segmentation and classification of range images the recognition of objects in three dimensional space is a desirable capability of a computer vision system range images which directly measure 3 d surface coordinates of a scene are well suited for this task in this paper we report a procedure to detect connected planar convex and concave surfaces of 3 d objects this is accomplished in three stages the first stage segments the range image into surface patches by a square error criterion clustering algorithm using surface points and associated surface normals the second stage classifies these patches as planar convex or concave based on a non parametric statistical test for trend curvature values and eigenvalue analysis in the final stage boundaries between adjacent surface patches are classified as crease or noncrease edges and this information is used to merge compatible patches to produce reasonable faces of the object s this procedure has been successfully applied to a large number of real and synthetic images four of which we present in this paper

strichartz type estimates in mixed besov spaces with application to critical nonlinear schrodinger equations abstract we study the cauchy problem for the nonlinear schrodinger equation with power nonlinearity in the fractional order sobolev space h s r n we consider the case where the nonlinear term is h s critical and the differentiability thereof is less than s we prove the existence of time global solutions of the cauchy problem for small initial data to this end we prove strichartz type estimates for linear inhomogeneous schrodinger equations in mixed besov spaces

global strong solutions for nonlinear schro dinger equations on considere l existence globale unique des solutions fortes pour les equations de schrodinger non lineaire a interaction en loi de puissance i u t u u p 1 u t r x r n u t 0 x u 0 x x r n ou t 0 r

on solutions of the initial value problem for the nonlinear schrodinger equations on considere le probleme aux valeurs initiales pour l equation de schrodinger non lineaire de la forme iu t u f u 2 u t x r r n u 0 x x x r n on etudie la regularite des solutions quand les fonctions initiales ne sont pas regulieres

diffusions for global optimizations we seek a global minimum of u 0 1 n to r the solution to d dt x t nabla u x t will find local minima the solution to dx t nabla u x t dt sqrt 2t dw t where w is standard n dimensional brownian motion and the boundaries are reflecting will concentrate near the global minima of u at least when temperature t is small the equilibrium distribution for x t is gibbs with density pi t x alpha exp u x t this suggests setting t t t downarrow 0 to find the global minima of u we give conditions on u x and t t such that the solution to dx t nabla u x t dt sqrt 2t dw t converges weakly to a distribution concentrated on the global minima of u

l c ℝn decay of classical solutions for nonlinear schrodinger equations on etudie le probleme aux valeurs initiales pour l equation de schrodinger non lineaire iu t u f u 2 u u o x x x r n t r 1 n 11 sous de bonnes hypotheses de regularite sur f et et des conditions de croissance et de signe sur f on montre que les normes maximum des solutions decroissent quand t au meme taux que celles des solutions de l equation de schrodinger libre

texture analysis through a markovian modelling and fuzzyclassification application to urban area extraction fromsatellite images herein we propose a complete procedure to analyze and classify the texture of an image we apply this scheme to solve a specific image processing problem urban areas detection in satellite images first we propose to analyze the texture through the modelling of the luminance field with eight different chain based models we then derived a texture parameter from these models the effect of the lattice anisotropy is corrected by a renormalization group technique coming from statistical physics this parameter which takes into account local conditional variances of the image is compared to classical methods of texture analysis afterwards we develop a modified fuzzy cmeans algorithm that includes an entropy term the advantage of such an algorithm is that the number of classes does not need to be known a priori besides this algorithm provides us with further information i e the probability that a given pixel belongs to a given cluster finally we introduce this information in a markovian model of segmentation some results on spot5 simulated images spot3 images and ers1 radar images are presented these images are provided by the french national space agency cnes and the european space agency esa

multiple resolution segmentation of textured images a multiple resolution algorithm is presented for segmenting images into regions with differing statistical behavior in addition an algorithm is developed for determining the number of statistically distinct regions in an image and estimating the parameters of those regions both algorithms use a causal gaussian autoregressive model to describe the mean variance and spatial correlation of the image textures together the algorithms can be used to perform unsupervised texture segmentation the multiple resolution segmentation algorithm first segments images at coarse resolution and then progresses to finer resolutions until individual pixels are classified this method results in accurate segmentations and requires significantly less computation than some previously known methods the field containing the classification of each pixel in the image is modeled as a markov random field segmentation at each resolution is then performed by maximizing the a posteriori probability of this field subject to the resolution constraint at each resolution the a posteriori probability is maximized by a deterministic greedy algorithm which iteratively chooses the classification of individual pixels or pixel blocks the unsupervised parameter estimation algorithm determines both the number of textures and their parameters by minimizing a global criterion based on the aic information criterion clusters corresponding to the individual textures are formed by alternately estimating the cluster parameters and repartitioning the data into those clusters concurrently the number of distinct textures is estimated by combining clusters until a minimum of the criterion is reached

estimating gaussian markov random field parameters in a nonstationary framework application to remote sensing imaging in this paper we tackle the problem of estimating textural parameters we do not consider the problem of texture synthesis but the problem of extracting textural features for tasks such as image segmentation we take into account nonstationarities occurring in the local mean we focus on gaussian markov random fields for which two estimation methods are proposed and applied in a nonstationary framework the first one consists of extracting conditional probabilities and performing a least square approximation this method is applied to a nonstationary framework dealing with the piecewise constant local mean this framework is adapted to practical tasks when discriminating several textures on a single image the blurring effect affecting edges between two different textures is thus reduced the second proposed method is based on renormalization theory statistics involved only concern variances of gaussian laws leading to cramer rao estimators this method is thus especially robust with respect to the size of sampling moreover nonstationarities of the local mean do not affect results we then demonstrate that the estimated parameters allow texture discrimination for remote sensing data the first proposed estimation method is applied to extract urban areas from spot images since discontinuities of the local mean are taken into account we obtain an accurate urban areas delineation finally we apply the renormalization based on method to segment ice in polar regions from avhrr data

simultaneous motion detection and background reconstruction with a conditional mixed state markov random field in this work we present a new way of simultaneously solving the problems of motion detection and background image reconstruction an accurate estimation of the background is only possible if we locate the moving objects meanwhile a correct motion detection is achieved if we have a good available background model the key of our joint approach is to define a single random process that can take two types of values instead of defining two different processes one symbolic motion detection and one numeric background intensity estimation it thus allows to exploit the spatio temporal interaction between a decision motion detection and an estimation intensity reconstruction problem consequently the meaning of solving both tasks jointly is to obtain a single optimal estimate of such a process the intrinsic interaction and simultaneity between both problems is shown to be better modeled within the so called mixed state statistical framework which is extended here to account for symbolic states and conditional random fields experiments on real sequences and comparisons with existing motion detection methods support our proposal further implications for video sequence inpainting will be also discussed

maximum likelihood reconstruction for emission tomography previous models for emission tomography et do not distinguish the physics of et from that of transmission tomography we give a more accurate general mathematical model for et where an unknown emission density x y z generates and is to be reconstructed from the number of counts n d in each of d detector units d within the model we give an algorithm for determining an estimate of which maximizes the probability p n of observing the actual detector count data n over all possible densities let independent poisson variables n b with unknown means b b 1 b represent the number of unobserved emissions in each of b boxes pixels partitioning an object containing an emitter suppose each emission in box b is detected in detector unit d with probability p b d d 1 d with p b d a one step transition matrix assumed known we observe the total number n n d of emissions in each detector unit d and want to estimate the unknown b b 1 b for each the observed data n has probability or likelihood p n the em algorithm of mathematical statistics starts with an initial estimate 0 and gives the following simple iterative procedure for obtaining a new estimate new from an old estimate old to obtain k k 1 2 new b old b dd 1 n d p b d old b p b d b 1 b

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

unsupervised texture segmentation using gabor filters abstract this paper presents a texture segmentation algorithm inspired by the multi channel filtering theory for visual information processing in the early stages of human visual system the channels are characterized by a bank of gabor filters that nearly uniformly covers the spatial frequency domain and a systematic filter selection scheme is proposed which is based on reconstruction of the input image from the filtered images texture features are obtained by subjecting each selected filtered image to a nonlinear transformation and computing a measure of energy in a window around each pixel a square error clustering algorithm is then used to integrate the feature images and produce a segmentation a simple procedure to incorporate spatial information in the clustering process is proposed a relative index is used to estimate the true number of texture categories

explicit wavefunctions for shape invariant potentials by operator techniques the authors obtain explicit expressions for the wavefunctions of all the known shape invariant potentials by using the operator method

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

bayesian morphology fast unsupervised bayesian image analysis abstract we consider the problems of image segmentation and classification and image restoration when the true image is made up of a small number of unordered colors our emphasis is on both performance and speed speed has become increasingly important for analyzing large images and multispectral images with many bands processing large image databases real time or near realtime image analysis and the online analysis of video bayesian image analysis provides an elegant solution to these problems but it is computationally expensive and the solutions it provides may be sensitive to unrealistic global properties of the models on which it is based the icm algorithm is faster and based on the local properties of the models underlying bayesian image analysis parameter estimation is performed iteratively via pseudolikelihood mathematical morphology is faster again and is widely considered to perform well but lacks a statistical basis method selection analogous to parameter estimation is done in a

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

weighted sobolev spaces and rapidly decreasing solutions of some nonlinear dispersive wave equations where d is a positive integer a is a d dimensional laplacian and the subscripts x t denote partial differentiations the initial value problems for 1 i 1 3 require the asymptotic conditions as x tends to infinity and one must specify spaces of functions satisfying the desired asymptotic conditions the usual choices of spaces are the sobolev spaces z p well posedness in hs of the initial value problems for 1 1 1 3 was established by many authors 3 5 8 12 181 it is of interest to know that eqs l l 1 3 have solutions decreasing faster than hs convergence as x tends to infinity in particular solutions in the schwartz spaces s for each t provided that their initial data are in s this is motivated by tanaka s result for the korteweg de vries equation 131 which establishes the existence of s solutions by the inverse scattering techniques and by the fact that eqs l l 1 3 have travelling solutions in s solitary waves which may play an important role of asymptotic behavior of solutions as t tends to infinity

the infinite hidden markov random field model hidden markov random field hmrf models are widely used for image segmentation as they appear naturally in problems where a spatially constrained clustering scheme is asked for a major limitation of hmrf models concerns the automatic selection of the proper number of their states i e the number of region clusters derived by the image segmentation procedure existing methods including likelihood or entropy based criteria and reversible markov chain monte carlo methods usually tend to yield noisy model size estimates while imposing heavy computational requirements recently dirichlet process dp infinite mixture models have emerged in the cornerstone of nonparametric bayesian statistics as promising candidates for clustering applications where the number of clusters is unknown a priori infinite mixture models based on the original dp or spatially constrained variants of it have been applied in unsupervised image segmentation applications showing promising results under this motivation to resolve the aforementioned issues of hmrf models in this paper we introduce a nonparametric bayesian formulation for the hmrf model the infinite hmrf model formulated on the basis of a joint dirichlet process mixture dpm and markov random field mrf construction we derive an efficient variational bayesian inference algorithm for the proposed model and we experimentally demonstrate its advantages over competing methodologies

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

simple parallel hierarchical and relaxation algorithms for segmenting noncausal markovian random fields the modeling and segmentation of images by mrf s markov random fields is treated these are two dimensional noncausal markovian stochastic processes two conceptually new algorithms are presented for segmenting textured images into regions in each of which the data are modeled as one of c mrf s the algorithms are designed to operate in real time when implemented on new parallel computer architectures that can be built with present technology a doubly stochastic representation is used in image modeling here a gaussian mrf is used to model textures in visible light and infrared images and an autobinary or autoternary etc mrf to model a priori information about the local geometry of textured image regions for image segmentation the true texture class regions are treated either as a priori completely unknown or as a realization of a binary or ternary etc mrf in the former case image segmentation is realized as true maximum likelihood estimation in the latter case it is realized as true maximum a posteriori likelihood segmentation in addition to providing a mathematically correct means for introducing geometric structure the autobinary or ternary etc mrf can be used in a generative mode to generate image geometries and artificial images and such simulations constitute a very powerful tool for studying the effects of these models and the appropriate choice of model parameters the first segmentation algorithm is hierarchical and uses a pyramid like structure in new ways that exploit the mutual dependencies among disjoint pieces of a textured region

tsallis based variational method for finding approximate wave functions abstract we introduce trial functions of a form that maximizes a tsallis information measure and use them in conjunction with the variational approach of cooper dawson and shepard cds that is based upon supersymmetry ideas

maximum likelihood discriminant analysis on the plane using a markovian model of spatial context abstract a method is presented for utilising spatial information in performing discriminant analysis on multivariate data at each point on a regular lattice as for example with landsat the spatial information is modelled as a particularly simple markov random field the discriminant analysis is based on the maximum likelihood method the results are compared with alternatives by monte carlo simulation and seem to be encouraging

on the covariance of two noncentral f random variables and the variance of the estimated liner discriminant function summary the covariance of two noncentral f random variables with a common covariance matrix is obtained from which the variance of their difference follows easily an application of this latter result in discriminant analysis is then given

approximate shape invariant potentials in quantum mechanics we introduce and explore the concept of approximate shape invariance of parametrized potential functions for non relativistic one dimensional quantum systems the supersymmetric partner v2 of an approximate shape invariant potential v1 does not exhibit the same shape as the original potential however by an appropriate choice of the values of the relevant parameters v2 can still be approximated by v1 we also propose a measure for the degree of shape invariance exhibited by a parametrized potential function in order to illustrate these ideas we consider a the lillo mantegna potentials admitting exact analytic power law ground state wavefunctions and b a family of potentials whose ground state eigenfunctions are given by the trial wavefunctions employed by cooper dawson and shepard in the susy based variational method

nonlinear schrodinger equations in the sobolev space of critical order the cauchy problem for the nonlinear schrodinger equations is considered in the sobolev spacehn 2 rn of critical ordern 2 where the embedding intol rn breaks down and any power behavior of interaction works as a subcritical nonlinearity under the interaction of exponential type the existence and uniqueness is proved for globalhn 2 solutions with small cauchy data

analysis of field experiments by least squares smoothing summary assuming a smooth trend plus independent error model for the environmental effects in the yields of a field plot experiment least squares smoothing methods are developed to estimate both the treatment effects and the unknown trend treatment estimates are closely related to those resulting from a generalized least squares analysis in which the covariance structure for the environmental effects has a particular form however the main emphases are on the accuracy of treatment estimates under a fixed smooth trend plus error model and the exploratory power of the basic method to isolate trend effects of unknown form although the detailed development is for the one dimensional case generalizations of the smoothness concept and extensions to two dimensions are also discussed application of the basic method is illustrated on three data sets and the results compared with other analyses

modified strichartz estimates with an application to the critical nonlinear schrodinger equation abstract the cauchy problem for the critical nonlinear schrodinger equation is considered in the sobolev space of fractional order some modified strichartz estimates are constructed and applied to the problem to obtain small global solutions with less regularity assumption for the nonlinear term

numerical study of transport properties in continuum percolation the authors present numerical simulations of ac conductance for a random resistor capacitor network the conductance obeys a probability density function p g varies as g alpha 0 alpha 1 they use a highly efficient propagation algorithm to calculate the effective conductance of a long strip of a lattice at low frequencies they find that for the concentration p of conducting bonds less than the percolation threshold pc the imaginary part of conductance is proportional to frequency im geff approximately omega and the real part of conductance shows an anomalous frequency dependence re geff approximately omega 2 alpha the results of simulations in such a continuum system are in agreement with the predictions of the effective medium and the maxwell garnett approximation they also calculate the non universal dc conductivity exponents in continuum percolation the results are consistent with earlier theoretical predictions and numerical calculations

a search for shape invariant solvable potentials the author investigates a simple method of constructing potentials which is related to the work of bhattacharjie and sudarshan 1962 and for which the schrodinger equation can be solved in terms of known special functions it turns out that this method can be related to supersymmetric quantum mechanics and this relationship can help to decide which special functions satisfying linear homogeneous second order differential equations can be solutions of the schrodinger equation with potentials of the form v x w2 x w x the author illustrates this procedure with the example of orthogonal polynomials and obtains explicit expressions of wavefunctions of a wide class of shape invariant potentials

a unified texture model based on a 2 d wold like decomposition a unified texture model that is applicable to a wide variety of texture types found in natural images is presented this model leads to the derivation of texture analysis and synthesis algorithms designed to estimate the texture parameters and to reconstruct the original texture field from these parameters the texture field is assumed to be a realization of a regular homogeneous random field which is characterized in general by a mixed spectral distribution the texture field is orthogonally decomposed into a purely indeterministic component and a deterministic component the deterministic component is further orthogonally decomposed into a harmonic component and a generalized evanescent component both analytical and experimental results show that the deterministic components should be parameterized separately from the purely indeterministic component the model is very efficient in terms of the number of parameters required to faithfully represent textures reconstructed textures are practically indistinguishable from the originals

on well posedness for nonlinear schrodinger equations with power nonlinearity in fractional order sobolev spaces abstract we study the well posedness for the nonlinear schrodinger equation nls i t u 1 2 u u p 1 u in r 1 n where p 1 c and prove that nls is locally well posed in h s if 2 s 4 and s 2 p 1 4 n 2 s to obtain a good lower bound for p we systematically use strichartz type estimates in fractional order besov spaces for the time variable

shape invariant potentials depending on n parameters transformed by translation shape invariant potentials in the sense of gendenshtein 1983 jetp lett 38 356 which depend on more than two parameters are not known to date cooper et al 1987 phys rev d 36 2458 posed the problem of finding a class of shape invariant potentials which depend on n parameters transformed by translation but it was not solved we analyse the problem using some properties of the riccati equation and find the general solution

algebraic nature of shape invariant and self similar potentials self similar potentials generalize the concept of shape invariance which was originally introduced to explore exactly solvable potentials in quantum mechanics in this paper it is shown that the previously introduced algebraic approach to the latter can be generalized to the former the infinite lie algebras introduced in this context are shown to be closely related to the q algebras the associated coherent states are investigated

a statistical model for positron emission tomography abstract positron emission tomography pet still in its research stages is a technique that promises to open new medical frontiers by enabling physicians to study the metabolic activity of the body in a pictorial manner much as in x ray transmission tomography and other modes of computerized tomography the quality of the reconstructed image in pet is very sensitive to the mathematical algorithm to be used for reconstruction in this article we tailor a mathematical model to the physics of positron emissions and we use the model to describe the basic image reconstruction problem of pet as a standard problem in statistical estimation from incomplete data we describe various estimation procedures such as the maximum likelihood ml method using the em algorithm the method of moments and the least squares method a computer simulation of a pet experiment is then used to demonstrate the ml and the least squares reconstructions the main purposes of this article are to report on what we believe is an

graphical and recursive models for contingency tables summary we discuss two classes of models for contingency tables graphical and recursive models both of which arise from restrictions that are expressible as conditional independencies of variable pairs the first of these is a subclass of hierarchical log linear models each of its models can be represented by an undirected graph in the second class each model corresponds to a particular kind of a directed graph instead and can be characterized by a nontrivial factorization of the joint distribution in terms of response variables we derive decomposable or multiplicative models as the intersecting class this result has useful consequences for exploratory types of analysis as well as for the model interpretation we can give an aid for detecting well fitting decomposable models in a transformation of the observed contingency table and each decomposable model may be interpreted with the help of an undirected or directed graph