probabilistic visual learning for object representation we present an unsupervised technique for visual learning which is based on density estimation in high dimensional spaces using an eigenspace decomposition two types of density estimates are derived for modeling the training data a multivariate gaussian for unimodal distributions and a mixture of gaussians model for multimodal distributions those probability densities are then used to formulate a maximum likelihood estimation framework for visual search and target detection for automatic object recognition and coding our learning technique is applied to the probabilistic visual modeling detection recognition and coding of human faces and nonrigid objects such as hands

further results on entropy and separability let be a bi stochastic quantum operation we obtain that s s for any quantum state if and only if there exists a unitary operator u such that u u that is is a unitary operation it is well known that a bipartite quantum state ab is separable if and only if it can be written as ab i i i i i i where i i 1 i and i are the normalized pure states of the subsystems and respectively which may not be orthogonal in general in this paper we also present some necessary and sufficient conditions for which the sets i are orthonormal vectors

on entropy preserving stochastic averages abstract when an n n doubly stochastic matrix a acts on r n on the left as a linear transformation and p is an n long probability vector we refer to the new probability vector ap as the stochastic average of the pair a p let n denote the set of pairs a p whose stochastic average preserves the entropy of p h ap h p n is a subset of b n n where b n is the birkhoff polytope and n is the probability simplex we characterize n and determine its geometry topology and combinatorial structure for example we find that a p n if and only if a t ap p we show that for any n n is a connected set and is in fact piecewise linearly contractible in b n n we write n as a finite union of product subspaces in two distinct ways we derive the geometry of the fibers a and p of n 3 is worked out in detail our analysis exploits the convexity of x log x and the structure of an efficiently computable bipartite graph that we associate to each ds matrix this graph also lets us represent such a matrix in a permutation equivalent block diagonal form where each block is doubly stochastic and fully indecomposable

phase transitions in coupled map lattices we clarify some aspects related to critical phenomena in 1d coupled map lattices in particular we explain why a model studied by chate and manneville did not seem to be in the same universality class as directed percolation contrary to first expectations we claim that this model is actually in this universality class but that scaling is extremely late we present a slightly modified model which seems to be in this universality class with respect to some properties but not all in contrast to directed percolation and to the model studied by chate and manneville our model shows a very complex sequence of singularities vaguely reminiscent of the richness of bifurcations in 1d maps

using advection to control the velocity of patterns in rings of maps traveling patterns are well known features of rings of symmetrically coupled maps which however propagate with rather small velocities of the order of 10 3 sites per step we show that it is easy to produce traveling patterns with velocities tunable over three orders of magnitude by simply breaking the symmetry of the coupling between neighbors this asymmetry arises naturally when the usual model of coupled map lattices is generalized to also include advection in addition asymmetries change the wavelength of waves traveling on the lattice 2002 elsevier science b v all rights reserved

spatio temporal intermittency in coupled map lattices abstract the transition to turbulence in a one dimensional array of maps coupled by diffusion is shown to display critical properties resembling those of directed percolation the analogy is supported by the reconstruction of a probabilistic cellular automation with closely similar statistical properties numerical results suggest however that spatio temporal intermittency does not belong to the same universality class as directed percolation

decision theoretic saliency computational principles biological plausibility and implications for neurophysiology and psychophysics a decision theoretic formulation of visual saliency first proposed for top down processing object recognition gao vasconcelos 2005a is extended to the problem of bottom up saliency under this formulation optimality is defined in the minimum probability of error sense under a constraint of computational parsimony the saliency of the visual features at a given location of the visual field is defined as the power of those features to discriminate between the stimulus at the location and a null hypothesis for bottom up saliency this is the set of visual features that surround the location under consideration discrimination is defined in an information theoretic sense and the optimal saliency detector derived for a class of stimuli that complies with known statistical properties of natural images it is shown that under the assumption that saliency is driven by linear filtering the optimal detector consists of what is usually referred to as the standard architecture of v1 a cascade of linear filtering divisive normalization rectification and spatial pooling the optimal detector is also shown to replicate the fundamental properties of the psychophysics of saliency stimulus pop out saliency asymmetries for stimulus presence versus absence disregard of feature conjunctions and weber s law finally it is shown that the optimal saliency architecture can be applied to the solution of generic inference problems in particular for the class of stimuli studied it performs the three fundamental operations of statistical inference assessment of probabilities implementation of bayes decision rule and feature selection

traveling waves induced by parameter fluctuations in rings of coupled maps abstract we describe a novel mechanism for inducing traveling wave attractors in rings of coupled maps traveling waves are easily produced when parameters controlling local dynamics vary from site to site we also present some statistical results regarding the distribution of periodic time evolutions

susan a new approach to low level image processing this paper describes a new approach to low level image processing in particular edge and corner detection and structure preserving noise reduction non linear filtering is used to define which parts of the image are closely related to each individual pixel each pixel has associated with it a local image region which is of similar brightness to that pixel the new feature detectors are based on the minimization of this local image region and the noise reduction method uses this region as the smoothing neighbourhood the resulting methods are accurate noise resistant and fast details of the new feature detectors and of the new noise reduction method are described along with test results

accumulation points in nonlinear parameter lattices abstract in 1963 myrberg determined a period doubling cascade of the quadratic map to accumulate at 1 401155189 as found later the geometric way with which model parameters approach this value has universal behavior and several characteristic exponents associated with it in the present paper we discuss the existence of an infinite number of points characterized by the simultaneous accumulation of two or more bifurcation cascades we present an accurate numerical determination of the vertices of a doubly infinite nonlinear lattice which lead to a point of double accumulation in addition we discuss the number theoretic nature of irrationalities characterizing vertices novel classes of universality with characteristic exponents are conjectured to exist near points of multiple accumulations

the design and use of steerable filters the authors present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters allowing one to adaptively steer a filter to any orientation and to determine analytically the filter output as a function of orientation steerable filters may be designed in quadrature pairs to allow adaptive control over phase as well as orientation the authors show how to design and steer the filters and present examples of their use in the analysis of orientation and phase angularly adaptive filtering edge detection and shape from shading one can also build a self similar steerable pyramid representation the same concepts can be generalized to the design of 3 d steerable filters

wavelet transformation for gray level corner detection abstract corners are very attractive features for many applications in computer vision in this paper a new gray level corner detection algorithm based on the wavelet transform is presented the wavelet transform is used because the evolution across scales of its magnitudes and orientations can be used to characterize localized signals like edges and corners most conventional corner detectors detect corners based on the edge detection information however these edge detectors perform poorly at corners adversely affecting their overall performance to overcome this drawback we first propose a new edge detector based on the ratio of the inter scale wavelet transform modulus this edge detector can correctly detect edges at the corner positions making accurate corner detection possible to reduce the number of points required to be processed we apply the non minima suppression scheme to the edge image and extract the minima image based on the orientation variance these non corner edge points are eliminated in order to locate the corner points we propose a new corner indicator based on the scale invariant property of the corner orientations by examining the corner indicator the corner points can be located accurately as shown by experiments with our algorithm in addition since wavelet transform possesses the smoothing effect inherently our algorithm is insensitive to noise contamination as well

pattern dynamics in spatiotemporal chaos pattern selection diffusion of defect and pattern competition intermettency abstract a class of coupled map lattices is investigated as a model for the spatiotemporal chaos as the parameters are changed phase transitions among the patterns are observed pattern selection through the chaotic motion of domain is observed chaos is suppressed by the selection selection of the zigzag pattern is studied where localized defects which separate the two anti phase domains are found they change chaotically in time and move randomly in space the diffusion of defect is related with its chaotic motion collapse of zigzag pattern and the defect turbulence are studied in connection with the crisis in high dimensional dynamical systems pattern selection with longer wavelengths is found in the stronger coupling regime transition from pattern selection phase to fully developed turbulence occurs via the intermittency selective flicker like noise and the pareto distribution of lifetime of pattern are observed at the intermittency regime for the quantitative characterization of each phase pattern distributions pattern transition matrix static and dynamical entropies lifetime distribution of pattern spatiotemporal power spectra and lyapunov spectra are calculated phase transition from the pattern selection to fully developed turbulence is investigated with the use of these quantifiers where some order parameters and critical indeces are introduced

traveling waves in nonequilibrium systems abstract the order parameter equation for the oscillatory instability of a spatially homogeneous state is used to examine traveling wave patterns in large aspect ratio systems with rectangular as well as circular geometries

skewed rotation symmetry group detection we present a novel and effective algorithm for affinely skewed rotation symmetry group detection from real world images we define a complete skewed rotation symmetry detection problem as discovering five independent properties of a skewed rotation symmetry group 1 the center of rotation 2 the affine deformation 3 the type of the symmetry group 4 the cardinality of the symmetry group and 5 the supporting region of the symmetry group in the image we propose a frieze expansion fe method that transforms rotation symmetry group detection into a simple 1d translation symmetry detection problem we define and construct a pair of rotational symmetry saliency maps complemented by a local feature method frequency analysis using discrete fourier transform dft is applied to the frieze expansion patterns feps to uncover the types cyclic dihedral and o 2 the cardinalities and the corresponding supporting regions concentric or otherwise of multiple rotation symmetry groups in an image the phase information of the fep is used to rectify affinely skewed rotation symmetry groups our result advances the state of the art in symmetry detection by offering a unique combination of region based feature based and frequency based approaches experimental results on 170 synthetic and natural images demonstrate superior performance of our rotation symmetry detection algorithm over existing methods

extended symbolic dynamics in bistable cml existence and stability of fronts abstract we consider a diffusive coupled map lattice cml for which the local map is piecewise affine and has two stable fixed points by introducing a spatio temporal coding we prove the one to one correspondence between the set of global orbits and the set of admissible codes this relationship is applied to the study of the uniform fronts dynamics it is shown that for any given velocity in 1 1 there is a parameter set for which the fronts with that velocity exist and their shape is unique the dependence of the fronts velocity on the local map s discontinuity is proved to be a devil s staircase moreover the linear stability of the global orbits which do not reach the discontinuity follows directly from our simple map for the fronts this statement is improved and as a consequence the velocity of all the propagating interfaces is computed for any parameter the fronts are shown to be also nonlinearly stable under some restrictions on the parameters actually these restrictions follow from the co existence of uniform fronts and non uniformly travelling fronts for strong coupling finally these results are extended to some c local maps

pattern dynamics of a coupled map lattice for open flow abstract the pattern dynamics of the one way coupled logistic lattice which can serve as a phenomenological model for open flow is investigated and shown to be extremely rich for medium and large coupling strengths we find spatially periodic quasiperiodic and chaotic patterns with temporal periodicity and analyze their stability with the help of a newly introduced spatial map criteria are established for predicting the down flow bifurcation behavior of the coupled map lattice and for selecting attractors through modulation of the boundary for smaller coupling strengths we find a novel regime in which chaotic defects form a periodic lattice that is shown to be the result of a boundary crisis

the improbability of harris interest points an elementary characterization of the map underlying harris corners also known as harris interest points or key points is provided two principal and basic assumptions made are 1 local image structure is captured in an uncommitted way simply using weighted raw image values around every image location to describe the local image information and 2 the lower the probability of observing the image structure present in a particular point the more salient or interesting this position is i e saliency is related to how uncommon it is to see a certain image structure how surprising it is through the latter assumption the axiomatization proposed makes a sound link between image saliency in computer vision on the one hand and on the other computational models of preattentive human visual perception where exactly the same definition of saliency has been proposed because of this link the characterization provides a compelling case in favor of harris interest points over other approaches

discriminant saliency the detection of suspicious coincidences and applications to visual recognition a discriminant formulation of top down visual saliency intrinsically connected to the recognition problem is proposed the new formulation is shown to be closely related to a number of classical principles for the organization of perceptual systems including infomax inference by detection of suspicious coincidences classification with minimal uncertainty and classification with minimum probability of error the implementation of these principles with computational parsimony by exploitation of the statistics of natural images is investigated it is shown that barlow s principle of inference by the detection of suspicious coincidences enables computationally efficient saliency measures which are nearly optimal for classification this principle is adopted for the solution of the two fundamental problems in discriminant saliency feature selection and saliency detection the resulting saliency detector is shown to have a number of interesting properties and act effectively as a focus of attention mechanism for the selection of interest points according to their relevance for visual recognition experimental evidence shows that the selected points have good performance with respect to 1 the ability to localize objects embedded in significant amounts of clutter 2 the ability to capture information relevant for image classification and 3 the richness of the set of visual attributes that can be considered salient

multiscale corner detection by using wavelet transform a multiscale corner detection algorithm based on the wavelet transform of contour orientation is proposed it can utilize both the information of the local extrema and modulus of transform results to detect corners and arcs effectively the ramp width of contour orientation profile which can be computed using the transformed modulus of two scales reveals the difference between corner and arc and is utilized in the determination of corner points the experimental results have shown that the detector is more effective than both the single and multiple scale detectors they also demonstrate that the detector is insensitive to boundary noise in addition the proposed method is more efficient than the other multiscale corner detector because it operates on fewer number of scales which can be implemented by a fast transform algorithm

robust space time intermittency and 1 f noise abstract we investigate a type of intermittency that occurs in space as well as time studying a one dimensional lattice of coupled quadratic maps this system naturally forms spatial domains motion of the domain walls causes spatially localized changes from chaotic to almost periodic behavior the almost periodic phases have eigenvalues quite close to one resulting in long lived laminar bursts with a 1 f low frequency spectrum this behavior has aspects of both crutchfield and pomeau manneville intermittency unlike pomeau manneville however the behavior that we observe here is quite robust under changes of parameters

kolmogorov sinai entropy for locally coupled piecewise linear maps abstract we present analytical results for the kolmogorov sinai entropy of a one dimensional lattice of locally coupled piecewise linear maps for some particular values of the coupling strength our results explain the numerically observed fact that the entropy of a lattice of chaotic maps increases for strong coupling

chaotic traveling waves in a coupled map lattice traveling waves triggered by a phase slip are studied in a coupled map lattice a local phase slip affects globally the system which is in strong contrast with kink propagation attractors with different velocities coexist and form quantized bands determined by the number of phase slips if the system size is not far from an integer multiple of the selected wavelength attractors are tori otherwise weak chaos induces modulation of waves or a chaotic itinerancy of traveling states with a long ranged temporal correlation supertransients before the formation of traveling waves are noted in the high nonlinearity regime in the weaker nonlinearity there are fluctuations of domain sizes and brownian like motion of domains propagation of chaotic domains by phase slips is also found

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

the curvature primal sketch in this paper we introduce a novel representation of the significant changes in curvature along the bounding contour of planar shape we call the representation the curvature primal sketch because of the close analogy to the primal sketch representation advocated by marr for describing significant intensity changes we define a set of primitive parameterized curvature discontinuities and derive expressions for their convolutions with the first and second derivatives of a gaussian we describe an implemented algorithm that computes the curvature primal sketch by matching the multiscale convolutions of a shape and illustrate its performance on a set of tool shapes several applications of the representation are sketched

mode locking in coupled map lattices abstract we study propagation of pulses along one way coupled map lattices which originate from the transition between two superstable states of the local map the velocity of the pulses exhibits a staircase like behaviour as the coupling parameter is varied for a piecewise linear local map we prove that the velocity of the wave has a devil s staircase dependence on the coupling parameter a wave travelling with rational velocity is found to be stable to parametric perturbations in a manner akin to rational mode locking for circle maps we provide evidence that mode locking is also present for a broader range of maps and couplings

local grayvalue invariants for image retrieval this paper addresses the problem of retrieving images from large image databases the method is based on local grayvalue invariants which are computed at automatically detected interest points a voting algorithm and semilocal constraints make retrieval possible indexing allows for efficient retrieval from a database of more than 1 000 images experimental results show correct retrieval in the case of partial visibility similarity transformations extraneous features and small perspective deformations

pattern formation in diffusive advective coupled map lattices we investigate pattern formation and evolution in coupled map lattices when advection is incorporated inaddition to the usual diffusive term all patterns may be suitably grouped into ve classes three periodic supporting static patterns and traveling waves and two nonperiodic relative frequencies are determined as afunction of all model parameters diffusion advection local nonlinearity and lattice size advection plays animportant role in coupled map lattices being capable of considerably altering pattern evolution for instance advection may induce synchronization making chaotic patterns evolve periodically as a byproduct we de scribe a practical algorithm for classifying generic pattern evolutions and for measuring velocities of travelingwaves doi 10 1103 physreve 69 066206 pacs number s 89 75 kd 05 45 xt 05 45 rai introduction

birkhoff s polytope and unistochastic matrices n 3 and n 4 the set of bistochastic or doubly stochastic n n matrices is a convex set called birkhoff s polytope which we describe in some detail our problem is to characterize the set of unistochastic matrices as a subset of birkhoff s polytope for n 3 we present fairly complete results for n 4 partial results are obtained an interesting difference between the two cases is that there is a ball of unistochastic matrices around the van der waerden matrix for n 3 while this is not the case for n 4

synchronization in two layer bistable coupled map lattices abstract the dynamics of a two layer bistable coupled map lattice cml is investigated a methodology for the construction of invariant domains in the phase space is developed and applied to the study of pattern formation and inter layer synchronization sufficient conditions for global synchronization are obtained the phenomena of pattern interaction and replication of form is also investigated finally possible instabilities of the synchronization mode and on off diagonal attractors are analyzed

curved glide reflection symmetry detection we generalize the concept of bilateral reflection symmetry to curved glide reflection symmetry in 2d euclidean space such that classic reflection symmetry becomes one of its six special cases we propose a local feature based approach for curved glide reflection symmetry detection from real unsegmented 2d images furthermore we apply curved glide reflection axis detection for curved reflection surface detection in 3d images our method discovers groups and connects statistically dominant local glide reflection axes in an axis parameter space aps without preassumptions on the types of reflection symmetries quantitative evaluations and comparisons against state of the art algorithms on a diverse 64 test image set and 1 125 swedish leaf data images show a promising average detection rate of the proposed algorithm at 80 and 40 percent respectively and superior performance over existing reflection symmetry detection algorithms potential applications in computer vision particularly biomedical imaging include saliency detection from unsegmented images and quantification of deviations from normality we make our 64 test image set publicly available

symmetry as a continuous feature symmetry is treated as a continuous feature and a continuous measure of distance from symmetry in shapes is defined the symmetry distance sd of a shape is defined to be the minimum mean squared distance required to move points of the original shape in order to obtain a symmetrical shape this general definition of a symmetry measure enables a comparison of the amount of symmetry of different shapes and the amount of different symmetries of a single shape this measure is applicable to any type of symmetry in any dimension the symmetry distance gives rise to a method of reconstructing symmetry of occluded shapes the authors extend the method to deal with symmetries of noisy and fuzzy data finally the authors consider grayscale images as 3d shapes and use the symmetry distance to find the orientation of symmetric objects from their images and to find locally symmetric regions in images

lyapunov analysis and information flow in coupled map lattices abstract lyapunov analysis for the coupled map lattices is presented the co moving lyapunov exponent is calculated which is related with the propagation of the disturbance in space the propagation speed agrees with the zero crossing point of the co moving lyapunov exponent the co moving mutual information flow is introduced which shows the selective transmission of the information at some speed lyapunov spectra and vectors are calculated spatial structures of the vectors are investigated possible analogy with the anderson localization problem is discussed

spatially periodic orbits in coupled map lattices we obtain the conditions that ensure the stability of spatially and temporally periodic orbits of coupled map lattices the stability matrices can be put in a circulant and block circulant form this allows us to reduce the problem to smaller matrices corresponding to the building blocks of spatial periodicity we find that additional conditions are imposed as we expand the size of the lattice for the traveling wave solution the analysis is considerably simplified we have analyzed both the one dimensional and higher dimensional lattices

focus of attention from local color symmetries in this paper a continuous valued measure for local color symmetry is introduced the new algorithm is an extension of the successful gray value based symmetry map proposed by reisfeld et al the use of color facilitates the detection of focus points fps on objects that are difficult to detect using gray value contrast only the detection of fps is aimed at guiding the attention of an object recognition system therefore fps have to fulfill three major requirements stability distinctiveness and usability the proposed algorithm is evaluated for these criteria and compared with the gray value based symmetry measure and two other methods from the literature stability is tested against noise object rotation and variations of lighting as a measure for the distinctiveness of fps the principal components of fp centered windows are compared with those of windows at randomly chosen points on a large database of natural images finally usability is evaluated in the context of an object recognition task

evaluation of interest point detectors many different low level feature detectors exist and it is widely agreed that the evaluation of detectors is important in this paper we introduce two evaluation criteria for interest points repeatability rate and information content repeatability rate evaluates the geometric stability under different transformations information content measures the distinctiveness of features different interest point detectors are compared using these two criteria we determine which detector gives the best results and show that it satisfies the criteria well

irregular shape symmetry analysis theory and application to quantitative galaxy classification this paper presents a set of imperfectly symmetric measures based on a series of geometric transformation operations for quantitatively measuring the amount of symmetry of arbitrary shapes the definitions of both bilateral symmetricity and rotational symmetricity give new insight into analyzing the geometrical property of a shape and enable characterizing arbitrary shapes in a new way we developed a set of criteria for quantitative galaxy classification using our proposed irregular shape symmetry measures our study has demonstrated the effectiveness of the proposed method for the characterization of the shape of the celestial bodies the concepts described in the paper are applicable to many fields such as mathematics artificial intelligence digital image processing robotics biomedicine etc

on quasiperiodic travelling waves in coupled map lattices we investigate quasiperiodic travelling waves qtws in lattices of diffusively coupled logistic maps starting from the assumption that any spatial structure can be broken down into simpler elementary structures a classification scheme for qtws is introduced within this framework the phenomenon of discrete velocities is reviewed and further investigated in addition a new technique is proposed for predicting whether qtws can occur for given parameter values and which they might be