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.

Developing alternatives for optimal representation of seafloor habitats and associated communities in Stellwagen Bank National Marine Sanctuary

The implementation of various types of marine protected areas is one of several management tools available for conserving representative examples of the biological diversity within marine ecosystems in general and National Marine Sanctuaries in particular. However, deciding where and how many sites to establish within a given area is frequently hampered by incomplete knowledge of the distribution of organisms and an understanding of the potential tradeoffs that would allow planners to address frequently competing interests in an objective manner. Fortunately, this is beginning to change. Recent studies on the continental shelf of the northeastern United States suggest that substrate and water mass characteristics are highly correlated with the composition of benthic communities and may therefore, serve as proxies for the distribution of biological biodiversity. A detailed geo-referenced interpretative map of major sediment types within Stellwagen Bank National Marine Sanctuary (SBNMS) has recently been developed, and computer-aided decision support tools have reached new levels of sophistication. We demonstrate the use of simulated annealing, a type of mathematical optimization, to identify suites of potential conservation sites within SBNMS that equally represent 1) all major sediment types and 2) derived habitat types based on both sediment and depth in the smallest amount of space. The Sanctuary was divided into 3610 0.5 min2 sampling units. Simulations incorporated constraints on the physical dispersion of sampling units to varying degrees such that solutions included between one and four site clusters. Target representation goals were set at 5, 10, 15, 20, and 25 percent of each sediment type, and 10 and 20 percent of each habitat type. Simulations consisted of 100 runs, from which we identified the best solution (i.e., smallest total area) and four nearoptimal alternates. We also plotted total instances in which each sampling unit occurred in solution sets of the 100 runs as a means of gauging the variety of spatial configurations available under each scenario. Results suggested that the total combined area needed to represent each of the sediment types in equal proportions was equal to the percent representation level sought. Slightly larger areas were required to represent all habitat types at the same representation levels. Total boundary length increased in direct proportion to the number of sites at all levels of representation for simulations involving sediment and habitat classes, but increased more rapidly with number of sites at higher representation levels. There were a large number of alternate spatial configurations at all representation levels, although generally fewer among one and two versus three- and four-site solutions. These differences were less pronounced among simulations targeting habitat representation, suggesting that a similar degree of flexibility is inherent in the spatial arrangement of potential protected area systems containing one versus several sites for similar levels of habitat representation. We attribute these results to the distribution of sediment and depth zones within the Sanctuary, and to the fact that even levels of representation were sought in each scenario. (PDF contains 33 pages.)

Velocity resolved - scalar modeled simulations of high Schmidt number turbulent transport

The objective of this thesis is to develop a framework to conduct velocity resolved - scalar modeled (VR-SM) simulations, which will enable accurate simulations at higher Reynolds and Schmidt (Sc) numbers than are currently feasible. The framework established will serve as a first step to enable future simulation studies for practical applications. To achieve this goal, in-depth analyses of the physical, numerical, and modeling aspects related to Sc>>1 are presented, specifically when modeling in the viscous-convective subrange. Transport characteristics are scrutinized by examining scalar-velocity Fourier mode interactions in Direct Numerical Simulation (DNS) datasets and suggest that scalar modes in the viscous-convective subrange do not directly affect large-scale transport for high Sc. Further observations confirm that discretization errors inherent in numerical schemes can be sufficiently large to wipe out any meaningful contribution from subfilter models. This provides strong incentive to develop more effective numerical schemes to support high Sc simulations. To lower numerical dissipation while maintaining physically and mathematically appropriate scalar bounds during the convection step, a novel method of enforcing bounds is formulated, specifically for use with cubic Hermite polynomials. Boundedness of the scalar being transported is effected by applying derivative limiting techniques, and physically plausible single sub-cell extrema are allowed to exist to help minimize numerical dissipation. The proposed bounding algorithm results in significant performance gain in DNS of turbulent mixing layers and of homogeneous isotropic turbulence. Next, the combined physical/mathematical behavior of the subfilter scalar-flux vector is analyzed in homogeneous isotropic turbulence, by examining vector orientation in the strain-rate eigenframe. The results indicate no discernible dependence on the modeled scalar field, and lead to the identification of the tensor-diffusivity model as a good representation of the subfilter flux. Velocity resolved - scalar modeled simulations of homogeneous isotropic turbulence are conducted to confirm the behavior theorized in these a priori analyses, and suggest that the tensor-diffusivity model is ideal for use in the viscous-convective subrange. Simulations of a turbulent mixing layer are also discussed, with the partial objective of analyzing Schmidt number dependence of a variety of scalar statistics. Large-scale statistics are confirmed to be relatively independent of the Schmidt number for Sc>>1, which is explained by the dominance of subfilter dissipation over resolved molecular dissipation in the simulations. Overall, the VR-SM framework presented is quite effective in predicting large-scale transport characteristics of high Schmidt number scalars, however, it is determined that prediction of subfilter quantities would entail additional modeling intended specifically for this purpose. The VR-SM simulations presented in this thesis provide us with the opportunity to overlap with experimental studies, while at the same time creating an assortment of baseline datasets for future validation of LES models, thereby satisfying the objectives outlined for this work.

Convex Relaxation for Low-Dimensional Representation: Phase Transitions and Limitations

There is a growing interest in taking advantage of possible patterns and structures in data so as to extract the desired information and overcome the curse of dimensionality. In a wide range of applications, including computer vision, machine learning, medical imaging, and social networks, the signal that gives rise to the observations can be modeled to be approximately sparse and exploiting this fact can be very beneficial. This has led to an immense interest in the problem of efficiently reconstructing a sparse signal from limited linear observations. More recently, low-rank approximation techniques have become prominent tools to approach problems arising in machine learning, system identification and quantum tomography.

In sparse and low-rank estimation problems, the challenge is the inherent intractability of the objective function, and one needs efficient methods to capture the low-dimensionality of these models. Convex optimization is often a promising tool to attack such problems. An intractable problem with a combinatorial objective can often be "relaxed" to obtain a tractable but almost as powerful convex optimization problem. This dissertation studies convex optimization techniques that can take advantage of low-dimensional representations of the underlying high-dimensional data. We provide provable guarantees that ensure that the proposed algorithms will succeed under reasonable conditions, and answer questions of the following flavor:

More specifically, i) Focusing on linear inverse problems, we generalize the classical error bounds known for the least-squares technique to the lasso formulation, which incorporates the signal model. ii) We show that intuitive convex approaches do not perform as well as expected when it comes to signals that have multiple low-dimensional structures simultaneously. iii) Finally, we propose convex relaxations for the graph clustering problem and give sharp performance guarantees for a family of graphs arising from the so-called stochastic block model. We pay particular attention to the following aspects. For i) and ii), we aim to provide a general geometric framework, in which the results on sparse and low-rank estimation can be obtained as special cases. For i) and iii), we investigate the precise performance characterization, which yields the right constants in our bounds and the true dependence between the problem parameters.

Code conversion from signed-digit to complement representation based on look-ahead optical logic operations

We present, for the first time to our knowledge, a generalized lookahead logic algorithm for number conversion from signed-digit to complement representation. By properly encoding the signed-digits, all the operations are performed by binary logic, and unified logical expressions can be obtained for conversion from modified-signed-digit (MSD) to 2's complement, trinary signed-digit (TSD) to 3's complement, and quarternary signed-digit (QSD) to 4's complement. For optical implementation, a parallel logical array module using an electron-trapping device is employed and experimental results are shown. This optical module is suitable for implementing complex logic functions in the form of the sum of the product. The algorithm and architecture are compatible with a general-purpose optoelectronic computing system. (C) 2001 Society of Photo-Optical Instrumentation Engineers.

Symmetric representation of an integral domain over a subdomain

Let F(θ) be a separable extension of degree n of a field F. Let Δ and D be integral domains with quotient fields F(θ) and F respectively. Assume that Δ ᴝ D. A mapping φ of Δ into the n x n D matrices is called a Δ/D rep if (i) it is a ring isomorphism and (ii) it maps d onto dI_n whenever d ϵ D. If the matrices are also symmetric, φ is a Δ/D symrep.

Every Δ/D rep can be extended uniquely to an F(θ)/F rep. This extension is completely determined by the image of θ. Two Δ/D reps are called equivalent if the images of θ differ by a D unimodular similarity. There is a one-to-one correspondence between classes of Δ/D reps and classes of Δ ideals having an n element basis over D.

The condition that a given Δ/D rep class contain a Δ/D symrep can be phrased in various ways. Using these formulations it is possible to (i) bound the number of symreps in a given class, (ii) count the number of symreps if F is finite, (iii) establish the existence of an F(θ)/F symrep when n is odd, F is an algebraic number field, and F(θ) is totally real if F is formally real (for n = 3 see Sapiro, “Characteristic polynomials of symmetric matrices” Sibirsk. Mat. Ž. 3 (1962) pp. 280-291), and (iv) study the case D = Z, the integers (see Taussky, “On matrix classes corresponding to an ideal and its inverse” Illinois J. Math. 1 (1957) pp. 108-113 and Faddeev, “On the characteristic equations of rational symmetric matrices” Dokl. Akad. Nauk SSSR 58 (1947) pp. 753-754).

The case D = Z and n = 2 is studied in detail. Let Δ’ be an integral domain also having quotient field F(θ) and such that Δ’ ᴝ Δ. Let φ be a Δ/Z symrep. A method is given for finding a Δ’/Z symrep ʘ such that the Δ’ ideal class corresponding to the class of ʘ is an extension to Δ’ of the Δ ideal class corresponding to the class of φ. The problem of finding all Δ/Z symreps equivalent to a given one is studied.

Number of Players and Relative Pitch Area per Player: Comparing Their Influence on Heart Rate and Physical Demands in Under-12 and Under-13 Football Players

The aim of the present study is to analyse the influence of different large-sided games (LSGs) on the physical and physiological variables in under-12s (U12) and -13s (U13) soccer players. The effects of the combination of different number of players per team, 7, 9, and 11 (P7, P9, and P11, respectively) with three relative pitch areas, 100, 200, and 300 m(2) (A100, A200, and A300, respectively), were analysed in this study. The variables analysed were: 1) global indicator such as total distance (TD); work:rest ratio (W:R); player-load (PL) and maximal speed (V-max); 2) heart rate (HR) mean and time spent in different intensity zones of HR (<75%, 75-84%, 84-90% and >90%), and; 3) five absolute (<8, 8-13, 13-16 and >16 Km h(-1)) and three relative speed categories (<40%, 40-60% and >60% V-max). The results support the theory that a change in format (player number and pitch dimensions) affects no similarly in the two players categories. Although it can seem that U13 players are more demanded in this kind of LSG, when the work load is assessed from a relative point of view, great pitch dimensions and/or high number of player per team are involved in the training task to the U12 players. The results of this study could alert to the coaches to avoid some types of LSGs for the U12 players such as:P11 played in A100, A200 or A300, P9 played in A200 or A300 and P7 played in A300 due to that U13>U12 in several physical and physiological variables (W:R, time spent in 84-90% HRmax, distance in 8-13 and 13-16 Km h(-1) and time spent in 40-60% V-max). These results may help youth soccer coaches to plan the progressive introduction of LSGs so that task demands are adapted to the physiological and physical development of participants.

Educação e escolarização quilombola: construções políticopedagógicas em Brejo dos Crioulos MG

Atualmente tem se apresentado, pelo movimento quilombola, a demanda de formulação de políticas educacionais para o povo quilombola, acompanhando as reivindicações para legitimação do direito ao território ocupado secularmente, assim como outros direitos demandados por este povo tradicional. O processo de educação e escolarização na educação básica de um território quilombola como o de Brejo dos Crioulos em Minas Gerais, sob a perspectiva da educação diferenciada, ou seja, orientada culturalmente, pode estar fortemente relacionado com a dimensão política da atuação dos quilombolas na luta pelo reconhecimento e legitimidade do território, do modo de vida, da sua identidade, da sua cultura e história. Contemplou-se nesta investigação o mapeamento e a análise dos processos educativos de Brejo dos Crioulos apontando suas propostas curriculares, seus avanços, assim como os limites relacionados à formulação e implementação de políticas direcionadas para o desenvolvimento educacional local. A investigação no território quilombola específico, nos moldes da pesquisa qualitativa enquanto lógica de investigação, abordou as ações do movimento quilombola estadual e local, a identidade coletiva e a territorialidade em relação ao ciclo de políticas disponível, como, por exemplo, a Lei n 10.639/03, atualizada por meio da Lei n 11.645/08 e diretrizes curriculares que alteram a Lei n 9.394/96, com o objetivo de incluir, no currículo oficial da rede de ensino, a obrigatoriedade do ensino da História e cultura afro-brasileira e indígena, e as Diretrizes Curriculares para Educação Quilombola, aprovadas em 05 de junho de 2012, Parecer MEC/CNE/CEB 16/2012, homologadas na Resolução MEC/CNE/CEB n 8, publicada em 20 de novembro de 2012. Além das práticas políticas quilombolas, foram analisadas as práticas de gestão educacional do poder público municipal de São João da Ponte e Varzelândia, municípios do norte mineiro que integram o território pesquisado. Com a inserção em campo, nos moldes explicitados, foi privilegiado o uso da observação direta para mapear e descrever em profundidade o cotidiano no território pesquisado. Com a inserção em campo, nos moldes explicitados, foi privilegiado o uso da observação direta para mapear e descrever em profundidade o cotidiano no território pesquisado, as representações políticas e educacionais, as mudanças e transformações atuais. A entrevista em forma de conversa é, também, uma das técnicas utilizadas para documentar as experiências e representações dos sujeitos quilombolas, professores, gestores e coordenadores envolvidos com a educação e escolarização no território de Brejo dos Crioulos, além de registros em áudio, vídeo e caderno de campo. O tratamento e a análise dos dados coletados obedecem a critérios metodológicos qualitativos de triangulação para apresentação dos resultados da pesquisa.

Characterisation of technology roadmaps: Purpose and format

A report on characterisation of technology roadmaps, its purpose and formats are presented. A fast-start process is developed to support the initiation of technology roadmapping in firms to address the industrial needs. The purpose of each roadmap is related to a number of planning aims: product, capability, integration, strategic, long-range, programme and process planning. The second set of categories are related to the format of the roadmap, based on observed structure: multiple or single layers, bars, tables, graphs, pictorial forms, flow diagrams and text. It is concluded that technology roadmaps processes a great potential for supporting the development and implementation of business product and technology strategy.

Effects of turbulent reynolds number on the performance of algebraic flame surface density models for large eddy simulation in the thin reaction zones regime: A direct numerical simulation analysis

A direct numerical simulation (DNS) database of freely propagating statistically planar turbulent premixed flames with a range of different turbulent Reynolds numbers has been used to assess the performance of algebraic flame surface density (FSD) models based on a fractal representation of the flame wrinkling factor. The turbulent Reynolds number Ret has been varied by modifying the Karlovitz number Ka and the Damköhler number Da independently of each other in such a way that the flames remain within the thin reaction zones regime. It has been found that the turbulent Reynolds number and the Karlovitz number both have a significant influence on the fractal dimension, which is found to increase with increasing Ret and Ka before reaching an asymptotic value for large values of Ret and Ka. A parameterisation of the fractal dimension is presented in which the effects of the Reynolds and the Karlovitz numbers are explicitly taken into account. By contrast, the inner cut-off scale normalised by the Zel'dovich flame thickness ηi/δz does not exhibit any significant dependence on Ret for the cases considered here. The performance of several algebraic FSD models has been assessed based on various criteria. Most of the algebraic models show a deterioration in performance with increasing the LES filter width. © 2012 Mohit Katragadda et al.

Analytical Representation of Contours

The interpretation and recognition of noisy contours, such as silhouettes, have proven to be difficult. One obstacle to the solution of these problems has been the lack of a robust representation for contours. The contour is represented by a set of pairwise tangent circular arcs. The advantage of such an approach is that mathematical properties such as orientation and curvature are explicityly represented. We introduce a smoothing criterion for the contour tht optimizes the tradeoff between the complexity of the contour and proximity of the data points. The complexity measure is the number of extrema of curvature present in the contour. The smoothing criterion leads us to a true scale-space for contours. We describe the computation of the contour representation as well as the computation of relevant properties of the contour. We consider the potential application of the representation, the smoothing paradigm, and the scale-space to contour interpretation and recognition.

Quantum Monte Carlo in the Interaction Representation --- Application to a Spin-Peierls Model

A quantum Monte Carlo algorithm is constructed starting from the standard perturbation expansion in the interaction representation. The resulting configuration space is strongly related to that of the Stochastic Series Expansion (SSE) method, which is based on a direct power series expansion of exp(-beta*H). Sampling procedures previously developed for the SSE method can therefore be used also in the interaction representation formulation. The new method is first tested on the S=1/2 Heisenberg chain. Then, as an application to a model of great current interest, a Heisenberg chain including phonon degrees of freedom is studied. Einstein phonons are coupled to the spins via a linear modulation of the nearest-neighbor exchange. The simulation algorithm is implemented in the phonon occupation number basis, without Hilbert space truncations, and is exact. Results are presented for the magnetic properties of the system in a wide temperature regime, including the T-->0 limit where the chain undergoes a spin-Peierls transition. Some aspects of the phonon dynamics are also discussed. The results suggest that the effects of dynamic phonons in spin-Peierls compounds such as GeCuO3 and NaV2O5 must be included in order to obtain a correct quantitative description of their magnetic properties, both above and below the dimerization temperature.

An Invariant Representation for Matching Trajectories across Uncalibrated Video Streams

We introduce a view-point invariant representation of moving object trajectories that can be used in video database applications. It is assumed that trajectories lie on a surface that can be locally approximated with a plane. Raw trajectory data is first locally approximated with a cubic spline via least squares fitting. For each sampled point of the obtained curve, a projective invariant feature is computed using a small number of points in its neighborhood. The resulting sequence of invariant features computed along the entire trajectory forms the view invariant descriptor of the trajectory itself. Time parametrization has been exploited to compute cross ratios without ambiguity due to point ordering. Similarity between descriptors of different trajectories is measured with a distance that takes into account the statistical properties of the cross ratio, and its symmetry with respect to the point at infinity. In experiments, an overall correct classification rate of about 95% has been obtained on a dataset of 58 trajectories of players in soccer video, and an overall correct classification rate of about 80% has been obtained on matching partial segments of trajectories collected from two overlapping views of outdoor scenes with moving people and cars.

A Neuromorphic Model for Achromatic and Chromatic Surface Representation of Natural Images

This study develops a neuromorphic model of human lightness perception that is inspired by how the mammalian visual system is designed for this function. It is known that biological visual representations can adapt to a billion-fold change in luminance. How such a system determines absolute lightness under varying illumination conditions to generate a consistent interpretation of surface lightness remains an unsolved problem. Such a process, called "anchoring" of lightness, has properties including articulation, insulation, configuration, and area effects. The model quantitatively simulates such psychophysical lightness data, as well as other data such as discounting the illuminant, the double brilliant illusion, and lightness constancy and contrast effects. The model retina embodies gain control at retinal photoreceptors, and spatial contrast adaptation at the negative feedback circuit between mechanisms that model the inner segment of photoreceptors and interacting horizontal cells. The model can thereby adjust its sensitivity to input intensities ranging from dim moonlight to dazzling sunlight. A new anchoring mechanism, called the Blurred-Highest-Luminance-As-White (BHLAW) rule, helps simulate how surface lightness becomes sensitive to the spatial scale of objects in a scene. The model is also able to process natural color images under variable lighting conditions, and is compared with the popular RETINEX model.

Boundary, Brightness, and Depth Interactions During Preattentive Representation and Attentive Recognition of Figure and Ground

This article applies a recent theory of 3-D biological vision, called FACADE Theory, to explain several percepts which Kanizsa pioneered. These include 3-D pop-out of an occluding form in front of an occluded form, leading to completion and recognition of the occluded form; 3-D transparent and opaque percepts of Kanizsa squares, with and without Varin wedges; and interactions between percepts of illusory contours, brightness, and depth in response to 2-D Kanizsa images. These explanations clarify how a partially occluded object representation can be completed for purposes of object recognition, without the completed part of the representation necessarily being seen. The theory traces these percepts to neural mechanisms that compensate for measurement uncertainty and complementarity at individual cortical processing stages by using parallel and hierarchical interactions among several cortical processing stages. These interactions are modelled by a Boundary Contour System (BCS) that generates emergent boundary segmentations and a complementary Feature Contour System (FCS) that fills-in surface representations of brightness, color, and depth. The BCS and FCS interact reciprocally with an Object Recognition System (ORS) that binds BCS boundary and FCS surface representations into attentive object representations. The BCS models the parvocellular LGN→Interblob→Interstripe→V4 cortical processing stream, the FCS models the parvocellular LGN→Blob→Thin Stripe→V4 cortical processing stream, and the ORS models inferotemporal cortex.