fast methods for the eikonal and related hamilton jacobi equations on unstructured meshes the fast marching method is a numerical algorithm for solving the eikonal equation on a rectangular orthogonal mesh in o m log m steps where m is the total number of grid points the scheme relies on an upwind finite difference approximation to the gradient and a resulting causality relationship that lends itself to a dijkstra like programming approach in this paper we discuss several extensions to this technique including higher order versions on unstructured meshes in rn and on manifolds and connections to more general static hamilton jacobi equations

a theoretical framework of regional cone beam tomography intuitively if only part of an object is to be reconstructed the information required to perform the reconstruction should be less than that required to perform global reconstruction global reconstruction is assumed by every published reconstruction formula with closed format the reduction of input information could lead to the simplification of data collection and the reduction of implementation cost the author has explored three basic issues of regional cone beam tomography 1 a completeness condition for regional reconstruction 2 an estimation formula and 3 a convergence condition the analysis of the first issue yields requirements for artifact free reconstruction and a convenient criterion for source curve design the closed format of the estimation formula developed permits efficient analysis the discussion of the third issue facilitates guidelines for selecting an appropriate interpolation technique for discrete input data

curve like structure extraction using minimal path propagation with backtracking minimal path techniques can efficiently extract geometrically curve like structures by finding the path with minimal accumulated cost between two given endpoints though having found wide practical applications e g line identification crack detection and vascular centerline extraction minimal path techniques suffer from some notable problems the first one is that they require setting two endpoints for each line to be extracted endpoint problem the second one is that the connection might fail when the geodesic distance between the two points is much shorter than the desirable minimal path shortcut problem in addition when connecting two distant points the minimal path connection might become inefficient as the accumulated cost increases over the propagation and results in leakage into some non feature regions near the starting point accumulation problem to address these problems this paper proposes an approach termed minimal path propagation with backtracking we found that the information in the process of backtracking from reached points can be well utilized to overcome the above problems and improve the extraction performance the whole algorithm is robust to parameter setting and allows a coarse setting of the starting point extensive experiments with both simulated and realistic data are performed to validate the performance of the proposed method

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

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

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

gain in stochastic resonance precise numerics versus linear response theory beyond the two mode approximation in the context of the phenomenon of stochastic resonance sr we study the correlation function the signal to noise ratio snr and the ratio of output over input snr i e the gain which is associated to the nonlinear response of a bistable system driven by time periodic forces and white gaussian noise these quantifiers for sr are evaluated using the techniques of linear response theory lrt beyond the usually employed two mode approximation scheme we analytically demonstrate within such an extended lrt description that the gain can indeed not exceed unity we implement an efficient algorithm based on work by greenside and helfand detailed in the appendix to integrate the driven langevin equation over a wide range of parameter values the predictions of lrt are carefully tested against the results obtained from numerical solutions of the corresponding langevin equation over a wide range of parameter values we further present an accurate procedure to evaluate the distinct contributions of the coherent and incoherent parts of the correlation function to the snr and the gain as a main result we show for subthreshold driving that both the correlation function and the snr can deviate substantially from the predictions of lrt and yet the gain can be either larger or smaller than unity in particular we find that the gain can exceed unity in the strongly nonlinear regime which is characterized by weak noise and very slow multifrequency subthreshold input signals with a small duty cycle this latter result is in agreement with recent analog simulation results by gingl et al icnf 2001 edited by g bosman world scientific singapore 2002 pp 545 548 fluct noise lett 1 l181 2001

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

on the use of a minimal path approach for target trajectory analysis vision based action recognition has multiple applications mainly focused in video surveillance systems the art of labeling each target behavior in crowded scenarios is a complicated field since usually we do not have visual confirmation of the parts of a target to infer its behavior thus trajectory analysis becomes a good choice to try to infer knowledge about target movements most of the contributions to this field involve a training period in which we obtain information a priori about the environment storing a dataset with all the possible usual routes based in the minimal path theory using geodesic active contours we present a novel architecture where no initial information about the scene is needed while it is possible to include it if necessary to specify constraints experimental results in two different application domains show the performance and flexibility of this method being able to be used in multiple trajectory analysis problems

reactive dynamics of inertial particles in nonhyperbolic chaotic flows anomalous kinetics of infective e g autocatalytic reactions in open nonhyperbolic chaotic flows are important for many applications in biological chemical and environmental sciences we present a scaling theory for the singular enhancement of the production caused by the universal underlying fractal patterns the key dynamical invariant quantities are the effective fractal dimension and effective escape rate which are primarily determined by the hyperbolic components of the underlying dynamical invariant sets the theory is general as it includes all previously studied hyperbolic reactive dynamics as a special case we introduce a class of dissipative embedding maps for numerical verification

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

crises sudden changes in chaotic attractors and transient chaos abstract the occurrence of sudden qualitative changes of chaotic dynamics as a parameter is varied is discussed and illustrated it is shown that such changes may result from the collision of an unstable periodic orbit and a coexisting chaotic attractor we call such collisions crises phenomena associated with crises include sudden changes in the size of chaotic attractors sudden appearances of chaotic attractors a possible route to chaos and sudden destructions of chaotic attractors and their basins this paper presents examples illustrating that crisis events are prevalent in many circumstances and systems and that just past a crisis certain characteristic statistical behavior whose type depends on the type of crisis occurs in particular the phenomenon of chaotic transients is investigated the examples discussed illustrate crises in progressively higher dimension and include the one dimensional quadratic map the two dimensional henon map systems of ordinary differential equations in three dimensions and a three dimensional map in the case of our study of the three dimensional map a new route to chaos is proposed which is possible only in invertible maps or flows of dimension at least three or four respectively based on the examples presented the following conjecture is proposed almost all sudden changes in the size of chaotic attractors and almost all sudden destruction or creations of chaotic attractors and their basins are due to crises

discriminative feature representation to improve projection data inconsistency for low dose ct imaging in low dose computed tomography ldct imaging the data inconsistency of measured noisy projections can significantly deteriorate reconstruction images to deal with this problem we propose here a new sinogram restoration approach the sinogram discriminative feature representation s dfr method different from other sinogram restoration methods the proposed method works through a 3 d representation based feature decomposition of the projected attenuation component and the noise component using a well designed composite dictionary containing atoms with discriminative features this method can be easily implemented with good robustness in parameter setting its comparison to other competing methods through experiments on simulated and real data demonstrated that the s dfr method offers a sound alternative in ldct

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

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

poincare map for scattering states for scattering states in classical mechanics a map is constructed which is an analogue to the poincare map for bound state trajectories iteration of this map indicates which parts of the phase space are filled by unstable trajectories that are sensitive to small changes in the initial conditions and which regions are filled by stable trajectories examples for this map are given by numerical calculations for scattering off a simple two dimensional model potential

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

optimal transportation with traffic congestion and wardrop equilibria in the classical monge kantorovich problem the transportation cost depends only on the amount of mass sent from sources to destinations and not on the paths followed by this mass thus it does not allow for congestion effects using the notion of traffic intensity we propose a variant taking into account congestion this variant is a continuous version of a well known traffic problem on networks that is studied both in economics and in operational research the interest of this problem is in its relations with traffic equilibria of wardrop type what we prove in the paper is exactly the existence and the variational characterization of equilibria in a continuous space setting

computation of unmeasured third generation vct views from measured views we compute unmeasured cone beam projections from projections measured by a third generation helical volumetric computed tomography system by solving a characteristic problem for an ultrahyperbolic differential equation john 1938 by working in the fourier domain we convert the second order pde into a family of first order ordinary differential equations a simple first order integration is used to solve the odes

two approximations of solutions of hamilton jacobi equations abstract equations of hamilton jacobi type arise in many areas of application including the calculus of variations control theory and differential games the associated initial value problems almost never have global time classical solutions and one must deal with suitable generalized solutions the correct class of generalized solutions has only recently been established by the authors this article establishes the convergence of a class of difference approximations to these solutions by obtaining explicit error estimates analogous results are proved by similar means for the method of vanishing viscosity author

the applicability of dip moveout azimuth moveout in the presence of caustics reflection seismic data continuation is the computation of data at source and receiver locations that differ from those in the original data using whatever data are available we develop a general theory of data continuation in the presence of caustics and illustrate it with three examples dip moveout dmo azimuth moveout amo and offset continuation this theory does not require knowledge of the reflector positions we construct the output data set from the input through the composition of three operators an imaging operator a modeling operator and a restriction operator this results in a single operator that maps directly from the input data to the desired output data we use the calculus of fourier integral operators to develop this theory in the presence of caustics for both dmo and amo we compute impulse responses in a constant velocity model and in a more complicated model in which caustics arise this analysis reveals errors that can be introduced by assuming for example a model with a constant vertical velocity gradient when the true model is laterally heterogeneous data continuation uses as input a subset common offset common angle of the available data which may introduce artifacts in the continued data one could suppress these artifacts by stacking over a neighborhood of input data using a small range of offsets or angles for example we test data continuation on synthetic data from a model known to generate imaging artifacts we show that stacking over input scattering angles suppresses artifacts in the continued data

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

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

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

data consistency based translational motion artifact reduction in fan beam ct a basic assumption in the classic computed tomography ct theory is that an object remains stationary in an entire scan in biomedical ct micro ct this assumption is often violated to produce high resolution images such as for our recently proposed clinical micro ct cmct prototype it is desirable to develop a precise motion estimation and image reconstruction scheme in this paper we first extend the helgason ludwig consistency condition hlcc from parallel beam to fan beam geometry when an object is subject to a translation then we propose a novel method to estimate the motion parameters only from sinograms based on the hlcc to reconstruct the moving object we formulate two generalized fan beam reconstruction methods which are in filtered backprojection and backprojection filtering formats respectively furthermore we present numerical simulation results to show that our approach is accurate and robust

stickiness in hamiltonian systems from sharply divided to hierarchical phase space we investigate the dynamics of chaotic trajectories in simple yet physically important hamiltonian systems with nonhierarchical borders between regular and chaotic regions with positive measures we show that the stickiness to the border of the regular regions in systems with such a sharply divided phase space occurs through one parameter families of marginally unstable periodic orbits and is characterized by an exponent ensuremath gamma 2 for the asymptotic power law decay of the distribution of recurrence times generic perturbations lead to systems with hierarchical phase space where the stickiness is apparently enhanced due to the presence of infinitely many regular islands and cantori in this case we show that the distribution of recurrence times can be composed of a sum of exponentials or a sum of power laws depending on the relative contribution of the primary and secondary structures of the hierarchy numerical verification of our main results are provided for area preserving maps mushroom billiards and the newly defined magnetic mushroom billiards

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

weakly noisy chaotic scattering received 30 april 2013 published 23 september 2013 the effect of a weak source of noise on the chaotic scattering is relevant to situations of physical interest we investigate how a weak source of additive uncorrelated gaussian noise affects both the dynamics and thetopology of a paradigmatic chaotic scattering problem as the one taking place in the open nonhyperbolic regimeof the h enon heiles hamiltonian system we have found long transients for the time escape distributions forcritical values of the noise intensity for which the particles escape slower as compared with the noiseless case an analysis of the survival probability of the scattering function versus the gaussian noise intensity shows asmooth curve with one local maximum and with one local minimum which are related to those long transientsand with the basin structure in phase space on the other hand the computation of the exit basins in phase spaceshows a quadratic curve for which the basin boundaries lose their fractal like structure as noise turned on doi 10 1103 physreve 88 032914 pacs number s 05

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

an inversion formula for cone beam reconstruction an analytic inversion formula allowing the reconstruction of a three dimensional object from x ray cone beams is given the formula is valid for the case where the source of the beams describes a bounded curve satisfying a set of weak conditions

interactive image segmentation via adaptive weighted distances an interactive algorithm for soft segmentation of natural images is presented in this paper the user first roughly scribbles different regions of interest and from them the whole image is automatically segmented this soft segmentation is obtained via fast linear complexity computation of weighted distances to the user provided scribbles the adaptive weights are obtained from a series of gabor filters and are automatically computed according to the ability of each single filter to discriminate between the selected regions of interest we present the underlying framework and examples showing the capability of the algorithm to segment diverse images

ordered upwind methods for static hamilton jacobi equations theory and algorithms we develop a family of fast methods for approximating the solutions to a wide class of static hamilton jacobi pdes these fast methods include both semi lagrangian and fully eulerian versions numerical solutions to these problems are typically obtained by solving large systems of coupled nonlinear discretized equations our techniques which we refer to as ordered upwind methods oums use partial information about the characteristic directions to decouple these nonlinear systems greatly reducing the computational labor our techniques are considered in the context of control theoretic and front propagation problems we begin by discussing existing oums focusing on those designed for isotropic problems we then introduce a new class of oums which decouple systems for general anisotropic problems we prove convergence of one such scheme to the viscosity solution of the corresponding hamilton jacobi pde next we introduce a set of finite differences methods based on an analysis of the role played by anisotropy in the context of front propagation and optimal trajectory problems the performance of the methods is analyzed and computational experiments are performed using test problems from computational geometry and seismology

fractal dimension in dissipative chaotic scattering the effect of weak dissipation on chaotic scattering is relevant to situations of physical interest we investigate how the fractal dimension of the set of singularities in a scattering function varies as the system becomes progressively more dissipative a crossover phenomenon is uncovered where the dimension decreases relatively more rapidly as a dissipation parameter is increased from zero and then exhibits a much slower rate of decrease we provide a heuristic theory and numerical support from both discrete time and continuous time scattering systems to establish the generality of this phenomenon our result is expected to be important for physical phenomena such as the advection of inertial particles in open chaotic flows among others

chaotic scattering modelled by an inclined billiard abstract chaotic scattering as observed in satellite encounters and in other problems is modelled by a simple billiard a point particle bounces on two disks and in addition is subjected to a constant acceleration in an appropriate limit this problem reduces to a piecewise linear mapping we consider a one parameter family of orbits obtained by starting the particle at rest from a constant height we find that this family exhibits chaotic scattering it has an infinite number of discontinuities forming a self similar cantor set with the help of symbolic dynamics the structure of the family can be completely elucidated

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

optimal riemannian distances preventing mass transfer we consider an optimization problem related to mass transportation given two probabilities f and f on an open subset r we let vary the cost of the transport among all distances associated with conformally flat riemannian metrics on which satisfy an integral constraint precisely an upper bound on the l norm of the riemannian coefficient then we search for an optimal distance which prevents as much as possible the transfer of f into f higher values of the riemannian coefficient make the connection more difficult but the problem is non trivial due to the presence of the integral constraint in particular the existence of a solution is a priori guaranteed only on the relaxed class of costs which are associated with possibly non riemannian finsler metrics our main result shows that a solution does exist in the initial class of riemannian distances 2000msc 49j45 53c60

characterization and source receiver continuation of seismic reflection data in reflection seismology one places sources and receivers on the earth s surface the source generates elastic waves in the subsurface that are reflected where the medium properties stiffness and density vary discontinuously in the field often there are obstructions to collect seismic data for all source receiver pairs desirable or needed for data processing and application of inverse scattering methods typically data are measured on the earth s surface we employ the term data continuation to describe the act of computing data that have not been collected in the field seismic data are commonly modeled by a scattering operator developed in a high frequency single scattering approximation we initially focus on the determination of the range of the forward scattering operator that models the singular part of the data in the mentioned approximation this encompasses the analysis of the properties of and the construction of a minimal elliptic projector that projects a space of distributions on the data acquisition manifold to the range of the mentioned scattering operator this projector can be directly used for the purpose of seismic data continuation and is derived from the global parametrix of a homogeneous pseudodifferential equation the solution of which coincides with the range of the scattering operator we illustrate the data continuation by a numerical example

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

wada basins and chaotic invariant sets in the henon heiles system the h enon heiles hamiltonian is investigated in the context of chaotic scattering in the range of energies where escaping from the scattering region is possible special attention is paid to the analysis of the different nature of the orbits and the the invariant sets such as the stable and unstable manifolds and the chaotic saddle furthermore a discussion on the average decay time associated to the typical chaotic transients which are present in this problem is presented the main goal of this paper is to show by using various computational methods that the corresponding exit basins of this open hamiltonian are not only fractal but they also verify the more restrictive property of wada we argue that this property is verified by typical open hamiltonian systems with three or more escapes

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

markov tree model of transport in area preserving maps abstract transport in an area preserving map with a mixture of regular and chaotic regions is described in terms of the flux through invariant cantor sets called cantori a model retaining a discrete set of cantori approaching a boundary circle gives the markov chain description of hanson cary and meiss the inclusion of cantori surrounding island chains and islands about islands etc gives a markov tree model with a slower decay rate the survival probability distribution is shown to decay asymptotically as a power law the decay exponent agrees reasonably well with the computations of karney and of chirikov and shepelyanski

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

bifurcation to chaotic scattering abstract we investigate a novel type of bifurcation to chaos which occurs in the context of chaotic scattering in chaotic scattering the deflection angle versus impact parameter is singular on a set of impact parameters which is fractal this behavior is caused by the presence of a chaotic invariant set of unstable bounded orbits in the bifurcation considered here the chaotic set arises abruptly in a sense to be discussed as the particle energy e decreases from above a critical value em to below we call this transition an abrupt bifurcation to fully developed chaotic scattering numerical computation of the dimension d of the chaotic set shows that in agreement with theoretical prediction d 1 in em e 1 near the abrupt bifurcatio

numerical approximation of the steiner problem in dimension 2 and 3 the aim of this work is to present some numerical computations of solutions of the steiner problem based on the recent phase field approximations proposed in 12 and analyzed in 5 4 our strategy consists in improving the regularity of the associated phase field solution by use of higher order derivatives in the cahn hilliard functional as in 6 we justify the convergence of this slightly modified version of the functional together with other technics that we employ to improve the numerical experiments in particular we are able to consider a large number of points in dimension 2 we finally present and justify an approximation method that is efficient in dimension 3 which is one of the major novelties of the paper

cone beam reconstruction with sources on a curve an inversion procedure is developed for reconstructing a function of compact support in mathbb r 3 from its divergent beam x ray transform with sources on a curve the results apply to many curves not satisfying the conditions of tuy siam j appl math 43 1983 pp 546 552 for example planar circles of sufficiently large radius in some cases estimates in sobolev norms are established for the inversion operator