image and texture segmentation using local spectral histograms we present a method for segmenting images consisting of texture and nontexture regions based on local spectral histograms defined as a vector consisting of marginal distributions of chosen filter responses local spectral histograms provide a feature statistic for both types of regions using local spectral histograms of homogeneous regions we decompose the segmentation process into three stages the first is the initial classification stage where probability models for homogeneous texture and nontexture regions are derived and an initial segmentation result is obtained by classifying local windows in the second stage we give an algorithm that iteratively updates the segmentation using the derived probability models the third is the boundary localization stage where region boundaries are localized by building refined probability models that are sensitive to spatial patterns in segmented regions we present segmentation results on texture as well as nontexture images our comparison with other methods shows that the proposed method produces more accurate segmentation results

multiple window parallel adaptive boundary finding in computer vision the problem considered in this paper is the estimation of highly variable object boundaries in noisy images boundaries may be those of a tank in an ir image a spinal canal in a cat scan a cloud in a visible light image etc or they may be internal to an object such as the boundary between a spherical surface and a cylindrical surface in a manufactured object the focus of the paper is on parallel multiple window boundary estimation algorithms here the image field is parti tioned into an array of rectangular windows and boundary finders are run simultaneously within the windows the boundary segments found within the windows are then seamed together to obtain meaningful global boundaries the entire procedure is treated within a maximum likelihood estimation framework that we have developed for boundary finding although our multiple window estimation approach can be used with a number of local boundary finding algorithms we concen trate on one which is based on dynamic programming and will produce the true maximum likelihood boundary some theoretical considera tions for boundary model design and boundary finding runtime are covered included is the use of a low computational cost f test for test ing whether a window contains a boundary and an analytical treatment which shows that use of coarse pixels with a chi square test or an f test improves the probability of correctly recognizing whether a boundary is present in a window

periodicity directionality and randomness wold features for image modeling and retrieval one of the fundamental challenges in pattern recognition is choosing a set of features appropriate to a class of problems in applications such as database retrieval it is important that image features used in pattern comparison provide good measures of image perceptual similarities we present an image model with a new set of features that address the challenge of perceptual similarity the model is based on the 2d wold decomposition of homogeneous random fields the three resulting mutually orthogonal subfields have perceptual properties which can be described as periodicity directionality and randomness approximating what are indicated to be the three most important dimensions of human texture perception the method presented improves upon earlier wold based models in its tolerance to a variety of local inhomogeneities which arise in natural textures and its invariance under image transformation such as rotation an image retrieval algorithm based on the new texture model is presented different types of image features are aggregated for similarity comparison by using a bayesian probabilistic approach the effectiveness of the wold model at retrieving perceptually similar natural textures is demonstrated in comparison to that of two other well known pattern recognition methods the wold model appears to offer a perceptually more satisfying measure of pattern similarity while exceeding the performance of these other methods by traditional pattern recognition criteria examples of natural scene wold texture modeling are also presented

texture analysis and classification with linear regression model based on wavelet transform the wavelet transform as an important multiresolution analysis tool has already been commonly applied to texture analysis and classification nevertheless it ignores the structural information while capturing the spectral information of the texture image at different scales in this paper we propose a texture analysis and classification approach with the linear regression model based on the wavelet transform this method is motivated by the observation that there exists a distinctive correlation between the sample images belonging to the same kind of texture at different frequency regions obtained by 2 d wavelet packet transform experimentally it was observed that this correlation varies from texture to texture the linear regression model is employed to analyze this correlation and extract texture features that characterize the samples therefore our method considers not only the frequency regions but also the correlation between these regions in contrast the pyramid structured wavelet transform pswt and the tree structured wavelet transform tswt do not consider the correlation between different frequency regions experiments show that our method significantly improves the texture classification rate in comparison with the multiresolution methods including pswt tswt the gabor transform and some recently proposed methods derived from these

texture synthesis and nonparametric resampling of random fields this paper introduces a nonparametric algorithm for bootstrapping a stationary random field and proves certain consistency properties of the algorithm for the case of mixing random fields the motivation for this paper comes from relating a heuristic texture synthesis algorithm popular in computer vision to general nonparametric bootstrapping of stationary random fields we give a formal resampling scheme for the heuristic texture algorithm and prove that it produces a consistent estimate of the joint distribution of pixels in a window of certain size under mixing and regularity conditions on the random field the joint distribution of pixels is the quantity of interest here because theories of human perception of texture suggest that two textures with the same joint distribution of pixel values in a suitably chosen window will appear similar to a human thus we provide theoretical justification for an algorithm that has already been very successful in practice and suggest an explanation for its perceptually good results

minimax entropy principle and its application to texture modeling this article proposes a general theory and methodology called the minimax entropy principle for building statistical models for images or signals in a variety of applications this principle consists of two parts the first is the maximum entropy principle for feature binding or fusion for a given set of observed feature statistics a distribution can be built to bind these feature statistics together by maximizing the entropy over all distributions that reproduce them the second part is the minimum entropy principle for feature selection among all plausible sets of feature statistics we choose the set whose maximum entropy distribution has the minimum entropy computational and inferential issues in both parts are addressed in particular a feature pursuit procedure is proposed for approximately selecting the optimal set of features the minimax entropy principle is then corrected by considering the sample variation in the observed feature statistics and an information criterion for feature pursuit is derived the minimax entropy principle is applied to texture modeling where a novel markov random field mrf model called frame filter random field and minimax entropy is derived and encouraging results are obtained in experiments on a variety of texture images the relationship between our theory and the mechanisms of neural computation is also discussed

exploring texture ensembles by efficient markov chain monte carlo toward a trichromacy theory of texture presents a mathematical definition of texture the julesz ensemble spl omega h which is the set of all images defined on z sup 2 that share identical statistics h then texture modeling is posed as an inverse problem given a set of images sampled from an unknown spl omega h sub we search for the statistics h sub which define the ensemble a spl omega h has an associated probability distribution q i h which is uniform over the images in spl omega h and has zero probability outside the authors previously 1999 showed q i h to be the limit distribution of the frame filter random field and minimax entropy model as the image lattice spl lambda spl rarr z sup 2 this conclusion establishes the intrinsic link between the scientific definition of texture on z sup 2 and the mathematical models of texture on finite lattices it brings two advantages the practice of texture image synthesis by matching statistics is put on a mathematical foundation and we need not learn the expensive frame model in feature pursuit model selection and texture synthesis an efficient markov chain monte carte algorithm is proposed for sampling julesz ensembles it generates random texture images by moving along the directions of filter coefficients and thus extends the traditional single site gibbs sampler we compare four popular statistical measures in the literature in terms of their descriptive abilities our experiments suggest that a small number of bins in marginal histograms are sufficient for capturing a variety of texture patterns

reduced complexity rotation invariant texture classification using a blind deconvolution approach in this paper we present a texture classification procedure that makes use of a blind deconvolution approach specifically the texture is modeled as the output of a linear system driven by a binary excitation we show that features computed from one dimensional slices extracted from the two dimensional autocorrelation function acf of the binary excitation allows representing the texture for rotation invariant classification purposes the two dimensional classification problem is thus reconduced to a more simple one dimensional one which leads to a significant reduction of the classification procedure computational complexity

texture segmentation using voronoi polygons textures are defined in terms of primitives called tokens a texture segmentation algorithm based on the voronoi tessellation is discussed the algorithm first builds the voronoi tessellation of the tokens that make up the textured image it then computes a feature vector for each voronoi polygon these feature vectors are used in a probabilistic relaxation labeling on the tokens to identify the interior and the border regions of the textures some experimental results are shown

equivalence of julesz ensembles and frame models in the past thirty years research on textures has been pursued along two different lines the first line of research pioneered by julesz 1962 ire transactions of information theory it 8 84 92 seeks essential ingredients in terms of features and statistics in human texture perception this leads us to a mathematical definition of textures in terms of julesz ensembles zhu et al ieee trans on pami vol 22 no 6 2000 a julesz ensemble is a set of images that share the same value of some basic feature statistics images in the julesz ensemble are defined on a large image lattice a mathematical idealization being z2 so that exact constraint on feature statistics makes sense the second line of research studies markov random field mrf models that characterize texture patterns on finite or small image lattice in a statistical way this leads us to a general class of mrf models called frame filter random field and maximum entropy zhu et al neural computation 9 1627 1660 in this article we bridge the two lines of research by the fundamental principle of equivalence of ensembles in statistical mechanics gibbs 1902 elementary principles of statistical mechanics yale university press we show that 1 as the size of the image lattice goes to infinity a frame model concentrates its probability mass uniformly on a corresponding julesz ensemble therefore the julesz ensemble characterizes the global statistical property of the frame models 2 for a large image randomly sampled from a julesz ensemble any local patch of the image given its environment follows the conditional distribution specified by a corresponding frame model therefore the frame model describes the local statistical property of the julesz ensemble and is an inevitable texture model on finite or small lattice if texture perception is decided by feature statistics the key to derive these results is the large deviation estimate of the volume of or the number of images in the julesz ensemble which we call the entropy function studying the equivalence of ensembles provides deep insights into questions such as the origin of mrf models typical images of statistical models and error rates in various texture related vision tasks yuille and coughlan ieee trans on pami vol 2 no 2 2000 the second thrust of this paper is to study texture distance based on the texture models of both small and large lattice systems we attempt to explain the asymmetry phenomenon observed in texture pop out experiments by the asymmetry of kullback leibler divergence our results generalize the traditional signal detection theory green and swets 1988 signal detection theory and psychophysics peninsula publishing for distance measures from iid cases to random fields our theories are verified by two groups of computer simulation experiments

dimensions of random average conformal repellers abstract this paper defines random average conformal repellers which are a generalization of random conformal repellers using the subadditive thermodynamic formalism the hausdorff dimension of random average conformal repellers is obtained as the root of the random pressure function

approximate random variate generation from infinitely divisible distributions with applications to bayesian inference summary stochastic processes with independent increments play a central role in bayesian nonparametric inference the distributions of the increments of these processes aside from fixed points of discontinuity are infinitely divisible and their laplace and or fourier transforms in the levy representation are usually known conventional bayesian inference in this context has been limited largely to providing point estimates of the random quantities of interest although markov chain monte carlo methods have been used to obtain a fuller analysis in the context of dirichlet process priors in this paper we propose and implement a general method for simulating infinitely divisible random variates when their fourier or laplace transforms are available in the levy representation theoretical justification is established by proving a convergence theorem that is a sampling form of a classical theorem in probability the results provide a method for implementing bayesian nonparametric inference by using a wide range of stochastic processes as priors

on the dimension of deterministic and random cantor like sets symbolic dynamics and the eckmann ruelle conjecture in this paper we unify and extend many of the known results on the dimension of deterministic and random cantor like sets in n and apply these results to study some problems in dynamical systems in particular we verify the eckmann ruelle conjecture for equilibrium measures for holder continuous conformal expanding maps and conformal axiom a topologically hyperbolic homeomorphims we also construct a holder continuous axiom a homeomorphism of positive topological entropy for which the unique measure of maximal entropy is ergodic and has different upper and lower pointwise dimensions almost everywhere this example shows that the non conformal holder continuous version of the eckmann ruelle conjecture is false

the earth mover s distance as a metric for image retrieval we investigate the properties of a metric between two distributions the earth mover s distance emd for content based image retrieval the emd is based on the minimal cost that must be paid to transform one distribution into the other in a precise sense and was first proposed for certain vision problems by peleg werman and rom for image retrieval we combine this idea with a representation scheme for distributions that is based on vector quantization this combination leads to an image comparison framework that often accounts for perceptual similarity better than other previously proposed methods the emd is based on a solution to the transportation problem from linear optimization for which efficient algorithms are available and also allows naturally for partial matching it is more robust than histogram matching techniques in that it can operate on variable length representations of the distributions that avoid quantization and other binning problems typical of histograms when used to compare distributions with the same overall mass the emd is a true metric in this paper we focus on applications to color and texture and we compare the retrieval performance of the emd with that of other distances

fundamental limits of bayesian inference order parameters and phase transitions for road tracking there is a growing interest in formulating vision problems in terms of bayesian inference and in particular the maximum a posteriori map estimator in this paper we consider the special case of detecting roads from aerial images and demonstrate that analysis of this ensemble enables us to determine fundamental bounds on the performance of the map estimate we demonstrate that there is a phase transition at a critical value of the order parameter below this phase transition it is impossible to detect the road by any algorithm we derive closely related order parameters which determine the time and memory complexity of search and the accuracy of the solution using the n search strategy our approach can be applied to other vision problems and we briefly summarize the results when the model uses the wrong prior we comment on how our work relates to studies of the complexity of visual search and the critical behaviour in the computational cost of solving np complete problems

triplet markov fields for the classification of complex structure data we address the issue of classifying complex data we focus on three main sources of complexity namely the high dimensionality of the observed data the dependencies between these observations and the general nature of the noise model underlying their distribution we investigate the recent triplet markov fields and propose new models in this class designed for such data and in particular allowing very general noise models in addition our models can handle the inclusion of a learning step in a consistent way so that they can be used in a supervised framework one advantage of our models is that whatever the initial complexity of the noise model parameter estimation can be carried out using state of the art bayesian clustering techniques under the usual simplifying assumptions as generative models they can be seen as an alternative in the supervised case to discriminative conditional random fields identifiability issues underlying the models in the nonsupervised case are discussed while the models performance is illustrated on simulated and real data exhibiting the mentioned various sources of complexity

statistical principles in image modeling images of natural scenes contain a rich variety of visual patterns to learn and recognize these patterns from natural images it is necessary to construct statistical models for these patterns in this review article we describe three statistical principles for modeling image patterns the sparse coding principle the minimax entropy principle and the meaningful alignment principle we explain these three principles and their relationships in the context of modeling images as compositions of gabor wavelets these three principles correspond to three regimes of composition patterns of gabor wavelets and these three regimes are connected by changes in scale or resolution

variational region based segmentation using multiple texture statistics this paper investigates variational region level criterion for supervised and unsupervised texture based image segmentation the focus is given to the demonstration of the effectiveness and robustness of this region based formulation compared to most common variational approaches the main contributions of this global criterion are twofold first the proposed methods circumvent a major problem related to classical texture based segmentation approaches existing methods even if they use different and various texture features are mainly stated as the optimization of a criterion evaluating punctual pixel likelihoods or similarity measure computed within a local neighborhood these approaches require sufficient dissimilarity between the considered texture features an additional limitation is the choice of the neighborhood size and shape these two parameters and especially the neighborhood size significantly influence the classification performances the neighborhood must be large enough to capture texture structures and small enough to guarantee segmentation accuracy these parameters are often set experimentally these limitations are mitigated with the proposed variational methods stated at the region level it resorts to an energy criterion defined on image where regions are characterized by nonparametric distributions of their responses to a set of filters in the supervised case the segmentation algorithm consists in the minimization of a similarity measure between region level statistics and texture prototypes and a boundary based functional that imposes smoothness and regularity on region boundaries in the unsupervised case the data driven term involves the maximization of the dissimilarity between regions the proposed similarity measure is generic and permits optimally fusing various types of texture features it is defined as a weighted sum of kullback leibler divergences between feature distributions the optimization of the proposed variational criteria is carried out using a level set formulation the effectiveness and the robustness of this formulation at region level compared to classical active contour methods are evaluated for various brodatz and natural images

outperforming the gibbs sampler empirical estimator for nearest neighbor random fields given a markov chain sampling scheme does the standard empirical estimator make best use of the data we show that this is not so and construct better estimators we restrict attention to nearest neighbor random fields and to gibbs samplers with deterministic sweep but our approach applies to any sampler that uses reversible variable at a time updating with deterministic sweep the structure of the transition distribution of the sampler is exploited to construct further empirical estimators that are combined with the standard empirical estimator to reduce asymptotic variance the extra computational cost is negligible when the random field is spatially homogeneous symmetrizations of our estimator lead to further variance reduction the performance of the estimators is evaluated in a simulation study of the ising model

prior learning and gibbs reaction diffusion this article addresses two important themes in early visual computation it presents a novel theory for learning the universal statistics of natural images and it proposes a general framework of designing reaction diffusion equations for image processing we studied the statistics of natural images including the scale invariant properties then generic prior models were learned to duplicate the observed statistics based on minimax entropy theory the resulting gibbs distributions have potentials of the form u i spl lambda s spl sigma sub spl alpha 1 sup k spl sigma sub x y spl lambda sup spl alpha f sup spl alpha i x y with s f sup 1 f sup 2 f sup k being a set of filters and spl lambda spl lambda sup 1 spl lambda sup 2 spl lambda sup k the potential functions the learned gibbs distributions confirm and improve the form of existing prior models such as line process but in contrast to all previous models inverted potentials were found to be necessary we find that the partial differential equations given by gradient descent on u i spl lambda s are essentially reaction diffusion equations where the usual energy terms produce anisotropic diffusion while the inverted energy terms produce reaction associated with pattern formation enhancing preferred image features we illustrate how these models can be used for texture pattern rendering denoising image enhancement and clutter removal by careful choice of both prior and data models of this type incorporating the appropriate features

a no reference texture regularity metric based on visual saliency this paper presents a no reference perceptual metric that quantifies the degree of perceived regularity in textures the metric is based on the similarity of visual attention va of the textural primitives and the periodic spatial distribution of foveated fixation regions throughout the image a ground truth eye tracking database for textures is also generated as part of this paper and is used to evaluate the performance of the most popular va models using the saliency map generated by the best va model the proposed texture regularity metric is computed it is shown through subjective testing that the proposed metric has a strong correlation with the mean opinion score for the perceived regularity of textures the proposed texture regularity metric can be used to improve the quality and performance of many image processing applications like texture synthesis texture compression and content based image retrieval

em and beyond the basic theme of the em algorithm to repeatedly use complete data methods to solve incomplete data problems is also a theme of several more recent statistical techniques these techniques multiple imputation data augmentation stochastic relaxation and sampling importance resampling combine simulation techniques with complete data methods to attack problems that are difficult or impossible for em

fusion of hidden markov random field models and its bayesian estimation in this paper we present a hidden markov random field hmrf data fusion model the proposed model is applied to the segmentation of natural images based on the fusion of colors and textons into julesz ensembles the corresponding exploration selection estimation ese procedure for the estimation of the parameters is presented this method achieves the estimation of the parameters of the gaussian kernels the mixture proportions the region labels the number of regions and the markov hyper parameter meanwhile we present a new proof of the asymptotic convergence of the ese procedure based on original finite time bounds for the rate of convergence

universal analytical forms for modeling image probabilities seeking probability models for images we employ a spectral approach where the images are decomposed using bandpass filters and probability models are imposed on the filter outputs also called spectral components we employ a two parameter family of probability densities called bessel k forms for modeling the marginal densities of the spectral components and demonstrate their fit to the observed histograms for video infrared and range images motivated by object based models for image analysis a relationship between the bessel parameters and the imaged objects is established using l sup 2 metric on the set of bessel k forms we propose a pseudometric on the image space for quantifying image similarities differences some applications including clutter classification and pruning of hypotheses for target recognition are presented

embedding gestalt laws in markov random fields the goal of this paper is to study a mathematical framework of 2d object shape modeling and learning for middle level vision problems such as image segmentation and perceptual organization for this purpose we pursue generic shape models which characterize the most common features of 2d object shapes in this paper shape models are learned from observed natural shapes based on a minimax entropy learning theory the learned shape models are gibbs distributions defined on markov random fields mrfs the neighborhood structures of these mrfs correspond to gestalt laws colinearity cocircularity proximity parallelism and symmetry thus both contour based and region based features are accounted for stochastic markov chain monte carlo mcmc algorithms are proposed for learning and model verification furthermore this paper provides a quantitative measure for the so called nonaccidental statistics and thus justifies some empirical observations of gestalt psychology by information theory our experiments also demonstrate that global shape properties can arise from interactions of local features

fuzzy model based clustering and its application in image segmentation a fuzzy generalized gaussian density ggd segmentation model is proposed a ggd based agglomerative fuzzy algorithm is developed a two stage fuzzy ggd segmentation algorithm is proposed this paper proposes a novel fuzzy model based unsupervised learning algorithm with boundary correction for image segmentation we propose a fuzzy generalized gaussian density ggd segmentation model and the ggd based agglomerative fuzzy algorithm for grouping image pixels the merits of algorithm are that it is not sensitive to initial parameters and that the number of groups can be estimated via the validation technique to minimize the objective function of the model we define a dissimilarity measure based on the kullbackleibler divergence of the ggds that computes the discrepancy between ggds in the space of generalized probability distributions to effectively segment images with various textures we propose a two stage fuzzy ggd segmentation algorithm the first stage adopts the proposed fuzzy algorithm to obtain initial segmentation and the second stage improves initial segmentation by image boundary correction experimental results show that our proposed method has a promising performance compared with existing approaches

ranks for pairs of spatial fields via metric based on grayscale morphological distances based on a set of morphological distances computed between the grayscale images spatial fields of similar size specifications the ratios of selected morphological distances and the ratios of areas of infima and suprema of grayscale images a new metric to quantify the degree of similarity between the grayscale images is proposed we denote the two spatial fields grayscale images respectively with f i and f j and the infima and suprema of these spatial fields with f i wedge f j and f i vee f j the three morphology based distances include 1 dilation distance d f i f j 2 erosion distance e f i f j and 3 median based distance m n f i f j by employing these parameters which play vital role in construction of parameter specific interaction matrices we provide a metric to designate every possible pair of images that can be considered out of a database consisting of a huge number of images we demonstrate the whole approach on 1 synthetic spatial fields 2 a set of 12 similar sized grayscale images representing cloud top temperatures of a specific region for 12 different time instants and 3 four spatial elevation fields to rank possible pairs of images

a multifractal formalism let x be a metric space and a borel probability measure on x for q t r and e x write formula then hq t and pq t are borel measures hq t is a multifractal generalization of the centered hausdorff measure and pq t is a multifractal generalization of the packing measure the measures hq t and pq t define for a fixed q in the usual way a generalized hausdorff dimension dimq e and a generalized packing dimension dimq e of subsets e of x we study the functions b q dimq supp b q dimq supp and their relation to the so called multifractal spectra functions of formula we prove among other things that f f is bounded from above by the legendre transform of b b and that equality holds for graph directed self similar measures and cookie cutter measures finally we discuss the connection with generalized renyi dimensions

digital image restoration using spatial interaction models this paper is concerned with developing fast nonrecursive algorithms for the minimum mean squared error restoration of degraded images the degradation is assumed to be due to a space invariant periodic nonseparable known point spread function and additive white noise our basic approach is to represent the images by a class of spatial interaction models namely the simultaneous autoregressve models and the conditional markov models defined on toroidal lattices and develop minimum mean squared error restoration algorithms using these models the restoration algorithms are optimal if the parameters characterizing the interaction models are exactly known however in practice the parameters are estimated from the images by using spatial interaction models we develop restoration algorithms that do not require the availability of the original image or its prototype the specific structure of the underlying lattice enables the implementation of the filters using fast fourier transform fft computations several restoration examples are given

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

multi level pixel based texture classification through efficient prototype selection via normalized cut this paper presents a new efficient technique for supervised pixel based classification of textured images a prototype selection algorithm that relies on the normalized cut criterion is utilized for automatically determining a subset of prototypes in order to characterize each texture class at the local level based on the outcome of a multichannel gabor filter bank then a simple minimum distance classifier fed with the previously determined prototypes is used to classify every image pixel into one of the given texture classes multi sized evaluation windows following a top down approach are used during classification in order to improve accuracy near frontiers of regions of different texture results with standard brodatz vistex and meastex compositions and with complex real images are presented and discussed the proposed technique is also compared with alternative texture classifiers

a multifractal analysis of equilibrium measures for conformal expanding maps and moran like geometric constructions in this paper we establish the complete multifractal formalism for equilibrium measures for holder continuous conformal expanding maps andexpanding markov moran like geometric constructions examples include markov maps of an interval beta transformations of an interval rational maps with hyperbolic julia sets and conformal toral endomorphisms we also construct a holder continuous homeomorphism of a compact metric space with an ergodic invariant measure of positive entropy for which the dimension spectrum is not convex and hence the multifractal formalism fails

texture synthesis and pattern recognition for partially ordered markov models abstract the uses of texture in image analysis are widespread ranging from remotely sensed data to medical imaging to military applications image processing tasks that use texture characteristics include classification region segmentation and synthesis of data while there are several approaches available for texture modeling the research presented here is concerned with stochastic texture models stochastic approaches view a texture as the realization of a random field and are most useful when the texture appears noisy or when it lacks smooth geometric features the model introduced in this paper is a subclass of markov random fields mrfs called partially ordered markov models pomms markov random fields are a class of stochastic models that incorporate spatial dependency between data points one major disadvantage of mrfs is that in general an explicit form of the joint probability of the random variables describing the model is not obtainable however a popular subclass of mrfs called markov mesh models mmms allows the explicit description of the joint probability in terms of spatially local conditional probabilities we show how pomms are a generalization of mmms and demonstrate the versatility of pomms to texture synthesis and pattern recognition in imaging specifically we give a fast one pass algorithm for simulating textures using pomms and introduce examples of heterogeneous models that suggest potential applications for object recognition purposes then we address an inverse problem where we present results from a series of statistical experiments designed to estimate parameters of stochastic texture models for both binary and gray value data although the applications in this paper focus on imaging in their most general form pomms can be found in areas such as probabilistic expert systems bayesian hierarchical modeling influence diagrams and random graphs and networks

the hausdorff and dynamical dimensions of self affine sponges a dimension gap result we construct a self affine sponge in mathbb r 3 whose dynamical dimension i e the supremum of the hausdorff dimensions of its invariant measures is strictly less than its hausdorff dimension this resolves a long standing open problem in the dimension theory of dynamical systems namely whether every expanding repeller has an ergodic invariant measure of full hausdorff dimension more generally we compute the hausdorff and dynamical dimensions of a large class of self affine sponges a problem that previous techniques could only solve in two dimensions the hausdorff and dynamical dimensions depend continuously on the iterated function system defining the sponge implying that sponges with a dimension gap represent a nonempty open subset of the parameter space

segmentation given partial grouping constraints we consider data clustering problems where partial grouping is known a priori we formulate such biased grouping problems as a constrained optimization problem where structural properties of the data define the goodness of a grouping and partial grouping cues define the feasibility of a grouping we enforce grouping smoothness and fairness on labeled data points so that sparse partial grouping information can be effectively propagated to the unlabeled data considering the normalized cuts criterion in particular our formulation leads to a constrained eigenvalue problem by generalizing the rayleigh ritz theorem to projected matrices we find the global optimum in the relaxed continuous domain by eigendecomposition from which a near global optimum to the discrete labeling problem can be obtained effectively we apply our method to real image segmentation problems where partial grouping priors can often be derived based on a crude spatial attentional map that binds places with common salient features or focuses on expected object locations we demonstrate not only that it is possible to integrate both image structures and priors in a single grouping process but also that objects can be segregated from the background without specific object knowledge

visually distinct patterns with matching subband statistics a commonly used representation of a visual pattern is a statistical distribution measured from the output of a bank of filters gaussian laplacian gabor etc both marginal and joint distributions of filter responses have been advocated and effectively used for a variety of vision tasks including texture classification texture synthesis object detection and image retrieval this paper examines the ability of these representations to discriminate between an arbitrary pair of visual stimuli examples of patterns are derived that provably possess the same marginal and joint statistical properties yet are visually distinct this is accomplished by showing sufficient conditions for matching the first k moments of the marginal distributions of a pair of images then given a set of filters we show how to match the marginal statistics of the subband images formed through convolution with the filter set next joint statistics are examined and images with similar joint distributions of subband responses are shown finally distinct periodic patterns are derived that possess approximately the same subband statistics for any arbitrary filter set

on the selection of an optimal wavelet basis for texture characterization although most of the theoretical and implementation aspects of wavelet based algorithms in texture characterization are well studied and understood many issues related to the choice of filter bank in texture processing remain unresolved the impact of the wavelet basis has been mentioned in a few papers whereas other more detailed investigations have considered only the choice of the wavelet basis in image coding for example regularity number of vanishing moments and a shift variance degree have been used for the filter evaluation in image coding but the utility of all these metrics in texture analysis has not yet been established therefore the scope of this paper was to investigate whether the properties of decomposition filters play an important role in texture description and which feature is dominant in the selection of an optimal filter bank we performed classification experiments with 23 brodatz textures our investigation shows that the selection of the decomposition filters has a significant influence on the result of texture characterization finally the paper ranks 19 orthogonal and biorthogonal filters and establishes the most relevant criteria for choice of decomposition filters in wavelet based texture characterization algorithms

gibbs random fields cooccurrences and texture modeling gibbs random field grf models and features from cooccurrence matrices are typically considered as separate but useful tools for texture discrimination the authors show an explicit relationship between cooccurrences and a large class of grf s this result comes from a new framework based on a set theoretic concept called the aura set and on measures of this set aura measures this framework is also shown to be useful for relating different texture analysis tools the authors show how the aura set can be constructed with morphological dilation how its measure yields cooccurrences and how it can be applied to characterizing the behavior of the gibbs model for texture in particular they show how the aura measure generalizes to any number of gray levels and neighborhood order some properties previously known for just the binary nearest neighbor grf finally the authors illustrate how these properties can guide one s intuition about the types of grf patterns which are most likely to form

parameter estimation of poisson mixture with automated model selection through byy harmony learning finite mixture is widely used in the fields of information processing and data analysis however its model selection i e the selection of components in the mixture for a given sample data set has been still a rather difficult task recently the bayesian ying yang byy harmony learning has provided a new approach to the gaussian mixture modeling with a favorite feature that model selection can be made automatically during parameter learning in this paper based on the same byy harmony learning framework for finite mixture we propose an adaptive gradient byy learning algorithm for poisson mixture with automated model selection it is demonstrated well by the simulation experiments that this adaptive gradient byy learning algorithm can automatically determine the number of actual poisson components for a sample data set with a good estimation of the parameters in the original or true mixture where the components are separated in a certain degree moreover the adaptive gradient byy learning algorithm is successfully applied to texture classification

on the dimensions of conformal repellers randomness and parameter dependency bowen s formula relates the hausdorff dimension of a conformai repeller to the zero of a pressure function we present an elementary self contained proof to show that bowen s formula holds for c1 conformai repellers we consider time dependent conformai repellers obtained as invariant subsets for sequences of conformally expanding maps within a suitable class we show that bowen s formula generalizes to such a repeller and that if the sequence is picked at random then the hausdorff dimension of the repeller almost surely agrees with its upper and lower box dimensions and is given by a natural generalization of bowen s formula for a random uniformly hyperbolic julia set on the riemann sphere we show that if the family of maps and the probability law depend realanalytically on parameters then so does its almost sure hausdorff dimension 1 random julia sets and their dimensions let u djj be an open connected subset of the riemann sphere avoiding at least three points and equipped with a hyperbolic metric let k c u be a compact subset we denote by at u the space of unramified conformai covering maps vf u with the requirement that the covering domain vf c k denote by df vf m the conformai derivative of see equation 2 4 and by df supf ik df the maximal value of this derivative over the set f 1k let t fn c k u be a sequence of such maps the intersection

multiscale hybrid linear models for lossy image representation in this paper we introduce a simple and efficient representation for natural images we view an image in either the spatial domain or the wavelet domain as a collection of vectors in a high dimensional space we then fit a piece wise linear model i e a union of affine subspaces to the vectors at each downsampling scale we call this a multiscale hybrid linear model for the image the model can be effectively estimated via a new algebraic method known as generalized principal component analysis gpca the hybrid and hierarchical structure of this model allows us to effectively extract and exploit multimodal correlations among the imagery data at different scales it conceptually and computationally remedies limitations of many existing image representation methods that are based on either a fixed linear transformation e g dct wavelets or an adaptive uni modal linear transformation e g pca or a multimodal model that uses only cluster means e g vq we will justify both quantitatively and experimentally why and how such a simple multiscale hybrid model is able to reduce simultaneously the model complexity and computational cost despite a small overhead of the model our careful and extensive experimental results show that this new model gives more compact representations for a wide variety of natural images under a wide range of signal to noise ratios than many existing methods including wavelets we also briefly address how the same hybrid linear modeling paradigm can be extended to be potentially useful for other applications such as image segmentation

markov random field texture models we consider a texture to be a stochastic possibly periodic two dimensional image field a texture model is a mathematical procedure capable of producing and describing a textured image we explore the use of markov random fields as texture models the binomial model where each point in the texture has a binomial distribution with parameter controlled by its neighbors and number of tries equal to the number of gray levels was taken to be the basic model for the analysis a method of generating samples from the binomial model is given followed by a theoretical and practical analysis of the method s convergence examples show how the parameters of the markov random field control the strength and direction of the clustering in the image the power of the binomial model to produce blurry sharp line like and blob like textures is demonstrated natural texture samples were digitized and their parameters were estimated under the markov random field model a hypothesis test was used for an objective assessment of goodness of fit under the markov random field model overall microtextures fit the model well the estimated parameters of the natural textures were used as input to the generation procedure the synthetic microtextures closely resembled their real counterparts while the regular and inhomogeneous textures did not

genetic algorithms for ambiguous labelling problems abstract consistent labelling problems frequently have more than one solution most work in the field has aimed at disambiguating early in the interpretation process using only local evidence this paper starts with a review of the literature on labelling problems and ambiguity based on this review we propose a strategy for simultaneously extracting multiple related solutions to the consistent labelling problem in a preliminary experimental study we show that an appropriately modified genetic algorithm is a robust tool for finding multiple solutions to the consistent labelling problem these solutions are related by common labellings of the most strongly constrained junctions we have proposed three run time measures of algorithm performance the maximum fitness of the genetic algorithm s population its shannon entropy and the total hamming distance between its distinct members the results to date indicate that when the shannon entropy falls below a certain threshold new solutions are unlikely to emerge and that most of the diversity in the population disappears within the first few generations

on the foundations of relaxation labeling processes a large class of problems can be formulated in terms of the assignment of labels to objects frequently processes are needed which reduce ambiguity and noise and select the best label among several possible choices relaxation labeling processes are just such a class of algorithms they are based on the parallel use of local constraints between labels this paper develops a theory to characterize the goal of relaxation labeling the theory is founded on a definition of con sistency in labelings extending the notion of constraint satisfaction in certain restricted circumstances an explicit functional exists that can be maximized to guide the search for consistent labelings this functional is used to derive a new relaxation labeling operator when the restrictions are not satisfied the theory relies on variational cal culus it is shown that the problem of finding consistent labelings is equivalent to solving a variational inequality a procedure nearly identical to the relaxation operator derived under restricted circum stances serves in the more general setting further a local convergence result is established for this operator the standard relaxation labeling formulas are shown to approximate our new operator which leads us to conjecture that successful applications of the standard methods are explainable by the theory developed here observations about con vergence and generalizations to higher order compatibility relations are described

iterative reweighted total generalized variation based poisson noise removal model total generalized variation tgv regularization model is one of the most effective methods for denoising and eliminating staircase effect however the tgv regularization model tends to blur edges as the existence of high order derivative in order to avoid the staircase effect while alleviating the edge blurring an iterative reweighted tgv based poisson noise removal model is presented under the assumption that each pixel of noisy image follows a poisson distribution the weight function incorporated in the tgv regularization term is derived from the expectation maximization em algorithm we design a new iterative weighted primal dual algorithm which is an improvement of the classic iterative reweighted algorithm numerical experimental results show the better performance of our model in removing noise effectively while preserving edges and eliminating staircase effect

nonlinear rayleigh functionals rayleigh functionals are the generalization of rayleigh quotients for matrices to nonlinear eigenvalue problems while analyzing the state of the art we address some problems concerning the existing definitions and give different new ones these new definitions are more general in that they allow complex eigenvalues and operators however in order to obtain local existence and uniqueness we need to restrict to target eigentriplets x y with right and left normalized eigenvectors x y such that y ht x 0 and to sufficiently good eigenvector approximations defining the rayleigh functional as there is a one sided and a two sided rayleigh quotient we introduce the one sided and the two sided rayleigh functional we estimate the quality of the rayleigh functional in terms of the angles between target eigenvectors and their approximations and derive perturbation bounds and first order perturbation results of the same kind and order as known for linear problems we show that stationarity holds in the same way we conclude with an analysis of the so called generalized rayleigh quotient proposed by lancaster for matrix polynomials we study the connection between this generalized rayleigh quotient and the two sided rayleigh functional and compare another variant without left eigenvector approximations with the one sided rayleigh functional

differentiation of srb states abstract let f be a diffeomorphism of a manifold m and f a generalized srb state for f if supp f is a hyperbolic compact set we show that the map is differentiable in a suitable functional setup and we compute the derivative when supp f is an attractor the derivative is given by where x is the vector field this formula can be extended to time dependent situations and also at least formally to nonuniformly hyperbolic situations the above results will find their use in the study of the onsager reciprocity relations and the fluctuation dissipation formula of nonequilibrium statistical mechanics

local convex and concave pattern aiming at the defect of local binary pattern lbp this paper presents a novel and efficient local second order derivative descriptor for image texture feature extraction based on local convex and concave pattern lccp lccp encodes local directional second order derivative feature of texture based on local convex and concave characteristic which can really capture the derivative information of texture than the center symmetric local derivative pattern cs ldp does the proposed multi resolution lccp not only encodes directional derivative information but also constructs spatial relationships in a given local region by bilinear interpolation extensions of multi resolution lccp based on uniform pattern and weighted pattern have also been discussed the performance of the proposed lccp and its extensions are assessed on the biometric recognition and texture classification under different challenges each image is divided into several regions from which histogram features are extracted and concatenate into an enhanced feature vector for match extensive experiments have validated the effectiveness of lccp and its extensions

recognition without correspondence using multidimensionalreceptive field histograms the appearance of an object is composed of local structure this local structure can be described and characterized by a vector of local features measured by local operators such as gaussian derivatives or gabor filters this article presents a technique where appearances of objects are represented by the joint statistics of such local neighborhood operators as such this represents a new class of appearance based techniques for computer vision based on joint statistics the paper develops techniques for the identification of multiple objects at arbitrary positions and orientations in a cluttered scene experiments show that these techniques can identify over 100 objects in the presence of major occlusions most remarkably the techniques have low complexity and therefore run in real time

optimizing gabor filter design for texture edge detection and classification an effective and efficient texture analysis method based on a new criterion for designing gabor filter sets is proposed the commonly used filter sets are usually designed for optimal signal representation we propose here an alternative criterion for designing the filter set we consider a set of filters and its response to pairs of harmonic signals two signals are considered separable if the corresponding two sets of vector responses are disjoint in at least one of the components we propose an algorithm for deriving the set of gabor filters that maximizes the fraction of separable harmonic signal pairs in a given frequency range the resulting filters differ significantly from the traditional ones we test these maximal harmonic discrimination mhd filters in several texture analysis tasks clustering recognition and edge detection it turns out that the proposed filters perform much better than the traditional ones in these tasks they can achieve performance similar to that of state of the art distribution based texton methods while being simpler and more computationally efficient

image representation using separable two dimensional continuous and discrete orthogonal moments this paper addresses bivariate orthogonal polynomials which are a tensor product of two different orthogonal polynomials in one variable these bivariate orthogonal polynomials are used to define several new types of continuous and discrete orthogonal moments some elementary properties of the proposed continuous chebyshev gegenbauer moments cgm gegenbauer legendre moments glm and chebyshev legendre moments clm as well as the discrete tchebichef krawtchouk moments tkm tchebichef hahn moments thm krawtchouk hahn moments khm are presented we also detail the application of the corresponding moments describing the noise free and noisy images specifically the local information of an image can be flexibly emphasized by adjusting parameters in bivariate orthogonal polynomials the global extraction capability is also demonstrated by reconstructing an image using these bivariate polynomials as the kernels for a reversible image transform comparisons with the known moments are performed and the results show that the proposed moments are useful in the field of image analysis furthermore the study investigates invariant pattern recognition using the proposed three moment invariants that are independent of rotation scale and translation and an example is given of using the proposed moment invariants as pattern features for a texture classification application

texture classification using windowed fourier filters we define a distance between textures for texture classification from texture features based on windowed fourier filters the definition of the distance relies on an interpretation of our texture attributes in terms of spectral density when the texture can be considered as a gaussian random field the distance between textures is then defined as a symmetrized kullback distance which is a simple function of the attributes and does not require any normalization an experimental analysis using gabor filters and in particular a comparison to quadratic distances shows the efficiency and robustness of the method

texture segmentation using gaussian markov random fields and neural oscillator networks we propose an image segmentation method based on texture analysis our method is composed of two parts the first part determines a novel set of texture features derived from a gaussian markov random fields gmrf model unlike a gmrf based approach our method does not employ model parameters as features or require the extraction of features for a fixed set of texture types a priori the second part is a 2d array of locally excitatory globally inhibitory oscillator networks legion after being filtered for noise suppression features are used to determine the local couplings in the network when legion runs the oscillators corresponding to the same texture tend to synchronize whereas different texture regions tend to correspond to distinct phases in simulations a large system of differential equations is solved for the first time using a recently proposed method for integrating relaxation oscillator networks we provide results on real texture images to demonstrate the performance of our method

texture classification using refined histogram in this correspondence we propose a novel efficient and effective refined histogram rh for modeling the wavelet subband detail coefficients and present a new image signature based on the rh model for supervised texture classification our rh makes use of a step function with exponentially increasing intervals to model the histogram of detail coefficients and the concatenation of the rh model parameters for all wavelet subbands forms the so called rh signature to justify the usefulness of the rh signature we discuss and investigate some of its statistical properties these properties would clarify the sufficiency of the signature to characterize the wavelet subband information in addition we shall also present an efficient rh signature extraction algorithm based on the coefficient counting technique which helps to speed up the overall classification system performance we apply the rh signature to texture classification using the well known databases experimental results show that our proposed rh signature in conjunction with the use of symmetrized kullback leibler divergence gives a satisfactory classification performance compared with the current state of the art methods

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

integrated active contours for texture segmentation we address the issue of textured image segmentation in the context of the gabor feature space of images gabor filters tuned to a set of orientations scales and frequencies are applied to the images to create the gabor feature space a two dimensional riemannian manifold of local features is extracted via the beltrami framework the metric of this surface provides a good indicator of texture changes and is used therefore in a beltrami based diffusion mechanism and in a geodesic active contours algorithm for texture segmentation the performance of the proposed algorithm is compared with that of the edgeless active contours algorithm applied for texture segmentation moreover an integrated approach extending the geodesic and edgeless active contours approaches to texture segmentation is presented we show that combining boundary and region information yields more robust and accurate texture segmentation results

texture classification by modeling joint distributions of local patterns with gaussian mixtures texture classification generally requires the analysis of patterns in local pixel neighborhoods statistically the underlying processes are comprehensively described by their joint probability density functions jpdfs even for small neighborhoods however stable estimation of jpdfs by joint histograms jhsts is often infeasible since the number of entries in the jhst exceeds by far the number of pixels in a typical texture region moreover evaluation of distance functions between jhsts is often computationally prohibitive practically the number of entries in a jhst is therefore reduced by considering only two pixel patterns leading to 2d jhsts known as cooccurrence matrices or by quantization of the gray levels in local patterns to only two gray levels yielding local binary patterns lbps both approaches result in a loss of information we introduce here a framework for supervised texture classification which reduces or avoids this information loss local texture neighborhoods are first filtered by a filter bank without further quantization the jpdf of the filter responses is then described parametrically by gaussian mixture models gmms we show that the parameters of the gmms can be reliably estimated from small image regions moreover distances between the thus modelled jpdfs of different texture patterns can be computed efficiently in closed form from their model parameters we furthermore extend this texture descriptor to achieve full invariance to rotation we evaluate the framework for different filter banks on the brodatz texture set we first show that combining the lbp difference filters with the gmm based density estimator outperforms the classical lbp approach and its codebook extensions when replacing these rather elementary difference filters by the wavelet frame transform wft the performance of the framework on all 111 brodatz textures exceeds the one obtained more recently by spin image and rift descriptors by lazebnik et al

texture classification using spectral histograms based on a local spatial frequency representation we employ a spectral histogram as a feature statistic for texture classification the spectral histogram consists of marginal distributions of responses of a bank of filters and encodes implicitly the local structure of images through the filtering stage and the global appearance through the histogram stage the distance between two spectral histograms is measured using spl chi sup 2 statistic the spectral histogram with the associated distance measure exhibits several properties that are necessary for texture classification a filter selection algorithm is proposed to maximize classification performance of a given dataset our classification experiments using natural texture images reveal that the spectral histogram representation provides a robust feature statistic for textures and generalizes well comparisons show that our method produces a marked improvement in classification performance finally we point out the relationships between existing texture features and the spectral histogram suggesting that the latter may provide a unified texture feature

segmentation based on fusion of range and intensity images using robust trimmed methods abstract this paper proposes a segmentation algorithm based on fusion of range and intensity images using robust trimmed methods based on the bayesian theory a priori knowledge is represented using the markov random field mrf a maximum a posteriori map estimator is constructed using the edge features extracted from both range and intensity images objects are represented by a number of local planar surfaces in range images and the parametric space for surface representation is constructed with the surface parameters estimated pixel by pixel based on the least trimmed squares lts method whereas in intensity images the trimmed variance is adopted as the feature for edge extraction a final edge map is obtained by the map estimator that is constructed using the likelihood functions based on the edge information obtained from range and intensity images finally an image is segmented using the fused edge map computer simulation results show that our new segmentation algorithm effectively segments test images independent of shadow noise and lighting environment

filtering for texture classification a comparative study in this paper we review most major filtering approaches to texture feature extraction and perform a comparative study filtering approaches included are laws masks 1980 ring wedge filters dyadic gabor filter banks wavelet transforms wavelet packets and wavelet frames quadrature mirror filters discrete cosine transform eigenfilters optimized gabor filters linear predictors and optimized finite impulse response filters the features are computed as the local energy of the filter responses the effect of the filtering is highlighted keeping the local energy function and the classification algorithm identical for most approaches for reference comparisons with two classical nonfiltering approaches co occurrence statistical and autoregressive model based features are given we present a ranking of the tested approaches based on extensive experiments

decay of correlations dedicated to micheline ishay i would like to thank p boyland l chierchia v donnay g de martino c gole j l lebowitz m lyubich m rychlik i g schwarz s vaienti and especially g gallavotti for helpful and enlightening discussions particularly warm thanks go to n chernov for carefully reading and finding a mistake in an early version the present paper benefits from several improvements due to his sharp criticism in addition i am indebted to p collet and most of all m wojtkowski for introducing me to the magical world of cones finally i thank j milnor director of the institute for mathematical sciences at stony brook university where i was visiting during part of this work and the italian c n r gnfm for providing travel funds

an integrated approach for scene understanding based on markov random field model in this paper we propose a markov random field model based approach as a unified and systematic way for modeling encoding and applying scene knowledge to the image understanding problem in our proposed scheme we formulate the image segmentation and interpretation problem as an integrated scheme and solve it through a general optimization algorithm more specifically the image is first segmented into a set of disjoint regions by a conventional region based segmentation technique which operates on image pixels and a region adjacency graph rag is then constructed from the resulting segmented regions based on the spatial adjacencies between regions our scheme then proceeds on the rag by defining the region merging and labeling problem based on the mrf models in the mrf model we specify the a priori knowledge about the optimal segmentation and interpretation in the form of clique functions and those clique functions are incorporated into the energy function to be minimized by a general optimization technique in the proposed scheme the image segmentation and interpretation processes cooperate in the simultaneous optimization process such that the erroneous segmentation and misinterpretation due to incomplete knowledge about each problem domain can be compensately recovered by continuous estimation of the single unified energy function we exploit the proposed scheme to segment and interpret natural outdoor scene images

two sided and alternating jacobi davidson we discuss two variants of a two sided jacobi davidson jd method which have asymptotically cubic convergence for nonnormal matrices and aim to find both right and left eigenvectors these methods can be seen as jacobi davidson analogs of ostrowski s two sided rayleigh quotient iteration rqi some relations between exact and inexact two sided jacobi davidson and exact and inexact two sided rayleigh quotient iteration are given together with convergence rates furthermore we introduce an alternating jacobi davidson process that can be seen as the jacobi davidson analog of parlett s alternating rayleigh quotient iteration the methods are extended to the generalized and polynomial eigenproblem advantages of the methods are illustrated by numerical examples

order parameters for detecting target curves in images when does high level knowledge help many problems in vision can be formulated as bayesian inference it is important to determine the accuracy of these inferences and how they depend on the problem domain in this paper we provide a theoretical framework based on bayesian decision theory which involves evaluating performance based on an ensemble of problem instances we pay special attention to the task of detecting a target in the presence of background clutter this framework is then used to analyze the detectability of curves in images we restrict ourselves to the case where the probability models are ergodic both for the geometry of the curve and for the imaging these restrictions enable us to use techniques from large deviation theory to simplify the analysis we show that the detectability of curves depend on a parameter k which is a function of the probability distributions characterizing the problem at critical values of k the target becomes impossible to detect on average our framework also enables us to determine whether a simpler approximate model is sufficient to detect the target curve and hence clarify how much information is required to perform specific tasks these results generalize our previous work yuille a l and coughlan j m 2000 pattern analysis and machine intelligence pami 22 2 160 173 by placing it in a bayesian decision theory framework by extending the class of probability models which can be analyzed and by analysing the case where approximate models are used for inference

binary partitioning perceptual grouping and restoration with semidefinite programming we introduce a novel optimization method based on semidefinite programming relaxations to the field of computer vision and apply it to the combinatorial problem of minimizing quadratic functionals in binary decision variables subject to linear constraints the approach is tuning parameter free and computes high quality combinatorial solutions using interior point methods convex programming and a randomized hyperplane technique apart from a symmetry condition no assumptions such as metric pairwise interactions are made with respect to the objective criterion as a consequence the approach can be applied to a wide range of problems applications to unsupervised partitioning figure ground discrimination and binary restoration are presented along with extensive ground truth experiments from the viewpoint of relaxation of the underlying combinatorial problem we show the superiority of our approach to relaxations based on spectral graph theory and prove performance bounds

estimation and choice of neighbors in spatial interaction models of images some aspects of statistical inference for a class of spatial interaction models for finite images are presented primarily the simultaneous autoregressive sar models and conditional markov cm models each of these models is characterized by a set of neighbors a set of coefficients and a noise sequence of specified characteristics we are concerned with two problems the estimation of the unknown parameters in both sar and cm models and the choice of an appropriate model from a class of such competing models assuming gaussian distributed variables we discuss maximum likelihood ml estimation methods in general the ml scheme leads to nonlinear optimization problems to avoid excessive computation an iterative scheme is given for sar models which gives approximate ml estimates in the gaussian case and reasonably good estimates in some non gaussian situations as well likewise for cm models an easily computable consistent estimate is given the asymptotic mean squared error mse of this estimate for a four neighbor cm model is shown tn be substantially less than the mse of the popular coding estimate asymptotically consistent decision rules are given for choosing an appropriate sar or cm model the usefulness of the estimation scheme and the decision rule for the choice of neighbors is illustrated by using synthetic patterns synthetic patterns obeying known sar and cm models are generated and the models corresponding to true and several competing neighbor sets are fitted the estimation scheme yields estimates close to the parameters of the true models and the decision rule for the choice of neighbors picks up the true model from the class of competing models

rigid body segmentation and shape description from dense optical flow under weak perspective we present an algorithm for identifying and tracking independently moving rigid objects from optical flow some previous attempts at segmentation via optical flow have focused on finding discontinuities in the flow field while discontinuities do indicate a change in scene depth they do not in general signal a boundary between two separate objects the proposed method uses the fact that each independently moving object has a unique epipolar constraint associated with its motion thus motion discontinuities based on self occlusion can be distinguished from those due to separate objects the use of epipolar geometry allows for the determination of individual motion parameters for each object as well as the recovery of relative depth for each point on the object the algorithm assumes an affine camera where perspective effects are limited to changes in overall scale no camera calibration parameters are required a kalman filter based approach is used for tracking motion parameters with time

relation between optimal nonlinearity and non gaussian noise enhancing a weak signal in a nonlinear system in the study of stochastic resonance it is often mentioned that nonlinearity can enhance a weak signal embedded in noise in order to give a systematic proof of the signal enhancement in nonlinear systems we derive an optimal nonlinearity that maximizes a signal to noise ratio snr the obtained optimal nonlinearity yields the maximum unbiased signal estimation performance which is known in the context of information theory it is found that a linear system is optimal for a gaussian noise but for a non gaussian noise there exist nonlinear systems that can achieve an snr higher than that obtained from linear systems this analysis refers to a system subjected to an additive non gaussian noise with a small signal input

natural image statistics for natural image segmentation we integrate a model for filter response statistics of natural images into a variational framework for image segmentation incorporated in a sound probabilistic distance measure the model drives level sets toward meaningful segmentations of complex textures and natural scenes despite its enhanced descriptive power our approach preserves the efficiency of level set based segmentation since each region comprises two model parameters only analyzing thousands of natural images we select suitable filter banks validate the statistical basis of our model and demonstrate that it outperforms variational segmentation methods using second order statistics

the effect of source amplitude and phase in matched field source localization traditional matched field processing is typically employed for localization of a source with unknown amplitude and phase at transmission the spectral information of the source is estimated via maximum likelihood and is used for localization with the bartlett processor maximum a posteriori estimation of the spectrum of the source is here proposed along with the estimation of source location and noise variance where the joint posterior probability distribution of all parameters is computed with gibbs sampling it is shown that the proposed method has a higher probability of correct localization than the traditional approach

the orthogonal rayleigh quotient iteration orqi method abstract this paper presents a new method for computing all the eigenvectors of a real n n symmetric band matrix t the algorithm computes an orthogonal matrix q q 1 q n and a diagonal matrix diag 1 n such that tq q the basic ideas are rather simple assume that q 1 q k 1 and 1 k 1 have already been computed then q k is obtained via the rayleigh quotient iteration rqi method starting from an arbitrary vector u 0 the rqi method generates a sequence of vectors u l l 1 2 and a sequence of scalars l l 0 1 2 the theory tells us that these two sequences converge almost always to an eigenpair u the appeal of the rqi method comes from the observation that the final rate of convergence is cubic furthermore if the starting point is forced to satisfy q t i u 0 0 for i 1 k 1 as our method does then all the coming vectors u l l 1 2 and their limit point u should stay orthogonal to q 1 q k 1 in practice orthogonality is lost because of rounding errors this difficulty is resolved by successive orthogonalization of u l against q 1 q k 1 the key for effective implementation of the algorithm is to use a selective orthogonalization scheme in which u l is orthogonalized only against close eigenvectors that is u l is orthogonalized against q i only if l i where is a small threshold value e g t 1000 an essential feature of the proposed orthogonalization scheme is the use of reorthogonalization the orqi method is supported by forward and backward error analysis preliminary experiments on medium size problems n 1000 are quite encouraging the average number of iterations per eigenvector was less than 13 while the overall number of flops required for orthogonalizations is often below n 3 2

wavelet modeling using finite mixtures of generalized gaussian distributions application to texture discrimination and retrieval this paper addresses statistical based texture modeling using wavelets we propose a new approach to represent the marginal distribution of the wavelet coefficients using finite mixtures of generalized gaussian mogg distributions the mogg captures a wide range of histogram shapes which provides better description and discrimination of texture than using single probability density functions pdf s as proposed by recent state of the art approaches moreover we propose a model similarity measure based on kullback leibler divergence kld approximation using monte carlo sampling methods through experiments on two popular texture data sets we show that our approach yields significant performance improvements for texture discrimination and retrieval as compared with recent methods of statistical based wavelet modeling