multiregion image segmentation by parametric kernel graph cuts the purpose of this study is to investigate multiregion graph cut image partitioning via kernel mapping of the image data the image data is transformed implicitly by a kernel function so that the piecewise constant model of the graph cut formulation becomes applicable the objective function contains an original data term to evaluate the deviation of the transformed data within each segmentation region from the piecewise constant model and a smoothness boundary preserving regularization term the method affords an effective alternative to complex modeling of the original image data while taking advantage of the computational benefits of graph cuts using a common kernel function energy minimization typically consists of iterating image partitioning by graph cut iterations and evaluations of region parameters via fixed point computation a quantitative and comparative performance assessment is carried out over a large number of experiments using synthetic grey level data as well as natural images from the berkeley database the effectiveness of the method is also demonstrated through a set of experiments with real images of a variety of types such as medical synthetic aperture radar and motion maps

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

on the stability of the quenched state in mean field spin glass models while the gibbs states of spin glass models have been noted to have an erratic dependence on temperature one may expect the mean over the disorder to produce a continuously varying quenched state the assumption of such continuity in temperature implies that in the infinite volume limit the state is stable under a class of deformations of the gibbs measure the condition is satisfied by the parisi ansatz along with an even broader stationarity property the stability conditions have equivalent expressions as marginal additivity of the quenched free energy implications of the continuity assumption include constraints on the overlap distribution which are expressed as the vanishing of the expectation value for an infinite collection of multi overlap polynomials the polynomials can be computed with the aid of a real replica calculation in which the number of replicas is taken to zero

characterization of invariant measures at the leading edge for competing particle systems we study systems of particles on a line which have a maximum are locally finite and evolve with independent increments quasi stationary states are defined as probability measures on the algebra generated by the gap variables for which joint distribution of gaps between particles is invariant under the time evolution examples are provided by poisson processes with densities of the form p d x e sx s dx with s 0 and linear superpositions of such measures we show that conversely any quasi stationary state for the independent dynamics with an exponentially bounded integrated density of particles corresponds to a superposition of poisson processes with densities p dx e sx s dx with s 0 restricted to the relevant algebra among the systems for which this question is of some relevance are spin glass models of statistical mechanics where the point process represents the collection of the free energies of distinct pure states the time evolution corresponds to the addition of a spin variable and the poisson measures described above correspond to the so called rem states

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

the parisi formula in this chapter we prove the parisi formula which gives the limiting value of the free energy per site for the sherrington kirkpatrick model at each temperature starting with the famous result of guerra that the parisi formula provided a bound for this free energy we make full use of poisson dirichlet cascades we then use the same techniques to prove in a strong sense that in presence of an external field the overlaps are positive

a level set model for image classification we present a supervised classification model based on a variational approach this model is devoted to find an optimal partition composed of homogeneous classes with regular interfaces the originality of the proposed approach concerns the definition of a partition by the use of level sets each set of regions and boundaries associated to a class is defined by a unique level set function we use as many level sets as different classes and all these level sets are moving together thanks to forces which interact in order to get an optimal partition we show how these forces can be defined through the minimization of a unique fonctional the coupled partial differential equations pde related to the minimization of the functional are considered through a dynamical scheme given an initial interface set zero level set the different terms of the pde s are governing the motion of interfaces such that at convergence we get an optimal partition as defined above each interface is guided by internal forces regularity of the interface and external ones data term no vacuum no regions overlapping several experiments were conducted on both synthetic and real images

on multilinear oscillatory singular integrals with rough kernels abstract in this paper for the multilinear oscillatory singular integral operators ta defined by t a f x p v r n e ip x y x y x y n m r m 1 a x y f y dy n 2 where p x y is a nontrivial and real valued polynomial defined on r n r n x is homogeneous of degree zero on r n a x has derivatives of order m in 0 l q s n 1 for some q 1 1 then for any p 1 ta is bounded on l p r n meanwhile the weighted lp boundedness of ta is also given

commutators of singular integrals and fractional integral operators the commutators of integral and differential operators are very important tools in harmonic analysis and pde recently the third author of this paper gave a survey front math china 2011 6 5 821 833 on some late results and put forward a few problems on commutators of many important operators in harmonic analysis in this paper we present some results about the commutators of singular integrals and fractional integrals with rough or variable kernels which can be seen as a supplement of the aforementioned survey

on ruelle s probability cascades and an abstract cavity method we construct in this work a markov process which describes a clustering mechanism through which equivalence classes on are progressively lumped together this clustering process gives a new description of ruelle s continuous probability cascades it also enables to introduce an abstract cavity method which mimicks certain features of the cavity method developed by physicists in the context of the sherrington kirkpatrick model

random overlap structures properties and applications to spin glasses random overlap structures rost s are random elements on the space of probability measures on the unit ball of a hilbert space where two measures are identified if they differ by an isometry in spin glasses they arise as natural limits of gibbs measures under the appropriate algebra of functions we prove that the so called cavity mapping on the space of rost s is continuous leading to a proof of the stochastic stability conjecture for the limiting gibbs measures of a large class of spin glass models similar arguments yield the proofs of a number of other properties of rost s that may be useful in future attempts at proving the ultrametricity conjecture lastly assuming that the ultrametricity conjecture holds the setup yields a constructive proof of the parisi formula for the free energy of the sherrington kirkpatrick model by making rigorous a heuristic of aizenman sims and starr

a multiphase level set framework for image segmentation using the mumford and shah model we propose a new multiphase level set framework for image segmentation using the mumford and shah model for piecewise constant and piecewise smooth optimal approximations the proposed method is also a generalization of an active contour model without edges based 2 phase segmentation developed by the authors earlier in t chan and l vese 1999 in scale space 99 m nilsen et al eds lncs vol 1682 pp 141 151 and t chan and l vese 2001 ieee ip 10 2 266 277 the multiphase level set formulation is new and of interest on its own by construction it automatically avoids the problems of vacuum and overlaps it needs only log n level set functions for n phases in the piecewise constant cases it can represent boundaries with complex topologies including triple junctionss in the piecewise smooth case only two level set functions formally suffice to represent any partition based on the four color theorem finally we validate the proposed models by numerical results for signal and image denoising and segmentation implemented using the osher and sethian level set method

influence of the noise model on level set active contour segmentation we analyze level set implementation of region snakes based on the maximum likelihood method for different noise models that belong to the exponential family we show that this approach can improve segmentation results in noisy images and we demonstrate that the regularization term can be efficiently determined using an information theory based approach i e the minimum description length principle the criterion to be optimized has no free parameter to be tuned by the user and the obtained segmentation technique is adapted to nonsimply connected objects

the thermodynamic limit in mean field spin glass models we present a simple strategy in order to show the existence and uniqueness of the infinite volume limit of thermodynamic quantities for a large class of mean field disordered models as for example the sherrington kirkpatrick model and the derrida p spin model the main argument is based on a smooth interpolation between a large system made of n spin sites and two similar but independent subsystems made of n 1 and n 2 sites respectively with n 1 n 2 n the quenched average of the free energy turns out to be subadditive with respect to the size of the system this gives immediately convergence of the free energy per site in the infinite volume limit moreover a simple argument based on concentration of measure gives the almost sure convergence with respect to the external noise similar results hold also for the ground state energy per site

broken replica symmetry bounds in the mean field spin glass model by using a simple interpolation argument in previous work we have proven the existence of the thermodynamic limit for mean field disordered models including the sherrington kirkpatrick model and the derrida p spin model here we extend this argument in order to compare the limiting free energy with the expression given by the parisi ansatz and including full spontaneous replica symmetry breaking our main result is that the quenched average of the free energy is bounded from below by the value given in the parisi ansatz uniformly in the size of the system moreover the difference between the two expressions is given in the form of a sum rule extending our previous work on the comparison between the true free energy and its replica symmetric sherrington kirkpatrick approximation we give also a variational bound for the infinite volume limit of the ground state energy per site

weighted jump and variational inequalities for rough operators abstract in this paper we systematically study weighted jump and variational inequalities for rough operators more precisely we show some weighted jump and variational inequalities for the families t t e e 0 of truncated singular integrals and m m t t 0 of averaging operators with rough kernels which are defined respectively by t e f x y e y y n f x y d y and m t f x 1 t n y t y f x y d y where the kernel belongs to l q s n 1 for q 1

spin glass computations and ruelle s probability cascades we study the parisi functional appearing in the parisi formula for the pressure of the sk model as a functional on ruelle s probability cascades rpc computation techniques for the rpc formulation of the functional are developed they are used to derive continuity and monotonicity properties of the functional retrieving a theorem of guerra we also detail the connection between the aizenman sims starr variational principle and the parisi formula as a final application of the techniques we rederive the almeida thouless line in the spirit of toninelli but relying on the rpc structure

nonlinear component analysis as a kernel eigenvalue problem a new method for performing a nonlinear form of principal component analysis is proposed by the use of integral operator kernel functions one can efficiently compute principal components in high dimensional feature spaces related to input space by some nonlinear map for instance the space of all possible five pixel products in 16 16 images we give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition

convex relaxed kernel mapping for image segmentation this paper investigates a convex relaxed kernel mapping formulation of image segmentation we optimize under some partition constraints a functional containing two characteristic terms 1 a data term which maps the observation space to a higher possibly infinite dimensional feature space via a kernel function thereby evaluating nonlinear distances between the observations and segments parameters and 2 a total variation term which favors smooth segment surfaces or boundaries the algorithm iterates two steps 1 a convex relaxation optimization with respect to the segments by solving an equivalent constrained problem via the augmented lagrange multiplier method and 2 a convergent fixed point optimization with respect to the segments parameters the proposed algorithm can bear with a variety of image types without the need for complex and application specific statistical modeling while having the computational benefits of convex relaxation our solution is amenable to parallelized implementations on graphics processing units gpus and extends easily to high dimensions we evaluated the proposed algorithm with several sets of comprehensive experiments and comparisons including 1 computational evaluations over 3d medical imaging examples and high resolution large size color photographs which demonstrate that a parallelized implementation of the proposed method run on a gpu can bring a significant speed up and 2 accuracy evaluations against five state of the art methods over the berkeley color image database and a multimodel synthetic data set which demonstrates competitive performances of the algorithm

construction of pure states in mean field models for spin glasses if a mean field model for spin glasses is generic in the sense that it satisfies the extended ghirlanda guerra identities and if the law of the overlaps has a point mass at the largest point q of its support we prove that one can decompose the configuration space into a sequence of sets ak such that generically the overlap of two configurations is equal to q if and only if they belong to the same set ak for the study of the overlaps each set ak can be replaced by a single point combining this with a recent result of panchenko a connection between ghirlanda guerra identities and ultrametricity ann probab 2008 to appear this proves that if the overlaps take only finitely many values ultrametricity occurs we give an elementary self contained proof of this result based on simple inequalities and an averaging argument

l p bounds for the commutators of singular integrals and maximal singular integrals with rough kernels the commutator of convolution type calderon zygmund singular integral operators with rough kernels p v x n are studied the authors established the l p 1 p boundedness of the commutators of singular integrals and maximal singular integrals with the kernel condition which is different from the condition h1 sn 1 mr 2000 subject classification 42b20 42b25 42b99

boundedness for the commutator of convolution operator a boundedness result is established for sublinear operators on homogeneous herz spaces as applications a new result about the weighted boundedness of commutators of convolution operators is obtained

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

region competition unifying snakes region growing and bayes mdl for multiband image segmentation we present a novel statistical and variational approach to image segmentation based on a new algorithm named region competition this algorithm is derived by minimizing a generalized bayes minimum description length mdl criterion using the variational principle the algorithm is guaranteed to converge to a local minimum and combines aspects of snakes balloons and region growing the classic snakes balloons and region growing algorithms can be directly derived from our approach we provide theoretical analysis of region competition including accuracy of boundary location criteria for initial conditions and the relationship to edge detection using filters it is straightforward to generalize the algorithm to multiband segmentation and we demonstrate it on gray level images color images and texture images the novel color model allows us to eliminate intensity gradients and shadows thereby obtaining segmentation based on the albedos of objects it also helps detect highlight regions

effective level set image segmentation with a kernel induced data term this study investigates level set multiphase image segmentation by kernel mapping and piecewise constant modeling of the image data thereof a kernel function maps implicitly the original data into data of a higher dimension so that the piecewise constant model becomes applicable this leads to a flexible and effective alternative to complex modeling of the image data the method uses an active curve objective functional with two terms an original term which evaluates the deviation of the mapped image data within each segmentation region from the piecewise constant model and a classic length regularization term for smooth region boundaries functional minimization is carried out by iterations of two consecutive steps 1 minimization with respect to the segmentation by curve evolution via euler lagrange descent equations and 2 minimization with respect to the regions parameters via fixed point iterations using a common kernel function this step amounts to a mean shift parameter update we verified the effectiveness of the method by a quantitative and comparative performance evaluation over a large number of experiments on synthetic images as well as experiments with a variety of real images such as medical satellite and natural images as well as motion maps

improving the accuracy of volumetric segmentation using pre processing boundary detection and image reconstruction the concentration edge detection and gegenbauer image reconstruction methods were previously shown to improve the quality of segmentation in magnetic resonance imaging in this study these methods are utilized as a pre processing step to the weibull e sd field segmentation it is demonstrated that the combination of the concentration edge detection and gegenbauer reconstruction method improves the accuracy of segmentation for the simulated test data and real magnetic resonance images used in this study

weighted graph cuts without eigenvectors a multilevel approach a variety of clustering algorithms have recently been proposed to handle data that is not linearly separable spectral clustering and kernel k means are two of the main methods in this paper we discuss an equivalence between the objective functions used in these seemingly different methods in particular a general weighted kernel k means objective is mathematically equivalent to a weighted graph clustering objective we exploit this equivalence to develop a fast high quality multilevel algorithm that directly optimizes various weighted graph clustering objectives such as the popular ratio cut normalized cut and ratio association criteria this eliminates the need for any eigenvector computation for graph clustering problems which can be prohibitive for very large graphs previous multilevel graph partitioning methods such as metis have suffered from the restriction of equal sized clusters our multilevel algorithm removes this restriction by using kernel k means to optimize weighted graph cuts experimental results show that our multilevel algorithm outperforms a state of the art spectral clustering algorithm in terms of speed memory usage and quality we demonstrate that our algorithm is applicable to large scale clustering tasks such as image segmentation social network analysis and gene network analysis

singular integrals with mixed homogeneity in triebel lizorkin spaces abstract in this paper we study the singular integral f x p v r n h y y y f x y d y in triebel lizorkin spaces here l log l s n 1 n 2 h is a measurable locally integrable function defined on 0 and is a norm which is homogeneous with respect to certain non isotropic dilations for the special case when is the usual euclidean norm we also consider the singular integral above in weighted triebel lizorkin spaces for some appropriate weights

boundedness of rough oscillatory singular integral on triebel lizorkin spaces we obtain appropriate sharp bounds on triebel lizorkin spaces for rough oscillatory integrals with polynomial phase by using these bounds and using an extrapolation argument we obtain some new and previously known results for oscillatory integrals under very weak size conditions on the kernel functions

an introduction to kernel based learning algorithms this paper provides an introduction to support vector machines kernel fisher discriminant analysis and kernel principal component analysis as examples for successful kernel based learning methods we first give a short background about vapnik chervonenkis theory and kernel feature spaces and then proceed to kernel based learning in supervised and unsupervised scenarios including practical and algorithmic considerations we illustrate the usefulness of kernel algorithms by discussing applications such as optical character recognition and dna analysis

weighted norm inequality for the singular integral with variable kernel and fractional differentiation abstract for 0 1 let d be the fractional differentiation operator and t be the singular integral operator with variable kernel which is defined by t f x r n x x y x y n f y d y let t and t denote the adjoint of t and the pseudo adjoint of t respectively let t 1 t 2 denote the product of t 1 and t 2 t 1 t 2 denote the pseudo product of t 1 and t 2 in this paper we give the weighted norm inequalities for commutators of these singular integral operators and the fractional differentiation operator d finally we extend all results to the morrey spaces

sar image segmentation based on level set approach and cal g _a 0 model this paper proposes an image segmentation method for synthetic aperture radar sar exploring statistical properties of sar data to characterize image regions we consider cal g a 0 distribution parameters for sar image segmentation combined to the level set framework the cal g a 0 distribution belongs to a class of cal g distributions that have been successfully used to model different regions in amplitude sar images for data modeling purpose such statistical data model is fundamental to deriving the energy functional to perform region mapping which is input into our level set propagation numerical scheme that splits sar images into homogeneous heterogeneous and extremely heterogeneous regions moreover we introduce an assessment procedure based on stochastic distance and the cal g a 0 model to quantify the robustness and accuracy of our approach our results demonstrate the accuracy of the algorithms regarding experiments on synthetic and real sar data

weighted norm inequalities for homogeneous singular integrals we prove weighted norm inequalities for homogeneous singular integrals when only a size condition is assumed on the restriction of the kernel to the unit sphere the same results hold for the operator obtained by modifying the centered hardy littlewood maximal operator over balls with a degree zero homogeneous function and also for the maximal singular integral

dti segmentation by statistical surface evolution we address the problem of the segmentation of cerebral white matter structures from diffusion tensor images dti a dti produces from a set of diffusion weighted mr images tensor valued images where each voxel is assigned with a 3 times 3 symmetric positive definite matrix this second order tensor is simply the covariance matrix of a local gaussian process with zero mean modeling the average motion of water molecules as we will show in this paper the definition of a dissimilarity measure and statistics between such quantities is a nontrivial task which must be tackled carefully we claim and demonstrate that by using the theoretically well founded differential geometrical properties of the manifold of multivariate normal distributions it is possible to improve the quality of the segmentation results obtained with other dissimilarity measures such as the euclidean distance or the kullback leibler divergence the main goal of this paper is to prove that the choice of the probability metric i e the dissimilarity measure has a deep impact on the tensor statistics and hence on the achieved results we introduce a variational formulation in the level set framework to estimate the optimal segmentation of a dti according to the following hypothesis diffusion tensors exhibit a gaussian distribution in the different partitions we must also respect the geometric constraints imposed by the interfaces existing among the cerebral structures and detected by the gradient of the dti we show how to express all the statistical quantities for the different probability metrics we validate and compare the results obtained on various synthetic data sets a biological rat spinal cord phantom and human brain dtis

weak type 1 1 bounds for rough operators ii in this paper we consider four operators arising in harmonic analysis in r n 1 they share one feature each is known to be bounded on lp for all 1 p o but for each it has been an open question whether a weak type 1 1 bound also holds in two cases we show that the weak 1 1 bound does hold and for the others we establish weaker estimates which are still sharper than the lp boundedness although the four operators are quite distinct they all involve convolution kernels which are related to the singular integrals of calderon and zygmund but which lack the smoothness required for the usual analysis in each case this defect is mitigated by the presence of some form of curvature consider the bochner riesz means

non negative patch alignment framework in this paper we present a non negative patch alignment framework npaf to unify popular non negative matrix factorization nmf related dimension reduction algorithms it offers a new viewpoint to better understand the common property of different nmf algorithms although multiplicative update rule mur can solve npaf and is easy to implement it converges slowly thus we propose a fast gradient descent fgd to overcome the aforementioned problem fgd uses the newton method to search the optimal step size and thus converges faster than mur experiments on synthetic and real world datasets confirm the efficiency of fgd compared with mur for optimizing npaf based on npaf we develop non negative discriminative locality alignment ndla experiments on face image and handwritten datasets suggest the effectiveness of ndla in classification tasks and its robustness to image occlusions compared with representative nmf related dimension reduction algorithms

estimates for singular integrals on homogeneous groups we consider singular integral operators and maximal singular integral operators with rough kernels on homogeneous groups we prove certain estimates for the operators that imply lp boundedness of them by an extrapolation argument under a sharp condition for the kernels also we prove some weighted lp inequalities for the operators