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Variational methods are among the most successful approaches to calculate the optical flow between two image frames. A particularly appealing formulation is based on total variation (TV) regularization and the robust L 1 norm in the data fidelity term. This formulation can preserve discontinuities in the flow field and offers an increased robustness against illumination changes, occlusions and noise. In this work we present a novel approach to solve the TV-L 1 formulation. Our method results in a very efficient numerical scheme, which is based on a dual formulation of the TV energy and employs an efficient point-wise thresholding step. Additionally, our approach can be accelerated by modern graphics processing units. We demonstrate the real-time performance (30 fps) of our approach for video inputs at a resolution of 320×240 pixels.
This article propose an energy for computing the optical flow, that fits the optical flow constraint using the L1-norm, and uses total variation as regularizer of the flow (component by component).
The energy is relaxed by introducing a coupling variable, which permits to solve it by alternating between TVL2 minimization (Chambolle's algorithm) and a point-wise thresholding.
The derivation of the thresholding conditions in eq (11) is simple but laborious.
- Dinstinguishes 3 possible behaviors of the optimum v*: \rho(v*) <0 , \rho(v*) > 0 and \rho(v*) = 0
- For each the optimum v^* can be determined.
- The thresholds are determined by plugging the optimums into the energy for each case, and then comparing the energy (searching for the minimum value).
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