stacs new active contour scheme for cardiac mr image segmentation the paper presents a novel stochastic active contour scheme stacs for automatic image segmentation designed to overcome some of the unique challenges in cardiac mr images such as problems with low contrast papillary muscles and turbulent blood flow stacs minimizes an energy functional that combines stochastic region based and edge based information with shape priors of the heart and local properties of the contour the minimization algorithm solves by the level set method the euler lagrange equation that describes the contour evolution stacs includes an annealing schedule that balances dynamically the weight of the different terms in the energy functional three particularly attractive features of stacs are 1 ability to segment images with low texture contrast by modeling stochastically the image textures 2 robustness to initial contour and noise because of the utilization of both edge and region based information 3 ability to segment the heart from the chest wall and the undesired papillary muscles due to inclusion of heart shape priors application of stacs to a set of 48 real cardiac mr images shows that it can successfully segment the heart from its surroundings such as the chest wall and the heart structures the left and right ventricles and the epicardium we compare stacs automatically generated contours with manually traced contours or the gold standard using both area and edge similarity measures this assessment demonstrates very good and consistent segmentation performance of stacs

statistical mechanics and phase transitions in clustering a new approach to clustering based on statistical physics is presented the problem is formulated as fuzzy clustering and the association probability distribution is obtained by maximizing the entropy at a given average variance the corresponding lagrange multiplier is related to the temperature and motivates a deterministic annealing process where the free energy is minimized at each temperature critical temperatures are derived for phase transitions when existing clusters split it is a hierarchical clustering estimating the most probable cluster parameters at various average variances

active contours without edges we propose a new model for active contours to detect objects in a given image based on techniques of curve evolution mumford shah 1989 functional for segmentation and level sets our model can detect objects whose boundaries are not necessarily defined by the gradient we minimize an energy which can be seen as a particular case of the minimal partition problem in the level set formulation the problem becomes a mean curvature flow like evolving the active contour which will stop on the desired boundary however the stopping term does not depend on the gradient of the image as in the classical active contour models but is instead related to a particular segmentation of the image we give a numerical algorithm using finite differences finally we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable also the initial curve can be anywhere in the image and interior contours are automatically detected

a review of statistical approaches to level set segmentation integrating color texture motion and shape since their introduction as a means of front propagation and their first application to edge based segmentation in the early 90 s level set methods have become increasingly popular as a general framework for image segmentation in this paper we present a survey of a specific class of region based level set segmentation methods and clarify how they can all be derived from a common statistical framework region based segmentation schemes aim at partitioning the image domain by progressively fitting statistical models to the intensity color texture or motion in each of a set of regions in contrast to edge based schemes such as the classical snakes region based methods tend to be less sensitive to noise for typical images the respective cost functionals tend to have less local minima which makes them particularly well suited for local optimization methods such as the level set method we detail a general statistical formulation for level set segmentation subsequently we clarify how the integration of various low level criteria leads to a set of cost functionals we point out relations between the different segmentation schemes in experimental results we demonstrate how the level set function is driven to partition the image plane into domains of coherent color texture dynamic texture or motion moreover the bayesian formulation allows to introduce prior shape knowledge into the level set method we briefly review a number of advances in this domain

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

noisy texture classification a higher order statistics approach abstract in this paper a novel texture classification scheme using higher order statistics hos functions as discriminating features is proposed it is well known that such statistical parameters are insensitive to additive gaussian noise in particular third order statistical parameters i e third order cumulants and bispectrum are insensitive to any symmetrically distributed noise and also exhibit the capability of better characterizing non gaussian signals by exploiting these hos properties it is possible to devise a robust method for classifying textures affected by noise with different distributions and even with very low signal to noise ratios

object and texture classification using higher order statistics the problem of the detection and classification of deterministic objects and random textures in a noisy scene is discussed an energy detector is developed in the cumulant domain by exploiting the noise insensitivity of higher order statistics an efficient implementation of this detector is described using matched filtering its performance is analyzed using asymptotic distributions in a binary hypothesis testing framework the object and texture discriminant functions are minimum distance classifiers in the cumulant domain and can be efficiently implemented using a bank of matched filters they are immune to additive gaussian noise and insensitive to object shifts important extensions which can handle object rotation and scaling are also discussed an alternative texture classifier is derived from a ml viewpoint and is statistically efficient at the expense of complexity the application of these algorithms to the texture modeling problem is indicated and consistent parameter estimates are obtained

k means type algorithms a generalized convergence theorem and characterization of local optimality the k means algorithm is a commonly used technique in cluster analysis in this paper several questions about the algorithm are addressed the clustering problem is first cast as a nonconvex mathematical program then a rigorous proof of the finite convergence of the k means type algorithm is given for any metric it is shown that under certain conditions the algorithm may fail to converge to a local minimum and that it converges under differentiability conditions to a kuhn tucker point finally a method for obtaining a local minimum solution is given

nonparametric ridge estimation we study the problem of estimating the ridges of a density function ridge estimation is an extension of mode finding and is useful for understanding the structure of a density it can also be used to find hidden structure in point cloud data we show that under mild regularity conditions the ridges of the kernel density estimator consistently estimate the ridges of the true density when the data are noisy measurements of a manifold we show that the ridges are close and topologically similar to the hidden manifold to find the estimated ridges in practice we adapt the modified mean shift algorithm proposed by ozertem and erdogmus j mach learn res 12 2011 1249 1286 some numerical experiments verify that the algorithm is accurate

constrained clustering as an optimization method a deterministic annealing approach to clustering is derived on the basis of the principle of maximum entropy this approach is independent of the initial state and produces natural hierarchical clustering solutions by going through a sequence of phase transitions it is modified for a larger class of optimization problems by adding constraints to the free energy the concept of constrained clustering is explained and three examples are are given in which it is used to introduce deterministic annealing the previous clustering method is improved by adding cluster mass variables and a total mass constraint the traveling salesman problem is reformulated as constrained clustering yielding the elastic net en approach to the problem more insight is gained by identifying a second lagrange multiplier that is related to the tour length and can also be used to control the annealing process the open path constraint formulation is shown to relate to dimensionality reduction by self organization in unsupervised learning a similar annealing procedure is applicable in this case as well

relative entropy and identification of gibbs measures in dynamical systems in this work we explore the idea of using the relative entropy of ergodic measures for the identification of gibbs measures in dynamical systems the question we face is how to estimate the thermodynamic potential together with a grammar from a sample produced by the corresponding gibbs state

generalised nonlocal image smoothing we propose a discrete variational approach for image smoothing consisting of nonlocal data and smoothness constraints that penalise general dissimilarity measures defined on image patches one of such dissimilarity measures is the weighted l 2 distance between patches in such a case we derive an iterative neighbourhood filter that induces a new similarity measure in the photometric domain it can be regarded as an extended patch similarity measure that evaluates not only the patch similarity of two chosen pixels but also the similarity of their corresponding neighbours this leads to a more robust smoothing process since the pixels selected for averaging are more coherent with the local image structure by slightly modifying the way the similarities are computed we obtain two related filters the nl means filter of buades et al siam multiscale model simul 4 2 490 530 2005b and the nds filter of mrazek et al geometric properties for incomplete data computational imaging and vision vol 31 pp 335 352 springer dordrecht 2006 in fact the proposed approach can be considered as a generalisation of the latter filter to the space of patches we also provide novel insights into relations of the nds filter with diffusion regularisation methods as well as with some recently proposed graph regularisation techniques we evaluate our method for the task of denoising greyscale and colour images degraded with gaussian and salt and pepper noise demonstrating that it compares very well to other more sophisticated approaches

efficient visual tracking using particle filter with incremental likelihood calculation in this paper we propose a particle filter that determines the weight of each particle employing the incremental likelihood calculation since there is usually a large overlap region between the two particles that are sequentially generated determining the weight of the particle has only a small time cost therefore the real time performance of the proposed tracker can be dramatically improved extensive experimental results for single object and multiple object tracking scenarios are presented to demonstrate the efficiency of the proposed approach finally an interesting color based active vision system is developed for a free floating space robot testbed to facilitate teleoperation

localizing region based active contours in this paper we propose a natural framework that allows any region based segmentation energy to be re formulated in a local way we consider local rather than global image statistics and evolve a contour based on local information localized contours are capable of segmenting objects with heterogeneous feature profiles that would be difficult to capture correctly using a standard global method the presented technique is versatile enough to be used with any global region based active contour energy and instill in it the benefits of localization we describe this framework and demonstrate the localization of three well known energies in order to illustrate how our framework can be applied to any energy we then compare each localized energy to its global counterpart to show the improvements that can be achieved next an in depth study of the behaviors of these energies in response to the degree of localization is given finally we show results on challenging images to illustrate the robust and accurate segmentations that are possible with this new class of active contour models

multi reference shape priors for active contours in this paper we present a new way of constraining the evolution of an active contour with respect to a set of fixed reference shapes this approach is based on a description of shapes by the legendre moments computed from their characteristic function this provides a region based representation that can handle arbitrary shape topologies moreover exploiting the properties of moments it is possible to include intrinsic affine invariance in the descriptor which solves the issue of shape alignment without increasing the number of d o f of the initial problem and allows introducing geometric shape variabilities our new shape prior is based on a distance in terms of descriptors between the evolving curve and the reference shapes minimizing the corresponding shape energy leads to a geometric flow that does not rely on any particular representation of the contour and can be implemented with any contour evolution algorithm we introduce our prior into a two class segmentation functional showing its benefits on segmentation results in presence of severe occlusions and clutter examples illustrate the ability of the model to deal with large affine deformation and to take into account a set of reference shapes of different topologies

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

on factor maps that send markov measures to gibbs measures let x and y be mixing shifts of finite type let be a factor map from x to y that is fiber mixing i e given x bar x in x with pi x pi bar x y in y there is z 1 y that is left asymptotic to x and right asymptotic to bar x we show that any markov measure on x projects to a gibbs measure on y under for a holder continuous potential in other words all hidden markov chains i e sofic measures realized by are gibbs measures in 2003 chazottes and ugalde gave a sufficient condition for a sofic measure to be a gibbs measure our sufficient condition generalizes their condition and is invariant under conjugacy and time reversal we provide examples demonstrating our result

local histogram based segmentation using the wasserstein distance we propose and analyze a nonparametric region based active contour model for segmenting cluttered scenes the proposed model is unsupervised and assumes pixel intensity is independently identically distributed our proposed energy functional consists of a geometric regularization term that penalizes the length of the partition boundaries and a region based image term that uses histograms of pixel intensity to distinguish different regions more specifically the region data encourages segmentation so that local histograms within each region are approximately homogeneous an advantage of using local histograms in the data term is that histogram differentiation is not required to solve the energy minimization problem we use wasserstein distance with exponent 1 to determine the dissimilarity between two histograms the wasserstein distance is a metric and is able to faithfully measure the distance between two histograms compared to many pointwise distances moreover it is insensitive to oscillations and therefore our model is robust to noise a fast global minimization method based on chan et al in siam j appl math 66 5 1632 1648 2006 bresson et al in j math imaging vis 28 2 151 167 2007 is employed to solve the proposed model the advantages of using this method are two fold first the computational time is less than that of the method by gradient descent of the associated euler lagrange equation chan et al in proc of ssvm pp 697 708 2007 second it is able to find a global minimizer finally we propose a variant of our model that is able to properly segment a cluttered scene with local illumination changes

measures for lattice systems abstract i review issues related with the presence or absence of gibbsianness in measures describing random fields in lattices after a brief exposition of the definition and properties of gibbs measures i discuss the phenomenon of non gibbsianness its examples characterization the proposed classification schemes and notions of generalized gibbsianness the review closes with comments on directions for further work

color image segmentation using adaptive mean shift and statistical model based methods in this paper we propose an unsupervised segmentation algorithm for color images based on gaussian mixture models gmms the number of mixture components is determined automatically by adaptive mean shift in which local clusters are estimated by repeatedly searching for higher density points in feature vector space for the estimation of parameters of gmms the mean field annealing expectation maximization em is employed the mean field annealing em provides a global optimal solution to overcome the local maxima problem in a mixture model by combining the adaptive mean shift and the mean field annealing em natural color images are segmented automatically without over segmentation or isolated regions the experiments show that the proposed algorithm can produce satisfactory segmentation without any a priori information

clustering via geometric median shift over riemannian manifolds the mean shift algorithms have been successfully applied to many areas such as data clustering feature analysis and image segmentation however they still have two limitations one is that they are ineffective in clustering data with low dimensional manifolds because of the use of the euclidean distance for calculating distances the other is that they sometimes produce poor results for data clustering and image segmentation this is because a mean may not be a point in a data set in order to overcome the two limitations we propose a novel approach for the median shift over riemannian manifolds that uses the geometric median and geodesic distances unlike the mean the geometric median of a data set is one of points in the set compared to the euclidean distance the geodesic distances can better describe data points distributed on riemannian manifolds based on these two facts we first present a novel density function that characterizes points on a manifold with the geodesic distance the shift of the geometric median over the riemannian manifold is derived from maximizing this density function after this we present an algorithm for geometric median shift over riemannian manifolds together with theoretical proofs of its correctness extensive experiments have demonstrated that our method outperforms the state of the art algorithms in data clustering image segmentation and noise filtering on both synthetic data sets and real image databases

stochastic global optimization methods part 1 clustering methods in this stochastic approach to global optimization clustering techniques are applied to identify local minima of a real valued objective function that are potentially global three different methods of this type are described their accuracy and efficiency are analyzed in detail

quantization based clustering algorithm in this paper a quantization based clustering algorithm qbca is proposed to cluster a large number of data points efficiently unlike previous clustering algorithms qbca places more emphasis on the computation time of the algorithm specifically qbca first assigns the data points to a set of histogram bins by a quantization function then it determines the initial centers of the clusters according to this point distribution finally qbca performs clustering at the histogram bin level rather than the data point level we also propose two approaches to improve the performance of qbca further i a shrinking process is performed on the histogram bins to reduce the number of distance computations and ii a hierarchical structure is constructed to perform efficient indexing on the histogram bins finally we analyze the performance of qbca theoretically and experimentally and show that the approach 1 can be easily implemented 2 identifies the clusters effectively and 3 outperforms most of the current state of the art clustering approaches in terms of efficiency

dream 2 s deformable regions driven by an eulerian accurate minimization method for image and video segmentation this paper deals with image and video segmentation using active contours we propose a general form for the energy functional related to region based active contours we compute the associated evolution equation using shape derivation tools and accounting for the evolving region based terms then we apply this general framework to compute the evolution equation from functionals that include various statistical measures of homogeneity for the region to be segmented experimental results show that the determinant of the covariance matrix appears to be a very relevant tool for segmentation of homogeneous color regions as an example it has been successfully applied to face segmentation in real video sequences

rational probability measures abstract the theory of finite automata and coding has been linked to probability theory since its foundation by the work of shannon and its further enrichment especially by schutzenberger in a parallel development symbolic dynamical systems whose behaviour is governed by a finite automaton have been studied under several aspects especially by hell robertson binkowska and kaminski 4 13 17 weiss has given to them the name of sofic systems and he has shown that they constitute a generalization of topological markov chains 20 since then adler and his associates have shown how theoretical development in this field could lead to a remarkable treatment of engineering problems in coding 1 in this paper we continue the exploration of this borderline area and present some new results probability measures on words are studied in their relation with coding and finite automata we particularly insist on the notion of a rational probability measure which although perhaps not quite new has not yet received all the attention it deserves in a first section we fix the notation and prove some preliminary results in particular the basic properties of rational probability measures are established the second section deals with probability measures for which the sequences obtained after some coding are mutually independent it contains two main results the first one gives conditions under which the restriction of a probability measure to a given free submonoid is a bernoulli measure it extends a result due to schutzenberger the second result is due to langlois and is published here for the first time in the two remaining sections we consider the problem of transferring a probability measure from one free monoid into another one several new results are proved which complement the ones previously obtained in collaboration with blanchard 5 6

an edge based algorithm for discontinuity adaptive color image smoothing abstract we present a new scheme to increase the performance of edge preserving image smoothing algorithm from the parameter tuning of a markov random field mrf function this method is based on an automatic control of the image smoothing strength in the mrf function in which the parameter control of the function depends on edge magnitude resulted from discontinuities of image intensity without any binary decision for the edge magnitude direct use of full edge magnitude could improve the performance of discontinuity preserving image smoothing technique

projections of gibbs states for holder potentials we give a short proof that the projection of a gibbs state for a holder continuous potential on a mixing shift of finite type under a 1 block fiber wise mixing factor map has a holder continuous g function this improves a number of previous results the key insight in the proof is to realize the measure of a cylinder set in terms of positive operators and use cone techniques

infinite to one codes and markov measures we study the structure of infinite to one continuous codes between subshifts of finite type and the behaviour of markov measures under such codes we show that if an infinite to one code lifts one markov measure to a markov measure then it lifts each markov measure to uncountably many markov measures and the fibre over each markov measure is isomorphic to any other fibre calling such a code markovian we characterize markovian codes through pressure we show that a simple condition on periodic points necessary for the existence of a code between two subshifts of finite type is sufficient to construct a markovian code several classes of markovian codes are studied in the process of proving illustrating and providing contrast to the main results a number of examples and counterexamples are given in particular we give a continuous code between two bernoulli shifts such that the defining vector of the image is not a clustering of the defining vector of the domain

image segmentation using active contours calculus of variations or shape gradients we consider the problem of segmenting an image through the minimization of an energy criterion involving region and boundary functionals we show that one can go from one class to the otherby solving poisson s orhelmholtz s equation with well chosen boundar y conditions using this equivalence we study the case of a large class of region functionals by standard methods of the calculus of variations and derive the corresponding euler lagrange equations we revisit this problem using the notion of a shape derivative and show that the same equations can be elegantly derived without going through the unnatural step of converting the region integrals into boundary integrals we also define a larger class of region functionals based on the estimation and comparison to a prototype of the probability density distribution of image features and show how the shape derivative tool allows us to easily compute the corresponding gateaux derivatives and euler lagrange equations finally we apply this new functional to the problem of regions segmentation in sequences of color images we briefly describe our numerical scheme and show some experimental results

transformations of gibbs measures we study local transformations of gibbs measures we establish sufficient conditions for the quasilocality of the images and obtain results on the existence and continuity properties of their relative energies general results are illustrated by simple examples

active contours driven by the salient edge energy model in this brief we present a new indicator i e salient edge energy for guiding a given contour robustly and precisely toward the object boundary specifically we define the salient edge energy by exploiting the higher order statistics on the diffusion space and incorporate it into a variational level set formulation with the local region based segmentation energy for solving the problem of curve evolution in contrast to most previous methods the proposed salient edge energy allows the curve to find only significant local minima relevant to the object boundary even in the noisy and cluttered background moreover the segmentation performance derived from our new energy is less sensitive to the size of local windows compared with other recently developed methods owing to the ability of our energy function to suppress diverse clutters the proposed method has been tested on various images and experimental results show that the salient edge energy effectively drives the active contour both qualitatively and quantitatively compared to various state of the art methods

analyticity of entropy rate of hidden markov chains we prove that under mild positivity assumptions the entropy rate of a hidden markov chain varies analytically as a function of the underlying markov chain parameters a general principle to determine the domain of analyticity is stated an example is given to estimate the radius of convergence for the entropy rate we then show that the positivity assumptions can be relaxed and examples are given for the relaxed conditions we study a special class of hidden markov chains in more detail binary hidden markov chains with an unambiguous symbol and we give necessary and sufficient conditions for analyticity of the entropy rate for this case finally we show that under the positivity assumptions the hidden markov chain itself varies analytically in a strong sense as a function of the underlying markov chain parameters

projection of markov measures may be gibbsian we study the induced measure obtained from a 1 step markov measure supported by a topological markov chain after the mapping of the original alphabet onto another one we give sufficient conditions for the induced measure to be a gibbs measure in the sense of bowen when the factor system is again a topological markov chain this amounts to constructing when it does exist the induced potential and proving its holder continuity this is achieved through a matrix method we provide examples and counterexamples to illustrate our results

efficient algorithm for level set method preserving distance function the level set method is a popular technique for tracking moving interfaces in several disciplines including computer vision and fluid dynamics however despite its high flexibility the original level set method is limited by two important numerical issues first the level set method does not implicitly preserve the level set function as a distance function which is necessary to estimate accurately geometric features s a the curvature or the contour normal second the level set algorithm is slow because the time step is limited by the standard courant friedrichs lewy cfl condition which is also essential to the numerical stability of the iterative scheme recent advances with graph cut methods and continuous convex relaxation methods provide powerful alternatives to the level set method for image processing problems because they are fast accurate and guaranteed to find the global minimizer independently to the initialization these recent techniques use binary functions to represent the contour rather than distance functions which are usually considered for the level set method however the binary function cannot provide the distance information which can be essential for some applications s a the surface reconstruction problem from scattered points and the cortex segmentation problem in medical imaging in this paper we propose a fast algorithm to preserve distance functions in level set methods our algorithm is inspired by recent efficient l1 optimization techniques which will provide an efficient and easy to implement algorithm it is interesting to note that our algorithm is not limited by the cfl condition and it naturally preserves the level set function as a distance function during the evolution which avoids the classical re distancing problem in level set methods we apply the proposed algorithm to carry out image segmentation where our methods prove to be 5 6 times faster than standard distance preserving level set techniques we also present two applications where preserving a distance function is essential nonetheless our method stays generic and can be applied to any level set methods that require the distance information

prototype selection for dissimilarity based classifiers a conventional way to discriminate between objects represented by dissimilarities is the nearest neighbor method a more efficient and sometimes a more accurate solution is offered by other dissimilarity based classifiers they construct a decision rule based on the entire training set but they need just a small set of prototypes the so called representation set as a reference for classifying new objects such alternative approaches may be especially advantageous for non euclidean or even non metric dissimilarities the choice of a proper representation set for dissimilarity based classifiers is not yet fully investigated it appears that a random selection may work well in this paper a number of experiments has been conducted on various metric and non metric dissimilarity representations and prototype selection methods several procedures like traditional feature selection methods here effectively searching for prototypes mode seeking and linear programming are compared to the random selection in general we find out that systematic approaches lead to better results than the random selection especially for a small number of prototypes although there is no single winner as it depends on data characteristics the k centres works well in general for two class problems an important observation is that our dissimilarity based discrimination functions relying on significantly reduced prototype sets 3 10 of the training objects offer a similar or much better classification accuracy than the best k nn rule on the entire training set this may be reached for multi class data as well however such problems are more difficult

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

the fuzzy potts model we consider the ferromagnetic q state potts model on the d dimensional lattice zd d or 2 suppose that the potts variables rho x x in zd are distributed in one of the q low temperature phases suppose that n not 1 q divides q partitioning the single site state space into n equal parts k1 kn we obtain a new random field sigma sigma x x in zd by defining fuzzy variables sigma x alpha if rho x in kalpha alpha 1 n we investigate the state induced on these fuzzy variables first we look at the conditional distribution of rho x given all values sigma y y in zd we find that below the coexistence point all versions of this conditional distribution are non quasilocal on a set of configurations which carries positive measure then we look at the conditional distribution of sigma x given all values sigma y y not x if the system is not at the coexistence point of a first order phase transition there exists a version of this conditional distribution that is almost surely quasilocal

the mean shift algorithm and its relation to kernel regression we investigate the connection between the asymptotic bias of the well known nadaraya watson kernel regression and the mean shift ms vector with the gaussian kernel we first show that the asymptotic bias for the univariate nadaraya watson kernel regression can be estimated using the ms scalar then we investigate the general d dimensional case d 1 and derive a formula for the asymptotic bias as a function of the ms vector we show that when the regression function is a linear function of its entries then the asymptotic bias can be represented as a linear function of the ms vector the ms algorithm for the univariate and the linear cases can be used to find points where the nadaraya watson kernel regression gives an unbiased estimate furthermore this connection suggests that exploiting the theoretical properties of the asymptotic bias of the nadaraya watson kernel regression may be helpful to show the convergence of the ms algorithm through the simulations we show that how the given theoretical results can be used to estimate the bias of the estimated clean signal by just observing the noisy signal having access to the bias of the estimator enables us to evaluate the accuracy of the estimated clean data which later will be used to design a quantizer

regularized multitask learning for multidimensional log density gradient estimation log density gradient estimation is a fundamental statistical problem and possesses various practical applications such as clustering and measuring nongaussianity a naive two step approach of first estimating the density and then taking its log gradient is unreliable because an accurate density estimate does not necessarily lead to an accurate log density gradient estimate to cope with this problem a method to directly estimate the log density gradient without density estimation has been explored and demonstrated to work much better than the two step method the objective of this letter is to improve the performance of this direct method in multidimensional cases our idea is to regard the problem of log density gradient estimation in each dimension as a task and apply regularized multitask learning to the direct log density gradient estimator we experimentally demonstrate the usefulness of the proposed multitask method in log density gradient estimation and mode seeking clustering

regularity properties and pathologies of position space renormalization group transformations scope and limitations of gibbsian theory we reconsider the conceptual foundations of the renormalization group rg formalism and prove some rigorous theorems on the regularity properties and possible pathologies of the rg map our main results apply to local in position space rg maps acting on systems of bounded spins compact single spin space regarding regularity we show that the rg map defined on a suitable space of interactions formal hamiltonians is always single valued and lipschitz continuous on its domain of definition this rules out a recently proposed scenario for the rg description of first order phase transitions on the pathological side we make rigorous some arguments of griffiths pearce and israel and prove in several cases that the renormalized measure is not a gibbs measure for any reasonable interaction this means that the rg map is ill defined and that the conventional rg description of first order phase transitions is not universally valid for decimation or kadanoff transformations applied to the ising model in dimension d 3 these pathologies occur in a full neighborhood 0 h e of the low temperature part of the first order phase transition surface for block averaging transformations applied to the ising model in dimension d 2 the pathologies occur at low temperatures for arbitrary magnetic field strength pathologies may also occur in the critical region for ising models in dimension d 4 we discuss the heuristic and numerical evidence on rg pathologies in the light of our rigorous theorems in addition we discuss critically the concept of gibbs measure which is at the heart of present day classical statistical mechanics we provide a careful and we hope pedagogical overview of the theory of gibbsian measures as well as the less familiar non gibbsian measures emphasizing the distinction between these two objects and the possible occurrence of the latter in different physical situations we give a rather complete catalogue of the known examples of such occurrences the main message of this paper is that despite a well established tradition gibbsiannessshould not be taken for granted

percolation path large deviations and weakly gibbs states we present a unified approach to establishing the gibbsian character of a wide class of non gibbsian states arising in the renormalisation group theory inside the realm of the pirogov sinai theory for lattice spin systems we prove that rg transformations applied to low temperature phases give rise to weakly gibbsian measures in other words we show that the griffiths pearce israel scenario of rg pathologies is carried by atypical configurations the renormalized measures are described by an effective interaction with relative energies well defined on a full measure set of configurations in this way we complete the first part of the dobrushin restoration program to give a gibbsian description to non gibbsian states a disagreement percolation estimate is used in the proof to bound the decay of quenched correlations through which the interaction potential is constructed the percolation is controlled via a novel type of pathwise large deviation theory

sequential gibbs measures and factor maps we define the notion of sequential gibbs measures inspired by on the classical notion of gibbs measures and recent examples from the study of non uniform hyperbolic dynamics extending previous results of kempton and pollicott factors of gibbs measures for full shifts entropy of hidden markov processes and connections to dynamical systems cambridge university press cambridge 2011 and chazottes and ugalde on the preservation of gibbsianness under symbol amalgamation entropy of hidden markov processes and connections to dynamical systems cambridge university press cambridge 2011 we show that the images of one block factor maps of a sequential gibbs measure are also a sequential gibbs measure with the same sequence of gibbs times we obtain some estimates on the regularity of the potential of the image measure at almost every point

relative pressure relative equilibrium states compensation functions and many to one codes between subshifts soit s x x t y y des applications continues d espaces metrisables compacts et soit x y une surjection continue avec t o s t o on etudie la notion de pression relative et on etudie certaines fonctions de pression relative maximales qui s associent aux etats d equilibres relatifs on relie ces idees a la notion de fonction de compensation et on montre qu une fonction de compensation existe toujours quand s et t sont des sous decalages

minimization of region scalable fitting energy for image segmentation intensity inhomogeneities often occur in real world images and may cause considerable difficulties in image segmentation in order to overcome the difficulties caused by intensity inhomogeneities we propose a region based active contour model that draws upon intensity information in local regions at a controllable scale a data fitting energy is defined in terms of a contour and two fitting functions that locally approximate the image intensities on the two sides of the contour this energy is then incorporated into a variational level set formulation with a level set regularization term from which a curve evolution equation is derived for energy minimization due to a kernel function in the data fitting term intensity information in local regions is extracted to guide the motion of the contour which thereby enables our model to cope with intensity inhomogeneity in addition the regularity of the level set function is intrinsically preserved by the level set regularization term to ensure accurate computation and avoids expensive reinitialization of the evolving level set function experimental results for synthetic and real images show desirable performances of our method

mean shift mode seeking and clustering mean shift a simple interactive procedure that shifts each data point to the average of data points in its neighborhood is generalized and analyzed in the paper this generalization makes some k means like clustering algorithms its special cases it is shown that mean shift is a mode seeking process on the surface constructed with a shadow kernal for gaussian kernels mean shift is a gradient mapping convergence is studied for mean shift iterations cluster analysis if treated as a deterministic problem of finding a fixed point of mean shift that characterizes the data applications in clustering and hough transform are demonstrated mean shift is also considered as an evolutionary strategy that performs multistart global optimization

density estimation with confidence sets exemplified by superclusters and voids in the galaxies abstract a method is presented for forming both a point estimate and a confidence set of semiparametric densities the final product is a three dimensional figure that displays a selection of density estimates for a plausible range of smoothing parameters the boundaries of the smoothing parameter are determined by a nonparametric goodness of fit test that is based on the sample spacings for each value of the smoothing parameter our estimator is selected by choosing the normal mixture that maximizes a function of the sample spacings a point estimate is selected from this confidence set by using the method of cross validation an algorithm to find the mixing distribution that maximizes the spacings functional is presented these methods are illustrated with a data set from the astronomy literature the measurements are velocities at which galaxies in the corona borealis region are moving away from our galaxy if the galaxies are clustered the velocity density will be multimodal with clusters correspond

distance regularized level set evolution and its application to image segmentation level set methods have been widely used in image processing and computer vision in conventional level set formulations the level set function typically develops irregularities during its evolution which may cause numerical errors and eventually destroy the stability of the evolution therefore a numerical remedy called reinitialization is typically applied to periodically replace the degraded level set function with a signed distance function however the practice of reinitialization not only raises serious problems as when and how it should be performed but also affects numerical accuracy in an undesirable way this paper proposes a new variational level set formulation in which the regularity of the level set function is intrinsically maintained during the level set evolution the level set evolution is derived as the gradient flow that minimizes an energy functional with a distance regularization term and an external energy that drives the motion of the zero level set toward desired locations the distance regularization term is defined with a potential function such that the derived level set evolution has a unique forward and backward fab diffusion effect which is able to maintain a desired shape of the level set function particularly a signed distance profile near the zero level set this yields a new type of level set evolution called distance regularized level set evolution drlse the distance regularization effect eliminates the need for reinitialization and thereby avoids its induced numerical errors in contrast to complicated implementations of conventional level set formulations a simpler and more efficient finite difference scheme can be used to implement the drlse formulation drlse also allows the use of more general and efficient initialization of the level set function in its numerical implementation relatively large time steps can be used in the finite difference scheme to reduce the number of iterations while ensuring sufficient numerical accuracy to demonstrate the effectiveness of the drlse formulation we apply it to an edge based active contour model for image segmentation and provide a simple narrowband implementation to greatly reduce computational cost