Joint Optical Flow and Temporally Consistent Semantic Segmentation

The importance and demands of visual scene understanding have been steadily increasing along with the active development of autonomous systems. Consequently, there has been a large amount of research dedicated to semantic segmentation and dense motion estimation. In this paper, we propose a method for jointly estimating optical flow and temporally consistent semantic segmentation, which closely connects these two problem domains and leverages each other. Semantic segmentation provides information on plausible physical motion to its associated pixels, and accurate pixel-level temporal correspondences enhance the accuracy of semantic segmentation in the temporal domain. We demonstrate the benefits of our approach on the KITTI benchmark, where we observe performance gains for flow and segmentation. We achieve state-of-the-art optical flow results, and outperform all published algorithms by a large margin on challenging, but crucial dynamic objects.Comment: 14 pages, Accepted for CVRSUAD workshop at ECCV 201

Currents and finite elements as tools for shape space

The nonlinear spaces of shapes (unparameterized immersed curves or submanifolds) are of interest for many applications in image analysis, such as the identification of shapes that are similar modulo the action of some group. In this paper we study a general representation of shapes that is based on linear spaces and is suitable for numerical discretization, being robust to noise. We develop the theory of currents for shape spaces by considering both the analytic and numerical aspects of the problem. In particular, we study the analytical properties of the current map and the $H^{-s}$ norm that it induces on shapes. We determine the conditions under which the current determines the shape. We then provide a finite element discretization of the currents that is a practical computational tool for shapes. Finally, we demonstrate this approach on a variety of examples

Plane-extraction from depth-data using a Gaussian mixture regression model

We propose a novel algorithm for unsupervised extraction of piecewise planar models from depth-data. Among other applications, such models are a good way of enabling autonomous agents (robots, cars, drones, etc.) to effectively perceive their surroundings and to navigate in three dimensions. We propose to do this by fitting the data with a piecewise-linear Gaussian mixture regression model whose components are skewed over planes, making them flat in appearance rather than being ellipsoidal, by embedding an outlier-trimming process that is formally incorporated into the proposed expectation-maximization algorithm, and by selectively fusing contiguous, coplanar components. Part of our motivation is an attempt to estimate more accurate plane-extraction by allowing each model component to make use of all available data through probabilistic clustering. The algorithm is thoroughly evaluated against a standard benchmark and is shown to rank among the best of the existing state-of-the-art methods.Comment: 11 pages, 2 figures, 1 tabl

Semi-Global Stereo Matching with Surface Orientation Priors

Semi-Global Matching (SGM) is a widely-used efficient stereo matching technique. It works well for textured scenes, but fails on untextured slanted surfaces due to its fronto-parallel smoothness assumption. To remedy this problem, we propose a simple extension, termed SGM-P, to utilize precomputed surface orientation priors. Such priors favor different surface slants in different 2D image regions or 3D scene regions and can be derived in various ways. In this paper we evaluate plane orientation priors derived from stereo matching at a coarser resolution and show that such priors can yield significant performance gains for difficult weakly-textured scenes. We also explore surface normal priors derived from Manhattan-world assumptions, and we analyze the potential performance gains using oracle priors derived from ground-truth data. SGM-P only adds a minor computational overhead to SGM and is an attractive alternative to more complex methods employing higher-order smoothness terms.Comment: extended draft of 3DV 2017 (spotlight) pape

On String Graph Limits and the Structure of a Typical String Graph

We study limits of convergent sequences of string graphs, that is, graphs with an intersection representation consisting of curves in the plane. We use these results to study the limiting behavior of a sequence of random string graphs. We also prove similar results for several related graph classes.Comment: 18 page

Commensurable continued fractions

We compare two families of continued fractions algorithms, the symmetrized Rosen algorithm and the Veech algorithm. Each of these algorithms expands real numbers in terms of certain algebraic integers. We give explicit models of the natural extension of the maps associated with these algorithms; prove that these natural extensions are in fact conjugate to the first return map of the geodesic flow on a related surface; and, deduce that, up to a conjugacy, almost every real number has an infinite number of common approximants for both algorithms.Comment: 41 pages, 10 figure