A Primal-Dual Algorithm for Link Dependent Origin Destination Matrix Estimation

Origin-Destination Matrix (ODM) estimation is a classical problem in transport engineering aiming to recover flows from every Origin to every Destination from measured traffic counts and a priori model information. In addition to traffic counts, the present contribution takes advantage of probe trajectories, whose capture is made possible by new measurement technologies. It extends the concept of ODM to that of Link dependent ODM (LODM), keeping the information about the flow distribution on links and containing inherently the ODM assignment. Further, an original formulation of LODM estimation, from traffic counts and probe trajectories is presented as an optimisation problem, where the functional to be minimized consists of five convex functions, each modelling a constraint or property of the transport problem: consistency with traffic counts, consistency with sampled probe trajectories, consistency with traffic conservation (Kirchhoff's law), similarity of flows having close origins and destinations, positivity of traffic flows. A primal-dual algorithm is devised to minimize the designed functional, as the corresponding objective functions are not necessarily differentiable. A case study, on a simulated network and traffic, validates the feasibility of the procedure and details its benefits for the estimation of an LODM matching real-network constraints and observations

Generalized Video Deblurring for Dynamic Scenes

Several state-of-the-art video deblurring methods are based on a strong assumption that the captured scenes are static. These methods fail to deblur blurry videos in dynamic scenes. We propose a video deblurring method to deal with general blurs inherent in dynamic scenes, contrary to other methods. To handle locally varying and general blurs caused by various sources, such as camera shake, moving objects, and depth variation in a scene, we approximate pixel-wise kernel with bidirectional optical flows. Therefore, we propose a single energy model that simultaneously estimates optical flows and latent frames to solve our deblurring problem. We also provide a framework and efficient solvers to optimize the energy model. By minimizing the proposed energy function, we achieve significant improvements in removing blurs and estimating accurate optical flows in blurry frames. Extensive experimental results demonstrate the superiority of the proposed method in real and challenging videos that state-of-the-art methods fail in either deblurring or optical flow estimation.Comment: CVPR 2015 ora

Full Flow: Optical Flow Estimation By Global Optimization over Regular Grids

We present a global optimization approach to optical flow estimation. The approach optimizes a classical optical flow objective over the full space of mappings between discrete grids. No descriptor matching is used. The highly regular structure of the space of mappings enables optimizations that reduce the computational complexity of the algorithm's inner loop from quadratic to linear and support efficient matching of tens of thousands of nodes to tens of thousands of displacements. We show that one-shot global optimization of a classical Horn-Schunck-type objective over regular grids at a single resolution is sufficient to initialize continuous interpolation and achieve state-of-the-art performance on challenging modern benchmarks.Comment: To be presented at CVPR 201

An Algorithmic Theory of Dependent Regularizers, Part 1: Submodular Structure

We present an exploration of the rich theoretical connections between several classes of regularized models, network flows, and recent results in submodular function theory. This work unifies key aspects of these problems under a common theory, leading to novel methods for working with several important models of interest in statistics, machine learning and computer vision. In Part 1, we review the concepts of network flows and submodular function optimization theory foundational to our results. We then examine the connections between network flows and the minimum-norm algorithm from submodular optimization, extending and improving several current results. This leads to a concise representation of the structure of a large class of pairwise regularized models important in machine learning, statistics and computer vision. In Part 2, we describe the full regularization path of a class of penalized regression problems with dependent variables that includes the graph-guided LASSO and total variation constrained models. This description also motivates a practical algorithm. This allows us to efficiently find the regularization path of the discretized version of TV penalized models. Ultimately, our new algorithms scale up to high-dimensional problems with millions of variables

Simultaneous Stereo Video Deblurring and Scene Flow Estimation

Videos for outdoor scene often show unpleasant blur effects due to the large relative motion between the camera and the dynamic objects and large depth variations. Existing works typically focus monocular video deblurring. In this paper, we propose a novel approach to deblurring from stereo videos. In particular, we exploit the piece-wise planar assumption about the scene and leverage the scene flow information to deblur the image. Unlike the existing approach [31] which used a pre-computed scene flow, we propose a single framework to jointly estimate the scene flow and deblur the image, where the motion cues from scene flow estimation and blur information could reinforce each other, and produce superior results than the conventional scene flow estimation or stereo deblurring methods. We evaluate our method extensively on two available datasets and achieve significant improvement in flow estimation and removing the blur effect over the state-of-the-art methods.Comment: Accepted to IEEE International Conference on Computer Vision and Pattern Recognition (CVPR) 201