shape preserving local histogram modification a novel approach for shape preserving contrast enhancement is presented in this paper contrast enhancement is achieved by means of a local histogram equalization algorithm which preserves the level sets of the image this basic property is violated by common local schemes thereby introducing spurious objects and modifying the image information the scheme is based on equalizing the histogram in all the connected components of the image which are defined based both on the grey values and spatial relations between pixels in the image and following mathematical morphology constitute the basic objects in the scene we give examples for both grey value and color images

on a class of hemivariational inequalities at resonance abstract we consider a class of noncoercive hemivariational inequalities involving the p laplacian at resonance we use the unilateral growth condition so the energy functional is nonsmooth nonconvex and its effective domain does not coincide with the whole space w 1 p 0 to avoid this difficulty we study the problem in finite dimensional spaces using the mountain pass theorem for locally lipschitz functionals and then we pass to the limit to obtain the existence of solutions

diffusion snakes introducing statistical shape knowledge into the mumford shah functional we present a modification of the mumford shah functional and its cartoon limit which facilitates the incorporation of a statistical prior on the shape of the segmenting contour by minimizing a single energy functional we obtain a segmentation process which maximizes both the grey value homogeneity in the separated regions and the similarity of the contour with respect to a set of training shapes we propose a closed form parameter free solution for incorporating invariance with respect to similarity transformations in the variational framework we show segmentation results on artificial and real world images with and without prior shape information in the cases of noise occlusion or strongly cluttered background the shape prior significantly improves segmentation finally we compare our results to those obtained by a level set implementation of geodesic active contours

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

nonlinear hemivariational inequalities at resonance in this paper we examine a semilinear hemivariational inequality at resonance in the first eigenvalue 1 of h01 z we prove two existence theorems for such problems our approach is variational and is based on the nonsmooth critical point theory of chang which uses the subdifferential calculus of clarke for locally lipschitz functions

minimization algorithms for multiple valued programmable logic arrays the performance of various heuristic algorithms for minimizing realizations of multiple valued functions by the charge coupled device ccd and cmos programmable logic arrays plas of h g kerkhoff and j t butler 1986 and j g samson 1988 respectively is analyzed the functions realized by the plas are in sum of products form where the sum is ordinary addition truncated to the highest logic value and the product represents the min operation of functions of the input variables that are the interval literal operations three heuristics proposed by g pomper and j a armstrong 1981 p w besslich 1986 and g w dueck and d m miller 1987 are compared over sets of random and random symmetric functions an exact minimization method that is a tree search using backtracking is described a reduction in the search space is achieved by considering constrained implicant sets and by eliminating some implicants altogether even with this improvement the time required for exact minimization is extremely high when compared to all three heuristics the case involving only prime implicants is considered and it is shown that such implicants have marginal value compared to constrained implicant sets the basis of comparison is the average number of product terms

on solutions for a hyperbolic system with differential inclusion and memory source term on the boundary in this paper we investigate the existence and uniform decay rates of global solutions for a hyperbolic system with a discontinuous and nonlinear multi valued term and a nonlinear memory source term on the boundary

abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity critical point theorems and applications to some nonlinear problems with strong resonance at infinity p bartolo and v benci istituto di matematica applicata via re david x0 bari ital and istituto di analisi matematica palazzo ateneo l ia scolai 2 bari italy received in revised form 20 december 1952

active contours for tracking distributions a new approach to tracking using active contours is presented the class of objects to be tracked is assumed to be characterized by a probability distribution over some variable such as intensity color or texture the goal of the algorithm is to find the region within the current image such that the sample distribution of the interior of the region most closely matches the model distribution two separate criteria for matching distributions are examined and the curve evolution equations are derived in each case the flows are shown to perform well in experiments

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

curve evolution implementation of the mumford shah functional for image segmentation denoising interpolation and magnification we first address the problem of simultaneous image segmentation and smoothing by approaching the mumford shah 1989 paradigm from a curve evolution perspective in particular we let a set of deformable contours define the boundaries between regions in an image where we model the data via piecewise smooth functions and employ a gradient flow to evolve these contours each gradient step involves solving an optimal estimation problem for the data within each region connecting curve evolution and the mumford shah functional with the theory of boundary value stochastic processes the resulting active contour model offers a tractable implementation of the original mumford shah model i e without resorting to elliptic approximations which have traditionally been favored for greater ease in implementation to simultaneously segment and smoothly reconstruct the data within a given image in a coupled manner various implementations of this algorithm are introduced to increase its speed of convergence we also outline a hierarchical implementation of this algorithm to handle important image features such as triple points and other multiple junctions next by generalizing the data fidelity term of the original mumford shah functional to incorporate a spatially varying penalty we extend our method to problems in which data quality varies across the image and to images in which sets of pixel measurements are missing this more general model leads us to a novel pde based approach for simultaneous image magnification segmentation and smoothing thereby extending the traditional applications of the mumford shah functional which only considers simultaneous segmentation and smoothing

existence of solutions for hyperbolic hemivariational inequalities in this paper we study a hyperbolic hemivariational inequality with a nonlinear pseudomonotone operator depending on the derivative of an unknown function and a linear monotone operator depending on an unknown function using the surjectivity result for l pseudomonotone operators an existence result for such inequalities is proved

multiple valued logic its status and its future multiple valued logic in which the number of discrete logic levels is not confined to two has been the subject of much research over many years the practical objective of this work has been to increase the information content of the digital signals in a system to a higher value than that provided by binary operation in this tutorial survey paper we will review the historical developments in this field both in circuit realizations and in methods of handling multiple valued design data and consider the present state of the art and future expectations

using prior shapes in geometric active contours in a variational framework in this paper we report an active contour algorithm that is capable of using prior shapes the energy functional of the contour is modified so that the energy depends on the image gradient as well as the prior shape the model provides the segmentation and the transformation that maps the segmented contour to the prior shape the active contour is able to find boundaries that are similar in shape to the prior even when the entire boundary is not visible in the image i e when the boundary has gaps a level set formulation of the active contour is presented the existence of the solution to the energy minimization is also established we also report experimental results of the use of this contour on 2d synthetic images ultrasound images and fmri images classical active contours cannot be used in many of these images

on coupled wave equation of kirchhoff type with nonlinear boundary damping and memory term in this paper we prove the existence of the solution to the mixed problem for coupled wave equation of kirchhoff type with nonlinear boundary damping and memory term moreover we discuss the uniform decay of the solution

energy decay for nondissipative distributed systems with boundary damping and source term abstract in this paper we consider energy decay for nondissipative distributed systems with boundary damping and source terms first we consider the wave equation u u h u u u second we consider the case h u u in both first and second cases we have the nonlinear boundary condition u 0 t k t s x u s d s a x g u 0 we study energy decay using the multiplier technique and equivalent energy

on weak solutions for hyperbolic differential inclusion with discontinuous nonlinearities abstract in this paper we study the existence of global weak solutions for hyperbolic differential inclusion with a discontinuous and nonlinear multi valued term and then investigate the asymptotic behavior of the solutions

variational methods for non differentiable functionals and their applications to partial differential equations the interest in extending the theory of nonlinear partial differential equations pde to pde with discontinuous nonlinearities dnde has been increasing daily the reasons are twofold 1 many free boundary problems may be reduced to boundary value problems of dnde cf chang 16 71 chang and jiang 9 and fleishman and mahar 121 2 sometimes in dealing with a pde problem it is beneficial to put the original pde into a large category for instance dnde cf chang 7 simply speaking a dnde is as follows

preferential image segmentation using trees of shapes a novel preferential image segmentation method is proposed that performs image segmentation and object recognition using mathematical morphologies the method preferentially segments objects that have intensities and boundaries similar to those of objects in a database of prior images a tree of shapes is utilized to represent the content distributions in images and curve matching is applied to compare the boundaries the algorithm is invariant to contrast change and similarity transformations of translation rotation and scale a performance evaluation of the proposed method using a large image dataset is provided experimental results show that the proposed approach is promising for applications such as object segmentation and video tracking with cluttered backgrounds

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

on the size of plas required to realize binary and multiple valued functions upper and lower bounds are shown for the average number of product terms required in the minimal realization as a function of the number of nonzero output values the variance in addition to the bounds allows conclusions to be drawn about how pla size determines the set of realizable functions although the bounds are most accurate when there are few nonzero values they are adequate for analyzing commercially available plas the analysis shows that for all but one commercially available pla the number of nonzero values is a statistically meaningful criterion for determining whether or not a given function is likely to be realized

scale sets image analysis this paper introduces a multi scale theory of piecewise image modelling called the scale sets theory and which can be regarded as a region oriented scale space theory the first part of the paper studies the general structure of a geometrically unbiased region oriented multi scale image description and introduces the scale sets representation a representation which allows to handle such a description exactly the second part of the paper deals with the way scale sets image analyses can be built according to an energy minimization principle we consider a rather general formulation of the partitioning problem which involves minimizing a two term based energy of the form c d where d is a goodness of fit term and c is a regularization term we describe the way such energies arise from basic principles of approximate modelling and we relate them to operational rate distorsion problems involved in lossy compression problems we then show that an important subset of these energies constitutes a class of multi scale energies in that the minimal cut of a hierarchy gets coarser and coarser as parameter increases this allows us to devise a fast dynamic programming procedure to find the complete scale sets representation of this family of minimal cuts considering then the construction of the hierarchy from which the minimal cuts are extracted we end up with an exact and parameter free algorithm to build scale sets image descriptions whose sections constitute a monotone sequence of upward global minima of a multi scale energy which is called the scale climbing algorithm this algorithm can be viewed as a continuation method along the scale dimension or as a minimum pursuit along the operational rate distorsion curve furthermore the solution verifies a linear scale invariance property which allows to completely postpone the tuning of the scale parameter to a subsequent stage for computational reasons the scale climbing algorithm is approximated by a pair wise region merging scheme however the principal properties of the solutions are kept some results obtained with mumford shah s piece wise constant model and a variant are provided and different applications of the proposed multi scale analyses are finally sketched

fast computation of a contrast invariant image representation this paper sets out a new representation of an image which is contrast independent the image is decomposed into a tree of shapes based on connected components of level sets which provides a full and nonredundant representation of the image a fast algorithm to compute the tree the fast level lines transform fllt is explained in detail some simple and direct applications of this representation are shown

optimal approximations by piecewise smooth functions and associated variational problems abstract this reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision in computer vision a fundamental problem is to appropriately decompose the domain r of a function g x y of two variables this problem starts by describing the physical situation which produces images assume that a three dimensional world is observed by an eye or camera from some point p and that g1 rho represents the intensity of the light in this world approaching the point sub 1 from a direction rho if one has a lens at p focusing this light on a retina or a film in both cases a plane domain r in which we may introduce coordinates x y then let g x y be the strength of the light signal striking r at a point with coordinates x y g x y is essentially the same as sub 1 rho possibly after a simple transformation given by the geometry of the imaging syste the function g x y defined on the plane domain r will be called an image what sort of function is g the light reflected off the surfaces si of various solid objects o sub i visible from p will strike the domain r in various open subsets r sub i when one object o1 is partially in front of another object o2 as seen from p but some of object o2 appears as the background to the sides of o1 then the open sets r1 and r2 will have a common boundary the edge of object o1 in the image defined on r and one usually expects the image g x y to be discontinuous along this boundary jhd

wavelet based level set evolution for classification of textured images we present a supervised classification model based on a variational approach this model is specifically devoted to textured images we want to get a partition of an image composed of texture regions separated by regular interfaces each kind of texture defines a class we use a wavelet packet transform to analyze the textures characterized by their energy distribution in each sub band in order to have an image segmentation according to the classes we model the regions and their interfaces by level set functions we define a functional on these level sets whose minimizers define the optimal classification according to texture a system of coupled pdes is deduced from the functional by solving this system each region evolves according to its wavelet coefficients and interacts with the neighbor regions in order to obtain a partition with regular contours experiments are shown on synthetic and real images

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

an optimization technique for the design of multiple valued pla s an optimization technique for the design of two types of multiple valued plas is described in a type i pla the multiple valued function is realized directly whereas in a type ii pla output encoding is used to encode the binary output of the pla in both types multiple function literal circuits are used for the purpose of minimization it is shown that the proposed technique leads to a considerably reduced size of pla when compared to the earlier techniques

non differentiable functionals and applications to elliptic problems with discontinuous nonlinearities abstract multiple critical points theorems for non differentiable functionals are established applications both to elliptic variational hemivariational inequalities and eigenvalue problems with discontinuous nonlinearities are then presented

an eigenvalue dirichlet problem involving the p laplacian with discontinuous nonlinearities a multiplicity result for an eigenvalue dirichlet problem involving the p laplacian with discontinuous nonlinearities is obtained the proof is based on a three critical points theorem for nondifferentiable functionals

natural image statistics for natural image segmentation we integrate a model for filter response statistics of natural images into a variational framework for image segmentation incorporated in a sound probabilistic distance measure the model drives level sets toward meaningful segmentations of complex textures and natural scenes despite its enhanced descriptive power our approach preserves the efficiency of level set based segmentation since each region comprises two model parameters only analyzing thousands of natural images we select suitable filter banks validate the statistical basis of our model and demonstrate that it outperforms variational segmentation methods using second order statistics

on the optimal design of multiple valued plas a description is given of the design and analysis of three types of multivalued plas programmable logic arrays type 1 plas realize functions directly in the form of the max of min of literal functions and constants in type 2 plas the body of the pla is binary and the output is encoded as a multiple valued logic value type 3 plas are the same as type 2 plas except for the use of 2 bit decoders and a permutation network on the input using the number of columns required to realize a given function as a measure to compare plas it is shown that type 3 plas are superior to type 2 which in turn are superior to type 1

input variable assignment and output phase optimization of pla s a pla minimization system having the following features is presented 1 minimization of both two level pla s and pla s with two bit decoders 2 optimal input variable assignment to the decoders 3 optimal output phase assignment and 4 essential prime implicants detection without generating all the prime implicants