Regularization Strategies for Discontinuity-Preserving Optical Flow Methods

Abstract

Abstract-The aim of this work is to study several strategies for the preservation of flow discontinuities in variational optical flow methods. We analyze the combination of robust functionals and diffusion tensors in the smoothness assumption. Our study includes the use of tensors based on decreasing functions, which has shown to provide good results. However, it presents several limitations and usually does not perform better than other basic approaches. It typically introduces instabilities in the computed motion fields in the form of independent blobs of vectors with large magnitude.We propose two alternatives to overcome these drawbacks: first, a simple approach that combines the decreasing function with a minimum isotropic smoothing; second, a method that looks for the best parameter configuration that preserves the important motion contours and avoid instabilities. It relies on the input images and the regularization parameter. It is fully automatic, providing a near-optimal value for many sequences, as shown in the experiments. Both proposals allow to detect the contours of the motion field and produce more stable solutions for a large range of parameters. In the experimental results, we present a detailed study and comparison of the different strategies.

Robust Discontinuity Preserving Optical Flow Methods

“…The iterative process stops when condition (12) is true or a maximum number of iterations is reached. Once it has converged, we go to the next inner iteration, m, and restart the variables in (10). If the parameters are correctly chosen, the method converges in few iterations.…”

“…It prevents the occurrence of instabilities. We fix it value to τ := 0.94 (see [10] for a detailed explanation).…”

“…where x is such that |∇I 1 (x )| is the rank τ × |Ω| among the image gradients and τ := 0.94 is a suitable value, as seen in Monzón et al [10].…”

“…Monzón et al [10] explored two mechanisms to overcome these drawbacks: on the one hand, they proposed a simple approach that ensures a minimum isotropic smoothing when using decreasing functions; on the other hand, they use a strategy that looks for the best parameter configuration preserving motion contours while avoiding instabilities.…”

Comparison of Optical Flow Methods under Stereomatching with Short Baselines

“…Metrics (16) and (18) apply equally to dense or sparse algorithms. Unlike (9), the metric (18) includes all the pixels of the images and not only the visible or valid pixels.…”