digital mechanics an informational process based on reversible universal cellular automata abstract this paper is written from the perspective of a computer scientist and addressed to theoretical physicists as a consequence it may seem somewhat unusual but rest assured everything is really quite simple the point of this paper is that the study of certain phenomena from computer science suggests that there are computer systems cellular automata that may be appropriate as models for microscopic physical phenomena cellular automata are now being used to model varied physical phenomena normally modelled by wave equations fluid dynamics ising models etc we hypothesize that there will be found a single cellular automaton rule that models all of microscopic physics and models it exactly we call this field dm for digital mechanics

maximal parabolic regularity for divergence operators including mixed boundary conditions abstract we show that elliptic second order operators a of divergence type fulfill maximal parabolic regularity on distribution spaces even if the underlying domain is highly non smooth the coefficients of a are discontinuous and a is complemented with mixed boundary conditions applications to quasilinear parabolic equations with non smooth data are presented

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

texture classification using the support vector machines in recent years support vector machines svms have demonstrated excellent performance in a variety of pattern recognition problems in this paper we apply svms for texture classification using translation invariant features generated from the discrete wavelet frame transform to alleviate the problem of selecting the right kernel parameter in the svm we use a fusion scheme based on multiple svms each with a different setting of the kernel parameter compared to the traditional bayes classifier and the learning vector quantization algorithm svms and in particular the fused output from multiple svms produce more accurate classification results on the brodatz texture album

adaptive image segmentation by combining photometric invariant region and edge information an adaptive image segmentation scheme is proposed employing the delaunay triangulation for image splitting the tessellation grid of the delaunay triangulation is adapted to the semantics of the image data by combining region and edge information to achieve robustness against imaging conditions e g shading shadows illumination and highlights photometric invariant similarity measures and edge computation are proposed experimental results on synthetic and real images show that the segmentation method is robust to edge orientation partially weak object boundaries and noisy but homogeneous regions furthermore the method is robust to a large degree to varying imaging conditions

discrete voronoi diagrams and the skiz operator a dynamic algorithm the voronoi diagram vd is a popular tool for partitioning the support of an image an algorithm is presented for constructing vd when the seed set which determines the voronoi regions can be modified by adding and removing seeds the number of pixels and seeds revisited for updating the diagram and the neighbor relationships among seeds is minimized a result on cocircular seeds is presented the adjacency or dual graph of the vd is readily obtained the use of the algorithm for constructing skeletons by influence zones skiz is demonstrated

equivalence between regularity theorems and heat kernel estimates for higher order elliptic operators and systems under divergence form we study the heat kernel of higher order elliptic operators or systems under divergence form on rn ellipticity is in the sense of garding inequality we show that for homogeneous operators gaussian upper bounds and holder regularity of the heat kernel is equivalent to local regularity of weak solutions we also show stability of such bounds under l perturbations of the coefficients or under perturbations with bounded coefficients lower order terms such a criterion allows us to obtain heat kernel bounds for operators or systems with uniformly continuous or vmo coefficients

improved bi dimensional emd and hilbert spectrum for the analysis of textures an improved bi dimensional empirical mode decomposition ibemd is proposed structure of image extremas represents the important feature of images and is useful for the information extraction and analysis the image extrema are classified into the five different sets which are called as the structural extrema the structural extrema are used instead of the classical extrema and the bemd bi dimensional empirical mode decomposition algorithms based on the structural extrema are more accurate through interpolating the up and down envelopes specially the ibemd has the least nmse normalised mean square error and the biggest snr signal to noise ratio for the mode decomposition and greatly improves the robustness of the bemd moreover quaternion hilbert transform based space spatial frequency tool is improved and applied to the texture analysis the experiments of texture analysis show that the new approach is efficient for the application in texture analysis

a bayesian segmentation methodology for parametric image models region based image segmentation methods require some criterion for determining when to merge regions this paper presents a novel approach by introducing a bayesian probability of homogeneity in a general statistical context the authors approach does not require parameter estimation and is therefore particularly beneficial for cases in which estimation based methods are most prone to error when little information is contained in some of the regions and therefore parameter estimates are unreliable the authors apply this formulation to three distinct parametric model families that have been used in past segmentation schemes implicit polynomial surfaces parametric polynomial surfaces and gaussian markov random fields the authors present results on a variety of real range and intensity images

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

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

a bayesian transformation model for wavelet shrinkage wavelet shrinkage estimators in general make the additive normal noise assumption and disregard the nonlinear nature of contamination we develop bayesian wavelet shrinkage estimators based on the power transformations in the linear model to accommodate a broad class of noise models in image processing applications we intend to admit under one roof the widespread additive model the product models common in imaging such as in synthetic aperture radar sar imagery as well as noise that may exist amid these two extremes tactful prior elicitation in this model such as the simultaneous assignment of mixture priors for wavelet coefficients and the transformation imparts flexibility and ample insight into the underlying structure the model permits estimation with unknown noise structure for reasonably unimodal and well behaved on the tails distributions wherein it can outperform common shrinkage estimators extensions with multiple transformations and markov random field priors are also considered for adaptation to local variations in contamination modern markov chain monte carlo mcmc bayesian computation has been used for simulations and several examples are reported

clock and category is quantum gravity algebraic we investigate the possibility that the quantum theory of gravity could be constructed discretely using algebraic methods the algebraic tools are similar to ones used in constructing topological quantum field theories the algebraic structures are related to ideas about the reinterpretation of quantum mechanics in a general relativistic context

noncommutativity and discrete physics this paper is an introduction to discrete physics based on a non commutative calculus of finite differences this gives a context for the feynman dyson derivation of non commutative electromagnetism and for generalizations of this result the paper discusses these ideas and their relations with quantum groups and topological quantum field theory 1998 elsevier science b v all rights reserved

local frequency features for texture classification abstract we propose a texture feature extraction method which allows very small training sets and due to its very local nature is suitable for classification of small textured structures the method is based on detection of local extremas along a set of direction vectors in the spatial image representation the local extremas are interpreted as identifying local frequencies and used to design features corresponding to the basal frequency characteristics amplitude and wavelength the good texture discrimination ability of these features is demonstrated on two images and in a quantitative comparison with features from gabor filtered images and co occurrence matrix features of the three images used in the quantitative comparison the local frequency features performed best on two of them we conclude that the new method is a promising feature extraction method for non stochastic textures and that it should be further explored

a metric approach to vector valued image segmentation we address the issue of low level segmentation of vector valued images focusing on the case of color natural images the proposed approach relies on the formulation of the problem in the metric framework as a voronoi tessellation of the image domain in this context a segmentation is determined by a distance transform and a set of sites our method consists in dividing the segmentation task in two successive sub tasks pre segmentation and hierarchical representation we design specific distances for both sub problems by considering low level image attributes and particularly color and lightness information then the interpretation of the metric formalism in terms of boundaries allows the definition of a soft contour map that has the property of producing a set of closed curves for any threshold finally we evaluate the quality of our results with respect to ground truth segmentation data

image segmentation using active contours driven by the bhattacharyya gradient flow this paper addresses the problem of image segmentation by means of active contours whose evolution is driven by the gradient flow derived from an energy functional that is based on the bhattacharyya distance in particular given the values of a photometric variable or of a set thereof which is to be used for classifying the image pixels the active contours are designed to converge to the shape that results in maximal discrepancy between the empirical distributions of the photometric variable inside and outside of the contours the above discrepancy is measured by means of the bhattacharyya distance that proves to be an extremely useful tool for solving the problem at hand the proposed methodology can be viewed as a generalization of the segmentation methods in which active contours maximize the difference between a finite number of empirical moments of the ldquoinsiderdquo and ldquooutsiderdquo distributions furthermore it is shown that the proposed methodology is very versatile and flexible in the sense that it allows one to easily accommodate a diversity of the image features based on which the segmentation should be performed as an additional contribution a method for automatically adjusting the smoothness properties of the empirical distributions is proposed such a procedure is crucial in situations when the number of data samples supporting a certain segmentation class varies considerably in the course of the evolution of the active contour in this case the smoothness properties of the empirical distributions have to be properly adjusted to avoid either over or underestimation artifacts finally a number of relevant segmentation results are demonstrated and some further research directions are discussed

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

hardy and bmo spaces associated to divergence form elliptic operators consider a second order divergence form elliptic operator l with complex bounded measurable coefficients in general operators based on l such as the riesz transform or square function may lie beyond the scope of the calderon zygmund theory they need not be bounded in the classical hardy bmo and even some l p spaces in this work we develop a theory of hardy and bmo spaces associated to l which includes in particular a molecular decomposition maximal and square function characterizations duality of hardy and bmo spaces and a john nirenberg inequality

location and density based hierarchical clustering using similarity analysis this paper presents a new approach to hierarchical clustering of point patterns two algorithms for hierarchical location and density based clustering are developed each method groups points such that maximum intracluster similarity and intercluster dissimilarity are achieved for point locations or point separations performance of the clustering methods is compared with four other methods the approach is applied to a two step texture analysis where points represent centroid and average color of the regions in image segmentation

text region extraction in a document image based on the delaunay tessellation in this paper delaunay triangulation is applied for the extraction of text areas in a document image by representing the location of connected components in a document image with their centroids the page structure is described as a set of points in two dimensional space when imposing delaunay triangulation on these points the text regions in the delaunay triangulation will have distinguishing triangular features from image and drawing regions for analysis the delaunay triangles are divided into four classes the study reveals that specific triangles in text areas can be clustered together and identified as text body using this method text regions in a document image containing fragments can also be recognized accurately experiments show the method is also very efficient

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

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

explicit estimates on the fundamental solution of higher order parabolic equations with measurable coefficients for some positive constants ci and all t 0 and x y 0 such estimates for uniformly elliptic operators have been proved under a variety of local regularity assumptions 14 17 and more recently for operators with measurable coefficients provided 2m n 8 this has been shown to be true in the limit case 2m n 3 11 while there are examples that show that 1 is not in general true when 2m n and h has measurable coefficients 10 in 6 estimates are obtained for singular or degenerate operators with measurable coefficients with the euclidean distance being replaced by one that reflects the behavior of the coefficients near the singularities we refer to 9 for a detailed account of much of the recent progress on the spectral theory of higher order elliptic operators the problem of sharpening such bounds was addressed recently the sharpness of estimates is checked by comparison against short time asymptotics of k t x y these were proved by tintarev 19 who showed following work of evgrafov and postnikov 12 that if 0 r if the coefficients a are smooth and if the symbol a x satisfies the strong doi 10 1006 jdeq 2000 3940 available online at http www idealibrary com on