This Article 
 Bibliographic References 
 Add to: 
On the Advantages of Polar and Log-Polar Mapping for Direct Estimation of Time-To-Impact from Optical Flow
April 1993 (vol. 15 no. 4)
pp. 401-410

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] L. Massone, G. Sandini, and V. Tagliasco, "Form-invariant topological mapping strategy for 2-d shape recognition,"CVGIP, vol. 30, no. 2, pp. 169-188, 1985.
[2] C. F. R. Weiman and G. Chaikin, "Logarithmic spiral grids for image processing and display,"CGIP, vol. 11, pp. 197-226, 1979.
[3] D. Marr,Vision. San Francisco: Freeman, 1982.
[4] D. H. Ballard and C. M. Brown,Computer Vision. Englewood Cliffs, NJ: Prentice-Hall, 1982.
[5] E. Hildreth,The Measurement of Visual Motion, Cambridge, MA: MIT Press, 1983.
[6] B. K. P. Horn,Robot Vision. Cambridge, MA: M.I.T. Press, 1986.
[7] E. L. Schwartz, "Spatial mapping in the primate sensory projection: Analytic structure and relevance to perception,"Biolog. Cybern., vol. 25, pp. 181-194, 1977.
[8] A. M. Chiang, "Ccd retina and neural net processor,"Proc. Workshop Hardware Implementation Neural Nets Synapses, (San Diego), 1988, pp. 171-182.
[9] P. J. Burt,Smart Sensing in Machine Vision. New York: Academic, 1988.
[10] J. Aloimonos, I. Weiss, and A. Bandyopadhyay, "Active vision,"Int. J Comput. Vision, vol. 1, no. 4, pp. 333-356, 1988.
[11] R. K. Bajcsy, "Active perception vs passive perception," inProc. Third IEEE Workshop Comput. Vision: Representation Contr., (Bellaire, MI), 1985, pp. 13-16.
[12] G. Sandini, P. Morasso, and M. Tistarelli, "Motor and spatial aspects in artificial vision," inProc. of 4th Int. Symp. Robotics Res.(Santa Cruz, CA), 1987, MIT Press.
[13] H. Inoue, H. Mizoguchi, Y. Murata, and M. Inaba, "A robot vision system with flexible multiple attention capability," inProc. ICAR, 1985, pp. 199-205.
[14] E. D. Dickmanns, "4d-dynamic scene analysis with integral spatio-temporal models," inProc. 5th Int. Symp. Robotics Res.(Tokyo), 1988, MIT Press.
[15] G. Sandini and P. Dario, "Active vision based on space-variant sensing," inProc. 5th Int. Symp. Robotics Res.(Tokyo), 1989, MIT Press.
[16] R. Jain, S. L. Bartlett, and N. O'Brien, "Motion stereo using ego-motion complex logarithmic mapping,"IEEE Trans. Pattern Anal. Machine Intell., vol. 9, no. 3, pp. 356-369, May 1987.
[17] S. L. Bartlett and R. C. Jain, "Depth determination using complex logarithmic mapping," inProc. SPIE Int. Conf. Intell. Robots Comput. Vision IX: Neural Biolog. 3-D Methods, (Boston, MA), 1990, pp. 4-9.
[18] G. Sandini and V. Tagliasco, "An anthropomorphic retina-like structure for scene analysis,"CGIP, vol. 14, no. 3, pp. 365-372, 1980.
[19] C. Braccini, G. Gambardella, G. Sandini, and V. Tagliasco, "A model of the early stages of the human visual system: Functional and topological transformation performed in the peripheral visual field,Biolog. Cybern., vol. 44, pp. 47-58, 1982.
[20] C. F. R. Weiman and R. D. Juday, "Tracking algorithms using log-polar mapped image coordinates," inSPIE Int. Conf. Intell. Robots Comput. Vision VIII: Algorithms Techn., (Philadelphia), Nov. 6-10, 1990, pp. 843-853, vol. 1192.
[21] M. Tistarelli and G. Sandini, "Estimation of depth from motion using an anthropomorphic visual sensor,"Image Vision Comput., vol. 8, no. 4, pp. 271-278, 1990.
[22] R. C. Nelson and J. Aloimonos, "Obstacle avoidance using flow field divergence,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-11, pp. 1102-1106, Oct. 1989.
[23] J. H. Rieger and D. T. Lawton, "Processing differential image motion," Tech. Rep., COINS Dept. Univ. of Mass., Amherst, 1984.
[24] J. Van der Spiegel et al., "A foveated retina-like sensor using ccd technology," inAnalog VLSI and Neural Network Implementations(C. Mead and M. Ismail, Eds.). Boston: Kluwer, 1989.
[25] D. H. Ballard, R. C. Nelson, and B. Yamauchi, "Animate vision,"Opt. News, vol. 15, no. 5, pp. 17-25, 1989.
[26] P. Morasso, G. Sandini, and M. Tistarelli, "Active vision: Integration of fixed and mobile cameras," inProc. NATO ARW Sensors Sensory Syst. Adv. Robots(Berlin, Heidelberg), 1986.
[27] E. Grosso, G. Sandini, and M. Tistarelli, "3d object reconstruction using stereo and motion,"IEEE Trans. Syst. Man Cybern.vol. SMC-19, no. 6, 1989.
[28] B. K. P. Horn and B. G. Schunck, "Determining optical flow,"Artificial Intell., vol. 17, no. 1-3, pp. 185-204, 1981.
[29] S. Uras, F. Girosi, A. Verri, and V. Terre, "Computational approach to motion perception,"Biolog. Cybern., vol. 60, pp. 69-87, 1988.
[30] E. DeMicheli, G. Sandini, M. Tistarelli, and V. Torre, "Estimation of visual motion and 3d motion parameters from singular points," inProc. of IEEE Int. Workshop Intell. Robots Syst.(Tokyo, Japan), 1988.
[31] G. Sandini and M. Tistarelli, "Active tracking strategy for monocular depth inference over multiple frames,"IEEE Trans. Patt. Anal. Machine Intell., vol. 12, no. 1, pp. 13-27, Jan. 1990.
[32] W. B. Thompson and J. K. Kearney, "Inexact vision," inProc. IEEE Workshop Motion: Represent. Anal., (Kiawah Island Resort), 1986, pp. 15-21.
[33] C. F. R. Weiman,Personal communication, Transition Research Corp. Int., 1990.
[34] V. Torre and T. A. Poggio, "On edge detection,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 147-163, Mar. 1986.
[35] M. Bertero, T. A. Poggio, and V. Torre, "Ill-posed problems in early vision,"Proc. IEEE, vol. 76, pp. 869-889, Aug. 1988.
[36] H. H. Nagel, "Extending the 'oriented smoothness constraint' into the temporal domain and the estimation of derivatives of optical flow," inProc. first Euro. Conf. Comput. Vision, (Antibes, France), 1990, pp. 139-148.
[37] Y. Aloimonos, "Purposive and qualitative active vision," inProc. Int. Workshop Active Contr. Visual Perception(Antibes, France), May 1990.

Index Terms:
CCD image sensors; motion estimation; log-polar mapping; direct estimation; time-to-impact; optical flow; anthropomorphic retina-like visual sensor; visual navigation; egomotion; tracking; CCD image sensors; motion estimation
M. Tistarelli, G. Sandini, "On the Advantages of Polar and Log-Polar Mapping for Direct Estimation of Time-To-Impact from Optical Flow," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 4, pp. 401-410, April 1993, doi:10.1109/34.206959
Usage of this product signifies your acceptance of the Terms of Use.