Optical flow estimation with consistent spatio-temporal coherence models

[EN] In this work we propose a new variational model for the consistent estimation of motion fields. The aim of this work is to develop appropriate spatio-temporal coherence models. In this sense, we propose two main contributions: a nonlinear flow constancy assumption, similar in spirit to the nonlinear brightness constancy assumption, which conveniently relates flow fields at different time instants; and a nonlinear temporal regularization scheme, which complements the spatial regularization and can cope with piecewise continuous motion fields. These contributions pose a congruent variational model since all the energy terms, except the spatial regularization, are based on nonlinear warpings of the flow field. This model is more general than its spatial counterpart, provides more accurate solutions and preserves the continuity of optical flows in time. In the experimental results, we show that the method attains better results and, in particular, it considerably improves the accuracy in the presence of large displacements.

TV-L1 optical flow estimation

[EN] This article describes an implementation of the optical flow estimation method introduced by Zach, Pock and Bischof. This method is based on the minimization of a functional containing a data term using the L norm and a regularization term using the total variation of the flow. The main feature of this formulation is that it allows discontinuities in the flow field, while being more robust to noise than the classical approach. The algorithm is an efficient numerical scheme, which solves a relaxed version of the problem by alternate minimization.

Horn-schunck optical flow with a multi-scale strategy

[EN] The seminal work of Horn and Schunck [8] is the first variational method for optical flow estimation. It introduced a novel framework where the optical flow is computed as the solution of a minimization problem. From the assumption that pixel intensities do not change over time, the optical flow constraint equation is derived. This equation relates the optical flow with the derivatives of the image. There are infinitely many vector fields that satisfy the optical flow constraint, thus the problem is ill-posed. To overcome this problem, Horn and Schunck introduced an additional regularity condition that restricts the possible solutions. Their method minimizes both the optical flow constraint and the magnitude of the variations of the flow field, producing smooth vector fields. One of the limitations of this method is that, typically, it can only estimate small motions. In the presence of large displacements, this method fails when the gradient of the image is not smooth enough. In this work, we describe an implementation of the original Horn and Schunck method and also introduce a multi-scale strategy in order to deal with larger displacements. For this multi-scale strategy, we create a pyramidal structure of downsampled images and change the optical flow constraint equation with a nonlinear formulation. In order to tackle this nonlinear formula, we linearize it and solve the method iteratively in each scale. In this sense, there are two common approaches: one that computes the motion increment in the iterations, like in ; or the one we follow, that computes the full flow during the iterations, like in. The solutions are incrementally refined ower the scales. This pyramidal structure is a standard tool in many optical flow methods.

Estimación del movimiento de objetos en secuencias de imágenes de intensidad y profundidad

Máster Universitario en Sistemas Inteligentes y Aplicaciones Numéricas en Ingeniería (SIANI)

Variational second order flow estimation for PIV sequences

[EN] We present in this paper a variational approach to accurately estimate simultaneously the velocity field and its derivatives directly from PIV image sequences. Our method differs from other techniques that have been presented in the literature in the fact that the energy minimization used to estimate the particles motion depends on a second order Taylor development of the flow. In this way, we are not only able to compute the motion vector field, but we also obtain an accurate estimation of their derivatives. Hence, we avoid the use of numerical schemes to compute the derivatives from the estimated flow that usually yield to numerical amplification of the inherent uncertainty on the estimated flow. The performance of our approach is illustrated with the estimation of the motion vector field and the vorticity on both synthetic and real PIV datasets.