GASP : Geometric Association with Surface Patches

A fundamental challenge to sensory processing tasks in perception and robotics is the problem of obtaining data associations across views. We present a robust solution for ascertaining potentially dense surface patch (superpixel) associations, requiring just range information. Our approach involves decomposition of a view into regularized surface patches. We represent them as sequences expressing geometry invariantly over their superpixel neighborhoods, as uniquely consistent partial orderings. We match these representations through an optimal sequence comparison metric based on the Damerau-Levenshtein distance - enabling robust association with quadratic complexity (in contrast to hitherto employed joint matching formulations which are NP-complete). The approach is able to perform under wide baselines, heavy rotations, partial overlaps, significant occlusions and sensor noise. The technique does not require any priors -- motion or otherwise, and does not make restrictive assumptions on scene structure and sensor movement. It does not require appearance -- is hence more widely applicable than appearance reliant methods, and invulnerable to related ambiguities such as textureless or aliased content. We present promising qualitative and quantitative results under diverse settings, along with comparatives with popular approaches based on range as well as RGB-D data.Comment: International Conference on 3D Vision, 201

Transport in time-dependent dynamical systems: Finite-time coherent sets

We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time, despite the chaotic nature of the system. We develop a novel probabilistic methodology based upon transfer operators that automatically detects maximally coherent sets. The approach is very simple to implement, requiring only singular vector computations of a matrix of transitions induced by the dynamics. We illustrate our new methodology on an idealized stratospheric flow and in two and three dimensional analyses of European Centre for Medium Range Weather Forecasting (ECMWF) reanalysis data

Learning and Matching Multi-View Descriptors for Registration of Point Clouds

Critical to the registration of point clouds is the establishment of a set of accurate correspondences between points in 3D space. The correspondence problem is generally addressed by the design of discriminative 3D local descriptors on the one hand, and the development of robust matching strategies on the other hand. In this work, we first propose a multi-view local descriptor, which is learned from the images of multiple views, for the description of 3D keypoints. Then, we develop a robust matching approach, aiming at rejecting outlier matches based on the efficient inference via belief propagation on the defined graphical model. We have demonstrated the boost of our approaches to registration on the public scanning and multi-view stereo datasets. The superior performance has been verified by the intensive comparisons against a variety of descriptors and matching methods

Convex Relaxations of SE(2) and SE(3) for Visual Pose Estimation

This paper proposes a new method for rigid body pose estimation based on spectrahedral representations of the tautological orbitopes of $SE(2)$ and $SE(3)$. The approach can use dense point cloud data from stereo vision or an RGB-D sensor (such as the Microsoft Kinect), as well as visual appearance data. The method is a convex relaxation of the classical pose estimation problem, and is based on explicit linear matrix inequality (LMI) representations for the convex hulls of $SE(2)$ and $SE(3)$. Given these representations, the relaxed pose estimation problem can be framed as a robust least squares problem with the optimization variable constrained to these convex sets. Although this formulation is a relaxation of the original problem, numerical experiments indicate that it is indeed exact - i.e. its solution is a member of $SE(2)$ or $SE(3)$ - in many interesting settings. We additionally show that this method is guaranteed to be exact for a large class of pose estimation problems.Comment: ICRA 2014 Preprin

Structural characterization of decomposition in rate-insensitive stochastic Petri nets

This paper focuses on stochastic Petri nets that have an equilibrium distribution that is a product form over the number of tokens at the places. We formulate a decomposition result for the class of nets that have a product form solution irrespective of the values of the transition rates. These nets where algebraically characterized by Haddad et al.~as $S\Pi^2$ nets. By providing an intuitive interpretation of this algebraical characterization, and associating state machines to sets of $T$-invariants, we obtain a one-to-one correspondence between the marking of the original places and the places of the added state machines. This enables us to show that the subclass of stochastic Petri nets under study can be decomposed into subnets that are identified by sets of its $T$-invariants

Approximate probabilistic verification of hybrid systems

Hybrid systems whose mode dynamics are governed by non-linear ordinary differential equations (ODEs) are often a natural model for biological processes. However such models are difficult to analyze. To address this, we develop a probabilistic analysis method by approximating the mode transitions as stochastic events. We assume that the probability of making a mode transition is proportional to the measure of the set of pairs of time points and value states at which the mode transition is enabled. To ensure a sound mathematical basis, we impose a natural continuity property on the non-linear ODEs. We also assume that the states of the system are observed at discrete time points but that the mode transitions may take place at any time between two successive discrete time points. This leads to a discrete time Markov chain as a probabilistic approximation of the hybrid system. We then show that for BLTL (bounded linear time temporal logic) specifications the hybrid system meets a specification iff its Markov chain approximation meets the same specification with probability $1$. Based on this, we formulate a sequential hypothesis testing procedure for verifying -approximately- that the Markov chain meets a BLTL specification with high probability. Our case studies on cardiac cell dynamics and the circadian rhythm indicate that our scheme can be applied in a number of realistic settings