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 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

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

extremal and barabanov semi norms of a semigroup generated by a bounded family of matrices abstract let s s i i i be an arbitrary family of complex n by n matrices where 1 n let s denote the joint spectral radius of s defined as s lim sup l sup i 1 i l i l s i 1 s i l 1 l which is independent of the norm used here a semi norm on c n is called extremal of s if it satisfies x 0 and x s i s x x x 1 x n c n and i i in this paper using an elementary analytical approach we show that if s is bounded in c n n then there always exists for s an extremal semi norm on c n if additionally s is compact in c n n this extremal semi norm has the barabanov type property i e to any x c n one can find an infinite sequence i n i with x s i 1 s i k s k x for each k 1 as a common starting point this directly implies the fundamental results barabanov s norm theorem berger wang s formula and elsner s reduction theorem

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

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

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

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

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

sets of matrices all infinite products of which converge an infinite product iit lmi of matrices converges on the right if limi m mi exists a set z ai i l of n x n matrices is called an rcp set rightconvergent product set if all infinite products with each element drawn from z converge such sets of matrices arise in constructing self similar objects like von koch s snowflake curve in various interpolation schemes in constructing wavelets of compact support and in studying nonhomogeneous markov chains this paper gives necessary conditions and also some sufficient conditions for a set x to be an rcp set these are conditions on the eigenvalues and left eigenspaces of matrices in 2 and finite products of these matrices necessary and sufficient conditions are given for a finite set z to be an rcp set having a limit function m d rit lad where d d d which is a continuous function on the space of all sequences d with the sequence topology finite rcp sets of column stochastic matrices are completely characterized some results are given on the problem of algorithmically deciding if a given set x is an rcp set

finiteness property of pairs of 2 2 sign matrices via real extremal polytope norms this paper deals with the joint spectral radius of a finite set of matrices we s ay that a set of matrices has the finiteness property if the maximal rate of growth in the multiplicative semigroup it generates is given by the powers of a finite product here we address the problem of establishing the finiteness properties of p airs of 2 2 sign matrices such problem is related to the conjecture that pairs of sign ma trices fulfil the finiteness property for any dimension this would imply by a recent result by j ungers and blondel that finite sets of rational matrices fulfil the finiteness property wh ich would be very important property in terms of the computation of the joint spectral radius the finiteness property of n n sign matrices remains open but the knowledge of its validity in the 2 2 case gives the hope to solve it by using some induction argument on the dimension as a main tool of our proof we make use of a procedure to compute a so called real polytope extremal norm for the set in particular we present an algorithm which under some suitable assumptions is able to check if a certain product in the multiplicative semig roup is spectrum maximizing for pairs of sign matrices we develop the computations exactly and hence are able to prove analytically the finiteness property on the other hand the algorithm c an be used in a floating point arithmetic and provide a general tool for approximating the join t spectral radius of a set of matrices

local gradient patterns lgp an effective local statistical feature extraction scheme for no reference image quality assessment abstract gradient features are known to be effective for full reference fr image quality assessment iqa however only a few metrics utilize gradient features for no reference nr iqa to investigate the potential benefits of gradient magnitude and phase for nr iqa we propose a novel and effective local statistical feature extraction metric namely local gradient patterns lgp for general purpose nr iqa using a gaussian partial derivative filter the image is first decomposed into two complementary components gradient magnitude and phase the local statistical features e g the conditional probability distributions are then extracted from the complementary components using the derived local gradient magnitude and phase pattern operators finally to facilitate nr iqa local statistical features that convey important structural information are mapped to the subjective mean opinion score of the image using a support vector regression svr procedure we evaluated our proposed lgp metric using images from two publicly available test databases the results confirm that the proposed lgp metric provides predictive performance that is superior to most state of the art nr iqa metrics and has an acceptable level of computational complexity

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

brief paper periodically switched stability induces exponential stability of discrete time linear switched systems in the sense of markovian probabilities the conjecture that periodically switched stability implies absolute asymptotic stability of random infinite products of a finite set of square matrices has recently been disproved under the guise of the finiteness conjecture in this paper we show that this conjecture holds in terms of markovian probabilities more specifically let s k c n x n 1 k k be arbitrarily given k matrices and s k k j j 1 1 k j k for each j 1 where n k 2 then we study the exponential stability of the following discrete time switched dynamics s x j s k j s k 1x 0 j 1 and x 0 c n where k j j 1 s k can be an arbitrary switching sequence for a probability row vector p p 1 p k r k and an irreducible markov transition matrix p r k x k with pp p we denote by m p p the markovian probability on s k corresponding to p p by using symbolic dynamics and ergodic theoretic approaches we show that if s possesses the periodically switched stability then i it is exponentially stable m p p almost surely ii the set of stable switching sequences k j j 1 s k has the same hausdorff dimension as s k thus the periodically switched stability of a discrete time linear switched dynamics implies that the system is exponentially stable for almost all switching sequences

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

the generalized spectral radius and extremal norms the generalized spectral radius also known under the name of joint spectral radius or after taking logarithms maximal lyapunov exponent of a discrete inclusion is examined we present a new proof for a result of barabanov which states that for irreducible sets of matrices an extremal norm always exists this approach lends itself easily to the analysis of further properties of the generalized spectral radius we prove that the generalized spectral radius is locally lipschitz continuous on the space of compact irreducible sets of matrices and show a strict monotonicity property of the generalized spectral radius sufficient conditions for the existence of extremal norms are obtained

the berger wang formula for the markovian joint spectral radius abstract the berger wang formula establishes equality between the joint and generalized spectral radii of a set of matrices for matrix products whose multipliers are applied not arbitrarily but in accordance with some markovian law there are also known analogs of the joint and generalized spectral radii however the known proofs of the berger wang formula hardly can be directly applied in the case of markovian products of matrices since they essentially rely on the arbitrariness of appearance of different matrices in the related matrix products nevertheless as has been shown by x dai 1 the berger wang formula is valid for the case of markovian analogs of the joint and the generalized spectral radii too although the proof in this case heavily exploits the more involved techniques of multiplicative ergodic theory in the paper we propose a matrix theory construction allowing to deduce the markovian analog of the berger wang formula from the classical berger wang formula

the generalized spectral radius theorem an analytic geometric proof abstract let be a bounded set of complex matrices m a 1 a m a i the generalized spectral radius theorem states that where and are defined as follows lim sup m 1 m where m sup a a m with a the spectral radius lim sup m 1 m where m sup a a m with any matrix norm we give an elementary proof based on analytic and geometric tools which is in some ways simpler than the first proof by berger and wang

diffraction of sh waves by a system of cracks solution by an integral equation method abstract a set of straight cracks in an infinite elastic medium under time harmonic sh wave loading is considered using the representation theorem for the displacements the problem is described by a system of integral equations numerical solutions for dynamic stress intensity factors of various crack configurations are presented and crack interaction phenomena are discussed

theories and ultra efficient computation of joint spectral radius for estimating first passage time distribution of markov set chain this technical note is concerned with the tail distribution of the first passage time of markov set chains msc an original two part idea a more progressive relation and a sortedness test is conceived to characterize such chains the theoretical construction based on this idea further results in an algorithm that can compute the tightest exponent bound of the tail distribution for high dimensional problem instances with surprising ease to understand the computational implication of this algorithm note that the problem is equivalent to computing the joint spectral radius jsr of a special independent column polytope one that defines markov set chains of nonnegative matrices in this context the reported algorithm can compute the exact jsr value for cases of 100 t 100 matrices in less than a second in matlab problems of this size is far beyond the scope of known jsr techniques it is worth noting that the fields of msc and jsr have not had significant overlap as one may expect despite their conceptual akiness meanwhile the present technical note is a contribution that belongs to both fields

on the limit products of a family of matrices in this paper we direct attention at bounded families of complex n n matrices in order to study their asymptotic behaviour we recall from linear algebra appl 322 2001 162 the concept of limit spectrum maximizing product and show that nondefective families always admit such limit products then we consider defective families in loc cite we proved that for finite families of 2 2 matrices defectivity is equivalent to the existence of defective such limit products this result led us to conjecture the validity of this property also for higher dimensions n 3 here instead by making use of the results obtained by bousch and mairesse j am math soc 15 2002 77 that disproved the well known finiteness conjecture we find some counterexamples to our conjecture in loc cite for all n 3 2002 elsevier science inc all rights reserved

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

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

convergence analysis of c2 hermite interpolatory subdivision schemes by explicit joint spectral radius formulas abstract subdivision schemes are popular iterative processes to build graphs of functions curves and surfaces we analyze the 2 point hermite c 2 subdivision scheme introduced by merrien in 26 for the analysis of its convergence and its smoothness properties we are concerned with the computation of the joint spectral radius of a family of 2 matrices associated with the scheme in this paper by an explicit computation of the joint spectral radius of such pairs of matrices we determine necessary and sufficient conditions for the scheme to be c 2 convergent whenever it reproduces cubic polynomials in addition we present two one parameter families of convergent subdivision schemes belonging to the class in 26 possessing interesting properties from the shape control point of view

a review of statistical approaches to level set segmentation integrating color texture motion and shape since their introduction as a means of front propagation and their first application to edge based segmentation in the early 90 s level set methods have become increasingly popular as a general framework for image segmentation in this paper we present a survey of a specific class of region based level set segmentation methods and clarify how they can all be derived from a common statistical framework region based segmentation schemes aim at partitioning the image domain by progressively fitting statistical models to the intensity color texture or motion in each of a set of regions in contrast to edge based schemes such as the classical snakes region based methods tend to be less sensitive to noise for typical images the respective cost functionals tend to have less local minima which makes them particularly well suited for local optimization methods such as the level set method we detail a general statistical formulation for level set segmentation subsequently we clarify how the integration of various low level criteria leads to a set of cost functionals we point out relations between the different segmentation schemes in experimental results we demonstrate how the level set function is driven to partition the image plane into domains of coherent color texture dynamic texture or motion moreover the bayesian formulation allows to introduce prior shape knowledge into the level set method we briefly review a number of advances in this domain

on the asymptotic regularity of a family of matrices abstract in this paper we consider bounded families f of complex n n matrices we give sufficient conditions under which the sequence k f 1 k k 1 where k f is the supremum of the spectral radii of all possible products of k matrices chosen in f is convergent to its supremum f the so called generalized spectral radius of f we also illustrate a possible practical application

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

the finite step realizability of the joint spectral radius of a pair of d d matrices one of which being rank one abstract we study the finite step realizability of the joint generalized spectral radius of a pair of real square matrices s 1 and s 2 one of which has rank 1 where 2 d let a denote the spectral radius of a square matrix a then we prove that there always exists a finite length word i 1 i m 1 2 m for some finite m 1 such that s i 1 s i m m sup n 1 max i 1 i n 1 2 n s i 1 s i n n in other words there holds the spectral finiteness property for s 1 s 2 explicit formula for computation of the joint spectral radius is derived this implies that the stability of the switched system induced by s 1 s 2 is algorithmically decidable in this case

an inequality for the spectral radius of an interval matrix abstract for an n n interval matrix a aij we say that a is majorized by the point matrix a a ij if aij aij when the jth column of a has the property that there exists a power a m containing in the same jth column at least one interval not degenerated to a point interval and aij aij otherwise denoting the generalized spectral radius in the sense of daubechies and lagarias of a by a and the usual spectral radius of a by a it is proved that if a is majorized by a then a a this inequality sheds light on the asymptotic stability theory of discrete time linear interval systems

a general solution to the antiplane problem of an arbitrarily located elliptical hole near the tip of a main crack abstract a general solution is obtained to the problem of the interaction between a main crack and an arbitrarily located and oriented elliptical hole near its tip under mode iii loading conditions the analysis is based on the complex potentials for the antiplane problem and the superposition principle the stress intensity factor at the main crack is obtained in a general series form and approximate closed form solutions are also derived using a perturbation procedure the present solution is shown to coincide with taylor expansion of exact solutions for collinear elliptical holes with specific aspect ratios numerical examples are provided to show the effect of the geometry location and orientation of the microdefect on the stress intensity factor of the main crack the present work should provide a valuable insight into main crack microdefect interaction phenomena in brittle materials

simultaneous schur stability let be a set of n n complex matrices denote by the multiplicative semi group generated by for an n n complex matrix a the spectrum of a and spectral radius of a are denoted by a and r a respectively motivated by a phenomenon in the closed unit disc of the complex plane we give a rigorous definition of simultaneous schur stability as follows is said to be simultaneously schur stable if r a 1 a and 1 a a is said to be asymptotically stable if there exists a norm on cn such that sup a a e 1 it is proved that for a bounded set of n n complex matrices is asymptotically stable if and only if it is simultaneously schur stable by way of simultaneous schur stability some applications are illustrated especially an analytic combinatorial proof of a recent result of considerable depth generalized gelfand spectral radius formula

b spline based globally optimal segmentation combining low level and high level information abstract image segmentation is an important step for large scale image analysis and object recognition variational based segmentation methods are widely studied due to their good performance but they still suffer from incapability to deal with images bearing weak contrast overlapped noise and cluttered texture to tackle this problem we propose a new statistical information analysis based multi scale and global optimization method for image segmentation this multi scale processing which is consistent with human s cognition mechanism enables us identify target at coarse scale the high level prior is obtained by the multiple gaussian kernel gray equalization and used as shape constraint in following fine scale an efficient energy functional is proposed with convexity and improved tv regularization in order to segment inhomogeneous target from noisy background a convex relaxation function is explicitly represented by cubic b spline basis for fast convergence and intrinsic smooth segmentation finally the energy functional is minimized by standard methods of split bregman gradient descent flow and the corresponding euler lagrange equation experimental results on synthetic and real world images validate the robustness and high accuracy boundaries detection for low contrast noisy and texture images

an active contour model based on local fitted images for image segmentation active contour models are popular and widely used for a variety of image segmentation applications with promising accuracy but they may suffer from limited segmentation performances due to the presence of intensity inhomogeneity to overcome this drawback a novel region based active contour model based on two different local fitted images is proposed by constructing a novel local hybrid image fitting energy which is minimized in a variational level set framework to guide the evolving of contour curves toward the desired boundaries the proposed model is evaluated and compared with several typical active contour models to segment synthetic and real images with different intensity characteristics experimental results demonstrate that the proposed model outperforms these models in terms of accuracy in image segmentation

extremal norms for positive linear inclusions abstract for finite dimensional linear semigroups which leave a proper cone invariant it is shown that irreducibility with respect to the cone implies the existence of an extremal norm in case the cone is simplicial a similar statement applies to absolute norms the semigroups under consideration may be generated by discrete time systems continuous time systems or continuous time systems with jumps the existence of extremal norms is used to extend results on the lipschitz continuity of the joint spectral radius beyond the known case of semigroups that are irreducible in the representation theory interpretation of the word

a max version of the generalized spectral radius theorem abstract let be a bounded set of n n nonnegative matrices in max algebra in this paper we propose the notions of the max algebra version of the generalized spectral radius of and the max algebra version of the joint spectral radius of the max algebra version of the generalized spectral radius theorem is established we propose the relationship between the generalized spectral radius of in the sense of daubechies and lagarias and its max algebra version moreover a generalization of elsner and van den driessche s lemma is presented as well

on the stability of takagi sugeno fuzzy systems with time varying uncertainties this paper studies the problems of stability analysis of takagi sugeno free fuzzy systems with time varying uncertainties in our prior study we represented the time varying uncertainty incurred in characteristic interval matrices in terms of the stability of takagi sugeno free fuzzy systems with consequent parameter uncertainties based on mayer s convergent theorem for powers of single interval matrix and its generalization we further proposed some sufficient conditions for the takagi sugeno free fuzzy system with time varying uncertainties to be globally asymptotically stable in this paper we propose the notion of simultaneously nilpotent interval matrices to investigate the takagi sugeno free fuzzy system with time varying uncertainties to be strongly stable within steps where relates to the dimension of interval matrices moreover a unique situation for the deterministic takagi sugeno free fuzzy system to be strongly stable within steps is derived as well where relates to the dimension of characteristic matrices for the deterministic takagi sugeno free fuzzy system

approximation of the joint spectral radius using sum of squares we provide an asymptotically tight computationally efficient approximation of the joint spectral radius of a set of matrices using sum of squares sos programming the approach is based on a search for an sos polynomial that proves simultaneous contractibility of a finite set of matrices we provide a bound on the quality of the approximation that unifies several earlier results and is independent of the number of matrices additionally we present a comparison between our approximation scheme and earlier techniques including the use of common quadratic lyapunov functions and a method based on matrix liftings theoretical results and numerical investigations show that our approach yields tighter approximations

the generalised berger wang formula and the spectral radius of linear cocycles using ergodic theory we prove two formulae describing the relationships between different notions of joint spectral radius for sets of bounded linear operators acting on a banach space the first formula was previously obtained by v s shulman and yu v turovski using operator theoretic ideas the second formula shows that the joint spectral radii corresponding to several standard measures of noncompactness share a common value when applied to a given precompact set of operators this result may be seen as an extension of classical formulae for the essential spectral radius given by r nussbaum a lebow and m schechter both results are obtained as a consequence of a more general theorem concerned with continuous operator cocycles defined over a compact dynamical system as a byproduct of our method we answer a question of j e cohen on the limiting behaviour of the spectral radius of a measurable matrix cocycle

bounded semigroups of matrices in this note are proved two conjectures of daubechies and lagarias the first asserts that if z is a bounded set of matrices such that all left infinite products converge then 8 generates a bounded semigroup the second asserts the equality of two differently defined joint spectral radii for a bounded set of matrices one definition involves the conventional spectral radius and one involves the operator norm

asymptotic stability and generalized gelfand spectral radius formula let be a set of n n complex matrices for m 1 2 let m be the set of all products of matrices in of length m denote by the multiplicative semigroup generated by is said to be asymptotically stable in the sense of dynamical systems if there is 0 1 such that there are bounded neighborhoods u v cn of the origin for which av mu for all a m m 1 2 for a bounded set of n n complex matrices it is shown that the following conditions are mutually equivalent i is asymptotically stable ii g9 lim supm supa m a 1 m 1 iii lim supm supa m a 1 m 1 where a stands for the spectral radius of a and iv there exists a positive number such that a 1 for all a this fact answers an open question raised by brayton and tong the generalized gelfand spectral radius formula that is g9 conjectured by daubechies and lagarias and proved by berger and wang using advanced tools from ring theory and then by elsner using analytic geometric tools follows immediately form the above asymptotic stability theorem

on the zero stability of variable stepsize multistep methods the spectral radius approach in this paper we illustrate a novel approach for studying the asymptotic behaviour of the solutions of linear difference equations with variable coefficients in particular we deal with the zero stability of the 3 step bdf method on grids with variable stepsize for the numerical solution of ivps for odes our approach is based on the theory of the spectral radius of a family of matrices and yields almost optimal results which give a slight improvement to the best results already known from the literature the success got on the chosen example suggests that our approach has a good potential for more general and harder stability analyses of numerical methods

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 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

rank one characterization of joint spectral radius of finite matrix family abstract in this paper we study the joint generalized spectral radius of a finite set of matrices in terms of its rank one approximation by singular value decomposition in the first part of the paper we show that any finite set of matrices with at most one element s rank being greater than one satisfies the finiteness property under the framework of invariant extremal norm formula for the computation of joint generalized spectral radius for this class of matrix family is derived based on that in the second part we further study the joint generalized spectral radius of finite sets of general matrices through constructing rank one approximations in terms of singular value decomposition and some new characterizations of joint generalized spectral radius are obtained several benchmark examples from applications as well as corresponding numerical computations are provided to illustrate the approach

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

contractibility of compact contractions in hilbert space for a finite set of compact contractions in a complex hilbert space h it is shown that r a 1 for all a in the multiplicative semigroup generated by if and only if there exists a positive integer n such that a 1 for all a in the multiplicative semigroup generated by with length greater than n here r a denotes the spectral radius of a as an application an answer is given to an infinite dimensional case of the finiteness conjecture for the generalized spectral radius attributed to j c lagarias and y wang linear algebra appl 214 1995 17

brief paper explicit construction of a barabanov norm for a class of positive planar discrete time linear switched systems we consider the stability under arbitrary switching of a discrete time linear switched system a powerful approach for addressing this problem is based on studying the most unstable switching law musl if the solution of the switched system corresponding to the musl converges to the origin then the switched system is stable for any switching law the musl can be characterized using optimal control techniques this variational approach leads to a hamilton jacobi bellman equation describing the behavior of the switched system under the musl the solution of this equation is sometimes referred to as a barabanov norm of the switched system although the barabanov norm was studied extensively it seems that there are few examples where it was actually computed in closed form in this paper we consider a special class of positive planar discrete time linear switched systems and provide a closed form expression for a corresponding barabanov norm and a musl the unit circle in this norm is a parallelogram

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

an algorithm for finding extremal polytope norms of matrix families in this paper the problem of the computation of the joint spectral radius of a finite set of matrices is considered we present an algorithm which under some suitable assumptions is able to check if a certain product in the multiplicative semigroup is spectrum maximizing the algorithm proceeds by attempting to construct a suitable extremal norm for the family namely a complex polytope norm as examples for testing our technique we first consider the set of two 2 dimensional matrices recently analyzed by blondel nesterov and theys to disprove the finiteness conjecture and then a set of 3 dimensional matrices arising in the zero stability analysis of the 4 step bdf formula for ordinary differential equations

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

on the accuracy of the ellipsoid norm approximation of the joint spectral radius the joint spectral radius of a set of matrices is a measure of the maximal asymptotic growth rate that can be obtained by forming long products of matrices taken from the set this quantity appears in a number of application contexts but is notoriously difficult to compute and to approximate we introduce in this paper an approximation hat rho that is based on ellipsoid norms that can be computed by convex optimization and that is such that the joint spectral radius belongs to the interval hat rho sqrt n hat rho where n is the dimension of the matrices we also provide a simple approximation for the special case where the entries of the matrices are non negative in this case the approximation is proved to be within a factor at most m m is the number of matrices of the exact value

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

computing the joint spectral radius this paper presents algorithms for finding an arbitrarily small interval that contains the joint spectral radius of a finite set of matrices it also presents a numerical criterion for verifying in certain cases that the joint spectral radius is the maximum of the spectral radii of the given matrices error bounds are derived for the case where calculations are done with finite precision and the matrices are not known exactly the algorithms are implemented and applied to estimate holder exponents of the orthonormal wavelets n constructed by daubechies for 3 n 8

a note on a gap result for norms of semigroups of matrices abstract let be a matrix norm and be a bounded set of n n complex matrices for each m 1 2 let m sup a a m where m a1a2 am ai bell proved that there is a gap in the possible growth of m if consists of finitely many n n complex matrices in this note based on a lemma by elsner we give an elementary proof of bell s theorem in bounded case

a global minimization hybrid active contour model with applications to oil spill images active contour model is popularly and widely used in the field of image segmentation which is based on superior theoretical properties and efficient numerical methods nevertheless one of the prominent disadvantages of this kind of model is the existence of local minima in its functional energy in this paper we propose a novel global minimization hybrid active contour model this model effectively integrates the edge information the local region information and the global region information of the image which is relatively sufficient to extract the object boundaries furthermore we introduce an efficient and fast numerical approach to globally minimize the proposed model which is through a dual formulation of the minimization problem and easy to implement the proposed model is robust enough to the initial condition and does not need to initialize the contour in a distance function and re initialize it periodically during the evolution process specially we applied the proposed model to segment oil spill images in which there usually exist the noise blurry boundaries and intensity inhomogeneity compared with the state of the art models experiment results demonstrate the performance and effectiveness of the proposed model with applications to synthetical and real images especially for oil spill images

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

on the elastic fields of an elliptical inhomogeneity under plane deformation a generalized and unified approach is presented for the two dimensional plane problem of an elliptical inhomogeneity in an isotropic elastic medium the analysis is based upon the use of conformal mapping and laurent series expansion of muskhelishvili s complex potentials the resulting elastic fields are derived explicitly in both transformed and physical planes for the inhomogeneity and the surrounding matrix the associated expressions are universal in the sense of being applicable to generalized geometries and applied loads the application of the general solution is illustrated by several examples and the resulting solutions are verified with those existing in the literature the results advanced here can be used as building blocks for dealing with more complex problems involving a wide variety of geometry and loading conditions

inequalities for numerical invariants of sets of matrices we prove three inequalities relating some invariants of sets of matrices such as the joint spectral radius one of the inequalities in which proof we use geometric invariant theory has the generalized spectral radius theorem of berger and wang as an immediate corollary

on the asymptotic properties of a family of matrices in this paper we consider bounded families f of complex n n matrices after introducing the concept of asymptotic order we investigate how the norm of products of matrices behaves as the number of factors goes to infinity in the case of defective families f u sing the asymptotic order allows us to get a deeper knowledge of the asymptotic behaviour than just considering the so called generalized spectral radius with reference to the well known finiteness conjecture for finite families we also introduce the concepts of spectrum maximizing product and limit spectrum maximizing product showing that for finite families of 2 2matrices defectivity is equivalent to the existence of defective such limit products 2001 elsevier science inc all rights reserved

resilient stabilization of switched linear control systems against adversarial switching this paper studies the problem of stabilizing discrete time switched linear control systems slcss using continuous input by a user against adversarial switching by an adversary it is assumed that at each time the adversary knows the user s decision on the continuous input but not vice versa a quantitative metric of stabilizability is proposed systems at the margin of stabilizability are further classified and studied via the notions of defectiveness and reducibility analytical bounds on the stabilizability metric are derived using semi norms with tight bounds provided by extremal norms numerical algorithms are also developed for computing this metric an application example in networked control systems is presented

completely convex formulation of the chan vese image segmentation model the active contours without edges model of chan and vese ieee transactions on image processing 10 2 266 277 2001 is a popular method for computing the segmentation of an image into two phases based on the piecewise constant mumford shah model the minimization problem is non convex even when the optimal region constants are known a priori in siam journal of applied mathematics 66 5 1632 1648 2006 chan esedo lu and nikolova provided a method to compute global minimizers by showing that solutions could be obtained from a convex relaxation in this paper we propose a convex relaxation approach to solve the case in which both the segmentation and the optimal constants are unknown for two phases and multiple phases in other words we propose a convex relaxation of the popular k means algorithm our approach is based on the vector valued relaxation technique developed by goldstein et al ucla cam report 09 77 2009 and brown et al ucla cam report 10 43 2010 the idea is to consider the optimal constants as functions subject to a constraint on their gradient although the proposed relaxation technique is not guaranteed to find exact global minimizers of the original problem our experiments show that our method computes tight approximations of the optimal solutions particularly we provide numerical examples in which our method finds better solutions than the method proposed by chan et al siam journal of applied mathematics 66 5 1632 1648 2006 whose quality of solutions depends on the choice of the initial condition

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 tree based approach to joint spectral radius determination abstract we suggest a novel method to determine the joint spectral radius of finite sets of matrices by validating the finiteness property it is based on finding a certain finite tree with nodes representing sets of matrix products our approach accounts for cases where one or several matrix products satisfy the finiteness property moreover is potentially functional even for reducible sets of matrices

a gel fand type spectral radius formula and stability of linear constrained switching systems abstract using ergodic theory in this paper we present a gel fand type spectral radius formula which states that the joint spectral radius is equal to the generalized spectral radius for a matrix multiplicative semigroup s restricted to a subset that need not carry the algebraic structure of s this generalizes the berger wang formula using it as a tool we study the absolute exponential stability of a linear switched system driven by a compact subshift of the one sided markov shift associated to s

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

the normed finiteness property of compact contraction operators we study the joint spectral radius given by a finite set of compact operators on a hilbert space it is shown that the normed finiteness property holds in this case that is if all the compact operators are contractions and the joint spectral radius is equal to 1 then there exists a finite product that has a spectral radius equal to 1 we prove an additional statement in that the requirement that the joint spectral radius be equal to 1 can be relaxed to the asking that the maximum norm of finite products of a length norm is equal to 1 the length of this product is related to the dimension of the subspace on which the set of operators is norm preserving

continuity of the generalized spectral radius in max algebra abstract let be an induced matrix norm associated with a monotone norm on r n and be the collection of all nonempty closed and bounded subsets of n n nonnegative matrices under this matrix norm for the hausdorff metric h between and is given by h max sup a inf b a b sup b inf a a b the max algebra system consists of the set of nonnegative numbers with sum a b max a b and the standard product ab for a b 0 for n n nonnegative matrices a b their product is denoted by a b where a b ij max 1 k n a ik b kj for each the max algebra version of the generalized spectral radius of is limsup m sup a m a 1 m where m a 1 a 2 a m a i here a is the maximum circuit geometric mean in this paper we prove that the max algebra version of the generalized spectral radius is continuous on the hausdorff metric space h the notion of the max algebra version of simultaneous nilpotence of matrices is also proposed necessary and sufficient conditions for the max algebra version of simultaneous nilpotence of matrices are presented as well

on the dynamic interaction between a microdefect and a main crack a generalized theoretical approach is presented for the dynamic interaction between an arbitrarily located and oriented microdefect and a finite main crack subjected to a plane incident wave the analysis is based upon the use of integral transform techniques and an appropriate superposition procedure the resulting dynamic stress intensity factors k text i ast and k text ii ast at the main crack are obtained by solving the appropriate singular integral equations using chebyshev polynomials for different incident waves the resulting solution is verified by comparison with existing results and numerical examples are provided to show the effect of the location and orientation of the microdefect and the frequency of the incident wave upon k text i ast and k text ii ast of the main crack the results advanced here can be used as building blocks in the fields of micromechanics damage and non destructive characterization of defects in solids

sufficient conditions for the stability of linear takagi sugeno free fuzzy systems in this paper we will study the stability issues of the linear takagi sugeno t s free fuzzy systems based on matrix norm we propose a new sufficient condition for the linear t s free fuzzy system to be globally asymptotically stable we then study the stability analysis in the case of systems with consequent parameter uncertainty based on mayer s convergent theorem we propose a sufficient condition which is easily implemented for the systems with consequent parameter uncertainty to be globally asymptotically stable

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

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

the finiteness conjecture for the generalized spectral radius of a set of matrices the generalized spectral radius g9 of a set of n n matrices is g9 lim supk g9k 1k where g9k sup a1a2 ak each ai the joint spectral radius g9 is g9 lim supk g9k 1k where g9k sup a1 ak each ai it is known that g9 g9 holds for any finite set of n n matrices the finiteness conjecture asserts that for any finite set of real n n matrices there exists a finite k such that g9 g9 g9k 1k the normed finiteness conjecture for a given operator norm asserts that for any finite set a1 am having all ai op 1 either g9 1 or g9 g9 g9k 1k 1 for some finite k it is shown that the finiteness conjecture is true if and only if the normed finiteness conjecture is true for all operator norms the normed finiteness conjecture is proved for a large class of operator norms extending results of gurvits in particular for polytope norms and for the euclidean norm explicit upper bounds are given for the least k having g9 g9k 1k these results imply upper bounds for generalized critical exponents for these norms

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

on asymptotic properties of matrix semigroups with an invariant cone recently several research efforts showed that the analysis of joint spectral characteristics of sets of matrices can be simplified when these matrices share an invariant cone we prove new results in this direction we prove that the joint spectral subradius is continuous in the neighborhood of sets of matrices that leave an embedded pair of cones invariant we show that both the averaged maximal spectral radius as well as the maximal trace where the maximum is taken on all the products of the same length t converge towards the joint spectral radius when t increases provided that the matrices share an invariant cone and additionally one of them is primitive

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