Duality based optical flow algorithms with applications

Lars Lau Raket
University of Copenhagen
University of Copenhagen, 2013

   title={Duality based optical flow algorithms},

   author={Rak{^e}t, L.L.},



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We consider the popular TV-L^1 optical flow formulation, and the so-called duality based algorithm for minimizing the TV-L^1 energy. The original formulation is extended to allow for vector valued images, and minimization results are given. In addition we consider different definitions of total variation regularization, and related formulations of the optical flow problem that may be used with a duality based algorithm. We present a highly optimized algorithmic setup to estimate optical flows, and give five novel applications. The first application is registration of medical images, where X-ray images of different hands, taken using different imaging devices are registered using a TV-L^1 optical flow algorithm. We propose to regularize the input images, using sparsity enhancing regularization of the image gradient to improve registration results. The second application is registration of 2D chromatograms, where registration only have to be done in one of the two dimensions, resulting in a vector valued registration problem with values having several hundred dimensions. We propose a novel method for solving this problem, where instead of a vector valued data term, the different channels are coupled through the regularization. This results in a simple formulation of the problem, that may be solved much more efficiently than the conventional coupling. In the third application of the TV-L^1 optical flow algorithm we consider the problem of interpolating frames in an image sequence. We propose to move the motion estimation from the surrounding frames directly to the unknown frame by parametrizing the optical flow objective function such that the interpolation assumption is directly modeled. This reparametrization is a powerful trick that results in a number of appealing properties, in particular the motion estimation becomes more robust to noise and large displacements, and the computational workload is more than halved compared to usual bidirectional methods. Finally we consider two applications of frame interpolation for distributed video coding. The first of these considers the use of depth data to improve interpolation, and the second considers using the information from partially decoded video frames to improve interpolation accuracy in high-motion video sequences.
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