existence of multiple weak solutions for asymptotically linear wave equations abstract we consider the problem of multiple existence of 2 periodic weak solutions to wave equations u x t h x t u x t f x t of space dimension 1 where h x t is asymptotically linear in both as 0 and as it is shown by variational methods that there exist at least three solutions under several conditions on h x t if f is sufficiently small one of the results reads as follows let b lim h x t and assume that the convergence is uniform with respect to x t and that b non resonant case then the following conditions guarantee the existence of at least three solutions for sufficiently small f a h x t h x t 0 is non decreasing resp non increasing in and sup x t h x t min b resp inf x t h x t max b to obtain these results we prove that a c 1 class functional which is bounded from above and satisfies a condition similar to the linking condition has at least three critical points under wps condition

multiple periodic solutions of ordinary differential equations with double resonance abstract in this paper we study by morse theory the existence of multiple periodic solutions of a class of ordinary differential equation with double resonance at infinity between two consecutive eigenvalues and with resonance at origin

soft color segmentation and its applications we propose an automatic approach to soft color segmentation which produces soft color segments with an appropriate amount of overlapping and transparency essential to synthesizing natural images for a wide range of image based applications although many state of the art and complex techniques are excellent at partitioning an input image to facilitate deriving a semantic description of the scene to achieve seamless image synthesis we advocate a segmentation approach designed to maintain spatial and color coherence among soft segments while preserving discontinuities by assigning to each pixel a set of soft labels corresponding to their respective color distributions we optimize a global objective function which simultaneously exploits the reliability given by global color statistics and flexibility of local image compositing leading to an image model where the global color statistics of an image is represented by a gaussian mixture model gmm whereas the color of a pixel is explained by a local color mixture model where the weights are defined by the soft labels to the elements of the converged gmm transparency is naturally introduced in our probabilistic framework which infers an optimal mixture of colors at an image pixel to adequately consider global and local information in the same framework an alternating optimization scheme is proposed to iteratively solve for the global and local model parameters our method is fully automatic and is shown to converge to a good optimal solution we perform extensive evaluation and comparison and demonstrate that our method achieves good image synthesis results for image based applications such as image matting color transfer image deblurring and image colorization

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 resonant neumann problems multiplicity of solutions abstract we consider a semilinear neumann problem with an asymptotically linear reaction term we assume that resonance occurs at infinity using variational methods based on the critical point theory together with the reduction technique and morse theory we show that the problem has at least four nontrivial smooth solutions

unsupervised hierarchical image segmentation through fuzzy entropy maximization we present an unsupervised multilevel segmentation scheme for automatically segmenting grayscale and color images fuzzy 2 partition entropy is combined with graph cut to form a bi level segmentation operator that splits a given region into 2 parts based on both global optimal threshold and local spatial coherence a multilevel segmentation scheme iteratively performs on selected regions and color channels producing a coarse to fine hierarchy of segments the presented algorithm is evaluated using the berkeley segmentation database and achieves competitive results compared with the state of the art methods the fuzzy c partition entropy has been widely adopted as a global optimization technique for finding the optimal thresholds when performing multilevel gray image segmentation nevertheless existing fuzzy c partition entropy approaches generally have two limitations i e partition number cneeds to be manually tuned for different input and the methods can process grayscale images only to address these two limitations an unsupervised multilevel segmentation algorithm is presented in this paper the core step of our algorithm is a bi level segmentation operator which uses binary graph cuts to maximize both fuzzy 2 partition entropy and segmentation smoothness by iteratively performing this bi level segmentation operator multilevel image segmentation is achieved in a hierarchical manner starting from the input color image our algorithm first picks the color channel that can best segment the image into two labels and then iteratively selects channels to further split each labels until convergence the experimental results demonstrate the presented hierarchical segmentation scheme can efficiently segment both grayscale and color images quantitative evaluations over classic gray images and the berkeley segmentation database show that our method is comparable to the state of the art multi scale segmentation methods yet has the advantage of being unsupervised efficient and easy to implement

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

a statistical approach to texture classification from single images we investigate texture classification from single images obtained under unknown viewpoint and illumination a statistical approach is developed where textures are modelled by the joint probability distribution of filter responses this distribution is represented by the frequency histogram of filter response cluster centres textons recognition proceeds from single uncalibrated images and the novelty here is that rotationally invariant filters are used and the filter response space is low dimensional classification performance is compared with the filter banks and methods of leung and malik ijcv 2001 schmid cvpr 2001 and cula and dana ijcv 2004 and it is demonstrated that superior performance is achieved here classification results are presented for all 61 materials in the columbia utrecht texture database we also discuss the effects of various parameters on our classification algorithm such as the choice of filter bank and rotational invariance the size of the texton dictionary as well as the number of training images used finally we present a method of reliably measuring relative orientation co occurrence statistics in a rotationally invariant manner and discuss whether incorporating such information can enhance the classifier s performance

multiple solutions for a class of semilinear elliptic problems with robin boundary condition abstract in this paper we show the existence of at least four nontrivial solutions for a class of semilinear elliptic problems with robin boundary condition and jumping nonlinearities solvability of oscillating equations with robin boundary condition is also investigated we prove the conclusions by using sub super solution method fucik spectrum theory mountain pass theorem in order intervals and morse theory

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

multiplicity of solutions for a class of the quasilinear elliptic equations at resonance abstract in this paper by morse theory we obtain the existence and multiplicity for a class of the quasilinear elliptic equations at resonance

image segmentation with a unified graphical model we propose a unified graphical model that can represent both the causal and noncausal relationships among random variables and apply it to the image segmentation problem specifically we first propose to employ conditional random field crf to model the spatial relationships among image superpixel regions and their measurements we then introduce a multilayer bayesian network bn to model the causal dependencies that naturally exist among different image entities including image regions edges and vertices the crf model and the bn model are then systematically and seamlessly combined through the theories of factor graph to form a unified probabilistic graphical model that captures the complex relationships among different image entities using the unified graphical model image segmentation can be performed through a principled probabilistic inference experimental results on the weizmann horse data set on the voc2006 cow data set and on the msrc2 multiclass data set demonstrate that our approach achieves favorable results compared to state of the art approaches as well as those that use either the bn model or crf model alone

algebraic list decoding of subspace codes subspace codes are collections of subspaces of a certain ambient vector space over a finite field koetter and kschischang introduced subspace codes in order to correct errors and erasures in noncoherent random linear network coding they have also studied a remarkable family of subspace codes obtained by evaluating certain linearized polynomials the koetter kschischang subspace codes are widely regarded as the counterpart of reed solomon codes in the domain of network error correction koetter and kschischang have furthermore devised an algebraic decoding algorithm for these codes analogous to the berlekamp welch decoding algorithm for reed solomon codes in this paper we develop list decoding algorithms for subspace codes thereby providing for certain code parameters a better tradeoff between rate and error correction capability than that of the koetter kschischang codes in a sense we are able to achieve for these codes what sudan was able to achieve for reed solomon codes in order to do so we have to modify and generalize the original koetter kschischang construction in many important respects the end result is this for any integer our list l decoder guarantees successful recovery of the message subspace provided that the normalized dimension of the error satisfies l l l 1 2 r where r is the packet rate which is a new parameter introduced in this paper as in the case of sudan s list decoding algorithm this exceeds the previously best known error correction radius 1 r established by koetter and kschischang only for low rates r

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

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

on the complexity of the rank syndrome decoding problem in this paper we propose two new generic attacks on the rank syndrome decoding rsd problem let c be a random n k rank code over gf q m and let y x e be a received word such that x in c and rank e r the first attack the support attack is combinatorial and permits to recover an error e of rank weight r in min o n k 3 m 3 q r lfloor km n rfloor o n k 3 m 3 q r 1 lfloor k 1 m n rfloor operations on gf q this new attack improves the exponent for the best generic attack for the rsd problem in the case n m by introducing the ratio m n in the exponential coefficient of the previously best known attacks the second attack the annulator polynomial attack is an algebraic attack based on the theory of q polynomials introduced by ore we propose a new algebraic setting for the rsd problem that permits to consider equations and unknowns in the extension field gf q m rather than in gf q as it is usually the case we consider two approaches to solve the problem in this new setting the linearization technique shows that if n ge k 1 r 1 1 the rsd problem can be solved in polynomial time more generally we prove that if lceil r 1 k 1 n 1 r rceil le k the rsd problem can be solved with an average complexity of o r 3 k 3 q r lceil r 1 k 1 n 1 r rceil operations in the base field gf q we also consider solving with grobner bases for which we discuss theoretical complexity we also consider hybrid solving with grobner bases on practical parameters as an example of application we use our new attacks on all recent cryptosystems parameters which repair the gpt cryptosystem we break all examples of published proposed parameters and some parameters are broken in less than 1 s in certain cases

efficient encryption from random quasi cyclic codes we propose a framework for constructing efficient code based encryption schemes that do not hide any structure in their public matrix the framework is in the spirit of the schemes first proposed by alekhnovich in 2003 and based on the difficulty of decoding random linear codes from random errors of low weight we depart somewhat from alekhnovich s approach and propose an encryption scheme based on the difficulty of decoding random quasi cyclic codes we propose two new cryptosystems instantiated within our framework the hamming quasi cyclic cryptosystem hqc based on the hamming metric and the rank quasi cyclic cryptosystem rqc based on the rank metric we give a security proof which reduces the indistinguishability under chosen plaintext attack security of our systems to a decision version of the well known problem of decoding random families of quasi cyclic codes for the hamming and rank metrics the respective mathsf qcsd and mathsf rqcsd problems we also provide an analysis of the decryption failure probability of our scheme in the hamming metric case for the rank metric there is no decryption failure our schemes benefit from a very fast decryption algorithm together with small key sizes of only a few thousand bits the cryptosystems are very efficient for low encryption rates and are very well suited to key exchange and authentication asymptotically for lambda the security parameter the public key sizes are respectively in mathcal o lambda 2 for hqc and in mathcal o left lambda frac 4 3 right for rqc practical parameter compares well to the systems based on ring learning parity with noise or the recent moderate density parity check codes system

a deterministic reduction for the gap minimum distance problem determining the minimum distance of a linear code is one of the most important problems in algorithmic coding theory the exact version of the problem was shown to be np complete by vardy the gap version of the problem was shown to be np hard for any constant factor under a randomized reduction in an earlier work it was shown in the same paper that the minimum distance problem is not approximable in randomized polynomial time to the factor 2log1 n unless np rtime 2polylog n in this paper we derandomize the reduction and thus prove that there is no deterministic polynomial time algorithm to approximate the minimum distance to any constant factor unless p np we also prove that the minimum distance is not approximable in deterministic polynomial time to the factor 2log1 n unless np dtime 2polylog n as the main technical contribution for any constant 2 3 1 we present a deterministic algorithm that given a positive integer s runs in time poly s and constructs a code c of length poly s with an explicit hamming ball of radius d c such that the projection at the first s coordinates sends the codewords in the ball surjectively onto a linear subspace of dimension s where d c denotes the minimum distance of c the codes are obtained by concatenating reed solomon codes with hadamard codes

on ideal lattices and learning with errors over rings the learning with errors lwe problem is to distinguish random linear equations which have been perturbed by a small amount of noise from truly uniform ones the problem has been shown to be as hard as worst case lattice problems and in recent years it has served as the foundation for a plethora of cryptographic applications unfortunately these applications are rather inefficient due to an inherent quadratic overhead in the use of lwe a main open question was whether lwe and its applications could be made truly efficient by exploiting extra algebraic structure as was done for lattice based hash functions and related primitives we resolve this question in the affirmative by introducing an algebraic variant of lwe called ring lwe and proving that it too enjoys very strong hardness guarantees specifically we show that the ring lwe distribution is pseudorandom assuming that worst case problems on ideal lattices are hard for polynomial time quantum algorithms applications include the first truly practical lattice based public key cryptosystem with an efficient security reduction moreover many of the other applications of lwe can be made much more efficient through the use of ring lwe

nontrivial solutions for elliptic resonant problems abstract nontrivial solutions for elliptic resonant problems are obtained via morse theory to compute the critical groups at infinity of the relevant functional we propose a new approach by combining the homotopy and reduction methods and the alexander duality theorem

discriminative random fields in this research we address the problem of classification and labeling of regions given a single static natural image natural images exhibit strong spatial dependencies and modeling these dependencies in a principled manner is crucial to achieve good classification accuracy in this work we present discriminative random fields drfs to model spatial interactions in images in a discriminative framework based on the concept of conditional random fields proposed by lafferty et al 2001 the drfs classify image regions by incorporating neighborhood spatial interactions in the labels as well as the observed data the drf framework offers several advantages over the conventional markov random field mrf framework first the drfs allow to relax the strong assumption of conditional independence of the observed data generally used in the mrf framework for tractability this assumption is too restrictive for a large number of applications in computer vision second the drfs derive their classification power by exploiting the probabilistic discriminative models instead of the generative models used for modeling observations in the mrf framework third the interaction in labels in drfs is based on the idea of pairwise discrimination of the observed data making it data adaptive instead of being fixed a priori as in mrfs finally all the parameters in the drf model are estimated simultaneously from the training data unlike the mrf framework where the likelihood parameters are usually learned separately from the field parameters we present preliminary experiments with man made structure detection and binary image restoration tasks and compare the drf results with the mrf results

coding for errors and erasures in random network coding the problem of error control in random linear network coding is considered a ldquononcoherentrdquo or ldquochannel obliviousrdquo model is assumed where neither transmitter nor receiver is assumed to have knowledge of the channel transfer characteristic motivated by the property that linear network coding is vector space preserving information transmission is modeled as the injection into the network of a basis for a vector space v and the collection by the receiver of a basis for a vector space u a metric on the projective geometry associated with the packet space is introduced and it is shown that a minimum distance decoder for this metric achieves correct decoding if the dimension of the space v capu is sufficiently large if the dimension of each codeword is restricted to a fixed integer the code forms a subset of a finite field grassmannian or equivalently a subset of the vertices of the corresponding grassmann graph sphere packing and sphere covering bounds as well as a generalization of the singleton bound are provided for such codes finally a reed solomon like code construction related to gabidulin s construction of maximum rank distance codes is described and a sudan style ldquolist 1rdquo minimum distance decoding algorithm is provided

on the hardness of the decoding and the minimum distance problems for rank codes we give a randomized reduction for the rank syndrome decoding problem and rank minimum distance problem for rank codes over extension fields our results are based on embedding linear codes in the hamming space into linear codes over an extension field equipped with the rank metric we prove that if any of the previous problems for the rank metric is in zpp rp cap corp then we would have np zpp we also give complexity results for the respective rank metric approximation problems

dancer fucik spectrum for fractional schrodinger operators with a steep potential well on rn abstract in this paper we study dancer fucik spectrum of the fractional schrodinger operators which is defined as the set of r 2 such that s u v x u u u in r n has a nontrivial solution u where the potential v has a steep potential well for sufficiently large parameter 0 it is allowed that s v has essential spectrum with finitely many eigenvalues below the infimum of e s s s v many difficulties are caused by general nonlocal operators we develop new techniques to overcome them to construct the first nontrivial curve of dancer fucik point spectrum by minimax methods to show some qualitative properties of the curve and to prove that the corresponding eigenfunctions are foliated schwartz symmetric as applications we obtain the existence of nontrivial solutions for nonlinear schrodinger equations with nonresonant nonlinearity

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

on asymptotically linear elliptic equations in r n abstract in this paper we obtain the existence of solution for asymptotically linear elliptic equations in r n we mainly focus on the resonant case the nonlinearity may not be sublinear

nontrivial solutions of semilinear equations at resonance in this paper we prove new existence results concerning nontrivial solutions to semilinear elliptic problem at resonance the methods used here are based on combining the minimax methods and the morse theory

computation of critical groups in resonance problems where the nonlinearity may not be sublinear under weaker assumptions that require 1 4 but not 1 7 as an applica tion we obtain new existence results for asymptotically linear elliptic boundary valueproblems at resonance we refer the reader to chang 2 for a wide exposition of morse theory the notionofcritical groups at innity was introduced in 1 2 criticalgroupcomputationsfirst we assume that g

dynamic trees for unsupervised segmentation and matching of image regions we present a probabilistic framework namely multiscale generative models known as dynamic trees dt for unsupervised image segmentation and subsequent matching of segmented regions in a given set of images beyond these novel applications of dts we propose important additions for this modeling paradigm first we introduce a novel dt architecture where multilayered observable data are incorporated at all scales of the model second we derive a novel probabilistic inference algorithm for dts structured variational approximation sva which explicitly accounts for the statistical dependence of node positions and model structure in the approximate posterior distribution thereby relaxing poorly justified independence assumptions in previous work finally we propose a similarity measure for matching dynamic tree models representing segmented image regions across images our results for several data sets show that dts are capable of capturing important component subcomponent relationships among objects and their parts and that dts perform well in segmenting images into plausible pixel clusters we demonstrate the significantly improved properties of the sva algorithm both in terms of substantially faster convergence rates and larger approximate posteriors for the inferred models when compared with competing inference algorithms furthermore results on unsupervised object recognition demonstrate the viability of the proposed similarity measure for matching dynamic structure statistical models

an overlapping tree approach to multiscale stochastic modeling and estimation recently a class of multiscale stochastic models has been introduced in which random processes and fields are described by scale recursive dynamic trees a major advantage of this framework is that it leads to an extremely efficient statistically optimal algorithm for least squares estimation in certain applications however estimates based on the types of multiscale models previously proposed may not be adequate as they have tended to exhibit a visually distracting blockiness we eliminate this blockiness by discarding the standard assumption that distinct nodes on a given level of the multiscale process correspond to disjoint portions of the image domain instead we allow a correspondence to overlapping portions of the image domain we use these so called overlapping tree models for both modeling and estimation in particular we develop an efficient multiscale algorithm for generating sample paths of a random field whose second order statistics match a prespecified covariance structure to any desired degree of fidelity furthermore we demonstrate that under easily satisfied conditions we can lift a random field estimation problem to one defined on an overlapped tree resulting in an estimation algorithm that is computationally efficient directly produces estimation error covariances and eliminates blockiness in the reconstructed imagery without any sacrifice in the resolution of fine scale detail

winding number constrained contour detection salient contour detection can benefit from the integration of both contour cues and region cues however this task is difficult due to different nature of region representations and contour representations to solve this problem this paper proposes an energy minimization framework based on winding number constraints in this framework both region cues such as color texture homogeneity and contour cues such as local contrast and continuity are represented in a joint objective function which has both region and contour labels the key problem is how to design constraints that ensure the topological consistency of the two kinds of labels our technique is based on the topological concept of winding number using a fast method for winding number computation a small number of linear constraints are derived to ensure label consistency our method is instantiated by ratio based energy functions by successfully integrating both region and contour cues our method shows advantages over competitive methods our method is extended to incorporate user interaction which leads to further improvements

non uniformly asymptotically linear p laplacian problems abstract we relax conditions on uniform convergences of f x s s p 2 s which are essential in many results on multiplicity for asymptotically linear p laplacian problems

the sensitivity of belief networks to imprecise probabilities an experimental investigation abstract bayesian belief networks are being increasingly used as a knowledge representation for reasoning under uncertainty some researchers have questioned the practicality of obtaining the numerical probabilities with sufficient precision to create belief networks for large scale applications in this work we investigate how precise the probabilities need to be by measuring how imprecision in the probabilities affects diagnostic performance we conducted a series of experiments on a set of real world belief networks for medical diagnosis in liver and bile disease we examined the effects on diagnostic performance of 1 varying the mappings from qualitative frequency weights into numerical probabilities 2 adding random noise to the numerical probabilities 3 simplifying from quaternary domains for diseases and findings absent mild moderate and severe to binary domains absent and present and 4 using test cases that contain diseases outside the network we found that even extreme differences in the probability mappings and large amounts of noise lead to only modest reductions in diagnostic performance we found no significant effect of the simplification from quaternary to binary representation we also found that outside diseases degraded performance modestly overall these findings indicate that even highly imprecise input probabilities may not impair diagnostic performance significantly and that simple binary representations may often be adequate these findings of robustness suggest that belief networks are a practical representation without requiring undue precision

a tree structured markov random field model for bayesian image segmentation we present a new image segmentation algorithm based on a tree structured binary mrf model the image is recursively segmented in smaller and smaller regions until a stopping condition local to each region is met each elementary binary segmentation is obtained as the solution of a map estimation problem with the region prior modeled as an mrf since only binary fields are used and thanks to the tree structure the algorithm is quite fast and allows one to address the cluster validation problem in a seamless way in addition all field parameters are estimated locally allowing for some spatial adaptivity to improve segmentation accuracy a split and merge procedure is also developed and a spatially adaptive mrf model is used numerical experiments on multispectral images show that the proposed algorithm is much faster than a similar reference algorithm based on flat mrf models and its performance in terms of segmentation accuracy and map smoothness is comparable or even superior

multiple positive solutions for a class of p superlinear elliptic problems abstract we study nonlinear elliptic dirichlet problems driven by the p laplacian and with a nonlinearity which consists of a p superlinear term perturbed by a p linear one using critical point theory coupled with suitable truncation techniques we show that the problem has two positive smooth solutions when the conditions are symmetric in the two semiaxes we have four nontrivial smooth solutions of constant sign finally for the semilinear problem using morse theory we produce a fifth nontrivial smooth solution

combining belief networks and neural networks for scene segmentation we are concerned with the problem of image segmentation in which each pixel is assigned to one of a predefined finite number of labels in bayesian image analysis this requires fusing together local predictions for the class labels with a prior model of label images following the work of bouman and shapiro 1994 we consider the use of tree structured belief networks tsbns as prior models the parameters in the tsbn are trained using a maximum likelihood objective function with the em algorithm and the resulting model is evaluated by calculating how efficiently it codes label images a number of authors have used gaussian mixture models to connect the label field to the image data we compare this approach to the scaled likelihood method of smyth 1994 and morgan and bourlard 1995 where local predictions of pixel classification from neural networks are fused with the tsbn prior our results show a higher performance is obtained with the neural networks we evaluate the classification results obtained and emphasize not only the maximum a posteriori segmentation but also the uncertainty as evidenced e g by the pixelwise posterior marginal entropies we also investigate the use of conditional maximum likelihood training for the tsbn and find that this gives rise to improved classification performance over the ml trained tsbn