Discrete and Continuous Optimization for Motion Estimation

The study of motion estimation reaches back decades and has become one of the central topics of research in computer vision. Even so, there are situations where current approaches fail, such as when there are extreme lighting variations, significant occlusions, or very large motions. In this thesis, we propose several approaches to address these issues. First, we propose a novel continuous optimization framework for estimating optical flow based on a decomposition of the image domain into triangular facets. We show how this allows for occlusions to be easily and naturally handled within our optimization framework without any post-processing. We also show that a triangular decomposition enables us to use a direct Cholesky decomposition to solve the resulting linear systems by reducing its memory requirements. Second, we introduce a simple method for incorporating additional temporal information into optical flow using inertial estimates of the flow, which leads to a significant reduction in error. We evaluate our methods on several datasets and achieve state-of-the-art results on MPI-Sintel. Finally, we introduce a discrete optimization framework for optical flow computation. Discrete approaches have generally been avoided in optical flow because of the relatively large label space that makes them computationally expensive. In our approach, we use recent advances in image segmentation to build a tree-structured graphical model that conforms to the image content. We show how the optimal solution to these discrete optical flow problems can be computed efficiently by making use of optimization methods from the object recognition literature, even for large images with hundreds of thousands of labels

Complementing Brightness Constancy with Deep Networks for Optical Flow Prediction

State-of-the-art methods for optical flow estimation rely on deep learning, which require complex sequential training schemes to reach optimal performances on real-world data. In this work, we introduce the COMBO deep network that explicitly exploits the brightness constancy (BC) model used in traditional methods. Since BC is an approximate physical model violated in several situations, we propose to train a physically-constrained network complemented with a data-driven network. We introduce a unique and meaningful flow decomposition between the physical prior and the data-driven complement, including an uncertainty quantification of the BC model. We derive a joint training scheme for learning the different components of the decomposition ensuring an optimal cooperation, in a supervised but also in a semi-supervised context. Experiments show that COMBO can improve performances over state-of-the-art supervised networks, e.g. RAFT, reaching state-of-the-art results on several benchmarks. We highlight how COMBO can leverage the BC model and adapt to its limitations. Finally, we show that our semi-supervised method can significantly simplify the training procedure

Algebraic Topology-Based Image Deformation : a Unified Model

In this paper, a new method for image deformation is presented. It is based upon decomposition of the deformation problem into basic physical laws. Unlike other methods that solve a differential or an energetic formulation of the physical laws involved, we encode the basic laws using computational algebraic topology. Conservative laws are translated into exact global values and constitutive laws are judiciously approximated. In order to illustrate the effectiveness of our model, we deal with both small- and large-scale deformation, utilizing elasticity theory and the viscous fluid model, respectively. The proposed approach is validated through a series of tests on optical flow estimation and image registration

Decomposition of Optical Flow on the Sphere

We propose a number of variational regularisation methods for the estimation and decomposition of motion fields on the $2$-sphere. While motion estimation is based on the optical flow equation, the presented decomposition models are motivated by recent trends in image analysis. In particular we treat $u+v$ decomposition as well as hierarchical decomposition. Helmholtz decomposition of motion fields is obtained as a natural by-product of the chosen numerical method based on vector spherical harmonics. All models are tested on time-lapse microscopy data depicting fluorescently labelled endodermal cells of a zebrafish embryo.Comment: The final publication is available at link.springer.co

A massively parallel multi-level approach to a domain decomposition method for the optical flow estimation with varying illumination

We consider a variational method to solve the optical flow problem with varying illumination. We apply an adaptive control of the regularization parameter which allows us to preserve the edges and fine features of the computed flow. To reduce the complexity of the estimation for high resolution images and the time of computations, we implement a multi-level parallel approach based on the domain decomposition with the Schwarz overlapping method. The second level of parallelism uses the massively parallel solver MUMPS. We perform some numerical simulations to show the efficiency of our approach and to validate it on classical and real-world image sequences

Estimating Sensor Motion from Wide-Field Optical Flow on a Log-Dipolar Sensor

Log-polar image architectures, motivated by the structure of the human visual field, have long been investigated in computer vision for use in estimating motion parameters from an optical flow vector field. Practical problems with this approach have been: (i) dependence on assumed alignment of the visual and motion axes; (ii) sensitivity to occlusion form moving and stationary objects in the central visual field, where much of the numerical sensitivity is concentrated; and (iii) inaccuracy of the log-polar architecture (which is an approximation to the central 20°) for wide-field biological vision. In the present paper, we show that an algorithm based on generalization of the log-polar architecture; termed the log-dipolar sensor, provides a large improvement in performance relative to the usual log-polar sampling. Specifically, our algorithm: (i) is tolerant of large misalignmnet of the optical and motion axes; (ii) is insensitive to significant occlusion by objects of unknown motion; and (iii) represents a more correct analogy to the wide-field structure of human vision. Using the Helmholtz-Hodge decomposition to estimate the optical flow vector field on a log-dipolar sensor, we demonstrate these advantages, using synthetic optical flow maps as well as natural image sequences