learning layered motion segmentations of video we present an unsupervised approach for learning a layered representation of a scene from a video for motion segmentation our method is applicable to any video containing piecewise parametric motion the learnt model is a composition of layers which consist of one or more segments the shape of each segment is represented using a binary matte and its appearance is given by the rgb value for each point belonging to the matte included in the model are the effects of image projection lighting and motion blur furthermore spatial continuity is explicitly modeled resulting in contiguous segments unlike previous approaches our method does not use reference frame s for initialization the two main contributions of our method are i a novel algorithm for obtaining the initial estimate of the model by dividing the scene into rigidly moving components using efficient loopy belief propagation and ii refining the initial estimate using swap and expansion algorithms which guarantee a strong local minima results are presented on several classes of objects with different types of camera motion e g videos of a human walking shot with static or translating cameras we compare our method with the state of the art and demonstrate significant improvements

nonsymmetric macdonald polynomials and demazure characters we establish a connection between a specialization of the nonsymmetric macdonald polynomials and the demazure characters of the corresponding affine kac moody algebra this allows us to obtain a representation theoretical interpretation of the coefficients of the expansion of the specialized symmetric macdonald polynomials in the basis formed by the irreducible characters of the associated finite lie algebra

new approach to the statistical properties of energy levels the joint distribution of energy eigenvalues of a hamiltonian is derived by means of the usual statistical laws of classical many body systems it makes a transition from the poisson type to the gaussian type depending on the value of a single parameter characteristic of the hamiltonian

c ondensation conditional density propagation forvisual tracking the problem of tracking curves in dense visual clutter is challenging kalman filtering is inadequate because it is based on gaussian densities which being unimo dal cannot represent simultaneous alternative hypotheses the condensation algorithm uses factored sampling previously applied to the interpretation of static images in which the probability distribution of possible interpretations is represented by a randomly generated set condensation uses learned dynamical models together with visual observations to propagate the random set over time the result is highly robust tracking of agile motion notwithstanding the use of stochastic methods the algorithm runs in near real time

scene segmentation from visual motion using global optimization this paper presents results from computer experiments with an algorithm to perform scene disposition and motion segmentation from visual motion or optic flow the maximum a posteriori map criterion is used to formulate what the best segmentation or interpretation of the scene should be where the scene is assumed to be made up of some fixed number of moving planar surface patches the bayesian approach requires first specification of prior expectations for the optic flow field which here is modeled as spatial and temporal markov random fields and secondly a way of measuring how well the segmentation predicts the measured flow field the markov random fields incorporate the physical constraints that objects and their images are probably spatially continuous and that their images are likely to move quite smoothly across the image plane to compute the flow predicted by the segmentation a recent method for reconstructing the motion and orientation of planar surface facets is used the search for the globally optimal segmentation is performed using simulated annealing

s matrix poles for chaotic quantum systems as eigenvalues of complex symmetric random matrices from isolated to overlapping resonances we study complex eigenvalues of large symmetric random matrices of the form where both and are real symmetric is a random gaussian and is such that when when the model can be used to describe the universal statistics of s matrix poles resonances in the complex energy plane we derive the ensuing distribution of the resonance widths which generalizes the well known distribution to the case of overlapping resonances we also consider a different class of almost real matrices when is random and uncorrelated with

weyl demazure and fusion modules for the current algebra of sl r 1 we construct a poincare birkhoff witt type basis for the weyl modules v chari a pressley weyl modules for classical and quantum affine algebras represent theory 5 2001 191 223 math qa 0004174 of the current algebra of as a corollary we prove the conjecture made in v chari a pressley weyl modules for classical and quantum affine algebras represent theory 5 2001 191 223 math qa 0004174 v chari a pressley integrable and weyl modules for quantum affine in quantum groups and lie theory durham 1999 in london math soc lecture note ser vol 290 cambridge univ press cambridge 2001 pp 48 62 math qa 0007123 on the dimension of the weyl modules in this case further we relate the weyl modules to the fusion modules defined in b feigin s loktev on generalized kostka polynomials and the quantum verlinde rule in differential topology infinite dimensional lie algebras and applications in amer math soc transl ser 2 vol 194 1999 pp 61 79 math qa 9812093 of the current algebra and the demazure modules in level one representations of the corresponding affine algebra in particular this allows us to establish substantial cases of the conjectures in b feigin s loktev on generalized kostka polynomials and the quantum verlinde rule in differential topology infinite dimensional lie algebras and applications in amer math soc transl ser 2 vol 194 1999 pp 61 79 math qa 9812093 on the structure and graded character of the fusion modules

the frequency structure of one dimensional occluding image signals we present a theoretical investigation of the frequency structure of 1d occluding image signals we show that image signal occlusion contains relevant information which is most easily extractable from its representation in the frequency domain for instance the occluding and occluded signal velocities may be identified as such and translucency phenomena may be understood in the terms of this theoretical investigation in addition it is found that the structure of occluding 1d signals is invariant under constant and linear models of signal velocity this theoretical framework can be used to describe the exact frequency structure of non fourier motion and bridges the gap between such visual phenomena and their understanding in the frequency domain

regular nilpotent elements and quantum groups we suggest new realizations of quantum groups uq corresponding to complex simple lie algebras and of affine quantum groups these new realizations are labeled by coxeter elements of the corresponding weyl group and have the following key feature the natural counterparts of the subalgebras u where is a maximal nilpotent subalgebra possess non singular characters

piecewise smooth dense optical flow via level sets we propose a new algorithm for dense optical flow computation dense optical flow schemes are challenged by the presence of motion discontinuities in state of the art optical flow methods over smoothing of flow discontinuities accounts for most of the error a breakthrough in the performance of optical flow computation has recently been achieved by brox et al our algorithm embeds their functional within a two phase active contour segmentation framework piecewise smooth flow fields are accommodated and flow boundaries are crisp experimental results show the superiority of our algorithm with respect to alternative techniques we also study a special case of optical flow computation in which the camera is static in this case we utilize a known background image to separate the moving elements in the sequence from the static elements tests with challenging real world sequences demonstrate the performance gains made possible by incorporating the static camera assumption in our algorithm

kernel based object tracking a new approach toward target representation and localization the central component in visual tracking of nonrigid objects is proposed the feature histogram based target representations are regularized by spatial masking with an isotropic kernel the masking induces spatially smooth similarity functions suitable for gradient based optimization hence the target localization problem can be formulated using the basin of attraction of the local maxima we employ a metric derived from the bhattacharyya coefficient as similarity measure and use the mean shift procedure to perform the optimization in the presented tracking examples the new method successfully coped with camera motion partial occlusions clutter and target scale variations integration with motion filters and data association techniques is also discussed we describe only a few of the potential applications exploitation of background information kalman tracking using motion models and face tracking

dynamic occlusion analysis in optical flow fields optical flow can be used to locate dynamic occlusion boundaries in an image sequence we derive an edge detection algorithm sensitive to changes in flow fields likely to be associated with occlusion the algorithm is patterned after the marr hildreth zero crossing detectors currently used to locate boundaries in scalar fields zero crossing detectors are extended to identify changes in direction and or magnitude in a vector valued flow field as a result the detector works for flow boundaries generated due to the relative motion of two overlapping surfaces as well as the simpler case of motion parallax due to a sensor moving through an otherwise stationary environment we then show how the approach can be extended to identify which side of a dynamic occlusion boundary corresponds to the occluding surface the fundamental principal involved is that at an occlusion boundary the image of the surface boundary moves with the image of the occluding surface such information is important in interpreting dynamic scenes results are demonstrated on optical flow fields automatically computed from real image sequences

image flow segmentation and estimation by constraint line clustering image flow is the velocity field in the image plane caused by the motion of the observer objects in the scene or apparent motion and can contain discontinuities due to object occlusion in the scene an algorithm that can estimate the image flow velocity field when there are discontinuities due to occlusions is described the constraint line clustering algorithm uses a statistical test to estimate the image flow velocity field in the presence of step discontinuities in the image irradiance or velocity field particular emphasis is placed on motion estimation and segmentation in situations such as random dot patterns where motion is the only cue to segmentation experimental results on a demanding synthetic test case and a real image are presented a smoothing algorithm for improving the velocity field estimate is also described the smoothing algorithm constructs a smooth estimate of the velocity field by approximating a surface between step discontinuities it is noted that the velocity field estimate can be improved using surface reconstruction between velocity field boundaries

probabilistic detection and tracking of motion boundaries we propose a bayesian framework for representing and recognizing local image motion in terms of two basic models translational motion and motion boundaries motion boundaries are represented using a non linear generative model that explicitly encodes the orientation of the boundary the velocities on either side the motion of the occluding edge over time and the appearance disappearance of pixels at the boundary we represent the posterior probability distribution over the model parameters given the image data using discrete samples this distribution is propagated over time using a particle filtering algorithm to efficiently represent such a high dimensional space we initialize samples using the responses of a low level motion discontinuity detector the formulation and computational model provide a general probabilistic framework for motion estimation with multiple non linear models

level dynamics for conservative and dissipative quantum systems we establish level dynamics for finite matrices employing a unified treatment of real symmetric complex hermitian quaternion real unitary and arbitrary complex matrices in all cases the level dynamics take the form of the classical hamiltonian flow of some fictitious many particle systems equilibrium statistical mechanics of the latter leads to the well known matrix ensembles of random matrix theory ginibre s ensemble in particular is thus associated with level dynamics of arbitrary complex matrices

map based stochastic diffusion for stereo matching and line fields estimation this paper proposes a stochastic approach to estimate the disparity field combined with line field in the maximum a posteriori map method based on markov random field mrf model it is important to optimize and converge the gibbs potential function corresponding to the perturbed disparity field the proposed optimization method stochastic diffusion takes advantage of the probabilistic distribution of the neighborhood fields to diffuse the gibbs potential space iteratively by using the neighborhood distribution in the non random and non deterministic diffusion both the estimation accuracy and the convergence speed are improved in the paper the hierarchical stochastic diffusion is also applied to the disparity field the hierarchical approach reduces the memory and computational load and increases the convergence speed of the potential space the paper also proposes an effective configuration of the neighborhood to be suitable for the hierarchical disparity structure according to the experiments the stochastic diffusion shows good estimation performance the line field improves the estimation at the object boundary and coincides with the object boundary with the useful contours the stochastic diffusion is applicable to any kind of field estimation given the appropriate definition of the field and mrf models

on determination of statistical properties of spectra from parametric level dynamics we analyse an approach aimed at determining statistical properties of spectra of a time periodic quantum chaotic system based on the parameter dynamics of their quasienergies in particular we show that application of the methods of statistical physics proposed previously in the literature taking into account appropriate integrals of motion of the parametric dynamics is fully justified even if the used integrals of motion do not determine the invariant manifold in a unique way the indetermination of the manifold is removed by applying dirac s theory of constrained hamiltonian systems and imposing appropriate primary first class constraints and a gauge transformation generated by them in the standard way the obtained results close the gap in the whole reasoning aiming at understanding statistical properties of spectra in terms of parametric dynamics

an investigation of smoothness constraints for the estimation of displacement vector fields from image sequences a mapping between one frame from an image sequence and the preceding or following frame can be represented as a displacement vector field in most situations the mere gray value variations do not provide sufficient information in order to estimate such a displacement vector field supplementary constraints are necessary for example the postulate that a displacement vector field varies smoothly as a function of the image position taken as a general requirement this creates difficulties at gray value transitions which correspond to occluding contours nagel therefore introduced the oriented smoothness requirement which restricts variations of the displacement vector field only in directions with small or no variation of gray values this contribution reports results of an investigation about how such an oriented smoothness constraint may be formulated and evaluated

quantum k theory on flag manifolds finite difference toda lattices and quantum groups let x y be homogeneous coordinates on cp a degree d holomorphic map cp 1 cp is uniquely determined up to a constant scalar factor by n 1 relatively prime degree d binary forms f0 x y fn x y omitting the condition that the forms are relatively prime we compactify the space of degree d holomorphic maps cp 1 cp to a complex projective space of dimension n 1 d 1 1 we denote this compactification of the space of maps by cp d this construction defines the compactification d r i 1cp ni 1 di of the space of degree d d1 dr maps from cp 1 to composing degree d holomorphic maps from cp 1 to the flag manifold x with the plucker embedding we embed the space of such maps into d the closure qmd of this space in d is often referred to as the drinfeld s compactification of the space of degree d maps from cp 1 to x and will be called the space of quasimaps following 14 it is a generally speaking singular irreducible projective variety of complex dimension dimx 2d1 2dr the flag manifold is a homogeneous space of the group slr 1 c and of its maximal compact subgroup sur 1 the action of these groups on x lifts naturally to the spaces d and qmd in addition to this action the spaces d and the subspaces qmd carry the circle action induced by the rotation of cp 1 defined by x y 7 x ey thus the product group g s sur 1 and its complex version gc c slr 1 c act on the quasimap spaces we will see later that qmd have g equivariant desingularizations qmd

design and use of linear models for image motion analysis linear parameterized models of optical flow particularly affine models have become widespread in image motion analysis the linear model coefficients are straightforward to estimate and they provide reliable estimates of the optical flow of smooth surfaces here we explore the use of parameterized motion models that represent much more varied and complex motions our goals are threefold to construct linear bases for complex motion phenomenas to estimate the coefficients of these linear modelss and to recognize or classify image motions from the estimated coefficients we consider two broad classes of motions i generic motion features such as motion discontinuities and moving barss and ii non rigid object specific motions such as the motion of human mouths for motion features we construct a basis of steerable flow fields that approximate the motion features for object specific motions we construct basis flow fields from example motions using principal component analysis in both cases the model coefficients can be estimated directly from spatiotemporal image derivatives with a robust multi resolution scheme finally we show how these model coefficients can be use to detect and recognize specific motions such as occlusion boundaries and facial expressions

analog hardware for detecting discontinuities in early vision the detection of discontinuities in motion intensity color and depth is a well studied but difficult problem in computer vision 6 we discuss the first hardware circuit that explicitly implements either analog or binary line processes in a deterministic fashion specifically we show that the processes of smoothing using a first order or membrane type of stabilizer and of segmentation can be implemented by a single two terminal nonlinear voltage controlled resistor the resistive fuse and we derive its current voltage relationship from a number of deterministic approximations to the underlying stochastic markov random fields algorthms the concept that the quadratic variation functionals of early vision can be solved via linear resistive networks minimizing power dissipation 37 can be extended to non convex variational functionals with analog or binary line processes being solved by nonlinear resistive networks minimizing the electrical co content

almost hermitian random matrices crossover from wigner dyson to ginibre eigenvalue statistics by using the method of orthogonal polynomials we analyze the statistical properties of complex eigenvalues of random matrices describing a crossover from hermitian matrices characterized by the wigner dyson statistics of real eigenvalues to strongly non hermitian ones whose complex eigenvalues were studied by ginibre two point statistical measures as e g spectral form factor number variance and small distance behavior of the nearest neighbor distance distribution p s are studied in more detail in particular we found that the latter function may exhibit unusual behavior p s ensuremath propto s 5 2 for some parameter values

weyl modules and q whittaker functions let g be a semi simple simply connected group over mathbb c following gerasimov et al comm math phys 294 97 119 2010 we use the q toda integrable system obtained by quantum group version of the kostant whittaker reduction cf etingof in am math soc trans ser 2 9 25 1999 sevostyanov in commun math phys 204 1 16 1999 to define the notion of q whittaker functions varpsi check lambda q z this is a family of invariant polynomials on the maximal torus t subset g here z in t depending on a dominant weight check lambda of g whose coefficients are rational functions in a variable q in mathbb c for a conjecturally the same but a priori different definition of the q toda system these functions were studied by ion duke math j 116 1 16 2003 and by cherednik int math res notices 20 3793 3842 2009 we shall denote the q whittaker functions from cherednik int math res notices 20 3793 3842 2009 by varpsi check lambda q z for g sl n these functions were extensively studied in gerasimov et al comm math phys 294 97 119 2010 comm math phys 294 121 143 2010 lett math phys 97 1 24 2011 we show that when g is simply laced the function hat varpsi check lambda q z varpsi check lambda q z cdot prod nolimits i in i prod nolimits r 1 langle alpha i check uplambda rangle 1 q r here i denotes the set of vertices of the dynkin diagram of g is equal to the character of a certain finite dimensional g mathsf t rtimes mathbb c module d check lambda the demazure module when g is not simply laced a twisted version of the above statement holds this result is known for varpsi check lambda replaced by varpsi check lambda cf sanderson in j algebraic combin 11 269 275 2000 and ion in duke math j 116 1 16 2003 however our proofs are algebro geometric and rely on our previous work braverman finkelberg in semi infinite schubert varieties and quantum k theory of flag manifolds arxiv 1111 2266 2011 and thus they are completely different from sanderson j algebraic combin 11 269 275 2000 and ion duke math j 116 1 16 2003 in particular we give an apparently new algebro geometric interpretation of the modules d check lambda

multimodal estimation of discontinuous optical flow using markov random fields the estimation of dense velocity fields from image sequences is basically an ill posed problem primarily because the data only partially constrain the solution it is rendered especially difficult by the presence of motion boundaries and occlusion regions which are not taken into account by standard regularization approaches in this paper the authors present a multimodal approach to the problem of motion estimation in which the computation of visual motion is based on several complementary constraints it is shown that multiple constraints can provide more accurate flow estimation in a wide range of circumstances the theoretical framework relies on bayesian estimation associated with global statistical models namely markov random fields the constraints introduced here aim to address the following issues optical flow estimation while preserving motion boundaries processing of occlusion regions fusion between gradient and feature based motion constraint equations deterministic relaxation algorithms are used to merge information and to provide a solution to the maximum a posteriori estimation of the unknown dense motion field the algorithm is well suited to a multiresolution implementation which brings an appreciable speed up as well as a significant improvement of estimation when large displacements are present in the scene experiments on synthetic and real world image sequences are reported

contour grouping based on contour skeleton duality in this paper we present a method for grouping relevant object contours in edge maps by taking advantage of contour skeleton duality regularizing contours and skeletons simultaneously allows us to combine both low level perceptual constraints as well as higher level model constraints in a very effective way the models are represented using paths in symmetry sets skeletons are treated as trajectories of an imaginary virtual robot in a discrete space of symmetric points obtained from pairs of edge segments boundaries are then defined as the maps obtained by grouping the associated pairs of edge segments along the trajectories casting the grouping problem in this manner makes it similar to the problem of simultaneous localization and mapping slam hence we adapt the state of the art probabilistic framework namely rao blackwellized particle filtering that has been successfully applied to slam we use the framework to maximize the joint posterior over skeletons and contours

intrackability characterizing video statistics and pursuing video representations videos of natural environments contain a wide variety of motion patterns of varying complexities which are represented by many different models in the vision literature in many situations a tracking algorithm is formulated as maximizing a posterior probability in this paper we propose to measure the video complexity by the entropy of the posterior probability called the intrackability to characterize the video statistics and pursue optimal video representations based on the definition of intrackability our study is aimed at three objectives firstly we characterize video clips of natural scenes by intrackability we calculate the intrackabilities of image points to measure the local inferential uncertainty and collect the histogram of the intrackabilities over the video in space and time as the global video statistics we find that a pca scatter plot based on the first two principle components of intrackability histograms can reflect the major variations i e image scaling and object density in natural video clips secondly we show that different video representations including deformable contours tracking kernels with various appearance features dense motion fields and dynamic texture models are connected by the change of intrackability and thus develop a simple criterion for model transition and for pursuing the optimal video representation thirdly we derive the connections between the intrackability measure and other criteria in the literature such as the shi tomasi texturedness measure conditional number and harris stephens r score and compare with the shi tomasi measure in tracking experiments

a generalisation of the calogero moser system abstract a generalised calogero moser many body system in which the particles possess extra internal degrees of freedom is introduced and solved by the method of olshanetsky and perelomov further the hierarchy of flows commuting with this system is obtained from a hierarchy of linear systems possessing sl n symmetry by the usual method of reduction thus they are shown to be integrable