on joint ruin probability for a bidimensional levy driven risk model with stochastic returns and heavy tailed claims abstract in this paper we study the joint ruin problem for two insurance companies that divide between them the losses in positive proportions 1 and 2 modeling an insurance and a re insurance company assume that the surplus process of i th i 1 2 company u i has the form of d u i t u i t d r i t i d p t t 0 with u i 0 x i 0 and p and r i two levy processes representing respectively a loss process and a stochastic return process supposing that the loss process p has a levy measure of consistent variation and the laplace exponent of r i i 1 2 satisfies some conditions an asymptotic estimate for this joint ruin problem is established

technical communique an improved stability criterion for fixed point state space digital filters using two s complement arithmetic a new stability criterion for fixed point state space digital filters using two s complement arithmetic is presented the effectiveness of the results obtained is shown by using a numerical example

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

a viscosity solutions approach to shape from shading the problem of recovering a lambertian surface from a single two dimensional image may be written as a first order nonlinear equation which presents the disadvantage of having several continuous and even smooth solutions a new approach based on hamilton jacobi bellman equations and viscosity solutions theories enables one to study non uniqueness phenomenon and thus to characterize the surface among the various solutions a consistent and monotone scheme approximating the surface is constructed thanks to the dynamic programming principle and numerical results are presented

tracking deformable objects in the plane using an active contour model the problems of segmenting a noisy intensity image and tracking a nonrigid object in the plane are discussed in evaluating these problems a technique based on an active contour model commonly called a snake is examined the technique is applied to cell locomotion and tracking studies the snake permits both the segmentation and tracking problems to be simultaneously solved in constrained cases a detailed analysis of the snake model emphasizing its limitations and shortcomings is presented and improvements to the original description of the model are proposed problems of convergence of the optimization scheme are considered in particular an improved terminating criterion for the optimization scheme that is based on topographic features of the graph of the intensity image is proposed hierarchical filtering methods as well as a continuation method based on a discrete sale space representation are discussed results for both segmentation and tracking are presented possible failures of the method are discussed

uniform asymptotics for the finite time ruin probabilities of two kinds of nonstandard bidimensional risk models abstract in this paper we consider uniform asymptotics for the finite time ruin probabilities of two kinds of nonstandard bidimensional renewal risk models with constant interest forces and diffusion generated by brownian motions in one of the models two classes of claims have different arrival times while in the another model two classes of claims share the same arrival times in both models two classes of claim sizes are both upper tail asymptotically independent and their distributions belong to the intersection of the long tailed distribution class and the dominatedly varying tailed distribution class and the inter arrival times follow a widely lower orthant dependence structure in each model we obtain three kinds of uniform asymptotics for the finite time ruin probabilities respectively

automatic 3d segmentation and quantification of lenticulostriate arteries from high resolution 7 tesla mra images we propose a novel hybrid approach for automatic 3d segmentation and quantification of high resolution 7 tesla magnetic resonance angiography mra images of the human cerebral vasculature our approach consists of two main steps first a 3d model based approach is used to segment and quantify thick vessels and most parts of thin vessels second remaining vessel gaps of the first step in low contrast and noisy regions are completed using a 3d minimal path approach which exploits directional information we present two novel minimal path approaches the first is an explicit approach based on energy minimization using probabilistic sampling and the second is an implicit approach based on fast marching with anisotropic directional prior we conducted an extensive evaluation with over 2300 3d synthetic images and 40 real 3d 7 tesla mra images quantitative and qualitative evaluation shows that our approach achieves superior results compared with a previous minimal path approach furthermore our approach was successfully used in two clinical studies on stroke and vascular dementia

shortest paths with higher order regularization this paper describes a new method of finding thin elongated structures in images and volumes we use shortest paths to minimize very general functionals of higher order curve properties such as curvature and torsion our method uses line graphs to find the optimal path on a given discretization often in the order of seconds on a single computer the curves are then refined using local optimization making it possible to recover very smooth curves we are able to place constraints on our curves such as maximum integrated curvature or a maximum curvature at any point of the curve to our knowledge we are the first to perform experiments in three dimensions with curvature and torsion regularization the largest graphs we process have over a hundred billion arcs experiments on medical images and in multi view reconstruction show the significance and practical usefulness of higher order regularization

technical communique stability of fixed point state space digital filters using two s complement arithmetic further insight the purpose of this note is to point out that for the digital filters using two s complement arithmetic the criterion in singh 2010 can be transformed into a simpler form the stability criteria in singh 2010 and mills et al 1978 are equivalent in some cases a third order example in which singh s criterion is satisfied and mills mullis roberts criterion fails is presented

a fast level set method for propagating interfaces a method is introduced to decrease the computational labor of the standard level set method for propagating interfaces the fast approach uses only points close to the curve at every time step we describe this new algorithm and compare its efficiency and accuracy with the standard level set approach

using dynamic programming for solving variational problems in vision dynamic programming is discussed as an approach to solving variational problems in vision dynamic programming ensures global optimality of the solution is numerically stable and allows for hard constraints to be enforced on the behavior of the solution within a natural and straightforward structure as a specific example of the approach s efficacy applying dynamic programming to the energy minimizing active contours is described the optimization problem is set up as a discrete multistage decision process and is solved by a time delayed discrete dynamic programming algorithm a parallel procedure for decreasing computational costs is discussed

closed form solutions for physically based shape modeling and recognition the authors present a closed form physically based solution for recovering a three dimensional 3 d solid model from collections of 3 d surface measurements given a sufficient number of independent measurements the solution is overconstrained and unique except for rotational symmetries the proposed approach is based on the finite element method fem and parametric solid modeling using implicit functions this approach provides both the convenience of parametric modeling and the expressiveness of the physically based mesh formulation and in addition can provide great accuracy at physical simulation a physically based object recognition method that allows simple closed form comparisons of recovered 3 d solid models is presented the performance of these methods is evaluated using both synthetic range data with various signal to noise ratios and using laser rangefinder data

some concepts of negative dependence abstract the theory of positive dependence notions cannot yield useful results for some widely used distributions such as the multinomial dirichlet and the multivariate hypergeometric some conditions of negative dependence that are satisfied by these distributions and which have practical meaning are introduced preservation results for some of these concepts are derived useful inequalities for some widely used distributions are obtained results of mallows 1969 that apply to the multinomial distributions are extended to more distributions examples are listed author

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

progressive minimal path method for segmentation of 2d and 3d line structures we propose a novel minimal path method for the segmentation of 2d and 3d line structures minimal path methods perform propagation of a wavefront emanating from a start point at a speed derived from image features followed by path extraction using backtracing usually the computation of the speed and the propagation of the wave are two separate steps and point features are used to compute a static speed we introduce a new continuous minimal path method which steers the wave propagation progressively using dynamic speed based on path features we present three instances of our method using an appearance feature of the path a geometric feature based on the curvature of the path and a joint appearance and geometric feature based on the tangent of the wavefront these features have not been used in previous continuous minimal path methods we compute the features dynamically during the wave propagation and also efficiently using a fast numerical scheme and a low dimensional parameter space our method does not suffer from discretization or metrication errors we performed qualitative and quantitative evaluations using 2d and 3d images from different application areas

stability of discrete time systems joined with a saturation operator on the state space this note studies the stability of discrete time dynamical systems acted upon by a saturation process in the state space a finite procedure is proposed to focus on the asymptotic behavior of systems which produces linear constraints imposed on lyapunov stein matrix inequalities to be solved a little linear algebra broadens the scope of stability test from that of the earlier liu michel s criterion

globally minimal surfaces by continuous maximal flows in this paper we address the computation of globally minimal curves and surfaces for image segmentation and stereo reconstruction we present a solution simulating a continuous maximal flow by a novel system of partial differential equations existing methods are either grid biased graph based methods or suboptimal active contours and surfaces the solution simulates the flow of an ideal fluid with isotropic velocity constraints velocity constraints are defined by a metric derived from image data an auxiliary potential function is introduced to create a system of partial differential equations it is proven that the algorithm produces a globally maximal continuous flow at convergence and that the globally minimal surface may be obtained trivially from the auxiliary potential the bias of minimal surface methods toward small objects is also addressed an efficient implementation is given for the flow simulation the globally minimal surface algorithm is applied to segmentation in 2d and 3d as well as to stereo matching results in 2d agree with an existing minimal contour algorithm for planar images results in 3d segmentation and stereo matching demonstrate that the new algorithm is robust and free from grid bias

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

3 d curvilinear structure detection filter via structure ball analysis curvilinear structure detection filters are crucial building blocks in many medical image processing applications where they are used to detect important structures such as blood vessels airways and other similar fibrous tissues unfortunately most of these filters are plagued by an implicit single structure direction assumption which results in a loss of signal around bifurcations this peculiarity limits the performance of all subsequent processes such as understanding angiography acquisitions computing an accurate segmentation or tractography or automatically classifying image voxels this paper presents a new 3 d curvilinear structure detection filter based on the analysis of the structure ball a geometric construction representing second order differences sampled in many directions the structure ball is defined formally and its computation on a discreet image is discussed a contrast invariant diffusion index easing voxel analysis and visualization is also introduced and different structure ball shape descriptors are proposed a new curvilinear structure detection filter is defined based on the shape descriptors that best characterize curvilinear structures the new filter produces a vesselness measure that is robust to the presence of x and y junctions along the structure by going beyond the single direction assumption at the same time it stays conceptually simple and deterministic and allows for an intuitive representation of the structure s principal directions sample results are provided for synthetic images and for two medical imaging modalities

finite time and infinite time ruin probabilities in a two dimensional delayed renewal risk model with sarmanov dependent claims abstract consider a two dimensional delayed renewal risk model with a constant interest rate where the claim sizes of the two classes form a sequence of independent and identically distributed random vectors following a common bivariate sarmanov distribution in the presence of heavy tailed claim sizes some asymptotic formulas are derived for the finite time and infinite time ruin probabilities

correspondence author s reply to comments on modified criterion for global asymptotic stability of fixed point state space digital filters using two s complement arithmetic automatica 46 2010 475 478

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

asymptotics for a delay claim risk model with diffusion dependence structures and constant force of interest abstract in the paper we consider an insurance risk model perturbed by diffusion with constant force of interest where each main claim may induce a delayed claim called a by claim if the main claims and by claims form a sequence of pairwise quasi asymptotically independent random variables with long tails and dominatedly varying tails and the main claim arrival process is an arbitrary counting process we obtain a uniformly asymptotic formula for finite time ruin probability for times in a finite interval particularly with a certain dependence structure among the inter arrival times of main claims the formula holds uniformly for all times when the claim sizes are consistently varying tailed where the result obtained also covers an asymptotic formula for the infinite time ruin probability

minimal surfaces based object segmentation a geometric approach for 3d object segmentation and representation is presented the segmentation is obtained by deformable surfaces moving towards the objects to be detected in the 3d image the model is based on curvature motion and the computation of surfaces with minimal areas better known as minimal surfaces the space where the surfaces are computed is induced from the 3d image volumetric data in which the objects are to be detected the model links between classical deformable surfaces obtained via energy minimization and intrinsic ones derived from curvature based flows the new approach is stable robust and automatically handles changes in the surface topology during the deformation

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

local or global minima flexible dual front active contours most variational active contour models are designed to find local minima of data dependent energy functionals with the hope that reasonable initial placement of the active contour will drive it toward a desirable local minimum as opposed to an undesirable configuration due to noise or complex image structure as such there has been much research into the design of complex region based energy functionals that are less likely to yield undesirable local minima when compared to simpler edge based energy functionals whose sensitivity to noise and texture is significantly worse unfortunately most of these more robust region based energy functionals are applicable to a much narrower class of imagery compared to typical edge based energies due to stronger global assumptions about the underlying image data devising new implementation algorithms for active contours that attempt to capture more global minimizers of already proposed image based energies would allow us to choose an energy that makes sense for a particular class of energy without concern over its sensitivity to local minima such implementations have been proposed for capturing global minima however sometimes the completely global minimum is just as undesirable as a minimum that is too local in this paper we propose a novel fast and flexible dual front implementation of active contours motivated by minimal path techniques and utilizing fast sweeping algorithms which is easily manipulated to yield minima with variable degrees of localness and globalness by simply adjusting the size of active regions the ability to gracefully move from capturing minima that are more local according to the initial placement of the active contour surface to minima that are more global allows this model to more easily obtain desirable minimizers which often are neither the most local nor the most global experiments on various 2d and 3d images and comparisons with some active contour models and region growing methods are also given to illustrate the properties of this model and its performance in a variety of segmentation applications

basic renewal theorems for random walks with widely dependent increments abstract in this paper we derive some basic renewal theorems for random walks with widely dependent increments which contain some common negatively dependent random variables r v s some positively dependent r v s and some others for this purpose we investigate uniform integrability for related counting processes and the strong law of large numbers for the widely dependent r v s

stability of linear discrete dynamics employing state saturation arithmetic this note is concerned with the stability of discrete time dynamical systems employing saturation arithmetic in the state space a matrix measure is introduced so that it can administer the proximity evaluation of a matrix to the set of diagonal matrices and the measure is utilized for making an additional condition to the lyapunov stein matrix inequality the solvability of the modified matrix inequality ensures not only the stability but also the absence of overflow oscillation under the state saturation arithmetic and this approach has the advantage of being free from auxiliary parameters as an application the obtained result is applied to the stability analysis of two dimensional dynamics numerical examples are given to illustrate the results

correspondence comments on modified criterion for global asymptotic stability of fixed point state space digital filters using two s complement arithmetic automatica 46 2010 475 478 a recently reported criterion singh v 2010 modified criterion for global asymptotic stability of fixed point state space digital filters using two s complement arithmetic automatica 46 475 478 which is a modified version of an earlier criterion due to mills mullis roberts for the global asymptotic stability of fixed point state space digital filters with two s complement arithmetic is reviewed pertaining to second order digital filters it is shown that singh s approach will never lead to a larger overflow stability region in the parameter space as compared to that obtainable via mills mullis roberts criterion

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

estimating shortest paths and minimal distances on digitized three dimensional surfaces abstract the estimation of minimal distances and shortest paths between points on a continuous three dimensional 3d surface given in digitized form is considered the suggested approach combines recently developed length estimators for digitized 3d curves with well known algorithms for computing shortest paths in sparse graphs to estimate the minimal distances and the corresponding shortest paths in a systematic computationally efficient way in comparison to differential geometry techniques for solving the continuous geodesic problem and to computational geometry algorithms for solving the discrete geodesic probelm the suggested hybrid continuous discrete approach is well suited to applications in which continuous surfaces are given in digitized form computation time must be relatively short and an approximate solution is acceptable in particular the suggested method can be used to efficiently obtain a good initial approximation as an input to other algorithms thus improving their speed of convergence and reducing their tendency to converge to insignificant local minima some confusion has recently arisen with respect to the relation between the design of length estimators and the optimization of local distances for distance transformations since 3d length estimation is a central concept in the suggested approach an effort is made to resolve discrepancies and to highlight the similarities and differences between these problems it is shown that while in two dimensions the design of length estimators and the design of local weights for distance transformations are rather similar in three dimensions digital geometry dictates that these problems are different the contexts in which each of the two approaches should be preferred are identified

technical communique stability analysis of a class of digital filters utilizing single saturation nonlinearity a novel criterion for the global asymptotic stability of a class of digital filters utilizing single saturation nonlinearity is presented an example showing the effectiveness of the present criterion is given

asymptotic ruin probabilities in a generalized bidimensional risk model perturbed by diffusion with constant force of interest abstract in the paper we study three types of finite time ruin probabilities in a diffusion perturbed bidimensional risk model with constant force of interest pairwise strongly quasi asymptotically independent claims and two general claim arrival processes and obtain uniformly asymptotic formulas for times in a finite interval when the claims are both long tailed and dominatedly varying tailed in particular with a certain dependence structure among the inter arrival times these formulas hold uniformly for all times when the claims are pairwise quasi asymptotically independent and consistently varying tailed

power watershed a unifying graph based optimization framework in this work we extend a common framework for graph based image segmentation that includes the graph cuts random walker and shortest path optimization algorithms viewing an image as a weighted graph these algorithms can be expressed by means of a common energy function with differing choices of a parameter q acting as an exponent on the differences between neighboring nodes introducing a new parameter p that fixes a power for the edge weights allows us to also include the optimal spanning forest algorithm for watershed in this same framework we then propose a new family of segmentation algorithms that fixes p to produce an optimal spanning forest but varies the power q beyond the usual watershed algorithm which we term the power watershed in particular when q 2 the power watershed leads to a multilabel scale and contrast invariant unique global optimum obtained in practice in quasi linear time placing the watershed algorithm in this energy minimization framework also opens new possibilities for using unary terms in traditional watershed segmentation and using watershed to optimize more general models of use in applications beyond image segmentation

derivatives with respect to metrics and applications subgradient marching algorithm this paper introduces a subgradient descent algorithm to compute a riemannian metric that minimizes an energy involving geodesic distances the heart of the method is the subgradient marching algorithm to compute the derivative of the geodesic distance with respect to the metric the geodesic distance being a concave function of the metric this algorithm computes an element of the subgradient in o n 2 log n operations on a discrete grid of n points it performs a front propagation that computes a subgradient of a discrete geodesic distance we show applications to landscape modeling and to traffic congestion both applications require the maximization of geodesic distances under convex constraints and are solved by subgradient descent computed with our subgradient marching we also show application to the inversion of travel time tomography where the recovered metric is the local minimum of a non convex variational problem involving geodesic distances

stability criterion for a class of fixed point digital filters using two s complement arithmetic a new stability criterion for a class of digital filters using two s complement arithmetic is presented the effectiveness of the obtained results is shown by using a numerical example

on a two dimensional risk model with time dependent claim sizes and risky investments abstract consider a two dimensional risk model in which two insurance companies divide between them the claims in some specified proportions suppose that the claim sizes and inter arrival times form a sequence of independent and identically distributed random pairs with each pair obeying a dependence structure and the surpluses of the two companies are invested into portfolios whose returns follow two different geometric levy processes when the claim size distribution is extended regularly varying tailed asymptotic expressions for the ruin probability of this two dimensional risk model are exhibited some numerical results are also presented to illustrate the accuracy of our asymptotic formulae

uniform asymptotics of the finite time ruin probability for all times abstract in this paper we study the asymptotics of the finite time ruin probability for a generalized renewal risk model with independent strong subexponential claim sizes and widely lower orthant dependent inter occurrence times this widely lower orthant dependence structure can include some common negative dependent random variables r v s such as negatively lower orthant dependent r v s some positive dependent r v s and some other dependent r v s for this generalized renewal risk model we show that the asymptotics of the finite time ruin probability hold uniformly for all times in the sense that the magnitude of the initial reserve of some insurance portfolio does not influence the length of the operating time further the uniform asymptotics of the random time ruin probability in the above model have been obtained

asymptotic ruin probabilities for a bidimensional renewal risk model with constant interest rate and dependent claims abstract this paper considers a bidimensional renewal risk model with constant interest rate and dependent regularly varying claims we assume that the total initial surplus of an insurance company is proportionally allocated to two kinds of insurance businesses the dependence among claim sizes stems from two aspects one is that the two kinds of claims share a common renewal claim number process and the another one is that each vector of claims follows a general dependence structure given in terms of survival copulas containing both asymptotic independence and asymptotic dependence cases under certain technical conditions we derive precise asymptotic formulae for the finite time and infinite time ruin probabilities

efficient algorithms for globally optimal trajectories we present serial and parallel algorithms for solving a system of equations that arises from the discretization of the hamilton jacobi equation associated to a trajectory optimization problem of the following type a vehicle starts at a prespecified point x sub o and follows a unit speed trajectory x t inside a region in spl rscr sup m until an unspecified time t that the region is exited a trajectory minimizing a cost function of the form spl int sub 0 sup t r x t dt q x t is sought the discretized hamilton jacobi equation corresponding to this problem is usually solved using iterative methods nevertheless assuming that the function r is positive we are able to exploit the problem structure and develop one pass algorithms for the discretized problem the first algorithm resembles dijkstra s shortest path algorithm and runs in time o n log n where n is the number of grid points the second algorithm uses a somewhat different discretization and borrows some ideas from a variation of dial s shortest path algorithm 1969 that we develop here it runs in time o n which is the best possible under some fairly mild assumptions finally we show that the latter algorithm can be efficiently parallelized for two dimensional problems and with p processors its running time becomes o n p provided that p o spl radic n log n

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

graph cuts and efficient n d image segmentation combinatorial graph cut algorithms have been successfully applied to a wide range of problems in vision and graphics this paper focusses on possibly the simplest application of graph cuts segmentation of objects in image data despite its simplicity this application epitomizes the best features of combinatorial graph cuts methods in vision global optima practical efficiency numerical robustness ability to fuse a wide range of visual cues and constraints unrestricted topological properties of segments and applicability to n d problems graph cuts based approaches to object extraction have also been shown to have interesting connections with earlier segmentation methods such as snakes geodesic active contours and level sets the segmentation energies optimized by graph cuts combine boundary regularization with region based properties in the same fashion as mumford shah style functionals we present motivation and detailed technical description of the basic combinatorial optimization framework for image segmentation via s t graph cuts after the general concept of using binary graph cut algorithms for object segmentation was first proposed and tested in boykov and jolly 2001 this idea was widely studied in computer vision and graphics communities we provide links to a large number of known extensions based on iterative parameter re estimation and learning multi scale or hierarchical approaches narrow bands and other techniques for demanding photo video and medical applications

an eulerian pde approach for computing tissue thickness we outline an eulerian framework for computing the thickness of tissues between two simply connected boundaries that does not require landmark points or parameterizations of either boundary thickness is defined as the length of correspondence trajectories which run from one tissue boundary to the other and which follow a smooth vector field constructed in the region between the boundaries a pair of partial differential equations pdes that are guided by this vector field are then solved over this region and the sum of their solutions yields the thickness of the tissue region unlike other approaches this approach does not require explicit construction of any correspondence trajectories an efficient stable and computationally fast solution to these pdes is found by careful selection of finite differences according to an up winding condition the behavior and performance of our method is demonstrated on two simulations and two magnetic resonance imaging data sets in two and three dimensions these experiments reveal very good performance and show strong potential for application in tissue thickness visualization and quantification

an improved time adaptive self organizing map for high speed shape modeling in this paper an improved active contour model based on the time adaptive self organizing map with a high convergence speed and low computational complexity is proposed for this purpose the active contour model based on the original time adaptive self organizing map is modified in two ways adaptation of the speed parameter and reduction of the number of neurons by adapting the speed parameter the neuron motion speed is determined based on the distance of each neuron from the shape boundary which results in an increase in the speed of convergence of the contour using a smaller number of neurons the computational complexity is reduced to achieve this the number of neurons used in the contour is determined based on the boundary curvature the proposed model is studied and compared with the original time adaptive self organizing map both models are used in several experiments including a tracking application results reveal the higher speed and very good performance of the proposed model for real time applications

graphical gaussian shape models and their application to image segmentation this paper presents a novel approach to shape modeling and a model based image segmentation procedure tailor made for the proposed shape model a common way to represent shape is based on so called key points and leads to shape variables which are invariant with respect to similarity transformations we propose a graphical shape model which relies on a certain conditional independence structure among the shape variables most often it is sufficient to use a sparse underlying graph reflecting both nearby and long distance key point interactions graphical shape models allow for specific shape modeling since e g for the subclass of decomposable graphical gaussian models both model selection procedures and explicit parameter estimates are available a further prerequisite to a successful application of graphical shape models in image analysis is provided by the toolbox of markov chain monte carlo methods offering highly flexible and effective methods for the exploration of a specified distribution for bayesian image segmentation based on a graphical gaussian shape model we suggest applying a hybrid approach composed of the well known gibbs sampler and the more recent slice sampler shape modeling as well as image analysis are demonstrated for the segmentation of vertebrae from two dimensional slices of computer tomography images

dynamic programming for detecting tracking and matching deformable contours the problem of segmenting an image into separate regions and tracking them over time is one of the most significant problems in vision terzopoulos et al 1987 proposed an approach to detect the contour regions of complex shapes assuming a user selected initial contour not very far from the desired solution we propose to further explore the information provided by the user s selected points and apply an optimal method to detect contours which allows a segmentation of the image the method is based on dynamic programming dp and applies to a wide variety of shapes it is exact and not iterative we also consider a multiscale approach capable of speeding up the algorithm by a factor of 20 although at the expense of losing the guaranteed optimality characteristic the problem of tracking and matching these contours is addressed for tracking the final contour obtained at one frame is sampled and used as initial points for the next frame then the same dp process is applied for matching a novel strategy is proposed where the solution is a smooth displacement field in which unmatched regions are allowed while cross vectors are not the algorithm is again based on dp and the optimal solution is guaranteed we have demonstrated the algorithms on natural objects in a large spectrum of applications including interactive segmentation and automatic tracking of the regions of interest in medical images

global minimum for active contour models a minimal path approach a new boundary detection approach for shape modeling is presented it detects the global minimum of an active contour model s energy between two end points initialization is made easier and the curve is not trapped at a local minimum by spurious edges we modify the snake energy by including the internal regularization term in the external potential term our method is based on finding a path of minimal length in a riemannian metric we then make use of a new efficient numerical method to find this shortest path it is shown that the proposed energy though based only on a potential integrated along the curve imposes a regularization effect like snakes we explore the relation between the maximum curvature along the resulting contour and the potential generated from the image the method is capable to close contours given only one point on the objects boundary by using a topology based saddle search routine we show examples of our method applied to real aerial and medical images

a fast minimal path active contour model a new minimal path active contour model for boundary extraction is presented implementing the new approach requires four steps 1 users place some initial end points on or near the desired boundary through an interactive interface 2 a potential searching window is defined between two end points 3 a graph search method based on conic curves is used to search the boundary and 4 a wriggling procedure is used to calibrate the contour and reduce sensitivity of the search results on the selected initial end points the last three steps are performed automatically in the proposed approach the potential window systematically provides a new node connection for the later graph search which is different from the row by row and column by column methods used in the classical graph search furthermore this graph search also suggests ways to design a wriggling procedure to evolve the contour in the direction nearly perpendicular to itself by creating a list of displacement vectors in the potential window the proposed minimal path active contour model speeds up the search and reduces the metrication error frequently encountered in the classical graph search methods e g the dynamic programming minimal path dpmp method

technical communique stability of discrete time systems joined with a saturation operator on the state space generalized form of liu michel s criterion a novel criterion for the global asymptotic stability of discrete time systems in a state space realization using saturation arithmetic was previously given by liu and michel in their approach as in most or probably all existing approaches the matrix p is assumed to be symmetric in this communique it is shown that their approach is such as to be extended to allow the use of an unsymmetric matrix p taking note of this a more general form of their criterion is presented a modified form of the criterion is also presented examples show the effectiveness of the generalized approach to the best of author s knowledge this communique is the first report of exploiting an unsymmetric p to obtain a stability condition with reduced conservatism

technical communique elimination of overflow oscillations in direct form digital filters using saturation arithmetic a novel frequency domain criterion for the elimination of limit cycles in a class of digital filters using saturation arithmetic is presented an example showing the effectiveness of the present criterion is given

technical communique modified criterion for global asymptotic stability of fixed point state space digital filters using two s complement arithmetic a criterion for the global asymptotic stability of fixed point state space digital filters using two s complement arithmetic is presented the criterion is a modified form of a well known criterion due to mills mullis and roberts the criterion is in the form of linear matrix inequality and hence computationally tractable an example shows the effectiveness of the modified criterion

boundary finding with parametrically deformable models segmentation using boundary finding is enhanced both by considering the boundary as a whole and by using model based global shape information the authors apply flexible constraints in the form of a probabilistic deformable model to the problem of segmenting natural 2 d objects whose diversity and irregularity of shape make them poorly represented in terms of fixed features or form the parametric model is based on the elliptic fourier decomposition of the boundary probability distributions on the parameters of the representation bias the model to a particular overall shape while allowing for deformations boundary finding is formulated as an optimization problem using a maximum a posteriori objective function results of the method applied to real and synthetic images are presented including an evaluation of the dependence of the method on prior information and image quality