diffusion snakes introducing statistical shape knowledge into the mumford shah functional we present a modification of the mumford shah functional and its cartoon limit which facilitates the incorporation of a statistical prior on the shape of the segmenting contour by minimizing a single energy functional we obtain a segmentation process which maximizes both the grey value homogeneity in the separated regions and the similarity of the contour with respect to a set of training shapes we propose a closed form parameter free solution for incorporating invariance with respect to similarity transformations in the variational framework we show segmentation results on artificial and real world images with and without prior shape information in the cases of noise occlusion or strongly cluttered background the shape prior significantly improves segmentation finally we compare our results to those obtained by a level set implementation of geodesic active contours

active contours without edges we propose a new model for active contours to detect objects in a given image based on techniques of curve evolution mumford shah 1989 functional for segmentation and level sets our model can detect objects whose boundaries are not necessarily defined by the gradient we minimize an energy which can be seen as a particular case of the minimal partition problem in the level set formulation the problem becomes a mean curvature flow like evolving the active contour which will stop on the desired boundary however the stopping term does not depend on the gradient of the image as in the classical active contour models but is instead related to a particular segmentation of the image we give a numerical algorithm using finite differences finally we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable also the initial curve can be anywhere in the image and interior contours are automatically detected

comparing images using the hausdorff distance the hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another efficient algorithms for computing the hausdorff distance between all possible relative positions of a binary image and a model are presented the focus is primarily on the case in which the model is only allowed to translate with respect to the image the techniques are extended to rigid motion the hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived the method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods it is shown that the method extends naturally to the problem of comparing a portion of a model against an image

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

the rectangle complexity of functions on two dimensional lattices let x be a non empty set let f z2x all vectors which occur have integer coefficients and for a1 a2 b1 b2 we write or 0 a block is a set of the form b z2 0 such that the complexity of f does not exceed b1b2 in this paper we prove the statement for b n 2 where n is any positive integer

localized nodal solutions for quasilinear schrodinger equations abstract in this paper we study the existence of localized nodal solutions for a class of semiclassical quasilinear schrodinger equations including as a special case the modified nonlinear schrodinger equation mnls e 2 v 1 2 v v 2 v x v v q 2 v 0 in r n v x 0 as x we establish for small e the existence of a sequence of localized nodal solutions concentrating near a given local minimum point of the potential function by developing new variational perturbation method to treat this class of non smooth variational problems the new method allows the perturbed variational functionals to share critical points with the original functional this method allows us to avoid any limiting process from the perturbed problems to the original problem and it is effective in dealing with multiple existence of solutions

balanced sequences and optimal routing the objective pursued in this paper is two fold the first part addresses the following combinatorial problem is it possible to construct an infinite sequence over n letters where each letter is distributed as evenly as possible and appears with a given rate the second objective of the paper is to use this construction in the framework of optimal routing in queuing networks we show under rather general assumptions that the optimal deterministic routing in stochastic event graphs is such a sequence

on the number of factors of sturmian words abstract we prove that for m 1 card a m 1 m i 1 m i 1 i where a m is the set of factors of length m of all the sturmian words and is the euler function this result was conjectured by dulucq and gouyou beauchamps 1987 who proved that this result implies that the language m 0 a m c is inherently ambiguous we also give a combinatorial version of the riemann hypothesis

balance properties of multi dimensional words a word u is called 1 balanced if for any two factors v and w of u of equal length we have 1 v i w i1 for each letter i where v i denotes the number of occurrences of i in the factor v the aim of this paper is to extend the notion of balance to multi dimensional words we first characterize all 1 balanced words on zn in particular we prove they are fully periodic for n 1 we then give a quantitative measure of non balancedness for some words on z2 with irrational density including two dimensional sturmian words

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

strong cocycle triviality for 2 shushifts we consider cocycles defined on two dimensional symbolic subshifts and develop a new approach to proving that every cocycle is trivial introducing the notion of semi safe subshifts we prove that every locally constant cocycle with values in a locally residually finite group is trivial and that the corresponding transfer function is itself locally constant

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

combinatorics of patterns of a bidimensional sturmian sequence resume nous etudions une generalisation des suites sturmiennes en construisant une surface plissee donnee par l approximation d un plan par trois sortes de faces carrees orientees suivant les trois plans de coordonnees a cette surface on associe par projection un pavage du plan par trois sortes de losanges on definit sur ce pavage une fonction de complexite en comptant le nombre de motifs distincts d une fenetre de taille donnee nous donnons en etudiant les prolongements des motifs la forme explicite de cette fonction dans le cas d une fenetre triangulaire et d une fenetre en forme de parallelogramme

on two multigrid algorithms for modeling variational multiphase image segmentation in this paper we present two related multigrid algorithms for multiphase image segmentation algorithm i solves the model by vese chan we first generalize our recently developed multigrid method to this multiphase segmentation model mg1 we also give a local fourier analysis for the local smoother which leads to a new and more effective smoother although mg1 is found many magnitudes faster than the fast method of additive operator splitting aos both algorithms are not robust with regard to the initial guess to overcome this dependence on the initial guess we consider a hierarchical segmentation model which achieves multiphase segmentation by repeated use of the chan vese two phase model our algorithm ii solves this model by a multigrid algorithm mg2 numerical experiments show that both algorithms are efficient and in particular mg2 is more robust than mg1 with respect to initial guesses ams subject classifications 68u10 65f10 65k10

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

a level set approach for computing solutions to incompressible two phase flow a level set approach for computing solutions to incompressible two phase flow is presented the interface between the two fluids is considered to be sharp and is described as the zero level set of a smooth function a new treatment of the level set method allows us to efficiently maintain the level set function as the signed distance from the interface we never have to explicitly reconstruct or find the zero level set consequently we are able to handle arbitrarily complex topologies large density and viscosity ratios and surface tension on relatively coarse grids we use a second order projection method along with a second order upwinded procedure for advecting the momentum and level set equations we consider the motion of air bubbles and water drops we also compute flows with multiple fluids such as air oil and water

iterative parameter choice and multigrid methods for anisotropic diffusion denoising anisotropic diffusion methods are well known for giving good qualitative results for image denoising this paper gives a review of the anisotropic diffusion methodology and its application to image denoising we propose a fixed point iteration using a multigrid solver to solve a regularized anisotropic diffusion equation which is not only well posed but also has a nontrivial steady state solution a new regularization parameter choice method brent ncp combining brent s method and the normalized cumulative periodogram information of the misfit is also introduced we test our algorithm on several common test images with different noise levels the experimental results demonstrate the effectiveness of the anisotropic diffusion with a multigrid approach and the broad applicability of the brent ncp parameter choice algorithm

matrix dependent prolongations and restrictions in a blackbox multigrid solver multigrid methods are studied for the solution of linear systems resulting from the 9 point discretization of a general linear second order elliptic partial differential equation in two dimensions the rate of convergence of standard multigrid methods often deteriorates when the coefficients in the differential equation are discontinuous or when dominating first order terms are present these difficulties may be overcome by choosing the prolongation and restriction operators in a special way a novel way to do this is proposed as a result a blackbox solver written in standard fortran 77 has been developed numerical experiments for several hard test problems are described and comparison is made with other algorithms the standard mg method and a method introduced by kettler a significant improvement of robustness and efficiency is found

existence of a least energy nodal solution for a schrodinger kirchhoff equation with potential vanishing at infinity in this paper we study a class of nonlocal schrodinger kirchhoff problems involving only continuous functions using a minimization argument and a quantitative deformation lemma we find a least energy nodal or sign changing solution to this problem moreover when the problem presents symmetry we show that it has infinitely many nontrivial solutions

maximal pattern complexity of two dimensional words the maximal pattern complexity of one dimensional words has been studied in several papers t kamae l zamboni sequence entropy and the maximal pattern complexity of infinite words ergodic theory dynam systems 22 4 2002 1191 1199 t kamae l zamboni maximal pattern complexity for discrete systems ergodic theory dynam systems 22 4 2002 1201 1214 t kamae h rao pattern complexity over l letters e comb j to appear t kamae y m xue two dimensional word with 2k maximal pattern complexity osaka j math 41 2 2004 257 265 we study the maximal pattern complexity p k of two dimensional words a two dimensional version of the notion of strong recurrence is introduced it is shown that if is strongly recurrent then either is doubly periodic or p k 2k k 1 2 accordingly we define a two dimensional pattern sturmian word as a strongly recurrent word with p k 2k examples of pattern sturmian words are given

image analysis using multigrid relaxation methods image analysis problems posed mathematically as variational principles or as partial differential equations are amenable to numerical solution by relaxation algorithms that are local iterative and often parallel although they are well suited structurally for implementation on massively parallel locally interconnected computational architectures such distributed algorithms are seriously handi capped by an inherent inefficiency at propagating constraints between widely separated processing elements hence they converge extremely slowly when confronted by the large representations of early vision application of multigrid methods can overcome this drawback as we showed in previous work on 3 d surface reconstruction in this paper we develop multiresolution iterative algorithms for computing lightness shape from shading and optical flow and we examine the efficiency of these algorithms using synthetic image inputs the multigrid methodology that we describe is broadly applicable in early vision notably it is an appealing strategy to use in conjunction with regularization analysis for the efficient solution of a wide range of ill posed image analysis problems

hybrid quasicrystals transport and localization in products of minimal sets we consider convex combinations of finite valued almost periodic sequences mainly substitution sequences and put them as potentials of one dimensional tight binding models we prove that these sequences are almost periodic we call such combinations hybrid quasicrystals and these studies are related to the minimality under the shift on both coordinates of the product space of the respective minimal hulls we observe a rich variety of behaviors on the quantum dynamical transport ranging from localization to transport

multigrid geometric active contour models geometric active contour models are very popular partial differential equation based tools in image analysis and computer vision we present a new multigrid algorithm for the fast evolution of level set based geometric active contours and compare it with other established numerical schemes we overcome the main bottleneck associated with most numerical implementations of geometric active contours namely the need for very small time steps to avoid instability by employing a very stable fully 2 d implicit explicit time integration numerical scheme the proposed scheme is more accurate and has improved rotational invariance properties compared with alternative split schemes particularly when big time steps are utilized we then apply properly designed multigrid methods to efficiently solve the occurring sparse linear system the combined algorithm allows for the rapid evolution of the contour and convergence to its final configuration after very few iterations image segmentation experiments demonstrate the efficiency and accuracy of the method

regular article a pde based fast local level set method we develop a fast method to localize the level set method of osher and sethian 1988 j comput phys 79 12 and address two important issues that are intrinsic to the level set method a how to extend a quantity that is given only on the interface to a neighborhood of the interface b how to reset the level set function to be a signed distance function to the interface efficiently without appreciably moving the interface this fast local level set method reduces the computational effort by one order of magnitude works in as much generality as the original one and is conceptually simple and easy to implement our approach differs from previous related works in that we extract all the information needed from the level set function or functions in multiphase flow and do not need to find explicitly the location of the interface in the space domain the complexity of our method to do tasks such as extension and distance reinitialization is o n where n is the number of points in space not o n log n as in works by sethian 1996 proc nat acad sci 93 1591 and helmsen and co workers 1996 spie microlithography ix p 253 this complexity estimation is also valid for quite general geometrically based front motion for our localized method

dream 2 s deformable regions driven by an eulerian accurate minimization method for image and video segmentation this paper deals with image and video segmentation using active contours we propose a general form for the energy functional related to region based active contours we compute the associated evolution equation using shape derivation tools and accounting for the evolving region based terms then we apply this general framework to compute the evolution equation from functionals that include various statistical measures of homogeneity for the region to be segmented experimental results show that the determinant of the covariance matrix appears to be a very relevant tool for segmentation of homogeneous color regions as an example it has been successfully applied to face segmentation in real video sequences

nodal solutions for singularly perturbed equations with critical exponential growth abstract the existence and concentration behavior of nodal solutions are established for the equation 2 u v z u f u in where is a domain in r 2 not necessarily bounded v is a positive holder continuous function and f c 1 is an odd function having critical exponential growth

complexity of trajectories in rectangular billiards to a trajectory of the billiard in a cube we assign its symbolic trajectory the sequence of numbers of coordinate planes to which the faces met by the trajectory are parallel the complexity of the trajectory is the number of different words of lengthn occurring in it we prove that for generic trajectories the complexity is well defined and calculate it confirming the conjecture of arnoux mauduit shiokawa and tamura amst

fast geodesic active contours we use an unconditionally stable numerical scheme to implement a fast version of the geodesic active contour model the proposed scheme is useful for object segmentation in images like tracking moving objects in a sequence of images the method is based on the weickert romeney viergever additive operator splitting aos scheme it is applied at small regions motivated by the adalsteinsson sethian level set narrow band approach and uses sethian s 1996 fast marching method for re initialization experimental results demonstrate the power of the new method for tracking in color movies

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

snakes shapes and gradient vector flow snakes or active contours are used extensively in computer vision and image processing applications particularly to locate object boundaries problems associated with initialization and poor convergence to boundary concavities however have limited their utility this paper presents a new external force for active contours largely solving both problems this external force which we call gradient vector flow gvf is computed as a diffusion of the gradient vectors of a gray level or binary edge map derived from the image it differs fundamentally from traditional snake external forces in that it cannot be written as the negative gradient of a potential function and the corresponding snake is formulated directly from a force balance condition rather than a variational formulation using several two dimensional 2 d examples and one three dimensional 3 d example we show that gvf has a large capture range and is able to move snakes into boundary concavities

region competition unifying snakes region growing and bayes mdl for multiband image segmentation we present a novel statistical and variational approach to image segmentation based on a new algorithm named region competition this algorithm is derived by minimizing a generalized bayes minimum description length mdl criterion using the variational principle the algorithm is guaranteed to converge to a local minimum and combines aspects of snakes balloons and region growing the classic snakes balloons and region growing algorithms can be directly derived from our approach we provide theoretical analysis of region competition including accuracy of boundary location criteria for initial conditions and the relationship to edge detection using filters it is straightforward to generalize the algorithm to multiband segmentation and we demonstrate it on gray level images color images and texture images the novel color model allows us to eliminate intensity gradients and shadows thereby obtaining segmentation based on the albedos of objects it also helps detect highlight regions

implicit explicit methods for time dependent partial differential equations implicit explicit imex schemes have been widely used especially in conjunction with spectral methods for the time integration of spatially discretized partial differential equations pdes of diffusion convection type typically an implicit scheme is used for the diffusion term and an explicit scheme is used for the convection term reaction diffusion problems can also be approximated in this manner in this work we systematically analyze the performance of such schemes propose improved new schemes and pay particular attention to their relative performance in the context of fast multigrid algorithms and of aliasing reduction for spectral methods for the prototype linear advection diffusion equation a stability analysis for first second third and fourth order multistep imex schemes is performed stable schemes permitting large time steps for a wide variety of problems and yielding appropriate decay of high frequency error modes are identified numerical experiments demonstrate that weak decay

optimal approximations by piecewise smooth functions and associated variational problems abstract this reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision in computer vision a fundamental problem is to appropriately decompose the domain r of a function g x y of two variables this problem starts by describing the physical situation which produces images assume that a three dimensional world is observed by an eye or camera from some point p and that g1 rho represents the intensity of the light in this world approaching the point sub 1 from a direction rho if one has a lens at p focusing this light on a retina or a film in both cases a plane domain r in which we may introduce coordinates x y then let g x y be the strength of the light signal striking r at a point with coordinates x y g x y is essentially the same as sub 1 rho possibly after a simple transformation given by the geometry of the imaging syste the function g x y defined on the plane domain r will be called an image what sort of function is g the light reflected off the surfaces si of various solid objects o sub i visible from p will strike the domain r in various open subsets r sub i when one object o1 is partially in front of another object o2 as seen from p but some of object o2 appears as the background to the sides of o1 then the open sets r1 and r2 will have a common boundary the edge of object o1 in the image defined on r and one usually expects the image g x y to be discontinuous along this boundary jhd

automatic prior shape selection for image edge detection with modified mumford shah model abstract edge detection plays an important role in the field of image processing in this paper we propose a novel variational model to automatically and adaptively detect one or more prior shapes from the given dictionary to guide the edge detection process in that way we can effectively detect the shapes of interest from the test image moreover an efficient algorithm based on the alternating direction method of multipliers admm is proposed to solve this model with guaranteed convergence a variety of numerical experiments show that the proposed method has achieved ideal performance for edge detection in images with missing information various types of noise and complicated background and even multiple objects

multigrid anisotropic diffusion a multigrid anisotropic diffusion algorithm for image processing is presented the multigrid implementation provides an efficient hierarchical relaxation method that facilitates the application of anisotropic diffusion to time critical processes through a multigrid v cycle the anisotropic diffusion equations are successively transferred to coarser grids and used in a coarse to fine error correction scheme when a coarse grid with a trivial solution is reached the coarse grid estimates of the residual error can be propagated to the original grid and used to refine the solution the main benefits of the multigrid approach are rapid intraregion smoothing and reduction of artifacts due to the elimination of low frequency error the theory of multigrid anisotropic diffusion is developed then the intergrid transfer functions relaxation techniques diffusion coefficients and boundary conditions are discussed the analysis includes the examination of the storage requirements the computational cost and the solution quality finally experimental results are reported that demonstrate the effectiveness of the multigrid approach

multiphase image segmentation via modica mortola phase transition we propose a novel multiphase segmentation model built upon the celebrated phase transition model of modica and mortola in material sciences and a properly synchronized fitting term that complements it the proposed sine sinc model outputs a single multiphase distribution from which each individual segment or phase can be easily extracted theoretical analysis is developed for the gamma convergence behavior of the proposed model and the existence of its minimizers since the model is not quadratic nor convex for computation we adopted the convex concave procedure cccp that has been developed in the literatures of both computational nonlinear pdes and neural computation numerical details and experiments on both synthetic and natural images are presented

variational optical flow computation in real time this paper investigates the usefulness of bidirectional multigrid methods for variational optical flow computations although these numerical schemes are among the fastest methods for solving equation systems they are rarely applied in the field of computer vision we demonstrate how to employ those numerical methods for the treatment of variational optical flow formulations and show that the efficiency of this approach even allows for real time performance on standard pcs as a representative for variational optic flow methods we consider the recently introduced combined local global method it can be considered as a noise robust generalization of the horn and schunck technique we present a decoupled as well as a coupled version of the classical gau spl szlig seidel solver and we develop several multigrid implementations based on a discretization coarse grid approximation in contrast with standard bidirectional multigrid algorithms we take advantage of intergrid transfer operators that allow for nondyadic grid hierarchies as a consequence no restrictions concerning the image size or the number of traversed levels have to be imposed in the experimental section we juxtapose the developed multigrid schemes and demonstrate their superior performance when compared to unidirectional multigrid methods and nonhierachical solvers for the well known 316 spl times 252 yosemite sequence we succeeded in computing the complete set of dense flow fields in three quarters of a second on a 3 06 ghz pentium4 pc this corresponds to a frame rate of 18 flow fields per second which outperforms the widely used gau spl szlig seidel method by almost three orders of magnitude

a robust multigrid approach for variational image registration models variational registration models are non rigid and deformable imaging techniques for accurate registration of two images as with other models for inverse problems using the tikhonov regularization they must have a suitably chosen regularization term as well as a data fitting term one distinct feature of registration models is that their fitting term is always highly nonlinear and this nonlinearity restricts the class of numerical methods that are applicable this paper first reviews the current state of the art numerical methods for such models and observes that the nonlinear fitting term is mostly avoided in developing fast multigrid methods it then proposes a unified approach for designing fixed point type smoothers for multigrid methods the diffusion registration model second order equations and a curvature model fourth order equations are used to illustrate our robust methodology analysis of the proposed smoothers and comparisons to other methods are given as expected of a multigrid method being many orders of magnitude faster than the unilevel gradient descent approach the proposed numerical approach delivers fast and accurate results for a range of synthetic and real test images

regularized laplacian zero crossings as optimal edge integrators we view the fundamental edge integration problem for object segmentation in a geometric variational framework first we show that the classical zero crossings of the image laplacian edge detector as suggested by marr and hildreth inherently provides optimal edge integration with regard to a very natural geometric functional this functional accumulates the inner product between the normal to the edge and the gray level image gradient along the edge we use this observation to derive new and highly accurate active contours based on this functional and regularized by previously proposed geodesic active contour geometric variational models we also incorporate a 2d geometric variational explanation to the haralick edge detector into the geometric active contour framework

an algebraic multigrid approach for image analysis we apply a new algebraic multigrid method for solving computer vision problems with constraints as particular examples we solve the shape from photometric stereo and image binarization problems a variational formulation is applied to the problem of shape reconstruction from three or more images of an object with the same viewing direction and different lighting conditions supplemented by some pointwise height constraints in order to obtain a smooth reconstruction we use a weight function that is singular at the constrained points resulting in an elliptic equation with singular coefficients which is solved efficiently by the algebraic multigrid algorithm as a second example a similar technique is applied to construct a threshold surface which interpolates between values at centers of edges this surface is then used for image binarization

on the location and profile of spike layer nodal solutions to nonlinear schrodinger equations abstract the existence and concentration behavior of a nodal solution are established for the equation e 2 u v x u f u in where is a domain in r n not necessarily bounded v is a positive holder continuous function and f c 1 r is an odd function having subcritical and superlinear growth under additional local condition on v it is proved that such a solution has just one positive and one negative peaks which are located around local minima of v

vectorial total variation based regularization for variational image registration to use interdependence between the primary components of the deformation field for smooth and non smooth registration problems the channel by channel total variation or standard vectorial total variation svtv based regularization has been extended to a more flexible and efficient technique allowing high quality regularization procedures based on this method this paper proposes a fast nonlinear multigrid nmg method for solving the underlying euler lagrange system of two coupled second order nonlinear partial differential equations numerical experiments using both synthetic and realistic images not only confirm that the recommended vtv based regularization yields better registration qualities for a wide range of applications than those of the svtv based regularization but also that the proposed nmg method is fast accurate and reliable in delivering visually pleasing registration results

configuration spaces transfer and 2 nodal solutions of a semiclassical nonlinear schrodinger equation we establish new lower bounds for the number of nodal bound states for the semiclassical nonlinear schrodinger equation varepsilon 2 delta u a x u u p 2 u with bounded and uniformly continuous potential a the solutions we obtain have precisely two nodal domains and their positive and negative parts concentrate near the set of minimum points of a our approach is independent of penalization techniques and yields in some cases the existence of infinitely many nodal solutions for fixed varepsilon via a dynamical systems approach we exhibit positively invariant sets of sign changing functions for the negative gradient flow of the associated energy functional we analyze these sets on the cohomology level with the help of dold s fixed point transfer in particular we estimate their cuplength in terms of the cuplength of equivariant configuration spaces of subsets of mathbb r n we also provide new estimates of the cuplength of configuration spaces

on high order denoising models and fast algorithms for vector valued images variational techniques for gray scale image denoising have been deeply investigated for many years however little research has been done for the vector valued denoising case and the very few existent works are all based on total variation regularization it is known that total variation models for denoising gray scaled images suffer from staircasing effect and there is no reason to suggest this effect is not transported into the vector valued models high order models on the contrary do not present staircasing in this paper we introduce three high order and curvature based denoising models for vector valued images their properties are analyzed and a fast multigrid algorithm for the numerical solution is provided ams subject classifications 68u10 65f10 65k10

approximation of functional depending on jumps by elliptic functional via t convergence we show how it is possible to approximate the mumford shah see 29 image segmentation functional by elliptic functionals defined on sobolev spaces the heuristic idea is to consider functionals h u z with z ranging between 0 and 1 and related to the set k the minimizing zh are near to 1 in a neighborhood of the set k and far from the neighborhood they are very small the neighborhood shrinks as h for a similar approach to the problem compare kulkarni see 25 the approximation of h to takes place in a variational sense the de giorgi f convergence

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

positive and sign changing clusters around saddle points of the potential for nonlinear elliptic problems we study the existence and asymptotic behavior of positive and sign changing multipeak solutions for the equation varepsilon 2 delta v v x v f v quad rm in mathbb r n where e is a small positive parameter f a superlinear subcritical and odd nonlinearity v a uniformly positive potential no symmetry on v is assumed it is known kang and wei in adv differ equ 5 899 928 2000 that this equation has positive multipeak solutions with all peaks approaching a local maximum of v it is also proved that solutions alternating positive and negative spikes exist in the case of a minimum see d aprile and pistoia in ann inst h poincare anal non lineaire 26 1423 1451 2009 the aim of this paper is to show the existence of both positive and sign changing multipeak solutions around a nondegenerate saddle point of v

least energy nodal solution for nonlinear schrodinger equation without ar condition abstract in this paper we are concerned with the existence of least energy nodal solution for the following stationary nonlinear schrodinger equation 0 1 u x v x u x f u x r n n 3 where 0 is a parameter v has double potential well and f has asymptotically linear growth or superlinear growth without ar condition by using variational methods we show that 0 1 has a least energy nodal solution

two dimensional iterated morphisms and discrete planes iterated morphisms of the free monoid are very simple combinatorial objects which produce infinite sequences by replacing iteratively letters by words the aim of this paper is to introduce a formalism for a notion of two dimensional morphisms we show that they can be iterated by using local rules and that they generate two dimensional patterns related to discrete approximations of irrational planes with algebraic parameters we associate such a two dimensional morphism with any usual pisot unimodular one dimensional iterated morphism over a three letter alphabet

combinatorial optimization of the discretized multiphase mumford shah functional the mumford shah model has been one of the most influential models in image segmentation and denoising the optimization of the multiphase mumford shah energy functional has been performed using level sets methods that optimize the mumford shah energy by evolving the level sets via the gradient descent these methods are very slow and prone to getting stuck in local optima due to the use of gradient descent after the reformulation of the 2 phase mumford shah functional on a graph several groups investigated the hierarchical extension of the graph representation to multi class the discrete hierarchical approaches are more effective than hierarchical or direct multiphase formulation using level sets however they provide approximate solutions and can diverge away from the optimal solution in this paper we present a discrete alternating optimization for the discretized vese chan approximation of the piecewise constant multiphase mumford shah functional that directly minimizes the multiphase functional without recursive bisection on the labels our approach handles the nonsubmodularity of the multiphase energy function and provides a global optimum if the image estimation data term is known apriori

generation and recognition of digital planes using multi dimensional continued fractions this paper extends in a multi dimensional framework pattern recognition techniques for generation or recognition of digital lines more precisely we show how the connection between chain codes of digital lines and continued fractions can be generalized by a connection between tilings and multi dimensional continued fractions this leads to a new approach for generating and recognizing digital hyperplanes

on a conjecture on bidimensional words we prove that given a double sequence w over the alphabet a i e a mapping from z2 to a if there exists a pair n0 m0 z2 such that pw n0 m0 1 100n0m0 then w has a periodicity vector where pw is the complexity function in rectangles of w