stability of cauchy jensen type functional equation in generalized fuzzy normed spaces in this paper we establish some stability results concerning the cauchy jensen functional equation in generalized fuzzy normed spaces the results of the present paper improve and extend some recent results

cubica independent component analysis by simultaneous third and fourth order cumulant diagonalization cubica which is an improved method for independent component analysis ica based on the diagonalization of cumulant tensors is proposed it is based on comon s algorithm but it takes third and fourth order cumulant tensors into account simultaneously the underlying contrast function is also mathematically much simpler and has a more intuitive interpretation it is therefore easier to optimize and approximate a comparison with comon s and three other ica algorithms on different data sets demonstrates its performance

fuzzy ψ contractive mappings in non archimedean fuzzy metric spaces this paper deals with some issues of fixed point theory involving fuzzy contractive mappings introduced by gregori and sapena we enlarge this class and prove a banach contraction theorem in m complete non archimedean fuzzy metric spaces under arbitrary t norms partially answering a question of gregori and sapena on fixed point theorems in fuzzy metric spaces fuzzy sets and systems 125 2002 245 252

unsupervised variational image segmentation classification using a weibull observation model studies have shown that the weibull distribution can model accurately a wide variety of images its parameters index a family of distributions which includes the exponential and approximations of the gaussian and the raleigh models widely used in image segmentation this study investigates the weibull distribution in unsupervised image segmentation and classification by a variational method the data term of the segmentation functional measures the conformity of the image intensity in each region to a weibull distribution whose parameters are determined jointly with the segmentation minimization of the functional is implemented by active curves via level sets and consists of iterations of two consecutive steps curve evolution via euler lagrange descent equations and evaluation of the weibull distribution parameters experiments with synthetic and real images are described which verify the validity of method and its implementation

improving feature space based image segmentation via density modification feature space based approaches have been popularly used to perform low level image analysis in this paper a density modification framework that enhances density map based discriminability of feature values in a feature space is proposed in order to aid feature space based segmentation in images the framework embeds a position dependent property associated with each sample in the feature space of an image into the corresponding density map and hence modifies it the property association and embedding operations in the framework is implemented using a fuzzy set theory based system devised with cues from beam theory of solid mechanics and the appropriateness of this approach is established qualitative and quantitative experimental results of segmentation in images are given to demonstrate the effectiveness of the proposed density modification framework and the usefulness of feature space based segmentation via density modification

stability of a general mixed additive cubic functional equation in non archimedean fuzzy normed spaces we establish some stability results concerning the general mixed additive cubic functional equation in non archimedean fuzzy normed spaces in addition we establish some results of approximately general mixed additive cubic mappings in non archimedean fuzzy normed spaces the results improve and extend some recent results

robust noise region based active contour model via local similarity factor for image segmentation abstract image segmentation using a region based active contour model could present difficulties when its noise distribution is unknown to overcome this problem this paper proposes a novel region based model for the segmentation of objects or structures in images by introducing a local similarity factor which relies on the local spatial distance within a local window and local intensity difference to improve the segmentation results by using this local similarity factor the proposed method can accurately extract the object boundary while guaranteeing certain noise robustness furthermore the proposed algorithm completely avoids the pre processing steps typical of region based contour model segmentation resulting in a higher preservation of image details experiments performed on synthetic images and real word images demonstrate that the proposed algorithm as compared with the state of art algorithms is more efficient and robust to higher noise level manifestations in the images

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

a fixed point theorem and the hyers ulam stability in non archimedean spaces abstract we prove a fixed point theorem in complete non archimedean normed spaces and show its applications in the hyers ulam stability of some functional equations

a generalization of joint diagonalization criteria for source separation in the field of blind source separation joint diagonalization based approaches constitute an important framework leading to useful algorithms such as the popular joint approximate diagonalization of eigenmatrices jade and simultaneous third order tensor diagonalization stotd algorithms however they are often restricted to the case of cumulants of order four in this paper we extend the results leading to jade and stotd to cumulants of any order greater than or equal to three by exhibiting a new family of contrast functions that constitutes then a unified framework for the above known results this also leads us to generalize some links between contrast functions and joint diagonalization criteria on which these algorithms are based in turn one contrast of the new family allows us to show that a function previously proposed as a separation criterion is also a contrast moreover for the two generalized jade and stotd contrasts the analytical optimal solution in the case of two sources is derived and shown to keep the same simple expression whatever the cumulant order finally some computer simulations illustrate the potential advantage one can take by considering statistics of different orders for the joint diagonalization of cumulant matrices

a geometric model for active contours in image processing we propose a new model for active contours based on a geometric partial differential equation our model is intrinsec stable satisfies the maximum principle and permits a rigorous mathematical analysis it enables us to extract smooth shapes we cannot retrieve angles and it can be adapted to find several contours simultaneously moreover as a consequence of the stability we can design robust algorithms which can be engineed with no parameters in applications numerical experiments are presented

the stability of the additive cauchy functional equation in non archimedean fuzzy normed spaces a stability result for the additive cauchy functional equation in non archimedean fuzzy normed spaces over a field with valuation is given by using the concept of countable extension of a t norm

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

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

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

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

a new stochastic variational pde model for soft mumford shah segmentation abstract in this paper a new stochastic variational pde model is developed using instead of hard segmentation soft segmentation in this way each pixel is allowed to belong to each image pattern with some probability our work proposes a functional with variable exponent which provides a more accurate model for image segmentation and denoising the diffusion resulting from the proposed model is a combination between tv based and isotropic smoothing the modeling procedure computational implementation and results are explored in detail and numerical examples of real and synthetic images are presented

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

perturbation of generalized derivations in fuzzy menger normed algebras in this paper we introduce a notion for fuzzy menger normed algebra then we will investigate continuity of algebraic operations in this space we will show that the class of all fuzzy menger normed algebras strictly contains the class of normed algebras finally we will prove hyers ulam rassias superstability of generalized derivation functional equationf ax by vw af x bf y vf w g v w x y v email protected x 0 a email protected c in complete fuzzy menger normed algebras a few applications of our results will be exhibited

comments on cubica independent component analysis by simultaneous third and fourth order cumulant diagonalization source separation based on joint diagonalization of cumulant matrices or tensors has led now to classical algorithms in a previous paper by blaschke and wiskott an algorithm based on the above principle is proposed it combines third and fourth order cumulants and it is claimed to possess interesting properties this comment has two objectives we point out imprecisions of statement and we give additional references of closely related works some of them presenting identical issues

an active contour model and its algorithms with local and global gaussian distribution fitting energies in this paper we propose an active contour model and its corresponding algorithms with detailed implementation for image segmentation in the proposed model the local and global region fitting energies are described by the combination of the local and global gaussian distributions with different means and variances respectively in this combination we increase a weighting coefficient by which we can adjust the ratio between the local and global region fitting energies then we present an algorithm for implementing the proposed model directly considering that in practice the selection of the weighting coefficient is troublesome we present a modified algorithm in order to overcome this problem and increase the flexibility by adaptively updating the weighting coefficient and the time step with the contour evolution this algorithm is less sensitive to the initialization of the contour and can speed up the convergence rate besides it is robust to the noise and can be used to extract the desired objects experiment results demonstrate that the proposed model and its algorithms are effective with application to both the synthetic and real world images

a level set approach for computing solutions to incompressible two phase flow a level set approach for computing solutions to incompressible two phase flow is presented the interface between the two fluids is considered to be sharp and is described as the zero level set of a smooth function a new treatment of the level set method allows us to efficiently maintain the level set function as the signed distance from the interface we never have to explicitly reconstruct or find the zero level set consequently we are able to handle arbitrarily complex topologies large density and viscosity ratios and surface tension on relatively coarse grids we use a second order projection method along with a second order upwinded procedure for advecting the momentum and level set equations we consider the motion of air bubbles and water drops we also compute flows with multiple fluids such as air oil and water

fuzzy bounded linear operators in this paper a notion of boundedness of a linear operator from a fuzzy normed linear space to another fuzzy normed linear space is introduced and two types strong and weak of fuzzy bounded linear operators are defined relation between fuzzy continuity and fuzzy boundedness is studied definitions of fuzzy bounded linear functionals are given and the notions of fuzzy dual spaces are developed the hahn banach theorem the open mapping theorem the closed graph theorem and the uniform boundedness principle theorem are established

fuzzy approximately cubic mappings we establish some stability results concerning the cubic functional equationf 2x y f 2x y 2f x y 2f x y 12f x in fuzzy normed spaces we discuss the fuzzy continuity of the cubic mappings and show that the existence of a solution for any approximately cubic mapping guarantees the completeness of the fuzzy normed space

on set valued nonlinear equations in menger probabilistic normed spaces we introduce the concept of probabilistic f j contractor couple which allows us to consider set valued nonlinear operator equations in a large class of probabilistic normed spaces our results complete those from cho et al nonlinear equations for fuzzy mappings in probabilistic normed spaces fuzzy sets and systems 110 2000 115 122 and fang on nonlinear equations for fuzzy mappings in probabilistic normed spaces fuzzy sets and systems 131 2002 357 364

multiscale roughness measure for color image segmentation color image segmentation is always an important technique in image processing system highly precise segmentation with low computation complexity can be achieved through roughness measurement which approximate the color histogram based on rough set theory however due to the imprecise description of neighborhood similarity the existing roughness measure tends to over focus on the trivial homogeneous regions but is not accurate enough to measure the color homogeneity this paper aims to construct a multiscale roughness measure through simulating the human vision we apply the theories of linear scale space and rough sets to generate the hierarchical roughness of color distribution under multiple scales this multiscale roughness can tolerate the disturbance of trivial regions and also can provide the multilevel homogeneity representation in vision which therefore produces precise and intuitive segmentation results furthermore we propose roughness entropy for scale selection the optimal scale for segmentation is decided by the entropy variation the proposed method shows the encouraging performance in the experiments based on berkeley segmentation database

an intensive restraint topology adaptive snake model and its application in tracking dynamic image sequence the aim of this work is to propose an improved intensive restraint topology adaptive snake model for detecting and tracking target contours with complex topological morphology from dynamic gray scale image sequences the image is discretized by orthogonal equidistant grid lines and snake nodes are constrained to move only from one grid vertex to another along grid lines thus the computation is much simpler than those of other t snakes since complicated calculation of intersection points of snake curve and grid lines is not required topological transformation is implemented through splitting snake nodes as well as automatically detecting and eliminating topological collision an adaptive weighted expansion energy term is introduced into snake s energy function driving the model to pass across the region with non uniform intensity distribution inside the target region the required manual interaction is reduced to only select a random point within the target region in the first frame of the image sequence for subsequent frames the detection result in the previous frame is regarded as the initial model in the current frame through experiments on simulated image data and clinical x ray coronary angiographic sequences the model s topological flexibility and lower computation cost compared with other t snakes are demonstrated also the sensitivity of the model to weights of the energy terms and grid size as well as the initial plan of the model is discussed based on experimental results

active contours driven by local image fitting energy a new region based active contour model that embeds the image local information is proposed in this paper by introducing the local image fitting lif energy to extract the local image information our model is able to segment images with intensity inhomogeneities moreover a novel method based on gaussian filtering for variational level set is proposed to regularize the level set function it can not only ensure the smoothness of the level set function but also eliminate the requirement of re initialization which is very computationally expensive experiments show that the proposed method achieves similar results to the lbf local binary fitting energy model but it is much more computationally efficient in addition our approach maintains the sub pixel accuracy and boundary regularization properties

on the stability of the additive cauchy functional equation in random normed spaces some stability results for the functional equations of cauchy and jensen in probabilistic setting are proved by using the fixed point method

a generalization of the hyers ulam rassias stability of jensen s equation in this paper we prove a generalization of the stability of the jensen s equation in the spirit of hyers ulam rassias and g vruta

on fuzzy metric spaces abstract in this paper we introduce the concept of a fuzzy metric space the distance between two points in a fuzzy metric space is a non negative upper semicontinuous normal and convex fuzzy number properties of fuzzy metric spaces are studied and some fixed point theorems are proved

fixed point theorems and the ulam hyers stability in non archimedean cone metric spaces abstract let x p be a metric space with a k valued non archimedean metric p in this paper we prove the existence and approximation of a fixed point for operators f x x satisfying the contractive condition in the form p f x f y q p x y where q k k is an increasing operator then we study the generalized ulam hyers stability of fixed point equations we next obtain an extension of the krasnoselskii fixed point theorem for the sum of two operators finally an application to functional equations is given

fuzzy versions of hyers ulam rassias theorem we introduce three reasonable versions of fuzzy approximately additive functions in fuzzy normed spaces more precisely we show under some suitable conditions that an approximately additive function can be approximated by an additive mapping in a fuzzy sense

weighted level set evolution based on local edge features for medical image segmentation level set methods have been widely used to implement active contours for image segmentation applications due to their good boundary detection accuracy in the context of medical image segmentation weak edges and inhomogeneities remain important issues that may hinder the accuracy of any segmentation method based on active contours implemented using level set methods this paper proposes a method based on active contours implemented using level set methods for segmentation of such medical images the proposed method uses a level set evolution that is based on the minimization of an objective energy functional whose energy terms are weighted according to their relative importance in detecting boundaries this relative importance is computed based on local edge features collected from the adjacent region located inside and outside of the evolving contour the local edge features employed are the edge intensity and the degree of alignment between the image s gradient vector flow field and the evolving contour s normal we evaluate the proposed method for segmentation of various regions in real mri and ct slices x ray images and ultra sound images evaluation results confirm the advantage of weighting energy forces using local edge features to reduce leakage these results also show that the proposed method leads to more accurate boundary detection results than the state of the art edge based level set segmentation methods particularly around weak edges

independent component analysis and simultaneous third order tensor diagonalization comon s 1994 well known scheme for independent component analysis ica is based on the maximal diagonalization in a least squares sense of a higher order cumulant tensor in a previous paper we proved that for fourth order cumulants the computation of an elementary jacobi rotation is equivalent to the computation of the best rank 1 approximation of a fourth order tensor in this paper we show that for third order tensors the computation of an elementary jacobi rotation is again equivalent to a best rank 1 approximation however here it is a matrix that has to be approximated this favorable computational load makes it attractive to do something third order like for fourth order cumulant tensors as well we show that simultaneous optimal diagonalization of third order tensor slices of the fourth order cumulant is a suitable strategy this simultaneous third order tensor diagonalization approach stotd is similar in spirit to the efficient jade algorithm

a generalization of the hyers ulam rassias stability of approximately additive mappings abstract in this paper we prove a generalization of the stability of approximately additive mappings in the spirit of hyers ulam and rassias

flux maximizing geometric flows several geometric active contour models have been proposed for segmentation in computer vision and image analysis the essential idea is to evolve a curve in 2d or a surface in 3d under constraints from image forces so that it clings to features of interest in an intensity image recent variations on this theme take into account properties of enclosed regions and allow for multiple curves or surfaces to be simultaneously represented however it is still unclear how to apply these techniques to images of narrow elongated structures such as blood vessels where intensity contrast may be low and reliable region statistics cannot be computed to address this problem we derive the gradient flows which maximize the rate of increase of flux of an appropriate vector field through a curve in 2d or a surface in 3d the key idea is to exploit the direction of the vector field along with its magnitude the calculations lead to a simple and elegant interpretation which is essentially parameter free and has the same form in both dimensions we illustrate its advantages with several level set based segmentations of 2d and 3d angiography images of blood vessels

fast geodesic active contours we use an unconditionally stable numerical scheme to implement a fast version of the geodesic active contour model the proposed scheme is useful for object segmentation in images like tracking moving objects in a sequence of images the method is based on the weickert romeney viergever additive operator splitting aos scheme it is applied at small regions motivated by the adalsteinsson sethian level set narrow band approach and uses sethian s 1996 fast marching method for re initialization experimental results demonstrate the power of the new method for tracking in color movies

active contours driven by global and local weighted signed pressure force for image segmentation abstract this paper proposes a new global and local weighted signed pressure force spf based active contour model acm to segment various types of images first by introducing the normalized global minimum absolute differences as the coefficients of global inner and outer region fitting centers a new global weighted spf gwspf is defined which makes the best of the difference information of inner and outer regions and improves segmentation performance second by introducing the normalized local minimum absolute differences as the coefficients of local inner and outer region fitting centers similarly a new local weighted spf lwspf is defined and added to the above global weighted spf third the global and local within class variances of the image are used to weight the gwspf and the lwspf which can automatically adjust the effect degrees of the gwspf and the lwspf experiments on many kinds of real world images have validated that the proposed model is superior to popular acms in segmentation accuracy in addition it is robust to the initial curve

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

independent component analysis jacobi like diagonalization of optimized composite order cumulants in the field of blind source separation jacobi like diagonalization based approaches constitute an important tool for independent component analysis ica recently simultaneous diagonalization of cumulant matrices of third and fourth order has been studied by a number of authors in this work we present an optimal parametrized composition of these cumulants that puts two classical contrasts namely the cumulantbased ica and the weighted fourth order contrast in a common framework it is shown that the optimal weight parameter depends on the a priori statistical knowledge of the original mixing sources following the same spirit of the ica algorithm we derive the analytical solution for the case of two sources finally a number of computer simulations have been performed to illustrate the behaviour of the jacobi like iterations for the maximization of the proposed parametrized contrast

hyers ulam stability of fuzzy fractional volterra integral equations with the kernel ψ function via successive approximation method abstract in this paper we investigative the hyers ulam stability and the hyers ulam rassias stability of fuzzy fractional volterra integral equations ffvies involving the kernel function we propose conditions for the existence uniqueness and stability of ffvie by employing the method of successive approximation to visualize the theoretical results some examples and numerical simulations are given

active contours driven by local likelihood image fitting energy for image segmentation accurate image segmentation is an essential step in image analysis and understanding where active contour models play an important part due to the noise low contrast and intensity inhomogeneity in images many segmentation algorithms suffer from limited accuracy this paper presents a novel region based active contour model for image segmentation by using the variational level set formulation in this model we construct the local likelihood image fitting llif energy functional by describing the neighboring intensities with local gaussian distributions the means and variances of local intensities in the llif energy functional are spatially varying functions which can be iteratively estimated during an energy minimization process to guide the contour evolving toward object boundaries to address diverse image segmentation needs we also expand this model to the multiphase level set multi scale gaussian kernels and narrowband formulations the proposed model has been compared with several state of the art active contour models on images with different modalities our results indicate that the proposed llif model achieves superior performance in image segmentation

finite dimensional fuzzy normed linear space abstract the concept of a fuzzy normed linear space is introduced it is proved that in a finite dimensional fuzzy normed linear space fuzzy norms are the same upto fuzzy equivalence finite dimensional fuzzy subspaces of a fuzzy normed linear space are proved to be necessarily complete fuzzy normed linear spaces

fuzzy topological vector spaces ii abstract some of the properties of fuzzy topological vector spaces are investigated also there are given necessary and sufficient conditions for a family of fuzzy sets in a vector space e to be the family of all neighborhoods of zero for a fuzzy linear topology

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

a nonparametric statistical method for image segmentation using information theory and curve evolution in this paper we present a new information theoretic approach to image segmentation we cast the segmentation problem as the maximization of the mutual information between the region labels and the image pixel intensities subject to a constraint on the total length of the region boundaries we assume that the probability densities associated with the image pixel intensities within each region are completely unknown a priori and we formulate the problem based on nonparametric density estimates due to the nonparametric structure our method does not require the image regions to have a particular type of probability distribution and does not require the extraction and use of a particular statistic we solve the information theoretic optimization problem by deriving the associated gradient flows and applying curve evolution techniques we use level set methods to implement the resulting evolution the experimental results based on both synthetic and real images demonstrate that the proposed technique can solve a variety of challenging image segmentation problems furthermore our method which does not require any training performs as good as methods based on training

nonparametric joint shape and feature priors for image segmentation in many image segmentation problems involving limited and low quality data employing statistical prior information about the shapes of the objects to be segmented can significantly improve the segmentation result however defining probability densities in the space of shapes is an open and challenging problem especially if the object to be segmented comes from a shape density involving multiple modes classes existing techniques in the literature estimate the underlying shape distribution by extending parzen density estimator to the space of shapes in these methods the evolving curve may converge to a shape from a wrong mode of the posterior density when the observed intensities provide very little information about the object boundaries in such scenarios employing both shape and class dependent discriminative feature priors can aid the segmentation process such features may involve e g intensity based textural or geometric information about the objects to be segmented in this paper we propose a segmentation algorithm that uses nonparametric joint shape and feature priors constructed by parzen density estimation we incorporate the learned joint shape and feature prior distribution into a maximum a posteriori estimation framework for segmentation the resulting optimization problem is solved using active contours we present experimental results on a variety of synthetic and real data sets from several fields involving multimodal shape densities experimental results demonstrate the potential of the proposed method

stability of multi additive mappings in non archimedean normed spaces abstract a function f v n w where v is a commutative semigroup w is a linear space and n 1 is an integer is called multi additive if it is additive in each variable in this paper we prove the generalized hyers ulam stability of multi additive mappings in non archimedean normed spaces using the so called direct method

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

an active contour model for image segmentation based on elastic interaction the task of image segmentation is to partition an image into non overlapping regions based on intensity or textural information the active contour methods provide an effective way for segmentation in which the boundaries of the objects are detected by evolving curves in this paper we propose a new edge based active contour method which uses a long range and orientation dependent interaction between image boundaries and the moving curves while maintaining the edge fidelity as a result this method has a large capture range and is able to detect sharp features of the images the velocity field for the moving curves generated by this elastic interaction is calculated using the fast fourier transform fft method level set representation is used for the moving curves so that the topological changes during the evolution are handled automatically this new method is derived based on the elastic interaction between line defects in solids dislocations although it is derived originally for two dimensional segmentation we also extend it to three dimensions the features of the new method are examined by experiments on both synthetic images and medical images of blood vessels comparisons are made with the existing active contour methods

fuzzy stability of the jensen functional equation we establish a generalized hyers ulam rassias stability theorem in the fuzzy sense in particular we introduce the notion of fuzzy approximate jensen mapping and prove that if a fuzzy approximate jensen mapping is continuous at a point then we can approximate it by an everywhere continuous jensen mapping as a fuzzy version of a theorem of schwaiger we also show that if every fuzzy approximate jensen type mapping from the natural numbers into a fuzzy normed space can be approximated by an additive mapping then the fuzzy norm is complete

integrated active contours for texture segmentation we address the issue of textured image segmentation in the context of the gabor feature space of images gabor filters tuned to a set of orientations scales and frequencies are applied to the images to create the gabor feature space a two dimensional riemannian manifold of local features is extracted via the beltrami framework the metric of this surface provides a good indicator of texture changes and is used therefore in a beltrami based diffusion mechanism and in a geodesic active contours algorithm for texture segmentation the performance of the proposed algorithm is compared with that of the edgeless active contours algorithm applied for texture segmentation moreover an integrated approach extending the geodesic and edgeless active contours approaches to texture segmentation is presented we show that combining boundary and region information yields more robust and accurate texture segmentation results

stability of additive mappings in non archimedean fuzzy normed spaces in this paper we introduce a notion of a non archimedean fuzzy norm and study the stability of the cauchy equation in the context of non archimedean fuzzy spaces in the spirit of hyers ulam rassias gavruta as a corollary the stability of the jensen equation is established we indeed present an interdisciplinary relation between the theory of fuzzy spaces the theory of non archimedean spaces and the theory of functional equations

a fixed point approach to the stability of functional equations in non archimedean metric spaces abstract in this note we prove a simple fixed point theorem for a special class of complete metric spaces namely complete non archimedean metric spaces which are connected with some problems coming from quantum physics p adic strings and superstrings we also show that this theorem is a very efficient and convenient tool for proving the hyers ulam stability of a quite wide class of functional equations in a single variable

a novel active contour model for image segmentation using distance regularization term abstract in this paper a novel active contour model r drlse model based on level set method is proposed for image segmentation the r drlse model is a variational level set approach that utilizes the region information to find image contours by minimizing the presented energy functional to avoid the time consuming re initialization step the distance regularization term is used to penalize the deviation of the level set function from a signed distance function the numerical implementation scheme of the model can significantly reduce the iteration number and computation time the results of experiments performed on some synthetic and real images show that the r drlse model is effective and efficient in particular our method has been applied to mr kidney image segmentation with desirable results

fuzzy normed space of operators and its completeness in this paper the new definition of the fuzzy norm of a linear operator from one fuzzy normed linear space into another is introduced and the boundedness of such an operator is described furthermore the space of all bounded linear operators endowed with this fuzzy norm is studied consequently its topological structure as well as completeness is given and that it can itself be made into a fuzzy normed linear space is also shown

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

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

kernel density estimation and intrinsic alignment for shape priors in level set segmentation in this paper we make two contributions to the field of level set based image segmentation firstly we propose shape dissimilarity measures on the space of level set functions which are analytically invariant under the action of certain transformation groups the invariance is obtained by an intrinsic registration of the evolving level set function in contrast to existing approaches to invariance in the level set framework this closed form solution removes the need to iteratively optimize explicit pose parameters the resulting shape gradient is more accurate in that it takes into account the effect of boundary variation on the object s pose secondly based on these invariant shape dissimilarity measures we propose a statistical shape prior which allows to accurately encode multiple fairly distinct training shapes this prior constitutes an extension of kernel density estimators to the level set domain in contrast to the commonly employed gaussian distribution such nonparametric density estimators are suited to model aribtrary distributions we demonstrate the advantages of this multi modal shape prior applied to the segmentation and tracking of a partially occluded walking person in a video sequence and on the segmentation of the left ventricle in cardiac ultrasound images we give quantitative results on segmentation accuracy and on the dependency of segmentation results on the number of training shapes