new estimates for solutions of lyapunov equations results for estimating the solution of differential and algebraic lyapunov matrix equations are obtained and some of the well known results are generalized

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

a variational method in image recovery this paper is concerned with a classical denoising and deblurring problem in image recovery our approach is based on a variational method by using the legendre fenchel transform we show how the nonquadratic criterion to be minimized can be split into a sequence of half quadratic problems easier to solve numerically first we prove an existence and uniqueness result and then we describe the algorithm for computing the solution and we give a proof of convergence finally we present some experimental results for synthetic and real images

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

simultaneous eigenvalue lower bounds for the lyapunov matrix equation simultaneous eigenvalue lower bounds for the solution of the lyapunov equation are presented the n summation and the n product bounds generalize existing bounds such as those for the trace and the determinant these bounds are stronger than the majority of the relevant bounds shown in the literature

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

double low rank matrix recovery for saliency fusion in this paper we address the problem of fusing various saliency detection methods such that the fusion result outperforms each of the individual methods we observe that the saliency regions shown in different saliency maps are with high probability covering parts of the salient object with image regions being represented by the saliency values of multiple saliency maps the object regions have strong correlation and thus lie in a low dimensional subspace meanwhile most of the background regions tend to have lower saliency values in various saliency maps they are also strongly correlated and lie in a low dimensional subspace that is independent of the object subspace therefore an image can be represented as the combination of two low rank matrices to obtain a unified low rank matrix that represents the salient object this paper presents a double low rank matrix recovery model for saliency fusion the inference process is formulated as a constrained nuclear norm minimization problem which is convex and can be solved efficiently with the alternating direction method of multipliers furthermore to reduce the computational complexity of the proposed saliency fusion method a saliency model selection strategy based on the sparse representation is proposed experiments on five datasets show that our method consistently outperforms each individual saliency detection approach and other state of the art saliency fusion methods

upper summation and product bounds for solution eigenvalues of the lyapunov matrix equation upper bounds for summations including the trace and for products including the determinant of the eigenvalues of the solution of the continuous algebraic lyapunov matrix equation are presented the majority of the bounds are tighter than those in the literature and some are new

gradient based iterative algorithms for generalized coupled sylvester conjugate matrix equations abstract by applying the hierarchical identification principle the gradient based iterative algorithm is suggested to solve a class of complex matrix equations with the real representation of a complex matrix as a tool the sufficient and necessary conditions for the convergence factor are determined to guarantee that the iterative solutions given by the proposed algorithm converge to the exact solution for any initial matrices also we solve the problem which is proposed by wu et al 2010 finally some numerical examples are provided to illustrate the effectiveness of the proposed algorithms and testify the conclusions suggested in this paper

discriminative saliency propagation with sink points salient object detection is still very challenging especially in images with complex or cluttered background in this paper we present an efficient and discriminative framework to address it in specially a discriminative similarity metric is first proposed by measuring the chi square distance in a new constructed feature space then we apply it to calculate a background based coarse saliency map by introducing distribution prior to remove foreground noises in the image boundaries based on manifold ranking a robust saliency propagation mechanism is further developed to highlight salient object and simultaneously suppress background region by setting appropriate sink points finally several simple refinement techniques are utilized to generate pixel wise and smooth saliency maps extensive experimental results show the superior performance of the proposed method in terms of different evaluation metrics in addition the proposed framework can be also applied to the existing saliency propagation methods for significant performance boosting we also believe that it is a good choice for subsequent applications based on the achieved high performance and acceptable computational overhead a discriminative similarity metric is proposed to distinguish similar regions we propose an efficient distribution guided background based weak saliency method a discriminative propagation mechanism is developed to optimize coarse saliency maps several new refinements are utilized to enhance the visual quality of the output we make a good balance between saliency detection accuracy and computational cost

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

exploiting information geometry to improve the convergence of nonparametric active contours this paper presents a fast converging riemannian steepest descent method for nonparametric statistical active contour models with application to image segmentation unlike other fast algorithms the proposed method is general and can be applied to any statistical active contour model from the exponential family which comprises most of the models considered in the literature this is achieved by first identifying the intrinsic statistical manifold associated with this class of active contours and then constructing a steepest descent on that manifold a key contribution of this paper is to derive a general and tractable closed form analytic expression for the manifold s riemannian metric tensor which allows computing discrete gradient flows efficiently the proposed methodology is demonstrated empirically and compared with other state of the art approaches on several standard test images a phantom positron emission tomography scan and a b mode echography of in vivo human dermis

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

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

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

eigenvalue bounds for algebraic riccati and lyapunov equations the majorization result of wimmer 2 relating the eigenvalues of the matrices involved in the lyapunov equation is extended to the algebraic riccati equation this result coupled with certain results on the eigenvalue bounds for sum and product of matrices yields several lower and upper bounds for the eigenvalues of the solution matrix of the algebraic riccati and lyapunov equations

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

new results for the bounds of the solution for the continuous riccati and lyapunov equations this paper presents upper and lower matrix bounds for the solution of the continuous algebraic matrix riccati equation furthermore a new lower matrix bound for the solution of the continuous algebraic lyapunov equation is also developed these are new results

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

a region merging prior for variational level set image segmentation in current level set image segmentation methods the number of regions is assumed to known beforehand as a result it remains constant during the optimization of the objective functional how to allow it to vary is an important question which has been generally avoided this study investigates a region merging prior related to regions area to allow the number of regions to vary automatically during curve evolution thereby optimizing the objective functional implicitly with respect to the number of regions we give a statistical interpretation to the coefficient of this prior to balance its effect systematically against the other functional terms we demonstrate the validity and efficiency of the method by testing on real images of intensity color and motion

constraining active contour evolution via lie groups of transformation we present a novel approach to constraining the evolution of active contours used in image analysis the proposed approach constrains the final curve obtained at convergence of curve evolution to be related to the initial curve from which evolution begins through an element of a desired lie group of plane transformations constraining curve evolution in such a way is important in numerous tracking applications where the contour being tracked in a certain frame is known to be related to the contour in the previous frame through a geometric transformation such as translation rotation or affine transformation for example it is also of importance in segmentation applications where the region to be segmented is known up to a geometric transformation our approach is based on suitably modifying the euler lagrange descent equations by using the correspondence between lie groups of plane actions and their lie algebras of infinitesimal generators and thereby ensures that curve evolution takes place on an orbit of the chosen transformation group while remaining a descent equation of the original functional the main advantage of our approach is that it does not necessitate any knowledge of nor any modification to the original curve functional and is extremely straightforward to implement our approach therefore stands in sharp contrast to other approaches where the curve functional is modified by the addition of geometric penalty terms we illustrate our algorithm on numerous real and synthetic examples

embedding overlap priors in variational left ventricle tracking we propose to embed overlap priors in variational tracking of the left ventricle lv in cardiac magnetic resonance mr sequences the method consists of evolving two curves toward the lv endo and epicardium boundaries we derive the curve evolution equations by minimizing two functionals each containing an original overlap prior constraint the latter measures the conformity of the overlap between the nonparametric kernel based intensity distributions within the three target regions lv cavity myocardium and background to a prior learned from a given segmentation of the first frame the bhattacharyya coefficient is used as an overlap measure different from existing intensity driven constraints the proposed priors do not assume implicitly that the overlap between the intensity distributions within different regions has to be minimal this prevents both the papillary muscles from being included erroneously in the myocardium and the curves from spilling into the background although neither geometric training nor preprocessing were used quantitative evaluation of the similarities between automatic and independent manual segmentations showed that the proposed method yields a competitive score in comparison with existing methods this allows more flexibility in clinical use because our solution is based only on the current intensity data and consequently the results are not bounded to the characteristics variability and mathematical description of a finite training set we also demonstrate experimentally that the overlap measures are approximately constant over a cardiac sequence which allows to learn the overlap priors from a single frame

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

bounds in the lyapunov matrix differential equation upper and lower bounds for the trace of the solution of the lyapunov matrix differential equation are derived it is shown that they are obtained as solutions to simple scalar differential equations as a special case the bounds for the stationary solution give ones for the solution to the lyapunov algebraic equation

saliency region detection based on markov absorption probabilities in this paper we present a novel bottom up salient object detection approach by exploiting the relationship between the saliency detection and the markov absorption probability first we calculate a preliminary saliency map by the markov absorption probability on a weighted graph via partial image borders as background prior unlike most of the existing background prior based methods which treated all image boundaries as background we only use the left and top sides as background for simplicity the saliency of each element is defined as the sum of the corresponding absorption probability by several left and top virtual boundary nodes which are most similar to it second a better result is obtained by ranking the relevance of the image elements with foreground cues extracted from the preliminary saliency map which can effectively emphasize the objects against the background whose computation is processed similarly as that in the first stage and yet substantially different from the former one at last three optimization techniques content based diffusion mechanism superpixelwise depression function and guided filter are utilized to further modify the saliency map generalized at the second stage which is proved to be effective and complementary to each other both qualitative and quantitative evaluations on four publicly available benchmark data sets demonstrate the robustness and efficiency of the proposed method against 17 state of the art methods

slic superpixels compared to state of the art superpixel methods computer vision applications have come to rely increasingly on superpixels in recent years but it is not always clear what constitutes a good superpixel algorithm in an effort to understand the benefits and drawbacks of existing methods we empirically compare five state of the art superpixel algorithms for their ability to adhere to image boundaries speed memory efficiency and their impact on segmentation performance we then introduce a new superpixel algorithm simple linear iterative clustering slic which adapts a k means clustering approach to efficiently generate superpixels despite its simplicity slic adheres to boundaries as well as or better than previous methods at the same time it is faster and more memory efficient improves segmentation performance and is straightforward to extend to supervoxel generation

upper and lower eigenvalue summation bounds of the lyapunov matrix differential equation and the application in a class time varying nonlinear system in this paper we first show a class relation between the eigenvalue of functional matrix derivative and the derivative of function matrix eigenvalue applying the relation we transform the time v

on bounds of the riccati and lyapunov matrix equations various bounds for the traces of the solutions of the algebraic riccati and lyapunov matrix equations are established in the continuous and discrete domain respectively the presented results give lower bounds for the sum of the eigenvalue of the matrix solutions

new spectral bounds on h2 norm of linear dynamical networks abstract in this paper we obtain new lower and upper bounds for the h 2 norm of a class of linear time invariant systems subject to exogenous noise inputs we show that the h 2 norm as a performance measure can be tightly bounded from below and above by some spectral functions of state and output matrices of the system in order to show the usefulness of our results we calculate bounds for the h 2 norm of some network models with specific coupling or graph structures e g systems with normal state matrices linear consensus networks with directed graphs and cyclic linear networks as a specific example the h 2 norm of a linear consensus network over a directed cycle graph is computed and shown how its performance scales with the network size our proposed spectral bounds reveal the important role and contribution of fast and slow dynamic modes of a system in the best and worst achievable performance bounds under white noise excitation finally we use several numerical simulations to show the superiority of our bounds over the existing bounds in the literature

a statistical overlap prior for variational image segmentation this study investigates variational image segmentation with an original data term referred to as statistical overlap prior which measures the conformity of overlap between the nonparametric distributions of image data within the segmentation regions to a learned statistical description this leads to image segmentation and distribution tracking algorithms that relax the assumption of minimal overlap and as such are more widely applicable than existing algorithms we propose to minimize active curve functionals containing the proposed overlap prior compute the corresponding euler lagrange curve evolution equations and give an interpretation of how the overlap prior controls such evolution we model the overlap measured via the bhattacharyya coefficient with a gaussian prior whose parameters are estimated from a set of relevant training images quantitative and comparative performance evaluations of the proposed algorithms over several experiments demonstrate the positive effects of the overlap prior in regard to segmentation accuracy and convergence speed

trace bounds on the solution of the algebraic matrix riccati and lyapunov equation lower and upper bounds on the trace of the positive semidefinite solution of the algebraic matrix riccati and lyapunov equation are derived the upper trace bound obtained in this note in many cases results in a tighter bound as compared to the upper bound for the maximal eigenvalue proposed in 1 and 2

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

image classification with the fisher vector theory and practice a standard approach to describe an image for classification and retrieval purposes is to extract a set of local patch descriptors encode them into a high dimensional vector and pool them into an image level signature the most common patch encoding strategy consists in quantizing the local descriptors into a finite set of prototypical elements this leads to the popular bag of visual words representation in this work we propose to use the fisher kernel framework as an alternative patch encoding strategy we describe patches by their deviation from an universal generative gaussian mixture model this representation which we call fisher vector has many advantages it is efficient to compute it leads to excellent results even with efficient linear classifiers and it can be compressed with a minimal loss of accuracy using product quantization we report experimental results on five standard datasets pascal voc 2007 caltech 256 sun 397 ilsvrc 2010 and imagenet10k with up to 9m images and 10k classes showing that the fv framework is a state of the art patch encoding technique

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

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

upper bounds for the eigenvalues of the solution of the lyapunov matrix equation eigenvalue upper bounds for the solution of the lyapunov matrix equation are presented for single eigenvalues summations of eigenvalues including the trace and products of eigenvalues including the determinant these bounds are compared to those for the trace and the extreme eigenvalues

a brief summary of the bounds on the solution of the algebraic matrix equations in control theory abstract in recent years several bounds have been reported for different measures of the extent or size of the solution of the algebraic matrix equations arising in control theory such as the riccati equation and the lyapunov equation this paper collects the bounds that have been presented up to now and summarizes them in an unified form this will prove particularly convenient for those wishing to get a ready estimate of the solution while solving the equations numerically or to develop theoretical results that rely on these bounds

adaptive metric learning for saliency detection in this paper we propose a novel adaptive metric learning algorithm aml for visual saliency detection a key observation is that the saliency of a superpixel can be estimated by the distance from the most certain foreground and background seeds instead of measuring distance on the euclidean space we present a learning method based on two complementary mahalanobis distance metrics 1 generic metric learning gml and 2 specific metric learning sml gml aims at the global distribution of the whole training set while sml considers the specific structure of a single image considering that multiple similarity measures from different views may enhance the relevant information and alleviate the irrelevant one we try to fuse the gml and sml together and experimentally find the combining result does work well different from the most existing methods which are directly based on low level features we devise a superpixelwise fisher vector coding approach to better distinguish salient objects from the background we also propose an accurate seeds selection mechanism and exploit contextual and multiscale information when constructing the final saliency map experimental results on various image sets show that the proposed aml performs favorably against the state of the arts

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

on solution bounds for three types of lyapunov matrix equations continuous discrete and unified equations an approach is proposed to obtain a series of solution bounds for the unified algebraic lyapunov matrix equation by making use of its feature i e a mediator between the continuous time and discrete time lyapunov equations due to the approach every existing solution bound for both the continuous and discrete equations becomes intact in the sense that it yields a corresponding bound for the unified equation the approach is endorsed by this simple fact the three types of lyapunov equations share the solution provided certain relationships are maintained among corresponding coefficient matrices of the equations some examples are presented to show that the proposed method actually produces new bounds and builds bridges over existing bounds

on some bounds in the algebraic riccati and lyanupov equations some bounds for the trace and determinant of the solution to the algebraic riccati and lyapunov matrix equations are presented these bounds give information on mean size of the solution to the equations in a simple way the obtained determinant bound for the lyapunov equation shows the improvement over the previously reported one

image segmentation using fuzzy region competition and spatial frequency information this paper presents a multiphase fuzzy region competition model that takes into account spatial and frequency information for image segmentation in the proposed energy functional each region is represented by a fuzzy membership function and a data fidelity term that measures the conformity of spatial and frequency data within each region to generalized gaussian densities whose parameters are determined jointly with the segmentation process compared with the classical region competition model our approach gives soft segmentation results via the fuzzy membership functions and moreover the use of frequency data provides additional region information that can improve the overall segmentation result to efficiently solve the minimization of the energy functional we adopt an alternate minimization procedure and make use of chambolle s fast duality projection algorithm we apply the proposed method to synthetic and natural textures as well as real world natural images experimental results show that our proposed method has very promising segmentation performance compared with the current state of the art approaches

iterative least squares solutions of coupled sylvester matrix equations abstract in this paper we present a general family of iterative methods to solve linear equations which includes the well known jacobi and gauss seidel iterations as its special cases the methods are extended to solve coupled sylvester matrix equations in our approach we regard the unknown matrices to be solved as the system parameters to be identified and propose a least squares iterative algorithm by applying a hierarchical identification principle and by introducing the block matrix inner product the star product for short we prove that the iterative solution consistently converges to the exact solution for any initial value the algorithms proposed require less storage capacity than the existing numerical ones finally the algorithms are tested on computer and the results verify the theoretical findings

a note on the lyapunov matrix equation in 5 bound for the determinant of the solution to the lyapunov matrix equation was reported this note gives an another bound for this value

eigenvalue upper bounds of the solution of the continuous riccati equation new upper bounds for the solution eigenvalues of the continuous algebraic matrix riccati equation are developed they include bounds of the extreme eigenvalues the summation and product of eigenvalues the trace and the determinant it is shown that the majority of the present eigenvalue bounds expressed in concise forms are less restrictive and sharper than existing results

linear shape from shading in many situations the reflectance function of a surface is approximately linear and there is an effielent closed form solution to the shape from shading problem when boundary conditions e g edges singular points are not available good estimates of shape may still be extracted by using the assumption of general viewing position an improved method for estimating the illuminant direction is also presented

lower bounds on the solution of lyapunov matrix and algebraic riccati equations in this note various lower bounds for all the eigenvalues of the solution matrix k of the lyapunov matrix equation are established a special case of this result is a generalization of that presented in 1 3 where lower bounds for the maximum and minimum eigenvalues of k are given moreover the approach used here enables one to establish various lower bounds for some of the largest eigenvalues of the solution matrix of the algebraic riccati equation

new upper estimates for the solution of the continuous algebraic lyapunov equation a new result for bounding the summations for solution eigenvalues of the algebraic lyapunov equation is presented this makes possible to generate the best known upper scalar solution estimates

a variational level set approach to multiphase motion a coupled level set method for the motion of multiple junctions of e g solid liquid and grain boundaries which follows the gradient flow for an energy functional consisting of surface tension proportional to length and bulk energies proportional to area is developed the approach combines the level set method of s osher and j a sethian with a theoretical variational formulation of the motion by f reitich and h m soner the resulting method uses as many level set functions as there are regions and the energy functional is evaluated entirely in terms of level set functions the gradient projection method leads to a coupled system of perturbed by curvature terms hamilton jacobi equations the coupling is enforced using a single lagrange multiplier associated with a constraint which essentially prevents a regions from overlapping and b the development of a vacuum the numerical implementation is relatively simple and the results agree with and go beyond the theory as given in 12 other applications of this methodology including the decomposition of a domain into subregions with minimal interface length are discussed finally some new techniques and results in level set methodology are presented

a six stimulus theory for stochastic texture we report a six stimulus basis for stochastic texture perception fragmentation of the scene by a chaotic process causes the spatial scene statistics to conform to a weibull distribution the parameters of the weibull distribution characterize the spatial structure of uniform stochastic textures of many different origins completely in this paper we report the perceptual significance of the weibull parameters we demonstrate the parameters to be sensitive to orthogonal variations in the imaging conditions specifically to the illumination conditions camera magnification and resolving power and the texture orientation apparently the weibull parameters form a six stimulus basis for stochastic texture description the results indicate that texture perception can be approached like the experimental science of colorimetry

unsupervised texture segmentation using markov random field models the problem of unsupervised segmentation of textured images is considered the only explicit assumption made is that the intensity data can be modeled by a gauss markov random field gmrf the image is divided into a number of nonoverlapping regions and the gmrf parameters are computed from each of these regions a simple clustering method is used to merge these regions the parameters of the model estimated from the clustered segments are then used in two different schemes one being all approximation to the maximum a posterior estimate of the labels and the other minimizing the percentage misclassification error the proposed approach is contrasted with the algorithm of s lakshamanan and h derin 1989 which uses a simultaneous parameter estimation and segmentation scheme the results of the adaptive segmentation algorithm of lakshamanan and derin are compared with a simple nearest neighbor classification scheme to show that if enough information is available simple techniques could be used as alternatives to computationally expensive schemes

bounds for the eigenvalues of the solution of the discrete riccati and lyapunov equations and the continuous lyapunov equation we present some bounds for the eigenvalues and certain sums and products of the eigenvalues of the solution of the discrete riccati and lyapunov matrix equations and the continuous lyapunov matrix equation nearly all of our bounds for the discrete riccati equation are new the bounds for the discrete and continuous lyapunov equations give a completion of some known bounds for the extremal eigenvalues and the determinant and the trace of the solution of the respective equation