Variational approaches for optical flow estimation

Christopher Finelli

Master Project

Section of Life Sciences and Technologies, EPFL

June 2015

Abstract

In computer vision, motion analysis constitutes an active research domain and is involved in several applications. The optical flow represents the most low-level characterization of motion, by estimating a dense displacement field describing the temporal evolution in a video sequence or between two consecutive frames. In a variational framework, the estimation of the optical flow is based on certain assumptions on the data and the use of regularizers, imposing prior constraints. Commonly, it is assumed that the intensity of the patterns stay constant throughout the motion. As for the regularization, the total variation (TV) functional and other TV-based regularizers have been extensively studied in the last decade. They have been shown to achieve good performances since this type of regularization preserves motion discontinuities at the object boundaries. However, it turns out that TV is not well adapted to vector fields. In this thesis, we consider a new class of Jacobian-based regularizers that generalizes the TV formalism. This regularization penalizes the Schatten p-norm of the Jacobian matrix and is thus related to the singular values. Furthermore, they are invariant to fundamental coordinate transformations. We propose a variational framework using ADMM that integrates Schatten p-norm regularization in an advanced optical flow model. Our numerical simulations reveal that the particular case of p = 1 better preserves the motion discontinuities that TV regularization. We illustrate that this results in a better motion estimation in certain classes of data.

image1 : Ground truth image2 : Estimation