Over-parameterized variational optical flow

Tal Nir

doi:10.1007/s11263-007-0051-2

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Over-parameterized variational optical flow

2007-06-30

PRE

Tal Nir *

Alfred M. Bruckstein⋆

Ron Kimmel

DOI：10.1007/s11263-007-0051-2

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Abstract

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A novel optical flow estimation process based on a spatio-temporal model with varying coefficients multiplying a set of basis functions at each pixel is introduced. Previous optical flow estimation methodologies did not use such an over parameterized representation of the flow field as the problem is ill-posed even without introducing any additional parameters: Neighborhood based methods of the Lucas-Kanade type determine the flow at each pixel by constraining the flow to be described by a few parameters in small neighborhoods. Modern variational methods represent the optic flow directly via the flow field components at each pixel. The benefit of over-parametrization becomes evident in the smoothness term, which instead of directly penalizing for changes in the optic flow, accumulates a cost of deviating from the assumed optic flow model. Our proposed method is very general and the classical variational optical flow techniques are special cases of it, when used in conjunction with constant basis functions. Experimental results with the novel flow estimation process yield significant improvements with respect to the best results published so far.

Keywords:

optical flow

variational methods

L-1 regularization

over-parametrization

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