor Using CCD Technology , 1989, Analog VLSI Implementation of Neural Systems.

[4]  Tomaso A. Poggio,et al.  On Edge Detection , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  Carl F. R. Weiman,et al.  Logarithmic spiral grids for image-processing and display , 1979 .

[6]  Dana H. Ballard,et al.  Computer Vision , 1982 .

[7]  M. Bertero,et al.  Ill-posed problems in early vision , 1988, Proc. IEEE.

[8]  M. Tistarelli,et al.  Estimation Of Visual Motion And 3d Motion Parameters From Singular Points , 1988, IEEE International Workshop on Intelligent Robots.

[9]  A. M. Chiang.  CCD Retina and Neural Net Processor , 1993 .

[10]  Giulio Sandini,et al.  Estimation of depth from motion using an anthropomorphic visual sensor , 1990, Image Vis. Comput..

[11]  Dana H. Ballard,et al.  Animate Vision , 1991, Artif. Intell..

[12]  Giulio Sandini,et al.  "Form-invariant" topological mapping strategy for 2D shape recognition , 1985, Comput. Vis. Graph. Image Process..

[13]  Ramesh C. Jain,et al.  Motion Stereo Using Ego-Motion Complex Logarithmic Mapping , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[14]  S. L. Bartlett,et al.  Depth determination using complex logarithmic mapping , 1991, Other Conferences.

[15]  J H Rieger,et al.  Processing differential image motion. , 1985, Journal of the Optical Society of America. A, Optics and image science.

[16]  Hans-Hellmut Nagel,et al.  Extending the 'Oriented Smoothness Constraint' into the Temporal Domain and the Estimation of Derivatives of Optical Flow , 1990, ECCV.

[17]  Peter J. Burt,et al.  `Smart Sensing' in machine vision , 1988 .

[18]  Giulio Sandini,et al.  Active Tracking Strategy for Monocular Depth Inference over Multiple Frames , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  Carl F. R. Weiman,et al.  Tracking Algorithms Using Log-Polar Mapped Image Coordinates , 1990, Other Conferences.

[20]  Giulio Sandini,et al.  Active vision: integration of fixed and mobile cameras , 1988 .

[21]  Yiannis Aloimonos,et al.  Obstacle Avoidance Using Flow Field Divergence , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[22]  E. D. Dickmanns,et al.  4 D-dynamic scene analysis with integral spatio-temporal models , 1988 .

[23]  Berthold K. P. Horn.  Robot vision , 1986, MIT electrical engineering and computer science series.

[24]  Giulio Sandini,et al.  An anthropomorphic retina-like structure for scene analysis , 1980 .

[25]  Yiannis Aloimonos,et al.  Purposive and qualitative active vision , 1990, [1990] Proceedings. 10th International Conference on Pattern Recognition.

[26]  Ellen C. Hildreth,et al.  Measurement of Visual Motion , 1984 .

[27]  Giulio Sandini,et al.  Active vision based on space-variant sensing , 1991 .

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