This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
On a Constraint Equation for the Estimation of Displacement Rates in Image Sequences
January 1989 (vol. 11 no. 1)
pp. 13-30

The commonly used constraint equation Delta g/sup T/u+g/sub t/=0 for the estimation of optical flow can only be justified by assumptions that are, in general, far too restrictive for image sequences of real world scenes. B.G. Schunck (1985, 86) recently argued that a constraint equation for the estimation of what he called image flow has to include a term containing the divergence of this image flow without presenting, however, a stringent derivation based on perspective projection from 3-D scene space. The present author derives a constraint equation based on a combination of perspective projection and notions from differential geometry. In addition, he demonstrates the quantitive effects of taking into account radiometric considerations based on the use of Lambertian reflection properties and isotropic illumination in scene space.

[1] R. O. Duda and P. E. Hart,Pattern Classification and Scene Analysis. New York: Wiley, 1973.
[2] O. D. Faugeras and G. Toscani, "The Calibration Problem for Stereo," inProc. IEEE Conf. Computer Vision and Pattern Recognition CVPR-86, Miami Beach, FL, June 22-26, 1986, pp. 15-20.
[3] A. Gelb, Ed.,Applied Optimal Estimation. Cambridge, MA: MIT Press, 1974.
[4] E. Hildreth,The Measurement of Visual Motion, Cambridge, MA: MIT Press, 1983.
[5] B. K. P. Horn,Robot Vision. Cambridge, MA: M.I.T. Press, 1986.
[6] B. K. P. Horn and B. G. Schunck, "Determining optical flow,"Artificial Intell., vol. 17, pp. 185-203, 1981.
[7] J. J. Koenderink and A. J. van Doorn, "How an ambulant observer can construct a model of the environment from the geometrical structure of the visual inflow," inKybernetik 1977, G. Hauske and E. Butenandt, Eds. Munich: Oldenbourg-Verlag, 1978, pp. 224-245.
[8] H. C. Longuet-Higgins and K. Prazdny, "The interpretation of moving retinal images,"Proc. Roy. Soc. London, vol. B208, pp. 385- 397, 1980.
[9] H.-H. Nagel, "Image sequences-ten (octal) years-from phenomenology towards a theoretical foundation, " inProc. 8th Int. Conf. Pattern Recognition, Paris, France, Oct. 27-31, 1986, pp. 1174-1185.
[10] S. Negahdaripour and B. K. P. Horn, "Direct passive navigation,"IEEE Trans. Patt. Anal. Machine Intell., vol. 9, no. 1, pp. 168-176, Jan 1987.
[11] B. G. Schunck, "Image flow: Fundamentals and future research," inProc. IEEE Conf. Computer Vision and Pattern Recognition CVPR- 85, San Francisco, CA, June 19-23, 1985, pp. 560-571.
[12] B. G. Schunck, "Image flow continuity equations for motion and density," inProc. Workshop Motion: Representation and Analysis, Charleston, SC, May 7-9, 1986, pp. 89-94.
[13] S. Ullman,The Interpretation of Visual Motion. Cambridge, MA: MIT Press, 1979.
[14] S. Ullman and E. C. Hildreth, "The measurement of visual motion," inPhysical and Biological Processing of Images, O. J. Braddick and A. C. Sleigh, Eds. New York: Springer-Verlag, 1983, pp. 154-176.
[15] A. M. Waxman, "An image flow paradigm," inProc. Workshop Computer Vision: Representation and Control, Annapolis, MD, Apr. 30-May 2, 1984, pp. 49-57.
[16] A. M. Waxman and S. Ullman, "Surface structure and three-dimensional motion from image flow kinematics,"Int. J. Robotics Res., vol. 4, no. 3, pp. 95-108, 1985.
[17] H. Westphal and H.-H. Nagel, "Towards the derivation of three-dimensional descriptions from image sequences for nonconvex moving objects,"Comput. Vision, Graphics, Image Processing, vol. 34, pp. 302-320, 1986.
[18] H. Westphal and H.-H. Nagel, "About the exploitation of reflectance properties to analyze images of moving objects,"Comput. Vision, Graphics, Image Processing, vol. 38, pp. 90-98, 1987.
[19] A. Verri and T. Poggio, "Motion field and optical flow: Qualitative properties," Artificial Intell. Lab. and Center for Biol. Inform. Processing, Massachusetts Inst. Technol., Cambridge, MA, AI Memo. 917, Dec. 1986; see alsoIEEE Trans. Pattern Anal. Machine Intell., to be published.

Index Terms:
picture processing; image sequences; constraint equation; optical flow; real world scenes; image flow; perspective projection; differential geometry; Lambertian reflection; isotropic illumination; optical information processing; picture processing; radiometry
Citation:
H H. Nagel, "On a Constraint Equation for the Estimation of Displacement Rates in Image Sequences," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 1, pp. 13-30, Jan. 1989, doi:10.1109/34.23110
Usage of this product signifies your acceptance of the Terms of Use.