three dimensional non planar crack growth by a coupled extended finite element and fast marching method a numerical technique for non planar three dimensional linear elastic crack growth simulations is proposed this technique couples the extended finite element method x fem and the fast marching method fmm in crack modeling using x fem the framework of partition of unity is used to enrich the standard finite element approximation by a discontinuous function and the two dimensional asymptotic crack tip displacement fields the initial crack geometry is represented by two level set functions and subsequently signed distance functions are used to maintain the location of the crack and to compute the enrichment functions that appear in the displacement approximation crack modeling is performed without the need to mesh the crack and crack propagation is simulated without remeshing crack growth is conducted using fmm unlike a level set formulation for interface capturing no iterations nor any time step restrictions are imposed in the fmm planar and non planar quasi static crack growth simulations are presented to demonstrate the robustness and versatility of the proposed technique copyright 2008 john wiley sons ltd

a parallel two scale method for eikonal equations numerous applications of eikonal equations prompted the development of many efficient numerical algorithms the heap cell method hcm is a recent serial two scale technique that has been shown to have advantages over other serial state of the art solvers for a wide range of problems a chacon and a vladimirsky siam j sci comput 34 2012 pp a547 a578 this paper presents a parallelization of hcm for a shared memory architecture the numerical experiments in r 3 show that the parallel hcm exhibits good algorithmic behavior and scales well resulting in a very fast and practical solver

hole filling in 3d volumetric objects the construction of hole filling or hole segmentation method for 3d volumetric images is a new challenging issue in computer science it needs a geometrical approach since from a topological point of view 3d holes tunnels are not well delimited subsets of three dimensional space in this paper the authors propose an original efficient flexible algorithm of hole filling for volumetric objects the algorithm has been tested on artificial objects and very complicated crack propagation tomography images the qualitative results quantitative results and features of proposed approach are presented in the paper according to our knowledge it is the first algorithm of hole filling for volumetric objects

3 d traveltimes and amplitudes by gridded rays seismic imaging in three dimensions requires the calculation of traveltimes and amplitudes of a wave propagating through an elastic medium they can be computed efficiently and accurately by integrating the eikonal equation on an elemental grid using finite difference methods unfortunately this approach to solving the eikonal equation is potentially unstable unless the grid sampling steps satisfy stability conditions or wavefront tracking algorithms are used we propose a new method for computing traveltimes and amplitudes in 3 d media that is simple fast unconditionally stable and robust defining the slowness vector as p px py pz and assuming an isotropic medium the ray velocity v is related to the slowness vector by the relation v p p p rays emerging from gridpoints on a horizontal plane are propagated downward a single vertical grid step to a new horizontal plane the components of the slowness vector are then interpolated to gridpoints on this next horizontal plane this is termed regriddi

an effective algorithm for the generation of patient specific purkinje networks in computational electrocardiology the purkinje network is responsible for the fast and coordinated distribution of the electrical impulse in the ventricle that triggers its contraction therefore it is necessary to model its presence to obtain an accurate patient specific model of the ventricular electrical activation in this paper we present an efficient algorithm for the generation of a patient specific purkinje network driven by measures of the electrical activation acquired on the endocardium the proposed method provides a correction of an initial network generated by means of a fractal law and it is based on the solution of eikonal problems both in the muscle and in the purkinje network we present several numerical results both in an ideal geometry with synthetic data and in a real geometry with patient specific clinical measures these results highlight an improvement of the accuracy provided by the patient specific purkinje network with respect to the initial one in particular a cross validation test shows an accuracy increase of 19 when only the 3 of the total points are used to generate the network whereas an increment of 44 is observed when a random noise equal to 20 of the maximum value of the clinical data is added to the measures

a level set approach to 3d reconstruction from range data this paper presents a method that uses the level sets of volumes to reconstruct the shapes of 3d objects from range data the strategy is to formulate 3d reconstruction as a statistical problem find that surface which is mostly likely given the data and some prior knowledge about the application domain the resulting optimization problem is solved by an incremental process of deformation we represent a deformable surface as the level set of a discretely sampled scalar function of three dimensions i e a volume such level set models have been shown to mimic conventional deformable surface models by encoding surface movements as changes in the greyscale values of the volume the result is a voxel based modeling technology that offers several advantages over conventional parametric models including flexible topology no need for reparameterization concise descriptions of differential structure and a natural scale space for hierarchical representations this paper builds on previous work in both 3d reconstruction and level set modeling it presents a fundamental result in surface estimation from range data an analytical characterization of the surface that maximizes the posterior probability it also presents a novel computational technique for level set modeling called the sparse field algorithm which combines the advantages of a level set approach with the computational efficiency and accuracy of a parametric representation the sparse field algorithm is more efficient than other approaches and because it assigns the level set to a specific set of grid points it positions the level set model more accurately than the grid itself these properties computational efficiency and subcell accuracy are essential when trying to reconstruct the shapes of 3d objects results are shown for the reconstruction objects from sets of noisy and overlapping range maps

an alternating direction method of multipliers for the numerical solution of a fully nonlinear partial differential equation involving the jacobian determinant we consider the dirichlet problem for a partial differential equation involving the jacobian determinant in two dimensions of space the problem consists in finding a vector valued function such that the determinant of its gradient is given pointwise in a bounded domain together with essential boundary conditions this problem was initially considered in dacorogna and moser ann inst h poincare anal non lineaire 7 1990 pp 1 26 and several theoretical generalizations have been derived since in this work we design a numerical algorithm for the approximation of the solution of such a problem for various kinds of boundary data the proposed method relies on an augmented lagrangian algorithm with biharmonic regularization and low order mixed finite element approximations an iterative method allows us to decouple the nonlinearity and the differential operators numerical experiments show the capabilities of the method for benchmarks and then for more demanding test problems an erratum has bee

contour detection and hierarchical image segmentation this paper investigates two fundamental problems in computer vision contour detection and image segmentation we present state of the art algorithms for both of these tasks our contour detector combines multiple local cues into a globalization framework based on spectral clustering our segmentation algorithm consists of generic machinery for transforming the output of any contour detector into a hierarchical region tree in this manner we reduce the problem of image segmentation to that of contour detection extensive experimental evaluation demonstrates that both our contour detection and segmentation methods significantly outperform competing algorithms the automatically generated hierarchical segmentations can be interactively refined by user specified annotations computation at multiple image resolutions provides a means of coupling our system to recognition applications

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

a gradient augmented level set method for unstructured grids we present and test a gradient augmented level set method for unstructured grids which has been designed to allow for easy integration in parallel flow solvers the means to this end is a hermite formulation where the gradient is stored and advected as an independent variable along with the level set function the method uses narrow band storage in conjunction with a fast marching method which is also designed to take advantage of the gradient augmentation we demonstrate through standard passive advection test cases that the proposed method is able to compute interface motion with performance comparable to popular high performing methods on structured grids

a new scheme for robust gradient vector estimation in color images gradient estimators are mostly designed to yield accurate and robust estimates of the gradient magnitude not the gradient direction this paper proposes a method for the accurate and robust estimation of both the gradient magnitude and direction it robustly estimates the gradient in the x and y directions the robustness against noise is achieved by prefiltering and postfiltering of the gradient in each direction to reduce edge blurring effects introduced by these filters the gradient in a certain direction is obtained by applying the prefilter and postfilter in the perpendicular direction the basic elements employed in each window are highpass lowpass and aggregation operators the highpass operator is used as a gradient estimator the lowpass operator is for prefiltering and postfiltering and the aggregation operator is for aggregating the prefiltered and postfiltered gradients four different combinations of highpass lowpass and aggregation operators are proposed mvd median mean mvd median max rcmg median mean and rcmg median max experimental results show that the rcmg median mean has the best performance in estimating the gradient and detecting the edges in noisy color images it is computationally more efficient than the state of the art gradient estimators and is able to accurately estimate the gradient direction as well as the gradient magnitude computer simulation results show that the proposed method outperforms other recently proposed color gradient estimators and edge detectors

evolution implementation and application of level set and fast marching methods for advancing fronts abstract a variety of numerical techniques are available for tracking moving interfaces in this review we concentrate on techniques that result from the link between the partial differential equations that describe moving interfaces and numerical schemes designed for approximating the solutions to hyperbolic conservation laws this link gives rise to computational techniques for tracking moving interfaces in two and three space dimensions under complex speed laws we discuss the evolution of these techniques the fundamental numerical approximations involved implementation details and applications in particular we review some work on three aspects of materials sciences semiconductor process simulations seismic processing and optimal structural topology design

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

wall distance search algorithm using voxelized marching spheres minimum distance to a solid wall is a commonly used parameter in turbulence closure formulations associated with the reynolds averaged form of the navier stokes equations rans this paper presents a new approach to efficiently compute the minimum distance between a set of points and a surface the method is based on sphere voxelization and uses fast integer arithmetic algorithms from the field of computer graphics using a simple test case where the number of points n p and surface elements n b can be independently specified the present method is empirically estimated to be o n p 0 8n b 0 5 an unstructured grid around an aircraft configuration dlr f6 is chosen as the test case for demonstration and validation multi processor computations up to 256 processors are conducted to study efficiency and scalability encouraging results are obtained with the sphere voxelization algorithm demonstrated to be more efficient than all of the alternate methods for computing minimum distances however a load imbalance does exist which negatively impacts the scalability for large number of cores a simple method for load re balancing is formulated and tested which results in significant improvements in both efficiency and scalability

linear systems with state and control constraints the theory and application of maximal output admissible sets the initial state of an unforced linear system is output admissible with respect to a constraint set y if the resulting output function satisfies the pointwise in time condition y t in y t or 0 the set of all possible such initial conditions is the maximal output admissible set o sub infinity the properties of o sub infinity and its characterization are investigated in the discrete time case it is generally possible to represent o sub infinity or a close approximation of it by a finite number of functional inequalities practical algorithms for generating the functions are described in the continuous time case simple representations of the maximal output admissible set are not available however it is shown that the discrete time results may be used to obtain approximate representations

a new incompressibility discretization for a hybrid particle mac grid representation with surface tension we take a particle based approach to incompressible free surface flow motivated by the fact that an explicit representation of the interface geometry and internal deformations gives precise feedback to an implicit solver for surface tension methods that enforce incompressibility directly on the particles are typically numerically inefficient compared to those that utilize a background grid however background grid discretizations suffer from inaccuracy near the free surface where they do not properly capture the interface geometry therefore our incompressibility discretization utilizes a particle based projection near the interface and a background mac grid based projection for efficiency in the vast interior of the liquid domain as well as a novel method for coupling these two disparate projections together we show that the overall coupled elliptic solver is second order accurate and remains second order accurate when used in conjunction with an appropriate temporal discretization for parabolic problems a similar second order accurate discretization is derived when the mac grid unknowns are located on faces as opposed to cell centers so that navier stokes viscosity can be solved for implicitly as well finally we present a fully implicit approach to surface tension that is robust enough to achieve a steady state solution in a single time step beyond stable implicit surface tension for our novel hybrid discretization we demonstrate preliminary results for both standard front tracking and the particle level set method

noise robust edge detector combining isotropic and anisotropic gaussian kernels a new noise robust edge detector is proposed which combines a small scaled isotropic gaussian kernel and large scaled anisotropic gaussian kernels angks to obtain edge maps of images its main advantage is that noise reduction is attained while maintaining high edge resolution from the angks anisotropic directional derivatives andds are derived to capture the locally directional variation of an image the andd based edge strength map esm is constructed its noise robustness is determined by the scale alone and its edge resolution by the ratio of the scale to the anisotropic factor moreover the edge stretch effect in anisotropic smoothing is revealed the andd based esm and the gradient based esm with a small scaled isotropic gaussian kernel are fused into a noise robust esm with high edge resolution and little edge stretch embedding the fused esm into the routine of canny detector a noise robust edge detector is developed which includes two additional modifications contrast equalization and noise dependent lower threshold the aggregate test receiver operating characteristic roc curves and the pratt s figure of merit fom are used to evaluate the proposed detector by abundant experiments the experimental results show that the proposed detector can obtain high quality edge maps for noise free and noisy images

brief paper convex invariant sets for discrete time lur e systems in this paper a method to estimate the domain of attraction of a class of discrete time lur e systems is presented a new notion of invariance denoted lnl invariance is introduced an algorithm to determinate the largest lnl invariant set for this class of systems is proposed moreover it is proven that the lnl invariant sets provided by this algorithm are polyhedral convex sets and constitute an estimation of the domain of attraction of the non linear system it is shown that any contractive set for the lur e system is contained in the lnl invariant set obtained applying the results of this paper two illustrative examples are given

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

solving the eikonal equation on an adaptive mesh a fast marching method fmm using the line of site calculation to solve the eikonal equation is applied to an adaptive mesh the criteria for refinement are the curvature of the propagating front it is shown empirically that for cases involving an initial front initiated from a single point in an open three dimensional domain and constant front propagating speed that the fmm with adaptive mesh refinement amr uses roughly an order of magnitude less cpu time and an order of magnitude less cpu memory than the non amr fmm to attain a similar level of accuracy it is also shown that the amr fmm refines when the curvature is caused by boundary irregularities and also non constant front propagating speed

identification of contact regions in semiconductor transistors by level set methods in this paper we present the formulation of level set methods for the inverse problem of identifying an interface in the coefficient of an elliptic equation from a boundary measurement this problem arises from the modeling of the identification of contact regions by boundary measurements for semiconductor transistors we propose the gauss newton direction as the interface velocity and implement the scheme for a parameterized class of interfaces

a morphological gradient approach to color edge detection a new color edge detector based on vector differences is proposed the basic technique gives as its output the maximum distance between the vectors within a mask when applied to scalar valued images the method reduces to the classic morphological gradient the technique is relatively computationally efficient and can also be readily applied to other vector valued images to improve the performance in the presence of noise a novel pairwise outlier rejection scheme is employed a quantitative evaluation using pratt s figure of merit shows the new technique to outperform other recently proposed color edge detectors in addition application to real images demonstrates the approach to be highly effective despite its low complexity

brief paper a set membership state estimation algorithm based on dc programming this paper presents a new approach to guaranteed state estimation for nonlinear discrete time systems with a bounded description of noise and parameters the sets of states that are consistent with the evolution of the system the measured outputs and bounded noise and parameters are represented by zonotopes dc programming and intersection operations are used to obtain a tight bound an example is given to illustrate the proposed algorithm

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

corner detection and classification using anisotropic directional derivative representations this paper proposes a corner detector and classifier using anisotropic directional derivative andd representations the andd representation at a pixel is a function of the oriented angle and characterizes the local directional grayscale variation around the pixel the proposed corner detector fuses the ideas of the contour and intensity based detection it consists of three cascaded blocks first the edge map of an image is obtained by the canny detector and from which contours are extracted and patched next the andd representation at each pixel on contours is calculated and normalized by its maximal magnitude the area surrounded by the normalized andd representation forms a new corner measure finally the nonmaximum suppression and thresholding are operated on each contour to find corners in terms of the corner measure moreover a corner classifier based on the peak number of the andd representation is given experiments are made to evaluate the proposed detector and classifier the proposed detector is competitive with the two recent state of the art corner detectors the he yung detector and cpda detector in detection capability and attains higher repeatability under affine transforms the proposed classifier can discriminate effectively simple corners y type corners and higher order corners

finite difference methods for the infinity laplace and p laplace equations abstract we build convergent discretizations and semi implicit solvers for the infinity laplacian and the game theoretical p laplacian the discretizations simplify and generalize earlier ones we prove convergence of the solution of the wide stencil finite difference schemes to the unique viscosity solution of the underlying equation we build a semi implicit solver which solves the laplace equation as each step it is fast in the sense that the number of iterations is independent of the problem size this is an improvement over previous explicit solvers which are slow due to the cfl condition

optimal control with budget constraints and resets we consider both discrete and continuous control problems constrained by a fixed budget of some resource which may be renewed upon entering a preferred subset of the state space in the discrete case we consider deterministic shortest path problems on graphs with a full budget reset in all preferred nodes in the continuous case we derive augmented pdes of optimal control which are then solved numerically on the extended state space with a full instantaneous budget reset on the preferred subset we introduce an iterative algorithm for solving these problems efficiently the method s performance is demonstrated on a range of computational examples including optimal path planning with constraints on prolonged visibility by a static enemy observer

robust second order accurate discretizations of the multi dimensional heaviside and dirac delta functions we present a robust second order accurate method for discretizing the multi dimensional heaviside and the dirac delta functions on irregular domains the method is robust in the following ways 1 integrations of source terms on a co dimension one surface are independent of the underlying grid and therefore stable under perturbations of the domain s boundary 2 the method depends only on the function value of a level function not on its derivatives we present the discretizations in tabulated form to make their implementations straightforward we present numerical results in two and three spatial dimensions to demonstrate the second order accuracy in the l 1 norm in the case of the solution of pdes with singular source terms in the case of evaluating the contribution of singular source terms on interfaces the method is also second order accurate in the l norm

brief nonlinear model predictive control with polytopic invariant sets ellipsoidal invariant sets have been widely used as target sets in model predictive control mpc these sets can be computed by constructing appropriate linear difference inclusions together with additional constraints to ensure that the ellipsoid lies within a given inclusion polytope the choice of inclusion polytope has a significant effect on the size of the target ellipsoid but the optimal inclusion polytope cannot in general be computed systematically this paper shows that use of polytopic invariant sets overcomes this difficulty allowing larger stabilizable sets without loss of performance in the interests of online efficiency consideration is focused on interpolation based mpc

stabilization of parametric active contours using a tangential redistribution term depending on implementation active contours have been classified as geometric or parametric active contours parametric contours irrespective of representation are known to suffer from the problem of irregular bunching and spacing out of curve points during the curve evolution in a spline based implementation of active contours this leads to occasional formation of loops locally and subsequently the curve blows up due to instabilities in this paper we analyze the reason for this problem and propose a solution to alleviate the same we propose an ordinary differential equation ode for controlling the curve parametrization during evolution by including a tangential force we show that the solution of the proposed ode is bounded we demonstrate the effectiveness of the proposed method for segmentation and tracking tasks on closed as well as open contours

ultimate boundedness control for uncertain discrete time systems via set induced lyapunov functions in this note linear discrete time systems affected by both parameter and input uncertainties are considered the problem of the synthesis of a feedback control assuring that the system state is ultimately bounded within a given compact set containing the origin with an assigned rate of convergence is investigated it is shown that the problem has a solution if and only if there exists a certain lyapunov function which does not belong to a preassigned class of functions e g the quadratic ones but it is determined by the target set in which ultimate boundedness is desired one of the advantages of this approach is that we may handle systems with control constraints no matching assumptions are made for systems with linearly constrained uncertainties it is shown that such a function may be derived by numerically efficient algorithms involving polyhedral sets the resulting compensator may be implemented as a linear variable structure control

rapid and brief communication color edge detection using the minimal spanning tree in this study the edge detection task in vector valued images is examined as a clustering problem using samples within a data window the minimal spanning tree mst provides the ordering of multivariate observations and facilitates the identification of similar classes the edge detector parameters like edge strength type and orientation are subsequently determined from the clustered data experiments and comparisons are performed revealing the enhanced performance of the proposed approach

fast marching methods fast marching methods are numerical schemes for computing solutions to the nonlinear eikonal equation and related static hamilton jacobi equations based on entropy satisfying upwind schemes and fast sorting techniques they yield consistent accurate and highly efficient algorithms they are optimal in the sense that the computational complexity of the algorithms is o n log n where n is the total number of points in the domain the schemes are of use in a variety of applications including problems in shape offsetting computing distances from complex curves and surfaces shape from shading photolithographic development computing first arrivals in seismic travel times construction of shortest geodesics on surfaces optimal path planning around obstacles and visibility and reflection calculations in this paper we review the development of these techniques including the theoretical and numerical underpinnings provide details of the computational schemes including higher order versions and demonstrate the techniques in a collection of different areas

color edge detection using vector order statistics a method is proposed whereby a color image is treated as a vector field and the edge information carried directly by the vectors is exploited a class of color edge detectors is defined as the minimum over the magnitudes of linear combinations of the sorted vector samples from this class a specific edge detector is obtained and its performance characteristics studied results of a quantitative evaluation and comparison to other color edge detectors using pratt s 1991 figure of merit and an artificially generated test image are presented edge detection results obtained for real color images demonstrate the efficiency of the detector

brief paper on the computation of convex robust control invariant sets for nonlinear systems in this paper we provide a method to compute robust control invariant sets for nonlinear discrete time systems a simple criterion to evaluate if a convex set in state space is a robust control invariant set for a nonlinear uncertain system is presented the criterion is employed to design an algorithm for computing a polytopic robust control invariant set the method is based on the properties of dc functions i e functions which can be expressed as the difference of two convex functions since the elements of a wide class of nonlinear functions have dc representation or at least admit an arbitrarily close approximation the method is quite general the algorithm requires relatively low computational resources

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

estimation of reactive fluxes in gradient stochastic systems using an analogy with electric circuits abstract we propose an approach for finding dominant reactive channels and calculating percentages of reactive flux through each channel in chemical systems driven by a deterministic potential force and a small thermal noise we assume that the temperature is low enough so that the reactive flux focuses around a finite number of paths connecting the reactant and the product states these paths can be found in a systematic way by solving a hamilton jacobi equation for the so called maxflux functional we argue that the name maxflux is misleading it should be called the resistivity functional instead once the network of transition paths is found one can define an equivalent electric circuit and find the currents through each of its wires these currents give estimates of the reactive flux along the corresponding transition paths we test our approach on the problem of finding transition paths in the alanine dipeptide with two dihedral angles where the reactive current can be computed exactly the percentages of the reactive flux through each reactive channel given by our approach turn out to be in remarkable agreement with the exact ones we apply this approach to the problem of finding escape paths of a co molecule from a myoglobin protein we find a collection of exit locations and establish percentages of the reactive flux through each of them

adaptively merging large scale range data with reflectance properties in this paper we tackle the problem of geometric and photometric modeling of large intricately shaped objects typical target objects we consider are cultural heritage objects when constructing models of such objects we are faced with several important issues that have not been addressed in the past issues that mainly arise due to the large amount of data that has to be handled we propose two novel approaches to efficiently handle such large amounts of data a highly adaptive algorithm for merging range images and an adaptive nearest neighbor search to be used with the algorithm we construct an integrated mesh model of the target object in adaptive resolution taking into account the geometric and or photometric attributes associated with the range images we use surface curvature for the geometric attributes and laser reflectance values for the photometric attributes this adaptive merging framework leads to a significant reduction in the necessary amount of computational resources furthermore the resulting adaptive mesh models can be of great use for applications such as texture mapping as we will briefly demonstrate additionally we propose an additional test for the k d tree nearest neighbor search algorithm our approach successfully omits back tracking which is controlled adaptively depending on the distance to the nearest neighbor since the main consumption of computational cost lies in the nearest neighbor search the proposed algorithm leads to a significant speed up of the whole merging process in this paper we present the theories and algorithms of our approaches with pseudo code and apply them to several real objects including large scale cultural assets

time to depth conversion and seismic velocity estimation using time migration velocity the objective was to build an efficient algorithm 1 to estimate seismic velocity from time migration velocity and 2 to convert time migrated images to depth we established theoretical relations between the time migration velocity and seismic velocity in two and three dimensions using paraxial ray tracing theory the relation in two dimensions implies that the conventional dix velocity is the ratio of the interval seismic velocity and the geometric spreading of image rays we formulated an inverse problem of finding seismic velocity from the dix velocity and developed a numerical procedure for solving it the procedure consists of two steps 1 computation of the geometric spreading of image rays and the true seismic velocity in time domain coordinates from the dix velocity 2 conversion of the true seismic velocity from the time domain to the depth domain and computation of the transition matrices from time domain coordinates todepth for step 1 we derived a partial differential equation pde i

polyhedral regions of local stability for linear discrete time systems with saturating controls the study and the determination of polyhedral regions of local stability for linear systems subject to control saturation is addressed the analysis of the nonlinear behavior of the closed loop saturated system is made by dividing the state space in regions of saturation inside each of these regions the system evolution can be represented by a linear system with an additive disturbance from this representation a necessary and sufficient condition relative to the contractivity of a given convex compact polyhedral set is stated consequently the polyhedral set can be associated with a lyapunov function and the local asymptotic stability of the saturated closed loop system inside the set is guaranteed furthermore it is shown how in some particular cases the compactness condition can be relaxed in order to ensure the asymptotic stability in unbounded polyhedra finally an application of the contractivity conditions is presented in order to determine local asymptotic stability regions for the closed loop saturated system

on the computation of set induced control lyapunov functions for continuous time systems the paper presents a computation oriented method for characterizing and obtaining local control lyapunov functions induced by particular star shaped nonconvex sets for continuous time nonlinear systems with bounded inputs for a given set the necessary and sufficient conditions for the induced function to be a nonconvex local control lyapunov function are provided the related convex problems for computing the exact region in which the function is decreasing and the optimal control input are presented the results are applied to the brockett integrator

shape matching and object recognition using shape contexts we present a novel approach to measuring similarity between shapes and exploit it for object recognition in our framework the measurement of similarity is preceded by 1 solving for correspondences between points on the two shapes 2 using the correspondences to estimate an aligning transform in order to solve the correspondence problem we attach a descriptor the shape context to each point the shape context at a reference point captures the distribution of the remaining points relative to it thus offering a globally discriminative characterization corresponding points on two similar shapes will have similar shape contexts enabling us to solve for correspondences as an optimal assignment problem given the point correspondences we estimate the transformation that best aligns the two shapes regularized thin plate splines provide a flexible class of transformation maps for this purpose the dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points together with a term measuring the magnitude of the aligning transform we treat recognition in a nearest neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image results are presented for silhouettes trademarks handwritten digits and the coil data set

prestack migration by split step dsr the double square root dsr prestack migration equation though defined for depth variable velocity can be used to image media with strong velocity variations using a phase shift plus interpolation pspi or split step correction the split step method is based on applying a phase shift correction to the extrapolated wavefield a correction that attempts to compensate for the lateral velocity variations i show how to extend dsr prestack migration to lateral velocity media and exemplify the method by applying the new algorithm to the marmousi data set the split step dsr migration is very fast and offers excellent imaging results

level set methods an overview and some recent results the level set method was devised by s osher and j a sethian 1988 j comput phys 79 12 49 as a simple and versatile method for computing and analyzing the motion of an interface in two or three dimensions bounds a possibly multiply connected region the goal is to compute and analyze the subsequent motion of under a velocity field v this velocity can depend on position time the geometry of the interface and the external physics the interface is captured for later time as the zero level set of a smooth at least lipschitz continuous function x t i e t x x t 0 is positive inside negative outside and is zero on t topological merging and breaking are well defined and easily performed in this review article we discuss recent variants and extensions including the motion of curves in three dimensions the dynamic surface extension method fast methods for steady state problems diffusion generated motion and the variational level set approach we also give a user s guide to the level set dictionary and technology and couple the method to a wide variety of problems involving external physics such as compressible and incompressible possibly reacting flow stefan problems kinetic crystal growth epitaxial growth of thin films vortex dominated flows and extensions to multiphase motion we conclude with a discussion of applications to computer vision and image processing

edge based image restoration in this paper we propose a new image inpainting algorithm that relies on explicit edge information the edge information is used both for the reconstruction of a skeleton image structure in the missing areas as well as for guiding the interpolation that follows the structure reconstruction part exploits different properties of the edges such as the colors of the objects they separate an estimate of how well one edge continues into another one and the spatial order of the edges with respect to each other in order to preserve both sharp and smooth edges the areas delimited by the recovered structure are interpolated independently and the process is guided by the direction of the nearby edges the novelty of our approach lies primarily in exploiting explicitly the constraint enforced by the numerical interpretation of the sequential order of edges as well as in the pixel filling method which takes into account the proximity and direction of edges extensive experiments are carried out in order to validate and compare the algorithm both quantitatively and qualitatively they show the advantages of our algorithm and its readily application to real world cases

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

irgs image segmentation using edge penalties and region growing this paper proposes an image segmentation method named iterative region growing using semantics irgs which is characterized by two aspects first it uses graduated increased edge penalty giep functions within the traditional markov random field mrf context model in formulating the objective functions second irgs uses a region growing technique in searching for the solutions to these objective functions the proposed irgs is an improvement over traditional mrf based approaches in that the edge strength information is utilized and a more stable estimation of model parameters is achieved moreover the irgs method provides the possibility of building a hierarchical representation of the image content and allows various region features and even domain knowledge to be incorporated in the segmentation process the algorithm has been successfully tested on several artificial images and synthetic aperture radar sar images

a combined extended finite element and level set method for biofilm growth this paper presents a computational technique based on the extended finite element method xfem and the level set method for the growth of biofilms the discontinuous derivative enrichment of the standard finite element approximation eliminates the need for the finite element mesh to coincide with the biofilm fluid interface and also permits the introduction of the discontinuity in the normal derivative of the substrate concentration field at the biofilm fluid interface the xfem is coupled with a comprehensive level set update scheme with velocity extensions which makes updating the biofilm interface fast and accurate without need for remeshing the kinetics of biofilms are briefly given and the non linear strong and weak forms are presented the non linear system of equations is solved using a newton raphson scheme example problems including 1d and 2d biofilm growth are presented to illustrate the accuracy and utility of the method the 1d results we obtain are in excellent agreement with previous 1d results obtained using finite difference methods our 2d results that simulate finger formation and finger tip splitting in biofilms illustrate the robustness of the present computational technique copyright 2007 john wiley sons ltd

anti impulse noise edge detection via anisotropic morphological directional derivatives traditional differential based edge detection suffers from abrupt degradation in performance when images are corrupted by impulse noises the morphological operators such as the median filters and weighted median filters possess the intrinsic ability to counteract impulse noise in this paper by combining the biwindow configuration with weighted median filters anisotropic morphological directional derivatives amdds robust to impulse noise are proposed to measure the local grayscale variation around a pixel for ideal step edges the amdd spatial response and directional representation are derived the characteristics and edge resolution of two kinds of typical biwindows are analyzed thoroughly in terms of the amdd spatial response and directional representation of ideal step edges the spatial matched filter is used to extract the edge strength map esm from the amdds of an image the spatial and directional matched filters are used to extract the edge direction map edm embedding the extracted esm and edm into the standard route of the differential based edge detection an anti impulse noise amdd based edge detector is constructed it is compared with the existing state of the art detectors on a recognized image dataset for edge detection evaluation the results show that it attains competitive performance in noise free and gaussian noise cases and the best performance in impulse noise cases

curvature and the evolution of fronts the evolution of a front propagating along its normal vector field with speedf dependent on curvaturek is considered the change in total variation of the propagating front is shown to depend only ondf dk only wherek changes sign analysis of the casef k 1 ek where e is a constant shows that curvature plays a role similar to that of viscosity in burgers equation for e 0 and non convex initial data the curvature blows up corners develop and an entropy condition can be formulated to provide an explicit construction for a weak solution beyond the singularity we then numerically show that the solution as e goes to zero converges to the constructed weak solution numerical methods based on finite difference schemes for marker particles along the front are shown to be unstable in regions where the curvature builds as a remedy we show that front tracking based on volume of fluid techniques can be used together with the entropy condition to provide transition from the classical to weak solution

design of steerable filters for feature detection using canny like criteria we propose a general approach for the design of 2d feature detectors from a class of steerable functions based on the optimization of a canny like criterion in contrast with previous computational designs our approach is truly 2d and provides filters that have closed form expressions it also yields operators that have a better orientation selectivity than the classical gradient or hessian based detectors we illustrate the method with the design of operators for edge and ridge detection we present some experimental results that demonstrate the performance improvement of these new feature detectors we propose computationally efficient local optimization algorithms for the estimation of feature orientation we also introduce the notion of shape adaptable feature detection and use it for the detection of image corners

a shearlet approach to edge analysis and detection it is well known that the wavelet transform provides a very effective framework for analysis of multiscale edges in this paper we propose a novel approach based on the shearlet transform a multiscale directional transform with a greater ability to localize distributed discontinuities such as edges indeed unlike traditional wavelets shearlets are theoretically optimal in representing images with edges and in particular have the ability to fully capture directional and other geometrical features numerical examples demonstrate that the shearlet approach is highly effective at detecting both the location and orientation of edges and outperforms methods based on wavelets as well as other standard methods furthermore the shearlet approach is useful to design simple and effective algorithms for the detection of corners and junctions

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

robustness of adaptive control under time delays for three dimensional curve tracking we analyze the robustness of a class of controllers that enable three dimensional curve tracking by a free moving particle the free particle tracks the closest point on the curve by building a strict lyapunov function and robustly forward invariant sets we show input to state stability under predictable tolerance and safety bounds that guarantee robustness under control uncertainty input delays and a class of polygonal state constraints including adaptive tracking and parameter identification under unknown control gains such an understanding may provide certified performance when the control laws are applied to real life systems

hole filling of a 3d model by flipping signs of a signed distance field in adaptive resolution when we use range finders to observe the shape of an object many occluded areas may occur these become holes and gaps in the model and make it undesirable for various applications we propose a novel method to fill holes and gaps to complete this incomplete model as an intermediate representation we use a signed distance field sdf which stores euclidean signed distances from a voxel to the nearest point of the mesh model by using an sdf we can obtain interpolating surfaces for holes and gaps the proposed method generates an interpolating surface that becomes smoothly continuous with real surfaces by minimizing the area of the interpolating surface since the isosurface of an sdf can be identified as being a real or interpolating surface from the magnitude of signed distances our method computes the area of an interpolating surface in the neighborhood of a voxel both before and after flipping the sign of the signed distance of the voxel if the area is reduced by flipping the sign then our method changes the sign for the voxel therefore we minimize the area of the interpolating surface by iterating this computation until convergence unlike methods based on partial differential equations pdes our method does not require any boundary condition and the initial state that we use is automatically obtained by computing the distance to the closest point of the real surface moreover because our method can be applied to an sdf of adaptive resolution our method efficiently interpolates large holes and gaps of high curvature we tested the proposed method with both synthesized and real objects and evaluated the interpolating surfaces

noise robust color edge detector using gradient matrix and anisotropic gaussian directional derivative matrix in this paper a noise robust color edge detector using gradient matrix and anisotropic gaussian directional derivative andd matrix is proposed in order to alleviate the conflict between high edge resolution and noise robustness in the color canny detector where the isotropic gaussian kernels and gradient matrix of the r g b components are used the andds of the three components of a color image are arranged into the andd matrix from its singular value decomposition svd the andd based color edge strength map cesm is constructed and is relevant to the pixelwise optimal fusion of the andds of the three components in the sense of color edge enhancement the merits and defects of the andd based cesm and gradient based cesm are contrasted to show their complementarity in color edge detection the two cesms are fused to develop a new color edge detector it is compared with the color canny detector and two recent color edge detectors the results show that the proposed detector attains better detection performance for noiseless and noisy color images corrupted by white gaussian noise or impulsive noise of small percentage a color edge detector using gradient matrix and andd matrix is proposed the svd of the andd matrix is used to determine cesm and cesd of a color image the new detector has both high edge resolution and noise robustness it attains better performance than the two existing color edge detectors

invariant approximations of the minimal robust positively invariant set this note provides results on approximating the minimal robust positively invariant mrpi set also known as the 0 reachable set of an asymptotically stable discrete time linear time invariant system it is assumed that the disturbance is bounded persistent and acts additively on the state and that the constraints on the disturbance are polyhedral results are given that allow for the computation of a robust positively invariant outer approximation of the mrpi set conditions are also given that allow one to a priori specify the accuracy of this approximation

a level set approach for the solution of a state constrained optimal control problem state constrained optimal control problems for linear elliptic partial differential equations are considered the corresponding first order optimality conditions in primal dual form are analyzed and linked to a free boundary problem resulting in a novel algorithmic approach with the boundary interface between the active and inactive sets as optimization variable the new algorithm is based on the level set methodology the speed function involved in the level set equation for propagating the interface is computed by utilizing techniques from shape optimization encouraging numerical results attained by the new algorithm are reported on

computing minimal surfaces via level set curvature flow given a fixed closed curve or curves in r sp3 there is an associated problem of finding a surface with mean curvature zero which has that curve or curves as its boundary in this paper a new approach to numerically solving the minimal surface problem is introduced the surface is represented as a level set of a global function phi r sp3 to r the family of surfaces evolve in time according to mean curvature flow a solution is found when a steady state condition is achieved a new system of interpolatory boundary conditions are used to maintain the connection between the surface and the fixed boundary contour several computer surfaces are shown including examples of topological changes

invariant sets computation for convex difference inclusions systems in this paper we introduce the convex difference inclusion cdi systems as a modeling framework useful to analyze set theory and invariance related issues for nonlinear and uncertain systems the dynamics of a cdi system is given by a set valued map whose values are convex compact subsets of the space and are determined by convex bounding functions necessary and sufficient boundary type conditions for invariance and contractiveness characteristic of the linear systems are given for the cdi systems lyapunov functions are proved to be induced by contractive sets for cdi systems as in the linear context a computational procedure for obtaining polytopic invariant and contractive sets for nonlinear systems based on the properties of the cdi systems is presented

robust and efficient upwind finite difference traveltime calculations in three dimensions first arrival traveltimes in complicated 3 d geologic media may be computed robustly and efficiently using an upwind finite difference solution of the 3 d eikonal equation an important application of this technique is computing traveltimes for imaging seismic data with 3 d prestack kirchhoff depth migration the method performs radial extrapolation of the three components of the slowness vector in spherical coordinates traveltimes are computed by numerically integrating the radial component of the slowness vector the original finite difference equations are recast into unitless forms that are more stable to numerical errors a stability condition adaptively determines the radial steps that are used to extrapolate computations are done in a rotated spherical coordinate system that places the small arc length regions of the spherical grid at the earth s surface z 0 plane this improves efficiency by placing large grid cells in the central regions of the grid where wavefields are complicated thereby

numerical schemes for the hamilton jacobi and level set equations on triangulated domains borrowing from techniques developed for conservation law equations numerical schemes which discretize the hamilton jacobi h j level set and eikonal equations on triangulated domains are presented the first scheme is a provably monotone discretization for the h j equations unfortunately the basic scheme lacks lipschitz continuity of the numerical hamiltonian by employing a virtual edge flipping technique local lipschitz continuity of the numerical flux is restored on acute triangulations next schemes are introduced and developed based on the weaker concept of positive coefficient approximations for homogeneous hamiltonians these schemes possess a discrete maximum principle on arbitrary triangulations and exhibit local lipschitz continuity of the numerical hamiltonian finally a class of petrov galerkin approximations is considered these schemes are stabilized via a least squares bilinear form the petrov galerkin schemes do not possess a discrete maximum principle but generalize to high order accuracy discretization of the level set equation also requires the numerical approximation of a mean curvature term a simple mass lumped galerkin approximation is presented in section 6 and analyzed using maximum principle analysis the use of unstructured meshes permits several forms of mesh adaptation which have been incorporated into numerical examples these numerical examples include discretizations of convex and nonconvex forms of the h j equation the eikonal equation and the level set equation

survey paper set invariance in control the properties of positively invariant sets are involved in many different problems in control theory such as constrained control robustness analysis synthesis and optimization in this paper we provide an overview of the literature concerning positively invariant sets and their application to the analysis and synthesis of control systems

a second order shape optimization approach for image segmentation the problem of segmentation of a given image using the active contour technique is considered an abstract calculus to find appropriate speed functions for active contour models in image segmentation or related problems based on variational principles is presented the speed method from shape sensitivity analysis is used to derive speed functions which correspond to gradient or newton type directions for the underlying optimization problem the newton type speed function is found by solving an elliptic problem on the current active contour in every time step numerical experiments comparing the classical gradient method with newton s method are presented

edge junction and corner detection using color distributions for over 30 years 1970 2000 researchers in computer vision have been proposing new methods for performing low level vision tasks such as detecting edges and corners one key element shared by most methods is that they represent local image neighborhoods as constant in color or intensity with deviations modeled as noise due to computational considerations that encourage the use of small neighborhoods where this assumption holds these methods remain popular the research presented models a neighborhood as a distribution of colors the goal is to show that the increase in accuracy of this representation translates into higher quality results for low level vision tasks on difficult natural images especially as neighborhood size increases we emphasize large neighborhoods because small ones often do not contain enough information we emphasize color because it subsumes gray scale as an image range and because it is the dominant form of human perception we discuss distributions in the context of detecting edges corners and junctions and we show results for each

information theoretic active polygons for unsupervised texture segmentation curve evolution models used in image segmentation and based on image region information usually utilize simple statistics such as means and variances hence can not account for higher order nature of the textural characteristics of image regions in addition the object delineation by active contour methods results in a contour representation which still requires a substantial amount of data to be stored for subsequent multimedia applications such as visual information retrieval from databases polygonal approximations of the extracted continuous curves are required to reduce the amount of data since polygons are powerful approximators of shapes for use in later recognition stages such as shape matching and coding the key contribution of this paper is the development of a new active contour model which nicely ties the desirable polygonal representation of an object directly to the image segmentation process this model can robustly capture texture boundaries by way of higher order statistics of the data and using an information theoretic measure and with its nature of the ordinary differential equations this new variational texture segmentation model is unsupervised since no prior knowledge on the textural properties of image regions is used another contribution in this sequel is a new polygon regularizer algorithm which uses electrostatics principles this is a global regularizer and is more consistent than a local polygon regularization in preserving local features such as corners

an efficient and stabilizing model predictive control of switched systems model predictive control mpc of switched systems typically requires an on line solution of a mixed integer program mip since the worst case complexity of the optimization problem increases exponentially with respect to the number of integer variables an on line implementation of the mpc for problems with large number of sub systems and or large horizons is usually expensive in this technical note we propose a stabilizing mpc formulation for state dependent switched systems that enables a tradeoff between the computational complexity of the mpc controller and the optimal performance of the closed loop system the proposed approach uses a pre terminal set in addition to the positively invariant terminal set which aids in reducing the on line complexity although at the expense of optimality examples are presented to illustrate the computational benefits of the proposed mpc strategy over existing mpc for switched systems

a hybrid particle level set method for improved interface capturing in this paper we propose a new numerical method for improving the mass conservation properties of the level set method when the interface is passively advected in a flow field our method uses lagrangian marker particles to rebuild the level set in regions which are underresolved this is often the case for flows undergoing stretching and tearing the overall method maintains a smooth geometrical description of the interface and the implementation simplicity characteristic of the level set method our method compares favorably with volume of fluid methods in the conservation of mass and purely lagrangian schemes for interface resolution the method is presented in three spatial dimensions