on the muskat problem with viscosity jump global in time results abstract the muskat problem models the filtration of two incompressible immiscible fluids of different characteristics in porous media in this paper we consider both the 2d and 3d setting of two fluids of different constant densities and different constant viscosities in this situation the related contour equations are non local not only in the evolution system but also in the implicit relation between the amplitude of the vorticity and the free interface among other extra difficulties no maximum principles are available for the amplitude and the slopes of the interface in l we prove global in time existence results for medium size initial stable data in critical spaces we also enhance previous methods by showing smoothing instant analyticity improving the medium size constant in 3d together with sharp decay rates of analytic norms the found technique is twofold giving ill posedness in unstable situations for very low regular solutions

on the numerical solution of the regularized birkhoff equations the birkhoff equations for the evolution of vortex sheets are regularized in a way proposed by krasny the convergence of numerical approximations to a fixed regularization is studied theoretically and numerically the numerical test problem is a two dimensional inviscid jet

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

geodesic active regions and level set methods for supervised texture segmentation this paper presents a novel variational framework to deal with frame partition problems in computer vision this framework exploits boundary and region based segmentation modules under a curve based optimization objective function the task of supervised texture segmentation is considered to demonstrate the potentials of the proposed framework the textured feature space is generated by filtering the given textured images using isotropic and anisotropic filters and analyzing their responses as multi component conditional probability density functions the texture segmentation is obtained by unifying region and boundary based information as an improved geodesic active contour model the defined objective function is minimized using a gradient descent method where a level set approach is used to implement the obtained pde according to this pde the curve propagation towards the final solution is guided by boundary and region based segmentation forces and is constrained by a regularity force the level set implementation is performed using a fast front propagation algorithm where topological changes are naturally handled the performance of our method is demonstrated on a variety of synthetic and real textured frames

global regularity for a birkhoff rott α approximation of the dynamics of vortex sheets of the 2d euler equations abstract we present an regularization of the birkhoff rott equation induced by the two dimensional euler equations for the vortex sheet dynamics we show that an initially smooth self avoiding vortex sheet remains smooth for all times under the regularized dynamics provided the initial density of vorticity is an integrable function over the curve with respect to the arc length measure

structure theorem and isomorphism test for graphs with excluded topological subgraphs we generalize the structure theorem of robertson and seymour for graphs excluding a fixed graph h as a minor to graphs excluding h as a topological subgraph we prove that for a fixed h every graph excluding h as a topological subgraph has a tree decomposition where each part is either almost embeddable to a fixed surface or has bounded degree with the exception of a bounded number of vertices furthermore we prove that such a decomposition is computable by an algorithm that is fixed parameter tractable with parameter h we present two algorithmic applications of our structure theorem to illustrate the mechanics of a typical application of the structure theorem we show that on graphs excluding h as a topological subgraph partial dominating set find k vertices whose closed neighborhood has maximum size can be solved in time f h k cdot n o 1 more significantly we show that on graphs excluding h as a topological subgraph graph isomorphism can be solved in time n f h this result unifies and generalizes two previously known important polynomial time solvable cases of graph isomorphism bounded degree graphs e m luks j comput system sci 25 1982 pp 42 65 and h minor free graphs i n ponomarenko zap nauchn sem leningrad otdel mat inst steklov lomi 174 1988 pp 147 177 182 the proof of this result needs a generalization of our structure theorem to the context of invariant treelike decomposition

finite time singularities for the free boundary incompressible euler equations in this paper we prove the existence of smooth initial data for the 2d free boundary incompressible euler equations also known for some particular scenarios as the water wave problem for which the smoothness of the interface breaks down in nite time into a splash singularity or a splat singularity

turning waves and breakdown for incompressible flows we consider the evolution of an interface generated between two immiscible incompressible and irrotational fluids specifically we study the muskat and water wave problems we show that starting with a family of initial data given by f0 the interface reaches a regime in finite time in which is no longer a graph therefore there exists a time t where the solution of the free boundary problem parameterized as f t blows up f l t in particular for the muskat problem this result allows us to reach an unstable regime for which the rayleigh taylor condition changes sign and the solution breaks down

a level set model for image classification we present a supervised classification model based on a variational approach this model is devoted to find an optimal partition composed of homogeneous classes with regular interfaces the originality of the proposed approach concerns the definition of a partition by the use of level sets each set of regions and boundaries associated to a class is defined by a unique level set function we use as many level sets as different classes and all these level sets are moving together thanks to forces which interact in order to get an optimal partition we show how these forces can be defined through the minimization of a unique fonctional the coupled partial differential equations pde related to the minimization of the functional are considered through a dynamical scheme given an initial interface set zero level set the different terms of the pde s are governing the motion of interfaces such that at convergence we get an optimal partition as defined above each interface is guided by internal forces regularity of the interface and external ones data term no vacuum no regions overlapping several experiments were conducted on both synthetic and real images

variational region based segmentation using multiple texture statistics this paper investigates variational region level criterion for supervised and unsupervised texture based image segmentation the focus is given to the demonstration of the effectiveness and robustness of this region based formulation compared to most common variational approaches the main contributions of this global criterion are twofold first the proposed methods circumvent a major problem related to classical texture based segmentation approaches existing methods even if they use different and various texture features are mainly stated as the optimization of a criterion evaluating punctual pixel likelihoods or similarity measure computed within a local neighborhood these approaches require sufficient dissimilarity between the considered texture features an additional limitation is the choice of the neighborhood size and shape these two parameters and especially the neighborhood size significantly influence the classification performances the neighborhood must be large enough to capture texture structures and small enough to guarantee segmentation accuracy these parameters are often set experimentally these limitations are mitigated with the proposed variational methods stated at the region level it resorts to an energy criterion defined on image where regions are characterized by nonparametric distributions of their responses to a set of filters in the supervised case the segmentation algorithm consists in the minimization of a similarity measure between region level statistics and texture prototypes and a boundary based functional that imposes smoothness and regularity on region boundaries in the unsupervised case the data driven term involves the maximization of the dissimilarity between regions the proposed similarity measure is generic and permits optimally fusing various types of texture features it is defined as a weighted sum of kullback leibler divergences between feature distributions the optimization of the proposed variational criteria is carried out using a level set formulation the effectiveness and the robustness of this formulation at region level compared to classical active contour methods are evaluated for various brodatz and natural images

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

number of nodal domains of eigenfunctions on non positively curved surfaces with concave boundary it is an open problem in general to prove that there exists a sequence of delta g eigenfunctions varphi j k on a riemannian manifold m g for which the number n varphi j k of nodal domains tends to infinity with the eigenvalue our main result is that n varphi j k rightarrow infty along a subsequence of eigenvalues of density 1 if m g is a non positively curved surface with concave boundary i e a generalized sinai or lorentz billiard unlike the recent closely related work of ghosh reznikov sarnak and of the authors on the nodal domain counting problem the surfaces need not have any symmetries

on the absence of splash singularities in the case of two fluid interfaces we show that splash singularities cannot develop in the case of locally smooth solutions of the two fluid interfaces in two dimensions more precisely we show that the scenario of formation of singularities discovered by castro cordoba fefferman gancedo gomez serrano 6 in the case of the water waves system in which the interface remains locally smooth but self intersects in finite time is completely prevented in the case of two fluid interfaces with positive densities

long time existence for a slightly perturbed vortex sheet consider a flat two dimensional vortex sheet perturbed initially by a small analytic disturbance by a formal perturbation analysis moore derived an approximate differential equation for the evolution of the vortex sheet we present a simplified derivation of moore s approximate equation and analyze errors in the approximation the result is used to prove existence of smooth solutions for long time if the initial perturbation is of size and is analytic in a strip m existence of a smooth solution of birkhoff s equation is shown for time t k2p if is sufficiently small with 1 as 0 for the particular case of sinusoidal data of wave length and amplitude e moore s analysis and independent numerical results show singularity development at time tc log o log log our results prove existence for t log if is sufficiently small with k 1 as 0 thus our existence results are nearly optimal

on the muskat problem global in time results in 2d and 3d this paper considers the three dimensional muskat problem in the stable regime we obtain a conservation law which provides an l 2 maximum principle for the fluid interface we also show global in time existence for strong and weak solutions with initial data controlled by explicit constants furthermore we refine the available estimates to obtain global existence and uniqueness for strong solutions with larger initial data than we previously had in 2d finally we provide global in time results in spaces with critical regularity giving solutions with bounded slope and time integrable bounded curvature

global existence singular solutions and ill posedness for the muskat problem the muskat or muskat leibenzon problem describes the evolution of the interface between two immiscible fluids in a porous medium or hele shaw cell under applied pressure gradients or fluid injection extraction in contras t to the hele shaw problem the one phase version of the muskat problem there are few nontrivial exact solutions or analytic results for the muskat problem for the stable forward muskat problem in which the higher viscosity fluid ex pands into the lower viscosity fluid we show global in time existence for initial data that is a small perturbation of a flat interface the initial data in this result ma y contain weak e g curvature singularities for the unstable backwa rd problem in which the higher viscosity fluid contracts we construct singular solution s that start off with smooth initial data but develop a point of infinite curvature at fi nite time c 2004 wiley periodicals inc

a priori estimates for fluid interface problems we consider the regularity of an interface between two incompressible and inviscid fluid flows in the presence of surface tension we obtain local in time estimates on the interface in h 3 2 k 1 and the velocity fields in h 3 2 k these estimates are obtained using geometric considerations which show that the kelvin helmholtz instabilities are a consequence of a curvature calculation 2007 wiley periodicals inc

finite time analyticity for the two and three dimensional rayleigh taylor instability the rayleigh taylor instability refers to the dynamics of the interface between two ideal irrotational fluids of different densities superposed one over the other and in relative motion the well posedness of this problem is considered for twoand three dimensional flows in the entire space and in the presence of a horizontal bottom in the entire space finite time analyticity of the interface is proven when the initial interface has sufficiently small gradients and is flat at infinity in the presence of a horizontal bottom the initial interface corrugations has also to be small initially but it is not required to vanish at infinity

duchon robert solutions for the rayleigh taylor and muskat problems abstract we construct analytic solutions to the euler equations with an interface between two fluids extending work of duchon and robert we also show that the estimates of duchon and robert yield global analytic solutions to the muskat problem with small initial data

motion recognition using nonparametric image motion models estimated from temporal and multiscale co occurrence statistics a new approach for motion characterization in image sequences is presented it relies on the probabilistic modeling of temporal and scale co occurrence distributions of local motion related measurements directly computed over image sequences temporal multiscale gibbs models allow us to handle both spatial and temporal aspects of image motion content within a unified statistical framework since this modeling mainly involves the scalar product between co occurrence values and gibbs potentials we can formulate and address several fundamental issues model estimation according to the ml criterion hence model training and learning and motion classification we have conducted motion recognition experiments over a large set of real image sequences comprising various motion types such as temporal texture samples human motion examples and rigid motion situations

a criterion for the equivalence of the birkhoff rott and euler descriptions of vortex sheet evolution in this article we consider the evolution of vortex sheets in the plane both as a weak solution of the two dimensional incompressible euler equations and as a weak solution of the birkhoff rott equations we begin by discussing the classical birkhoff rott equations with respect to arbitrary parametrizations of the sheet we introduce a notion of weak solution to the birkhoff rott system and we prove consistency of this notion with the classical formulation of the equations our main purpose in this paper is to present a sharp criterion for the equivalence of the weak euler and weak birkhoff rott descriptions of vortex sheet dynamics

on the energy of inviscid singular flows abstract it is known that the energy of a weak solution to the euler equation is conserved if it is slightly more regular than the besov space b 3 1 3 when the singular set of the solution is or belongs to a smooth manifold we derive various l p space regularity criteria dimensionally equivalent to the critical one in particular if the singular set is a hypersurface the energy of u is conserved provided the one sided non tangential limits to the surface exist and the non tangential maximal function is l 3 integrable while the maximal function of the pressure is l 3 2 integrable the results directly apply to prove energy conservation of the classical vortex sheets in both 2d and 3d at least in those cases where the energy is finite

linear stability of compressible vortex sheets in two dimensional elastodynamics abstract the linear stability of rectilinear compressible vortex sheets is studied for two dimensional isentropic elastic flows this problem has a free boundary and the boundary is characteristic a necessary and sufficient condition is obtained for the linear stability of the rectilinear vortex sheets more precisely it is shown that besides the stable supersonic zone the elasticity exerts an additional stable subsonic zone we also find that there is a class of states in the interior of subsonic zone where the stability of such states is weaker than the stability of other states in the sense that there is an extra loss of tangential derivatives with respect to the source terms this is a new feature that the euler flow does not possess one of the difficulties for the elastic flow is that the non differentiable points of the eigenvalues may coincide with the roots of the lopatinskii determinant as a result the kreiss symmetrization cannot be applied directly instead we perform an upper triangularization of the system to separate only the outgoing modes at all points in the frequency space so that an exact estimate of the outgoing modes can be obtained moreover all the outgoing modes are shown to be zero due to the l 2 regularity of solutions the estimates for the incoming modes can be derived directly from the lopatinskii determinant this new approach avoids the lengthy computation and estimates for the outgoing modes when kreiss symmetrization is applied this method can also be applied to the euler flow and mhd flow

an intensity texture model based level set method for image segmentation in this paper a novel level set segmentation model integrating the intensity and texture terms is proposed to segment complicated two phase nature images firstly an intensity term based on the global division algorithm is proposed which can better capture intensity information of image than the chan vese model cv particularly the cv model is a special case of the proposed intensity term under a certain condition secondly a texture term based on the adaptive scale local variation degree aslvd algorithm is proposed the aslvd algorithm adaptively incorporates the amplitude and frequency components of local intensity variation thus it can extract the non stationary texture feature accurately finally the intensity term and the texture term are jointly incorporated into level set and used to construct effective image segmentation model named as the intensity texture model since the intensity term and the texture term are complementary for image segmentation the intensity texture model has strong ability to accurately segment those complicated two phase nature images experimental results demonstrate the effectiveness of the proposed intensity texture model an intensity term based on the so called global division algorithm is proposed we extract the amplitude and frequency components of local intensity variation we propose the adaptive scale local variation degree algorithm as texture term the intensity and texture terms are integrated into level set energy functional

almost optimal convergence of the point vortex method for vortex sheets using numerical filtering standard numerical methods for the birkhoff rott equation for a vortex sheet are unstable due to the amplification of roundoff error by the kelvin helmholtz instability a nonlinear filtering method was used by krasny to eliminate this spurious growth of round off error and accurately compute the birkhoff rott solution essentially up to the time it becomes singular in this paper convergence is proved for the discretized birkhoff rott equation with krasny filtering and simulated roundoff error the convergence is proved for a time almost up to the singularity time of the continuous solution the proof is in an analytic function class and uses a discrete form of the abstract cauchy kowalewski theorem in order for the proof to work almost up to the singularity time the linear and nonlinear parts of the equation as well as the effects of krasny filtering are precisely estimated the technique of proof applies directly to other ill posed problems such as rayleigh taylor unstable interfaces in incompressible inviscid and irrotational fluids as well as to saffman taylor unstable interfaces in hele shaw cells

global regularity and convergence of a birkhoff rott α approximation of the dynamics of vortex sheets of the two dimensional euler equations we present an regularization of the birkhoff rott equation br equation induced by the two dimensional euler equations for the vortex sheet dynamics we show the convergence of the solutions of euler equations to a weak solution of the euler equations for initial vorticity being a finite radon measure of fixed sign which includes the vortex sheets case we also show that provided the initial density of vorticity is an integrable function over the curve with respect to the arc length measure i an initially lipschitz chord arc vortex sheet curve evolving under the br equation remains lipschitz for all times ii an initially holder c1 0 1 chord arc curve remains in c1 for all times and finally iii an initially holder cn n 1 0 1 closed chord arc curve remains so for all times in all these cases the weak euler and the br descriptions of the vortex sheet motion are equivalent 2009 wiley periodicals inc

the weisfeiler leman dimension of planar graphs is at most 3 we prove that the weisfeiler leman wl dimension of the class of all finite planar graphs is at most 3 in particular every finite planar graph is definable in first order logic with counting using at most 4 variables the previously best known upper bounds for the dimension and number of variables were 14 and 15 respectively first we show that for dimension 3 and higher the wl algorithm correctly tests isomorphism of graphs in a minor closed class whenever it determines the orbits of the automorphism group of every arc colored 3 connected graph belonging to this class then we prove that apart from several exceptional graphs which have wl dimension at most 2 the individualization of two appropriately chosen vertices of a colored 3 connected planar graph followed by the one dimensional wl algorithm produces the discrete vertex partition this implies that the three dimensional wl algorithm determines the orbits of arc colored 3 connected planar graphs as a byproduct of the proof we get a classification of the 3 connected planar graphs with fixing number 3

well posedness theory for aggregation sheets in this paper we consider distribution solutions to the aggregation equation rho t mathrm div rho mathbf u 0 mathbf u nabla v rho in mathbb r d where the density concentrates on a co dimension one manifold we show that an evolution equation for the manifold itself completely determines the dynamics of such solutions we refer to such solutions aggregation sheets when the equation for the sheet is linearly well posed we show that the fully non linear evolution is also well posed locally in time for the class of bi lipschitz surfaces moreover we show that if the initial sheet is c1 then the solution itself remains c1 as long as it remains lipschitz lastly we provide conditions on the kernel g s frac mathrm d v mathrm d s that guarantee the solution remains a bi lipschitz surface globally in time and construct explicit solutions that either collapse or blow up in finite time when these conditions fail

texture modeling by multiple pairwise pixel interactions a markov random field model with a gibbs probability distribution gpd is proposed for describing particular classes of grayscale images which can be called spatially uniform stochastic textures the model takes into account only multiple short and long range pairwise interactions between the gray levels in the pixels an effective learning scheme is introduced to recover structure and strength of the interactions using maximal likelihood estimates of the potentials in the gpd as desired parameters the scheme is based on an analytic initial approximation of the estimates and their subsequent refinement by a stochastic approximation experiments in modeling natural textures show the utility of the proposed model

finite time analyticity for the two and three dimensional kelvin helmholtz instability the well posed property for the finite time vortex sheet problem with analytic initial data was first conjectured by birkhoff in two dimensions and is shown here to hold both in two and three dimensions incompressible inviscid and irrotational flow with a velocity jump across an interface is assumed in two dimensions global existence of a weak solution to the euler equation with such initial conditions is established in three dimensions a lagrangian representation of the vortex sheet analogous to the birkhoff equation in two dimensions is presented

rayleigh taylor breakdown for the muskat problem with applications to water waves the muskat problem models the evolution of the interface between two different fluids in porous media the rayleigh taylor condition is natural to reach linear stability of the muskat problem we show that the rayleigh taylor condition may hold initially but break down in finite time as a consequence of the method used we prove the existence of water waves turning

image segmentation using active contours calculus of variations or shape gradients we consider the problem of segmenting an image through the minimization of an energy criterion involving region and boundary functionals we show that one can go from one class to the otherby solving poisson s orhelmholtz s equation with well chosen boundar y conditions using this equivalence we study the case of a large class of region functionals by standard methods of the calculus of variations and derive the corresponding euler lagrange equations we revisit this problem using the notion of a shape derivative and show that the same equations can be elegantly derived without going through the unnatural step of converting the region integrals into boundary integrals we also define a larger class of region functionals based on the estimation and comparison to a prototype of the probability density distribution of image features and show how the shape derivative tool allows us to easily compute the corresponding gateaux derivatives and euler lagrange equations finally we apply this new functional to the problem of regions segmentation in sequences of color images we briefly describe our numerical scheme and show some experimental results

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

absence of splash singularities for surface quasi geostrophic sharp fronts and the muskat problem in this paper for both the sharp front surface quasi geostrophic equation and the muskat problem we rule out the splash singularity blow up scenario in other words we prove that the contours evolving from either of these systems cannot intersect at a single point while the free boundary remains smooth splash singularities have been shown to hold for the free boundary incompressible euler equation in the form of the water waves contour evolution problem our result confirms the numerical simulations in earlier work in which it was shown that the curvature blows up because the contours collapse at a point here we prove that maintaining control of the curvature will remove the possibility of pointwise interphase collapse another conclusion that we provide is a better understanding of earlier work in which squirt singularities are ruled out in this case a positive volume of fluid between the contours cannot be ejected in finite time

isomorphism of graphs which are pairwise k separable a polynomial time algorithm for testing isomorphism of graphs which are pairwise k separable for fixed k is given the pairwise k separable graphs are those graphs where each pair of distinct vertices are k separable this is a natural generalization of the bounded valence test of luks the subgroup of automorphisms of a hypergraph whose restriction to the vertices is in a given k group for fixed k is constructed in polynomial time

computational complexity of quantum satisfiability we connect both discrete and algebraic complexity theory with the satisfiability problem in certain non boolean lattices specifically quantum logic was introduced in 1936 by garrett birkhoff and john von neumann as a framework for capturing the logical peculiarities of quantum observables in the 1d case it coincides with boolean propositional logic but starting with dimension two violates the distributive law we introduce the weak and strong satisfiability problem for quantum logic propositional formulae it turns out that in dimension two both are also np complete for higher dimensional spaces rd and cd with d 3 fixed on the other hand we show both problems to be complete for the nondeterministic blum shub smale bss model of real computation this provides a unified view on both turing and real bss complexity theory and extends the still relatively scarce list of problems established npr complete with one perhaps closest in spirit to the classical cook levin theorem more precisely strong satisfiability of terms is complete while that of terms i e those in conjunctive form can be decided in polynomial time in dimensions d 2 the decidability of the infinite dimensional case being still open we proceed to investigate the case of indefinite finite dimensions here weak satisfiability still belongs to npr and strong satisfiability is still hard the latter in fact turns out as polynomial time equivalent to the feasibility of noncommutative integer polynomial equations over matrix rings

a nonparametric statistical method for image segmentation using information theory and curve evolution in this paper we present a new information theoretic approach to image segmentation we cast the segmentation problem as the maximization of the mutual information between the region labels and the image pixel intensities subject to a constraint on the total length of the region boundaries we assume that the probability densities associated with the image pixel intensities within each region are completely unknown a priori and we formulate the problem based on nonparametric density estimates due to the nonparametric structure our method does not require the image regions to have a particular type of probability distribution and does not require the extraction and use of a particular statistic we solve the information theoretic optimization problem by deriving the associated gradient flows and applying curve evolution techniques we use level set methods to implement the resulting evolution the experimental results based on both synthetic and real images demonstrate that the proposed technique can solve a variety of challenging image segmentation problems furthermore our method which does not require any training performs as good as methods based on training

wavelet based level set evolution for classification of textured images we present a supervised classification model based on a variational approach this model is specifically devoted to textured images we want to get a partition of an image composed of texture regions separated by regular interfaces each kind of texture defines a class we use a wavelet packet transform to analyze the textures characterized by their energy distribution in each sub band in order to have an image segmentation according to the classes we model the regions and their interfaces by level set functions we define a functional on these level sets whose minimizers define the optimal classification according to texture a system of coupled pdes is deduced from the functional by solving this system each region evolves according to its wavelet coefficients and interacts with the neighbor regions in order to obtain a partition with regular contours experiments are shown on synthetic and real images

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

on the nonlinear instability of euler and prandtl equations in this paper we give examples of nonlinearly unstable solutions of euler equations in the whole space 2 the half space the periodic strip the strip 1 1 and the periodic torus 2 with an application to vortex sheets using the same methods we prove an instability result for prandtl type boundary layers that appear in and 2000 john wiley sons inc

a stability criterion for two fluid interfaces and applications we derive a new stability criterion for two fluid interfaces that ensures the existence of stable local solutions that do not break down too fast due to kelvin helmholtz instabilities it can be seen both as a two fluid generalization of the rayleigh taylor criterion and as a nonlinear version of the kelvin stability condition we show that gravity can control the inertial effects of the shear up to frequencies that are high enough for the surface tension to play a relevant role this explains why surface tension is a necessary condition for well posedness while the low frequency main dynamics of interfacial waves are unaffected by it in order to derive a practical version of this criterion we work with a nondimensionalized version of the equations and allow for the possibility of various asymptotic regimes such as the shallow water limit this limit being singular we have to derive a new symbolic analysis of the dirichlet neumann operator that includes an infinitely smoothing tail accounting for the contribution of the bottom we then validate our criterion by comparison with experimental data in two important settings air water interfaces and internal waves the good agreement we observe allows us to discuss the scenario of wave breaking and the behavior of water brine interfaces and to propose a formula for the maximal amplitude of interfacial waves we also show how to rigorously justify two fluid asymptotic models used for applications and how to relate some of their properties to kelvin helmholtz instabilities

global vortex sheet solutions of euler equations in the plane abstract for any curve close enough to a straight line there is a global solution of euler equations having for all positive time a vortex sheet and admitting the given curve as the initial sheet

texture classification using spectral histograms based on a local spatial frequency representation we employ a spectral histogram as a feature statistic for texture classification the spectral histogram consists of marginal distributions of responses of a bank of filters and encodes implicitly the local structure of images through the filtering stage and the global appearance through the histogram stage the distance between two spectral histograms is measured using spl chi sup 2 statistic the spectral histogram with the associated distance measure exhibits several properties that are necessary for texture classification a filter selection algorithm is proposed to maximize classification performance of a given dataset our classification experiments using natural texture images reveal that the spectral histogram representation provides a robust feature statistic for textures and generalizes well comparisons show that our method produces a marked improvement in classification performance finally we point out the relationships between existing texture features and the spectral histogram suggesting that the latter may provide a unified texture feature

filtering for texture classification a comparative study in this paper we review most major filtering approaches to texture feature extraction and perform a comparative study filtering approaches included are laws masks 1980 ring wedge filters dyadic gabor filter banks wavelet transforms wavelet packets and wavelet frames quadrature mirror filters discrete cosine transform eigenfilters optimized gabor filters linear predictors and optimized finite impulse response filters the features are computed as the local energy of the filter responses the effect of the filtering is highlighted keeping the local energy function and the classification algorithm identical for most approaches for reference comparisons with two classical nonfiltering approaches co occurrence statistical and autoregressive model based features are given we present a ranking of the tested approaches based on extensive experiments

local well posedness for fluid interface problems in this paper we prove the local well posedness of the fluid interface problem with surface tension where the velocity fields are not assumed to be irrotational and the fluid domains are not assumed to be simply connected viewed as a lagrangian system with the configuration space being an infinite dimensional manifold possessing many symmetries this problem is reduced to the evolution of the interface determined by its mean curvature and the evolution of the rotational part of the velocity fields determined by the symmetries this framework also applies to several other fluid surface problems which are outlined in the paper

a generalized birkhoff rott equation for two dimensional active scalar problems in this paper we derive evolution equations for the two dimensional active scalar problem when the solution is supported on one dimensional curves these equations are a generalization of the birkhoff rott equation when vorticity is the active scalar the formulation is lagrangian and it is valid for nonlocal kernels bf k that may include both a gradient and an incompressible term we develop a numerical method for implementing the model which achieves second order convergence in space and fourth order in time we verify the model by simulating classic active scalar problems such as the vortex sheet problem in the case of inviscid incompressible flow and the collapse of delta ring solutions in the case of pure aggregation finding excellent agreement we then study two examples with kernels of mixed type i e kernels that contain both incompressible and gradient flows the first example is a vortex density model which arises in superfluids we analyze the effect of the added gradient component

relational queries computable in polynomial time we characterize the polynomial time computable queries as those expressible in relational calculus plus a least fixed point operator and a total ordering on the universe we also show that even without the ordering one application of fixed point suffices to express any query expressible with several alternations of fixed point and negation this proves that the fixed point query hierarchy suggested by chandra and harel collapses at the first fixed point level it is also a general result showing that in finite model theory one application of fixed point suffices

fixed point definability and polynomial time on graphs with excluded minors we give a logical characterization of the polynomial time properties of graphs embeddable in some surface for every surface s a property p of graphs embeddable in s is decidable in polynomial time if and only if it is definable in fixed point logic with counting it is a consequence of this result that for every surface s there is a k such that a simple combinatorial algorithm namely the k dimensional weisfeiler lehman algorithm decides isomorphism of graphs embeddable in s in polynomial time we also present without proof generalizations of these results to arbitrary classes of graphs with excluded minors