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A. Verri, T. Poggio, "Motion Field and Optical Flow: Qualitative Properties," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 5, pp. 490498, May, 1989.  
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@article{ 10.1109/34.24781, author = {A. Verri and T. Poggio}, title = {Motion Field and Optical Flow: Qualitative Properties}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {11}, number = {5}, issn = {01628828}, year = {1989}, pages = {490498}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.24781}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  Motion Field and Optical Flow: Qualitative Properties IS  5 SN  01628828 SP490 EP498 EPD  490498 A1  A. Verri, A1  T. Poggio, PY  1989 KW  computer vision; qualitative properties; motion field; 2D vector field; 3D velocity field; optical flow; computer vision VL  11 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
It is shown that the motion field the 2D vector field which is the perspective projection on the image plane of the 3D velocity field of a moving scene, and the optical flow, defined as the estimate of the motion field which can be derived from the firstorder variation of the image brightness pattern, are in general different, unless special conditions are satisfied. Therefore, dense optical flow is often illsuited for computing structure from motion and for reconstructing the 3D velocity field by algorithms which require a locally accurate estimate of the motion field. A different use of the optical flow is suggested. It is shown that the (smoothed) optical flow and the motion field can be interpreted as vector fields tangent to flows of planar dynamical systems. Stable qualitative properties of the motion field, which give useful informations about the 3D velocity field and the 3D structure of the scene, usually can be obtained from the optical flow. The idea is supported by results from the theory of structural stability of dynamical systems.
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