A new visual object tracking algorithm using Bayesian Kalman filter

This paper proposes a new visual object tracking algorithm using a novel Bayesian Kalman filter (BKF) with simplified Gaussian mixture (BKF-SGM). The new BKF-SGM employs a GM representation of the state and noise densities and a novel direct density simplifying algorithm for avoiding the exponential complexity growth of conventional KFs using GM. Together with an improved mean shift (MS) algorithm, a new BKF-SGM with improved MS (BKF-SGM-IMS) algorithm with more robust tracking performance is also proposed. Experimental results show that our method can successfully handle complex scenarios with good performance and low arithmetic complexity. © IEEEpublished_or_final_versio

Fisher-Rao distance and pullback SPD cone distances between multivariate normal distributions

Data sets of multivariate normal distributions abound in many scientific areas like diffusion tensor imaging, structure tensor computer vision, radar signal processing, machine learning, just to name a few. In order to process those normal data sets for downstream tasks like filtering, classification or clustering, one needs to define proper notions of dissimilarities between normals and paths joining them. The Fisher-Rao distance defined as the Riemannian geodesic distance induced by the Fisher information metric is such a principled metric distance which however is not known in closed-form excepts for a few particular cases. In this work, we first report a fast and robust method to approximate arbitrarily finely the Fisher-Rao distance between multivariate normal distributions. Second, we introduce a class of distances based on diffeomorphic embeddings of the normal manifold into a submanifold of the higher-dimensional symmetric positive-definite cone corresponding to the manifold of centered normal distributions. We show that the projective Hilbert distance on the cone yields a metric on the embedded normal submanifold and we pullback that cone distance with its associated straight line Hilbert cone geodesics to obtain a distance and smooth paths between normal distributions. Compared to the Fisher-Rao distance approximation, the pullback Hilbert cone distance is computationally light since it requires to compute only the extreme minimal and maximal eigenvalues of matrices. Finally, we show how to use those distances in clustering tasks.Comment: 25 page

Planning in partially-observable switching-mode continuous domains

Continuous-state POMDPs provide a natural representation for a variety of tasks, including many in robotics. However, most existing parametric continuous-state POMDP approaches are limited by their reliance on a single linear model to represent the world dynamics. We introduce a new switching-state dynamics model that can represent multi-modal state-dependent dynamics. We present the Switching Mode POMDP (SM-POMDP) planning algorithm for solving continuous-state POMDPs using this dynamics model. We also consider several procedures to approximate the value function as a mixture of a bounded number of Gaussians. Unlike the majority of prior work on approximate continuous-state POMDP planners, we provide a formal analysis of our SM-POMDP algorithm, providing bounds, where possible, on the quality of the resulting solution. We also analyze the computational complexity of SM-POMDP. Empirical results on an unmanned aerial vehicle collisions avoidance simulation, and a robot navigation simulation where the robot has faulty actuators, demonstrate the benefit of SM-POMDP over a prior parametric approach.National Science Foundation (U.S.). Division of Information and Intelligent Systems (Grant 0546467

Doctor of Philosophy

dissertationScene labeling is the problem of assigning an object label to each pixel of a given image. It is the primary step towards image understanding and unifies object recognition and image segmentation in a single framework. A perfect scene labeling framework detects and densely labels every region and every object that exists in an image. This task is of substantial importance in a wide range of applications in computer vision. Contextual information plays an important role in scene labeling frameworks. A contextual model utilizes the relationships among the objects in a scene to facilitate object detection and image segmentation. Using contextual information in an effective way is one of the main questions that should be answered in any scene labeling framework. In this dissertation, we develop two scene labeling frameworks that rely heavily on contextual information to improve the performance over state-of-the-art methods. The first model, called the multiclass multiscale contextual model (MCMS), uses contextual information from multiple objects and at different scales for learning discriminative models in a supervised setting. The MCMS model incorporates crossobject and interobject information into one probabilistic framework, and thus is able to capture geometrical relationships and dependencies among multiple objects in addition to local information from each single object present in an image. The second model, called the contextual hierarchical model (CHM), learns contextual information in a hierarchy for scene labeling. At each level of the hierarchy, a classifier is trained based on downsampled input images and outputs of previous levels. The CHM then incorporates the resulting multiresolution contextual information into a classifier to segment the input image at original resolution. This training strategy allows for optimization of a joint posterior probability at multiple resolutions through the hierarchy. We demonstrate the performance of CHM on different challenging tasks such as outdoor scene labeling and edge detection in natural images and membrane detection in electron microscopy images. We also introduce two novel classification methods. WNS-AdaBoost speeds up the training of AdaBoost by providing a compact representation of a training set. Disjunctive normal random forest (DNRF) is an ensemble method that is able to learn complex decision boundaries and achieves low generalization error by optimizing a single objective function for each weak classifier in the ensemble. Finally, a segmentation framework is introduced that exploits both shape information and regional statistics to segment irregularly shaped intracellular structures such as mitochondria in electron microscopy images

Computational Techniques for Stochastic Reachability

As automated control systems grow in prevalence and complexity, there is an increasing demand for verification and controller synthesis methods to ensure these systems perform safely and to desired specifications. In addition, uncertain or stochastic behaviors are often exhibited (such as wind affecting the motion of an aircraft), making probabilistic verification desirable. Stochastic reachability analysis provides a formal means of generating the set of initial states that meets a given objective (such as safety or reachability) with a desired level of probability, known as the reachable (or safe) set, depending on the objective. However, the applicability of reachability analysis is limited in the scope and size of system it can address. First, generating stochastic reachable or viable sets is computationally intensive, and most existing methods rely on an optimal control formulation that requires solving a dynamic program, and which scales exponentially in the dimension of the state space. Second, almost no results exist for extending stochastic reachability analysis to systems with incomplete information, such that the controller does not have access to the full state of the system. This thesis addresses both of the above limitations, and introduces novel computational methods for generating stochastic reachable sets for both perfectly and partially observable systems. We initially consider a linear system with additive Gaussian noise, and introduce two methods for computing stochastic reachable sets that do not require dynamic programming. The first method uses a particle approximation to formulate a deterministic mixed integer linear program that produces an estimate to reachability probabilities. The second method uses a convex chance-constrained optimization problem to generate an under-approximation to the reachable set. Using these methods we are able to generate stochastic reachable sets for a four-dimensional spacecraft docking example in far less time than it would take had we used a dynamic program. We then focus on discrete time stochastic hybrid systems, which provide a flexible modeling framework for systems that exhibit mode-dependent behavior, and whose state space has both discrete and continuous components. We incorporate a stochastic observation process into the hybrid system model, and derive both theoretical and computational results for generating stochastic reachable sets subject to an observation process. The derivation of an information state allows us to recast the problem as one of perfect information, and we prove that solving a dynamic program over the information state is equivalent to solving the original problem. We then demonstrate that the dynamic program to solve the reachability problem for a partially observable stochastic hybrid system shares the same properties as for a partially observable Markov decision process (POMDP) with an additive cost function, and so we can exploit approximation strategies designed for POMDPs to solve the reachability problem. To do so, however, we first generate approximate representations of the information state and value function as either vectors or Gaussian mixtures, through a finite state approximation to the hybrid system or using a Gaussian mixture approximation to an indicator function defined over a convex region. For a system with linear dynamics and Gaussian measurement noise, we show that it exhibits special properties that do not require an approximation of the information state, which enables much more efficient computation of the reachable set. In all cases we provide convergence results and numerical examples