HUMAN DETECTION USING SPARSE REPRESENTATION

The problem of human detection is challenging, more so, when faced with adverse conditions such as occlusion and background clutter. This paper addresses the problem of human detection by representing an extracted feature of an image using a sparse linear combination of chosen dictionary atoms. The detection along with the scale finding, is done by using the coefficients obtained from sparse representation. This is of particular interest as we address the problem of scale using a scale-embedded dictionary where the conventional methods detect the object by running the detection window at all scales.

Covariance profiles: a signature representation for object sets

We consider the problem of extracting a signature representation of similar entities employing covariance descriptors. Covariance descriptors can efficiently represent objects and are robust to scale and pose changes. We posit that covariance descriptors corresponding to similar objects share a common geometrical structure which can be extracted through joint diagonalization. We term this diagonalizing matrix as the Covariance Profile (CP). CP can be used to measure the distance of a novel object to an object set through the diagonality measure. We demonstrate how CP can be employed on images as well as for videos, for applications such as face recognition and object-track clustering.

Fragment-based real-time object tracking: a sparse representation approach

Real-time object tracking is a critical task in many computer vision applications. Achieving rapid and robust tracking while handling changes in object pose and size, varying illumination and partial occlusion, is a challenging task given the limited amount of computational resources. In this paper we propose a real-time object tracker in l(1) framework addressing these issues. In the proposed approach, dictionaries containing templates of overlapping object fragments are created. The candidate fragments are sparsely represented in the dictionary fragment space by solving the l(1) regularized least squares problem. The non zero coefficients indicate the relative motion between the target and candidate fragments along with a fidelity measure. The final object motion is obtained by fusing the reliable motion information. The dictionary is updated based on the object likelihood map. The proposed tracking algorithm is tested on various challenging videos and found to outperform earlier approach.

Classification, representation, and automatic extraction of deformation features in sheet metal parts

This paper presents classification, representation and extraction of deformation features in sheet-metal parts. The thickness is constant for these shape features and hence these are also referred to as constant thickness features. The deformation feature is represented as a set of faces with a characteristic arrangement among the faces. Deformation of the base-sheet or forming of material creates Bends and Walls with respect to a base-sheet or a reference plane. These are referred to as Basic Deformation Features (BDFs). Compound deformation features having two or more BDFs are defined as characteristic combinations of Bends and Walls and represented as a graph called Basic Deformation Features Graph (BDFG). The graph, therefore, represents a compound deformation feature uniquely. The characteristic arrangement of the faces and type of bends belonging to the feature decide the type and nature of the deformation feature. Algorithms have been developed to extract and identify deformation features from a CAD model of sheet-metal parts. The proposed algorithm does not require folding and unfolding of the part as intermediate steps to recognize deformation features. Representations of typical features are illustrated and results of extracting these deformation features from typical sheet metal parts are presented and discussed. (C) 2013 Elsevier Ltd. All rights reserved.

Entropy of quantum states: Ambiguities

The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states. As pointed out to us by Sorkin, this happens if the GNS representation (of the algebra of observables in some quantum state) is reducible, and some representations in the decomposition occur with non-trivial degeneracy. This non-unique entropy can occur at zero temperature. We will argue elsewhere in detail that the degeneracies in the GNS representation can be interpreted as an emergent broken gauge symmetry, and play an important role in the analysis of emergent entropy due to non-Abelian anomalies. Finally, we establish the analogue of an H-theorem for this entropy by showing that its evolution is Markovian, determined by a stochastic matrix.

Burst error correction using partial fourier matrices and block sparse representation

There is a strong relation between sparse signal recovery and error control coding. It is known that burst errors are block sparse in nature. So, here we attempt to solve burst error correction problem using block sparse signal recovery methods. We construct partial Fourier based encoding and decoding matrices using results on difference sets. These constructions offer guaranteed and efficient error correction when used in conjunction with reconstruction algorithms which exploit block sparsity.

The projective plane, J-holomorphic curves and Desargues' theorem

By a theorem of Gromov, for an almost complex structure J on CP2 tamed by the standard symplectic structure, the J-holomorphic curves representing the positive generator of homology form a projective plane. We show that this satisfies the Theorem of Desargues if and only if J is isomorphic to the standard complex structure. This answers a question of Ghys. (C) 2013 Published by Elsevier Masson SAS on behalf of Academie des sciences.

A NEAR OPTIMAL PROJECTION FOR SPARSE REPRESENTATION BASED CLASSIFICATION

Sparse representation based classification (SRC) is one of the most successful methods that has been developed in recent times for face recognition. Optimal projection for Sparse representation based classification (OPSRC)1] provides a dimensionality reduction map that is supposed to give optimum performance for SRC framework. However, the computational complexity involved in this method is too high. Here, we propose a new projection technique using the data scatter matrix which is computationally superior to the optimal projection method with comparable classification accuracy with respect OPSRC. The performance of the proposed approach is benchmarked with various publicly available face database.

Large deviation function and fluctuation theorem for classical particle transport

We analytically evaluate the large deviation function in a simple model of classical particle transfer between two reservoirs. We illustrate how the asymptotic long-time regime is reached starting from a special propagating initial condition. We show that the steady-state fluctuation theorem holds provided that the distribution of the particle number decays faster than an exponential, implying analyticity of the generating function and a discrete spectrum for its evolution operator.

Reduced Grobner bases and Macaulay-Buchberger Basis Theorem over Noetherian rings

In this paper, we extend the characterization of Zx]/(f), where f is an element of Zx] to be a free Z-module to multivariate polynomial rings over any commutative Noetherian ring, A. The characterization allows us to extend the Grobner basis method of computing a k-vector space basis of residue class polynomial rings over a field k (Macaulay-Buchberger Basis Theorem) to rings, i.e. Ax(1), ... , x(n)]/a, where a subset of Ax(1), ... , x(n)] is an ideal. We give some insights into the characterization for two special cases, when A = Z and A = ktheta(1), ... , theta(m)]. As an application of this characterization, we show that the concept of Border bases can be extended to rings when the corresponding residue class ring is a finitely generated, free A-module. (C) 2014 Elsevier B.V. All rights reserved.

A perturbed martingale approach to global optimization

A new global stochastic search, guided mainly through derivative-free directional information computable from the sample statistical moments of the design variables within a Monte Carlo setup, is proposed. The search is aided by imparting to the directional update term additional layers of random perturbations referred to as `coalescence' and `scrambling'. A selection step, constituting yet another avenue for random perturbation, completes the global search. The direction-driven nature of the search is manifest in the local extremization and coalescence components, which are posed as martingale problems that yield gain-like update terms upon discretization. As anticipated and numerically demonstrated, to a limited extent, against the problem of parameter recovery given the chaotic response histories of a couple of nonlinear oscillators, the proposed method appears to offer a more rational, more accurate and faster alternative to most available evolutionary schemes, prominently the particle swarm optimization. (C) 2014 Elsevier B.V. All rights reserved.

An integral fluctuation theorem for systems with unidirectional transitions

The fluctuations of a Markovian jump process with one or more unidirectional transitions, where R-ij > 0 but R-ji = 0, are studied. We find that such systems satisfy an integral fluctuation theorem. The fluctuating quantity satisfying the theorem is a sum of the entropy produced in the bidirectional transitions and a dynamical contribution, which depends on the residence times in the states connected by the unidirectional transitions. The convergence of the integral fluctuation theorem is studied numerically and found to show the same qualitative features as systems exhibiting microreversibility.

Sparse Representation Based Acoustic Rangefinders: From Sensor Platforms to Mobile Devices

Acoustic rangerfinders are a promising technology for accurate proximity detection, a critical requirement for many emerging mobile computing applications. While state-of-the-art systems deliver robust ranging performance, the computational intensiveness of their detection mechanism expedites the energy depletion of the associated devices that are typically powered by batteries. The contribution of this article is fourfold. First, it outlines the common factors that are important for ranging. Second, it presents a review of acoustic rangers and identifies their potential problems. Third, it explores the design of an information processing framework based on sparse representation that could potentially address existing challenges, especially for mobile devices. Finally, it presents mu-BeepBeep: a low energy acoustic ranging service for mobile devices, and empirically evaluates its benefits.

Robust tracking with interest points: A sparse representation approach

Visual tracking is an important task in various computer vision applications including visual surveillance, human computer interaction, event detection, video indexing and retrieval. Recent state of the art sparse representation (SR) based trackers show better robustness than many of the other existing trackers. One of the issues with these SR trackers is low execution speed. The particle filter framework is one of the major aspects responsible for slow execution, and is common to most of the existing SR trackers. In this paper,(1) we propose a robust interest point based tracker in l(1) minimization framework that runs at real-time with performance comparable to the state of the art trackers. In the proposed tracker, the target dictionary is obtained from the patches around target interest points. Next, the interest points from the candidate window of the current frame are obtained. The correspondence between target and candidate points is obtained via solving the proposed l(1) minimization problem. In order to prune the noisy matches, a robust matching criterion is proposed, where only the reliable candidate points that mutually match with target and candidate dictionary elements are considered for tracking. The object is localized by measuring the displacement of these interest points. The reliable candidate patches are used for updating the target dictionary. The performance and accuracy of the proposed tracker is benchmarked with several complex video sequences. The tracker is found to be considerably fast as compared to the reported state of the art trackers. The proposed tracker is further evaluated for various local patch sizes, number of interest points and regularization parameters. The performance of the tracker for various challenges including illumination change, occlusion, and background clutter has been quantified with a benchmark dataset containing 50 videos. (C) 2014 Elsevier B.V. All rights reserved.

Markov chains, R-trivial monoids and representation theory

We develop a general theory of Markov chains realizable as random walks on R-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via Mobius inversion along a lattice, a condition for diagonalizability of the transition matrix and some techniques for bounding the mixing time. In addition, we discuss several examples, such as Toom-Tsetlin models, an exchange walk for finite Coxeter groups, as well as examples previously studied by the authors, such as nonabelian sandpile models and the promotion Markov chain on posets. Many of these examples can be viewed as random walks on quotients of free tree monoids, a new class of monoids whose combinatorics we develop.