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Against Quantitative Optical Flow

A. Verri and T. Poggio, Proc. 1st. International Conference on Computer Vision, London, June 1987.

A key task in machine vision is to obtain the 3D motion field from a sequence of images, for tasks such as segmenting the different moving objects and recovering the 3D structure of surfaces. One popular approach is optical flow. In order to find the 3D "velocity field" of the image sequence, the 2D "motion field" (the projection of the velocity field onto the image plane) must first be found. In optical flow techniques, the "optical flow" field (the perceived motion field due to the time-dependent variation of brightness at points in the image plane) is (usually) assumed to coincide with the motion field.

Using a number of examples Verri and Poggio prove that, in the general case, the motion field and optical flow field only coincide at points of high image gradient (edges, including texture edges), showing that optical flow cannot be used to reconstruct the 2D motion field in a point-to-point manner. However, they go on to show that useful qualitative properties of the 3D velocity field, such as its discontinuities, can be reconstructed directly from the optical flow field.

The take-home message is this: any research that purports to produce dense motion fields using optical flow techniques is provably wrong in the general case.

PAB 9/3/2005

The performance characterisation spin on this is that dense optical flow fields must be accompanied by estimates of error, which would generally be expected to be large away from edges and texture. Notice also, that what is true for optical flow MUST also be true for stereo algorithms, which are just a special case. If we wish to believe that stereo can produce accurate and useful dense data we may be guilty of fooling ourselves. If dense data can only be achieved by interpolating from the edges, then there is no independent information on smooth surfaces.

NAT 10/3/2005

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