interactive decision making for multiobjective linear fractional programming problems with block angular structure involving fuzzy numbers abstract in this paper by considering the experts vague or fuzzy understanding of the nature of the parameters in the problem formulation process multiobjective linear fractional programming problems with block angular structure involving fuzzy numbers are formulated through the use of the level sets of fuzzy numbers an extended pareto optimality concept called the pareto optimality is introduced to generate a candidate for the satisficing solution which is also pareto optimal the decision maker is asked to specify the degree and the reference objective values it is shown that the corresponding pareto optimal solution can be easily obtained by solving the minimax problems for which the dantzig wolfe decomposition method and ritter s partitioning procedure are applicable then a linear programming based interactive decision making method with decomposition procedures for deriving a satisficing solution for the decision maker efficiently from an pareto optimal solution set is presented an illustrative numerical example is provided to demonstrate the feasibility of the proposed method

finite element methods for active contour models and balloons for 2 d and 3 d images the use of energy minimizing curves known as snakes to extract features of interest in images has been introduced by kass witkin and terzopoulos 1987 a balloon model was introduced by cohen 1991 as a way to generalize and solve some of the problems encountered with the original method a 3 d generalization of the balloon model as a 3 d deformable surface which evolves in 3 d images is presented it is deformed under the action of internal and external forces attracting the surface toward detected edgels by means of an attraction potential we also show properties of energy minimizing surfaces concerning their relationship with 3 d edge points to solve the minimization problem for a surface two simplified approaches are shown first defining a 3 d surface as a series of 2 d planar curves then after comparing finite element method and finite difference method in the 2 d problem we solve the 3 d model using the finite element method yielding greater stability and faster convergence this model is applied for segmenting magnetic resonance images

automatic ventricular cavity boundary detection from sequential ultrasound images using simulated annealing an automatic algorithm has been developed for high speed detection of cavity boundaries in sequential 2 d echocardiograms using an optimization algorithm called simulated annealing sa the algorithm has three stages 1 a predetermined window of size n m is decimated to size n m after low pass filtering 2 an iterative radial gradient algorithm is employed to determine the center of gravity cg of the cavity 3 64 radii which originate from the cg defined in stage 2 are bounded by the high probability region each bounded radius is defined as a link in a 1 d 64 member cyclic markov random field this algorithm is unique in that it compounds spatial and temporal information along with a physical model in its decision rule whereas most other algorithms base their decisions on spatial data alone this is the first implementation of a relaxation algorithm for edge detection in echocardiograms results attained using this algorithm on real data have been highly encouraging

tension in active shapes the concept of tension is introduced in the framework of active contours with prior shape information and it is used to improve image segmentation in particular two properties of this new quantity are shown 1 high values of the tension correspond to undesired equilibrium points of the cost function under minimization and 2 tension decreases if a curve is split into two or more parts based on these ideas a tree is generated whose nodes are different local minima of the cost function deeper nodes in the tree are expected to correspond to lower values of the cost function in this way the search for the global optimum is reduced to visiting and pruning a binary tree the proposed method has been applied to the problem of fish segmentation from low quality underwater images qualitative and quantitative comparison with existing algorithms based on the euler lagrange diffusion equations shows the superiority of the proposed approach in avoiding undesired local minima

the integration of image segmentation maps using region and edge information we present an algorithm that integrates multiple region segmentation maps and edge maps it operates independently of image sources and specific region segmentation or edge detection techniques user specified weights and the arbitrary mixing of region edge maps are allowed the integration algorithm enables multiple edge detection region segmentation modules to work in parallel as front ends the solution procedure consists of three steps a maximum likelihood estimator provides initial solutions to the positions of edge pixels from various inputs an iterative procedure using only local information without edge tracing then minimizes the contour curvature finally regions are merged to guarantee that each region is large and compact the channel resolution width controls the spatial scope of the initial estimation and contour smoothing to facilitate multiscale processing experimental results are demonstrated using data from different types of sensors and processing techniques the results show an improvement over individual inputs and a strong resemblance to human generated segmentation

non autonomous second order hamiltonian systems abstract we study the existence of periodic solutions for a second order non autonomous dynamical system containing variable kinetic energy terms our assumptions balance the interaction between the kinetic energy and the potential energy with neither one dominating the other we study sublinear problems and the existence of non constant solutions

attractable snakes based on the greedy algorithm for contour extraction abstract while most improved snakes were built under the original variational scheme this paper presents an attractable snake based on the greedy snake williams and shah cvgip image understanding 55 1 1992 14 26 by use of a direct feedback mechanism that is seamlessly consistent with the search strategy of the greedy algorithm the proposed approach is capable of inheriting the simplicity and efficiency of that algorithm and performing competitively with related snakes to avoid undesirable local minima an overall optimal edge detector is designed a suitable synthetic convergent criterion is proposed which enables snakes to converge normally or oscillatingly on target objects an adaptive interpolation scheme that encourages snakes to accurately sense the details of object shapes is also described this model is applied to extract contours from various images with encouraging results

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

multiple objective linear fractional programming this paper presents a simplex based solution procedure for the multiple objective linear fractional programming problem by 1 departing slightly from the traditional notion of efficiency and 2 augmenting the feasible region as in goal programming the solution procedure solves for all weakly efficient vertices of the augmented feasible region the article discusses the difficulties that must be addressed in multiple objective linear fractional programming and motivates the solution algorithm that is developed

periodic second order superlinear hamiltonian systems abstract we consider periodic solutions for superlinear second order non autonomous dynamical systems including both kinetic and potential terms we study the existence of nontrivial and ground state solutions

taylor series approach to fuzzy multiobjective linear fractional programming this paper presents the use of a taylor series for fuzzy multiobjective linear fractional programming problems fmolfp the taylor series is a series expansion that a representation of a function in the proposed approach membership functions associated with each objective of fuzzy multiobjective linear fractional programming problem transformed by using a taylor series are unified thus the problem is reduced to a single objective practical applications and numerical examples are used in order to show the efficiency and superiority of the proposed approach

probe based automatic target recognition in infrared imagery a probe based approach combined with image modeling is used to recognize targets in spatially resolved single frame forward looking infrared flir imagery a probe is a simple mathematical function that operates locally on pixel values and produces an output that is directly usable by an algorithm an empirical probability density function of the probe values is obtained from a local region of the image and used to estimate the probability that a target of known shape is present target shape information is obtained from three dimensional 3 d computer aided design cad models knowledge of the probe values along with probe probability density functions and target shape information allows the likelihood ratio between a target hypothesis and background hypothesis to be written the generalized likelihood ratio test is then used to accept one of the target poses or to choose the background hypothesis we present an image model for infrared images the resulting recognition algorithm and experimental results on three sets of real and synthetic flir imagery

brownian strings segmenting images with stochastically deformable contours this paper describes an image segmentation technique in which an arbitrarily shaped contour was deformed stochastically until it fitted around an object of interest the evolution of the contour was controlled by a simulated annealing process which caused the contour to settle into the global minimum of an image derived energy function the nonparametric energy function was derived from the statistical properties of previously segmented images thereby incorporating prior experience since the method was based on a state space search for the contour with the best global properties it was stable in the presence of image errors which confound segmentation techniques based on local criteria such as connectivity unlike snakes and other active contour approaches the new method could handle arbitrarily irregular contours in which each interpixel crack represented an independent degree of freedom furthermore since the contour evolved toward the global minimum of the energy the method was more suitable for fully automatic applications than the snake algorithm which frequently has to be reinitialized when the contour becomes trapped in local energy minima high computational complexity was avoided by efficiently introducing a random local perturbation in a time independent of contour length providing control over the size of the perturbation and assuring that resulting shape changes were unbiased the method was illustrated by using it to find the brain surface in magnetic resonance head images and to track blood vessels in angiograms

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

an integrated approach to 2d object recognition a multilevel markov random field mrf energy environment has been developed that simultaneously performs delineation representation and classification of two dimensional objects by using a global optimization technique this environment supports a multipolar shape representation which establishes a dynamic mrf structure this structure is initialized as a single center polar representation and uses minimum description length tests to determine whether to establish new polar centers the polar representations at these centers are compared with a database of such representations in order to identify pieces of objects and the results of these comparisons are used to compile evidence for global object identifications this method is potentially more robust than conventional multistaged approaches to object recognition because it incorporates all the information about the objects into a single adaptive decision process and its use of a multipolar representation allows it to handle partially occluded objects

deformable contour method a constrained optimization approach in this paper a class of deformable contour methods using a constrained optimization approach of minimizing a contour energy function satisfying an interior homogeneity constraint is proposed the class is defined by any positive potential function describing the contour interior characterization an evolutionary strategy is used to derive the algorithm a similarity threshold tv can be used to determine the interior size and shape of the contour sensitivity and significance of tv and a spreadness measure are also discussed and shown experiments on noisy images and the convergence to a minimum energy gap contour are included the developed method has been applied to a variety of medical images from ct abdominal section mri image slices of brain brain tumor a pig heart ultrasound image sequence to visual blood cell images as the results show the algorithm can be adapted to a broad range of medical images containing objects with vague complex and or irregular shape boundary inhomogeneous and noisy interior and contour with small gaps

periodic solutions for second order systems with not uniformly coercive potential abstract the existence and multiplicity of periodic solutions are obtained for the nonautonomous second order systems with locally coercive potential that is f t x as x for a e t in some positive measure subset of 0 t by using an analogy of egorov s theorem the properties of subadditive functions the least action principle and a three critical point theorem proposed by brezis and nirenberg

region based strategies for active contour models the variational method has been introduced by kass et al 1987 in the field of object contour modeling as an alternative to the more traditional edge detection edge thinning edge sorting sequence since the method is based on a pre processing of the image to yield an edge map it shares the limitations of the edge detectors it uses in this paper we propose a modified variational scheme for contour modeling which uses no edge detection step but local computations instead only around contour neighborhoods as well as an anticipating strategy that enhances the modeling activity of deformable contour curves many of the concepts used were originally introduced to study the local structure of discontinuity in a theoretical and formal statement by leclerc zucker 1987 but never in a practical situation such as this one the first part of the paper introduces a region based energy criterion for active contours and gives an examination of its implications as compared to the gradient edge map energy of snakes then a simplified optimization scheme is presented accounting for internal and external energy in separate steps this leads to a complete treatment which is described in the last sections of the paper 4 and 5 the optimization technique used here is mostly heuristic and is thus presented without a formal proof but is believed to fill a gap between snakes and other useful image representations such as split and merge regions or mixed line labels image fields

a general discrete contour model in two three and four dimensions for topology adaptive multichannel segmentation we present a discrete contour model for the segmentation of image data with any dimension of image domain and value range the model consists of a representation using simplex meshes and a mechanical formulation of influences that drive an iterative segmentation the object s representation as well as the influences are valid for any dimension of the image domain the image influences introduced here can combine information from independent channels of higher dimensional value ranges additionally the topology of the model automatically adapts to objects contained in images noncontextual tests have validated the ability of the model to reproducibly delineate synthetic objects in particular images with a signal to noise ratio of snr spl les 0 5 are delineated within two pixels of their ground truth contour contextual validations have shown the applicability of the model for medical image analysis in image domains of two three and four dimensions in single as well as multichannel value ranges

a class of constrained clustering algorithms for object boundary extraction boundary extraction is a key task in many image analysis operations this paper describes a class of constrained clustering algorithms for object boundary extraction that includes several well known algorithms proposed in different fields deformable models constrained clustering data ordering and traveling salesman problems the algorithms belonging to this class are obtained by the minimization of a cost function with two terms a quadratic regularization term and an image dependent term defined by a set of weighting functions the minimization of the cost function is achieved by lowpass filtering the previous model shape and by attracting the model units toward the centroids of their attraction regions to define a new algorithm belonging to this class the user has to specify a regularization matrix and a set of weighting functions that control the attraction of the model units toward the data the usefulness of this approach is twofold it provides a unified framework for many existing algorithms in pattern recognition and deformable models and allows the design of new recursive schemes

goal programming with linear fractional criteria abstract in this paper we present an extension of goal programming to include linear fractional criteria the extension forms a natural link between goal programming gp and multiple objective linear fractional programming molfp

a goal programming procedure for fuzzy multiobjective linear fractional programming problem abstract this paper presents a goal programming gp procedure for fuzzy multiobjective linear fractional programming fmolfp problems in the proposed approach which is motivated by mohamed fuzzy sets and systems 89 1997 215 gp model for achievement of the highest membership value of each of fuzzy goals defined for the fractional objectives is formulated in the solution process the method of variable change on the under and over deviational variables of the membership goals associated with the fuzzy goals of the model is introduced to solve the problem efficiently by using linear goal programming lgp methodology the approach is illustrated by two numerical examples

markov random field texture models we consider a texture to be a stochastic possibly periodic two dimensional image field a texture model is a mathematical procedure capable of producing and describing a textured image we explore the use of markov random fields as texture models the binomial model where each point in the texture has a binomial distribution with parameter controlled by its neighbors and number of tries equal to the number of gray levels was taken to be the basic model for the analysis a method of generating samples from the binomial model is given followed by a theoretical and practical analysis of the method s convergence examples show how the parameters of the markov random field control the strength and direction of the clustering in the image the power of the binomial model to produce blurry sharp line like and blob like textures is demonstrated natural texture samples were digitized and their parameters were estimated under the markov random field model a hypothesis test was used for an objective assessment of goodness of fit under the markov random field model overall microtextures fit the model well the estimated parameters of the natural textures were used as input to the generation procedure the synthetic microtextures closely resembled their real counterparts while the regular and inhomogeneous textures did not

an image analysis problem in electron microscopy abstract this article considers the problem of identifying the irregular boundary of a magnetic domain in a thin multilayer film using data in the form of an electron micrograph two approaches are illustrated both of which are based on the concept of two smooth intensity surfaces one corresponding to the domain and one corresponding to the background so that the objective is to determine the boundary between the parts of the image where the two surfaces are present in the first a hierarchical bayesian approach priors are assumed for the set of domain background states and for the two intensity surfaces and restoration is carried out using a version of besag s icm procedure it is shown that it is important to initialize the method efficiently the second approach uses a template like model for the boundary and also relies on a bayesian approach the results from the second approach can be used as an end in themselves or as a way of initializing the more flexible first approach several illustrati

deformable shape detection and description via model based region grouping a method for deformable shape detection and recognition is described deformable shape templates are used to partition the image into a globally consistent interpretation determined in part by the minimum description length principle statistical shape models enforce the prior probabilities on global parametric deformations for each object class once trained the system autonomously segments deformed shapes from the background while not merging them with adjacent objects or shadows the formulation can be used to group image regions obtained via any region segmentation algorithm e g texture color or motion the recovered shape models can be used directly in object recognition experiments with color imagery are reported

an interactive fuzzy satisficing method for multiobjective linear fractional programming problems abstract we present a new interactive fuzzy decision making method for solving multiobjective linear fractional programming problems by assuming that the decision maker dm has fuzzy goals for each of the objective functions through the interaction with the dm the fuzzy goals of the dm are quantified by eliciting the corresponding membership functions including nonlinear functions after determining the membership functions if the dm specifies reference membership values the minimax problem is solved by combined use of the bisection method and the linear programming method and the dm is supplied with the corresponding pareto optimal solution together with the trade off rates between the membership functions then by considering the current values of the membership functions as well as the trade off rates the dm responds by updating his her reference membership values in this way the compromise or satisficing solution for the dm can be derived efficiently from among a pareto optimal solution set by updating his her reference membership values on the basis of the proposed method a time sharing computer program is written and an illustrative numerical example is demonstrated along with the computer outputs

a fuzzy satisficing method for large scale linear programming problems with block angular structure abstract in this paper we focus on large scale linear programming problems with block angular structure for which the dantzig wolfe decomposition method has been successfully applied by considering the vague nature of human judgements we assume that the decision maker may have a fuzzy goal for the objective function and fuzzy constraints for the coupling constraints having elicited the corresponding linear membership functions through the interaction with the decision maker if we adopt the convex fuzzy decision for combining them it is shown that under some appropriate conditions the formulated problem can be reduced to a number of independent linear subproblems and the overall satisficing solution for the decision maker is directly obtained just only solving the subproblems

fuzzy approaches for multiple objective linear fractional optimization abstract the problem of finding a solution to a multiple objective linear fractional program arises in several real world situations in this paper we advocate that fuzzy sets theory provides a basis for solving this problem with sufficient consistency and rigorousness after representing imprecise aspirations of the decision maker by structured linguistic variables or converting the original problem via approximations or change of variables into a multiple objective linear program techniques of fuzzy linear programming may be used to reach a satisfactory solution it is shown that under reasonable restrictions this solution is efficient pareto optimal for the original problem numerical examples are also included for illustration

infinitely many periodic solutions for a second order nonautonomous system in this paper we are interested in multiplicity results for a second order nonautonomous system infinitely many solutions follow from a recent variational principle by b ricceri

compact object recognition using energy function based optimization describes a method of recognizing objects whose contours can be represented in smoothly varying polar coordinate form both low and high level information about the object contour smoothness and edge sharpness at the low level and contour shape at the high level are incorporated into a single energy function that defines a 1d cyclic markov random field 1dcmrf this 1dcmrf is based on a polar coordinate object representation whose center can be initialized at any location within the object the recognition process is based on energy function minimization which is implemented by simulated annealing

new existence of periodic solutions for second order non autonomous hamiltonian systems abstract by using mountain pass theorem and local link theorem some existence theorems are obtained for periodic solutions of second order non autonomous hamiltonian systems under local superquadratic condition and other suitable conditions

on deformable models for visual pattern recognition this paper reviews model based methods for non rigid shape recognition these methods model match and classify non rigid shapes which are generally problematic for conventational algorithms using rigid models issues including model representation optimization criteria formulation model matching and classification are examined in detail with the objective to provide interested researchers a roadmap for exploring the field this paper emphasizes on 2d deformable models their potential applications and future research directions particularly on deformable pattern classification are discussed

a general variational principle and some of its applications abstract in this paper given a reflexive real banach space x and two sequentially weakly lower semicontinuous functionals on x with strongly continuous and coercive we are mainly interested in the existence of infinitely many local minima of the functional for each sufficiently large r

a mountain pass theorem 143 in other words the mountain separating 0 and e may even be assumed of zero altitude and the conclusion is still true moreover as we shall show if c a the critical point can be chosen with llx ll r it is interesting to ask whether this extension of the ambrosetti rabinowitz theorem remains true in the infinite dimensional case we prove here that if 1 is strengthened a little to the form 1 there exist real numbers u r r such that 0 a for every x e a x e x y a moreover if c a the critical point can be chosen with r i x0 i r roughly speaking in brief the mountain pass theorem continues to hold for a mountain of zero altitude provided it also has non zero thickness in addition if c a the pass itself occurs precisely on the mountain i e satisfying r llroll r there are two interesting and immediate corollaries the first one says that a c function which has iwo local minimum points also has a third critical point the second states that a u periodic c function with a local minimum e has a critical point x e ku k 0 1 2 the precise statements of the above results will be given in the next sec tions the proof depends upon a lemma of clark 3 formulated here in a version suitable to our purpose in section 3 some applications are presen ted for the forced pendulum equation 2

multiple periodic solutions for second order systems with changing sign potential this paper deals with the multiplicity of solutions of a second order nonautonomous system we extend a previous result of the author relaxing the assumptions on the sign of the potential

a bayesian approach to dynamic contours through stochastic sampling and simulated annealing in many applications of image analysis simply connected objects are to be located in noisy images during the last 5 6 years active contour models have become popular for finding the contours of such objects connected to these models are iterative algorithms for finding the minimizing energy curves making the curves behave dynamically through the iterations these approaches do however have several disadvantages the numerical algorithms that are in use constrain the models that can be used furthermore in many cases only local minima can be achieved in this paper the author discusses a method for curve detection based on a fully bayesian approach a model for image contours which allows the number of nodes on the contours to vary is introduced iterative algorithms based on stochastic sampling is constructed which make it possible to simulate samples from the posterior distribution making estimates and uncertainty measures of specific quantities available further simulated annealing schemes making the curve move dynamically towards the global minimum energy configuration are presented in theory no restrictions on the models are made in practice however computational aspects must be taken into consideration when choosing the models much more general models than the one used for active contours may however be applied the approach is applied to ultrasound images of the left ventricle and to magnetic resonance images of the human brain and show promising results

precise segmentation of multimodal images we propose new techniques for unsupervised segmentation of multimodal grayscale images such that each region of interest relates to a single dominant mode of the empirical marginal probability distribution of grey levels we follow the most conventional approaches in that initial images and desired maps of regions are described by a joint markov gibbs random field mgrf model of independent image signals and interdependent region labels however our focus is on more accurate model identification to better specify region borders each empirical distribution of image signals is precisely approximated by a linear combination of gaussians lcg with positive and negative components we modify an expectation maximization em algorithm to deal with the lcgs and also propose a novel em based sequential technique to get a close initial lcg approximation with which the modified em algorithm should start the proposed technique identifies individual lcg models in a mixed empirical distribution including the number of positive and negative gaussians initial segmentation based on the lcg models is then iteratively refined by using the mgrf with analytically estimated potentials the convergence of the overall segmentation algorithm at each stage is discussed experiments show that the developed techniques segment different types of complex multimodal medical images more accurately than other known algorithms

periodic solutions for a class of nonautonomous second order hamiltonian systems abstract in this paper some existence theorems of periodic solutions of a class of the nonautonomous second order hamiltonian systems x t b t x t h t x t 0 t 0 t are obtained by a mountain pass theorem and a local link theorem

a fuzzy satisficing method for large scale multiobjective linear programming problems with block angular structure abstract in this paper we focus on large scale multiobjective linear programming problems with the block angular structure by considering the imprecise nature of human judgements we assume that the decision maker may have a fuzzy goal for each of the objective functions having elicited the corresponding linear membership functions through the interaction with the decision maker we adopt the fuzzy decision for aggregating them then it is shown that the formulated problem can be reduced to one master problem and a number of linear subproblems and the satisficing solution for the decision maker can be obtained by directly applying the dantzig wolfe decomposition method