analyticity of periodic traveling free surface water waves with vorticity we prove that the prole of a periodic traveling wave propagating at the surface of water above a at bed in a ow with a real analytic vorticity must be real analytic provided the wave speed exceeds the horizontal uid velocity throughout the ow the real analyticity of each streamline be

intrinsic ultracontractivity and eigenfunction estimates for schrodinger operators let d be a domain in rn n 2 and let h h0 v where h0 is a divergence form uniformly elliptic operator with dirichlet boundary conditions and v is in the kato class intrinsic ultracontractivity is proved for the semigroup of h when d is holder domain of order 0 or a uniformly holder domain of order for 0 2 for every 2 there exists a uniformly holder domain of order for which the dirichlet laplacian is not intrinsically ultracontractive for a large class of domains it is shown that the heat kernels for h0 and h decay at the same rate at the boundary applications are given to the lifetime of conditioned brownian motion some of our results seem to be new even for smooth domains

the martin boundary in non lipschitz domains the martin boundary with respect to the laplacian and with respect to uniformly elliptic operators in divergence form can be identified with the euclidean boundary in c domains where x bx loglog 1 x logloglog 1 x b small a counterexample shows that this result is very nearly sharp

approximation of an arbitrary filter and its recursive implementation abstract filtering is one of the important techniques in computer vision it has been widely used in edge detection image restoration range image segmentation etc however the efficient implementation of an arbitrary filter has been a challenging problem until now in this paper a novel method is proposed to implement an arbitrary filter firstly an efficient recursive structure is proposed to implement any polynomial exponential type pet filter the computational complexity and structure are independent of its filter mask size or its bandwidth secondly a new method is proposed lagurre spectrum decomposition method to obtain the pet approximation of any filters as an example the above method is applied to the approximation and implementation of gaussian filters and experiments have shown that a perfect approximation can be obtained with only third order lagurre bases and therefore only a fourth order recursive filter is needed to implement gaussian filters finally the comparison of the present method with the known ones shows that 1 lagurre polynomial bases are orthogonal with each other so the filter approximation is simple 2 the bases are complete and the completeness guarantees the approximation error can be reduced to zero 3 the method can be used to design both gaussian and any other filters

analytic solutions for a stefan problem with gibbs thomson correction we provide existence of a unique smooth solution for a class of oneand two phase stefan problems with gibbs thomson correction in arbitrary space dimensions in addition it is shown that the moving interface depends analytically on the temporal and spatial variables of crucial importance for the analysis is the property of maximal lpregularity for the linearized problem which is fully developed in this paper as well

curvature evolution of nonconvex lens shaped domains we study the curvature flow of planar nonconvex lens shaped domains con sidered as special symmetric networks with two triple junctions we show that the evolv ing domain becomes convex in finite time then it shrinks homothetically to a point as proved in 22 our theorem is the analog of the result of grayson 13 for curvature flow of closed planar embedded curves

a representation for shape based on peaks and ridges in the difference of low pass transform this paper defines a multiple resolution representation for the two dimensional gray scale shapes in an image this representation is constructed by detecting peaks and ridges in the difference of lowpass dolp transform descriptions of shapes which are encoded in this representation may be matched efficiently despite changes in size orientation or position motivations for a multiple resolution representation are presented first followed by the definition of the dolp transform techniques are then presented for encoding a symbolic structural description of forms from the dolp transform this process involves detecting local peaks and ridges in each bandpass image and in the entire three dimensional space defined by the dolp transform linking adjacent peaks in different bandpass images gives a multiple resolution tree which describes shape peaks which are local maxima in this tree provide landmarks for aligning manipulating and matching shapes detecting and linking the ridges in each dolp bandpass image provides a graph which links peaks within a shape in a bandpass image and describes the positions of the boundaries of the shape at multiple resolutions detecting and linking the ridges in the dolp three space describes elongated forms and links the largest peaks in the tree the principles for determining the correspondence between symbols in pairs of such descriptions are then described such correspondence matching is shown to be simplified by using the correspondence at lower resolutions to constrain the possible correspondence at higher resolutions

frequency domain analysis and synthesis of image pyramid generating kernels construction of image pyramids is described as a two di mensional decimation process frequently employed generating kernels are compared to the optimal kernel that assures minimal information loss after the resolution reduction i e the one corresponding to an ideal low pass filter physically realizable optimal generating kernels are presented the amount of computation required for generation of the image pyramid can be reduced significantly by employing half band filters as components of the optimal kernel image pyramids generated by the optimal kernel show a better command of details than the ones generated by a simple 4 4 averaging or a computationally equivalent kernel

on the quasi geostrophic equations on compact closed surfaces in r3 abstract the quasi geostrophic equations on compact surfaces in r 3 without boundary are studied by means of the theory of quasi linear parabolic evolution equations based on maximal l p regularity it is shown that the problem is globally strongly well posed in l q the solutions regularize instantly and form a global semiflow in the proper state manifold and as time goes to infinity a solution converges exponentially to a constant in the topology of the state space

on minimal parabolic functions and time homogeneous parabolic h transforms burdzy was supported in part by nsf grant dms 9700721 saliosbury was supported in part by a grant from nserc a portion of this research took place during his stay at the fields institute

a short proof of boundary harnack principle abstract we give a direct analytic proof of the classical boundary harnack principle for solutions to linear uniformly elliptic equations in either divergence or non divergence form

nonlinear analytic semiflows in this paper a local existence and regularity theory is given for nonlinear parabolic initial value problems x t f x t and quasilinear initial value problems x t a x t x t f x t this theory extends the theory of daprato and grisvard of 1979 and shows how various properties like analyticity of solutions can be derived as a direct corollary of the existence theorem

well posedness and stability results for a quasilinear periodic muskat problem abstract we study the muskat problem describing the spatially periodic motion of two fluids with equal viscosities under the effect of gravity in a vertical unbounded two dimensional geometry we first prove that the classical formulation of the problem is equivalent to a nonlocal and nonlinear evolution equation expressed in terms of singular integrals and having only the interface between the fluids as unknown secondly we show that this evolution equation has a quasilinear structure which is at a formal level not obvious and we also disclose the parabolic character of the equation exploiting these aspects we establish the local well posedness of the problem for arbitrary initial data in h s s with s 3 2 2 determine a new criterion for the global existence of solutions and uncover a parabolic smoothing property besides we prove that the zero steady state solution is exponentially stable

application of scale space to image coding the continuous formulation of scale space is briefly reviewed it is shown that deriving a discrete formulation of scale space requires the solution to a more general problem the optimum approximation of a signal by local patterns the consequences of the theory for the laplacian image pyramid are discussed a pyramid coding scheme based on the discrete scale space formulation is derived preliminary coding results on real images are presented down to 1 b pixel the quality of the coded images is usually very close to that of the originals bit rates below 0 5 b pixel imply a too coarse quantization or even deletion of the prediction error image at the smallest scale and consequently always result in images that are noticeably unsharp in the intermediate region different degrees of quantization noise and unsharpness are present at comparable data rates the linear variation coder generates less quantization noise in uniform regions while the scale space coder gives a slightly better edge reproduction

a center manifold analysis for the mullins sekerka model abstract the mullins sekerka model is a nonlocal evolution model for hypersurfaces which arises as a singular limit for the cahn hilliard equation we show that classical solutions exist globally and tend to spheres exponentially fast provided that they are close to a sphere initially our analysis is based on center manifold theory and on maximal regularity

scale space derived from b splines this paper proposes a scale space theory based on b spline kernels our aim is twofold 1 present a general framework and show how b splines provide a flexible tool to design various scale space representations in particular we focus on the design of continuous scale space and dyadic scale space frame representations a general algorithm is presented for fast implementation of continuous scale space at rational scales in the dyadic case efficient frame algorithms are derived using b spline techniques to analyze the geometry of an image the relationship between several scale space approaches is explored the behavior of edge models the properties of completeness causality and other properties in such a scale space representation are examined in the framework of b splines it is shown that besides the good properties inherited from the gaussian kernel the b spline derived scale space exhibits many advantages for modeling visual mechanism including the efficiency compactness orientation feature and parallel structure

lifetimes of conditioned diffusions we investigate when an upper bound on expected lifetimes of conditioned diffusions associated with elliptic operators in divergence and non divergence form can be found the critical value of the parameter is found for each of the following classes of domains l p domains p n 1 uniformly regular twistedl p domains p n 1 and twisted holder domains 1 3 a related parabolic boundary harnack principle is proved

the heat equation shrinks ising droplets to points let d be a bounded smooth enough domain of r 2 for l 0 consider the continuous time zero temperature heat bath dynamics for the nearest neighbor ising model on z l 2 the square lattice with lattice spacing 1 l with initial condition such that sigma x 1 if x in d and sigma x otherwise we prove the following classical conjecture due to h spohn in the diffusive limit where time is rescaled by l 2 and l tends to infinity the boundary of the droplet of spins follows a deterministic anisotropic curve shortening flow such that the normal velocity is given by the local curvature times an explicit function of the local slope locally in a suitable reference frame the evolution of the droplet boundary follows the one dimensional heat equation to our knowledge this is the first proof of mean curvature type droplet shrinking for a lattice model with genuine microscopic dynamics an important ingredient is our recent work where the case of convex d was solved the other crucial point in the proof is obtaining precise regularity estimates on the deterministic curve shortening flow this builds on geometric and analytic ideas of grayson gage hamilton gage li chou zhu and others

recursive regularization filters design properties and applications least squares approximation problems that are regularized with specified highpass stabilizing kernels are discussed for each problem there is a family of discrete regularization filters r filters which allow an efficient determination of the solutions these operators are stable symmetric lowpass filters with an adjustable scale factor two decomposition theorems for the z transform of such systems are presented one facilitates the determination of their impulse response while the other allows an efficient implementation through successive causal and anticausal recursive filtering a case of special interest is the design of r filters for the first and second order difference operators these results are extended for two dimensional signals and for illustration purposes are applied to the problem of edge detection this leads to a very efficient implementation 8 multiplies 10 adds per pixel of the optimal canny edge detector based on the use of a separable second order r filter

optical flow a curve evolution approach a novel approach for the computation of optical flow based on an l sup 1 type minimization is presented it is shown that the approach has inherent advantages since it does not smooth the flow velocity across the edges and hence preserves edge information a numerical approach based on computation of evolving curves is proposed for computing the optical flow field computations are carried out on a number of real image sequences in order to illustrate the theory as well as the numerical approach

on the affine heat equation for non convex curves 1998 american mathematical society first published in journal of the american mathematical society vol 11 no 3 july 1998 published by the american mathematical society

image representations using multiscale differential operators differential operators have been widely used for multiscale geometric descriptions of images the efficient computation of these differential operators is always desirable moreover it has not been clear whether such representations are invertible for certain applications it is usually required that such representations should be invertible so that one can facilitate the processing of information in the transform domain and then recover it in this paper such problems are studied we consider multiscale differential representations of images using different types of operators such as the directional derivative operators and laplacian operators in particular we provide a general approach to represent images by their multiscale and multidirectional derivative components for practical implementation efficient pyramid like algorithms are derived using the spline technique for both the the composition and reconstruction of images it is shown that using these representations various meaningful geometric information of images can be extracted at multiple scales therefore these representations can be used for edge based image processing purposes furthermore the intrinsic relationships of the proposed representations with the compact wavelet models and some classical multiscale approaches are also elucidated in the paper

multiple resolution representation and probabilistic matching of 2 d gray scale shape one approach to pattern classification is to match a structural description of a pattern to models which describe the structural properties of pattern classes the central problem in structural pattern matching is to determine the correspondence between the symbols which comprise a model and symbols which describe a pattern the difficulty of determining this correspondence depends critically on the representation that is used to describe patterns this correspondence presents a probabilistic representation for structural models of pattern classes both pattern descriptions and models for pattern classes are based on symbols which represent grayscale information at multiple resolutions a pattern description is given by a tree of symbols with attribute values structural models are represented by a tree of symbols with probabilistic attributes the position and scale resolution of the symbols as well as other features are represented by these attributes an algorithm is presented for determining the correspondence between symbols in a description of a pattern and symbols in a model of a pattern class this algorithm uses the connectivity between symbols at different scales to constrain the search for correspondence an interactive training program for learning models of pattern classes is described and some conclusions from the work are presented

a stable manifold theorem for the curve shortening equation on presente une famille de solutions homothetiques de l equation pour une courbe planaire x kn et on demontre l existence de varietes non lineaires stables et instables autour de telles solutions

cyclic schemes for pde based image analysis we investigate a class of efficient numerical algorithms for many partial differential equations pdes in image analysis they are applicable to parabolic or elliptic pdes that have bounded coefficients and lead to space discretisations with symmetric matrices our schemes are easy to implement and well suited for parallel implementations on gpus since they are based on the explicit diffusion scheme in the parabolic case and the jacobi method in the elliptic case by supplementing these methods with cyclically varying time step sizes or relaxation parameters we achieve efficiency gains of several orders of magnitude we call the resulting algorithms fast explicit diffusion fed and fast jacobi fj methods to achieve a good compromise between efficiency and accuracy we show that one should use parameter cycles that result from factorisations of box filters for these cycles we establish stability results in the euclidean norm our schemes perform favourably in a number of applications including isotropic nonlinear diffusion filters with widely varying diffusivities as well as anisotropic diffusion methods for image filtering inpainting and regularisation in computer vision moreover they are equally suited for higher dimensional problems as well as higher order pdes and they can also be interpreted as efficient first order methods for smooth optimisation problems

front propagation and phase field theory the connection between the weak theories for a class of geometric equations and the asymptotics of appropriately rescaled reaction diffusion equations is rigorously established two different scalings are studied in the first the limiting geometric equation is a first order equation in the second it is a generalization of the mean curvature equation intrinsic definitions for the geometric equations are obtained and uniqueness under a geometric condition on the initial surface is proved in particular in the case of the mean curvature equation this condition is satisfied by surfaces that are strictly starshaped that have positive mean curvature or that satisfy a condition that interpolates between the positive mean curvature and the starshape conditions

boundary harnack principle for symmetric stable processes in this paper we study potential theoretic properties of the symmetric stable processes 0 2 establishing the boundary harnack principle for ratios of harmonic functions on any open sets identifying the martin boundary with the euclidean boundary for open sets with a certain interior fatness property and extending earlier results on intrinsic ultracontractivity and the conditional gauge theorem to certain open sets

multiphase thermomechanics with interfacial structure 2 evolution of an isothermal interface paper 1 1988 g 1 of this series began an investigation whose goal is a thermomechanics of two phase continua based on gibbs s notion of a sharp phase interface endowed with thermomechanical structure in that paper a balance law balance of capillary forces was introduced and then applied in conjunction with suitable statements of the first two laws of thermodynamics the chief results are thermodynamic restrictions on constitutive equations exact and approximate free boundary conditions at the interface and a hierarchy of free boundary problems the simplest versions of these problems the mullins sekerka problems are essentially the classical stefan problem with the free boundary condition u 0 for the temperature replaced by the condition u h k where k is the curvature of the free boundary and h 0 is a material constant this dependence on curvature renders the problem difficult and apart from numerical studies involving linearization stability there are almost no supporting theoretical results

efficient synthesis of gaussian filters by cascaded uniform filters gaussian filtering is an important tool in image processing and computer vision in this paper we discuss the background of gaussian filtering and look at some methods for implementing it consideration of the central limit theorem suggests using a cascade of simple filters as a means of computing gaussian filters among simple filters uniform coefficient finite impulse response digital filters are especially economical to implement the idea of cascaded uniform filters has been around for a while 13 16 we show that this method is economical to implement has good filtering characteristics and is appropriate for hardware implementation we point out an equivalence to one of burt s methods 1 3 under certain circumstances as an extension we describe an approach to implementing a gaussian pyramid which requires approximately two addition operations per pixel per level per dimension we examine tradeoffs in choosing an algorithm for gaussian filtering and finally discuss an implementation

fast convolution with laplacian of gaussian masks we present a technique for computing the convolution of an image with log laplacian of gaussian masks it is well known that a log of variance a can be decomposed as a gaussian mask and a log of variance 1 we take advantage of the specific spectral characteristics of these filters in our computation the log is a bandpass filter we can therefore fold the spectrum of the image after low pass filtering without loss of information which is equivalent to reducing the resolution we present a complete evaluation of the parameters involved together with a complexity analysis that leads to the paradoxical result that the computation time decreases when increases we illustrate the method on two images

dynamic active contours for visual tracking visual tracking using active contours is usually set in a static framework the active contour tracks the object of interest in a given frame of an image sequence a subsequent prediction step ensures good initial placement for the next frame this approach is unnatural the curve evolution gets decoupled from the actual dynamics of the objects to be tracked true dynamical approaches exist all being marker particle based and thus prone to the shortcomings of such particle based implementations in particular topological changes are not handled naturally in this framework the now classical level set approach is tailored for evolutions of manifolds of codimension one however dynamic curve evolution is at least a codimension two problem we propose an efficient level set based approach for dynamic curve evolution which addresses the artificial separation of segmentation and prediction while retaining all the desirable properties of the level set formulation it is based on a new energy minimization functional which for the first time puts dynamics into the geodesic active contour framework

regularity of solutions to a free boundary problem modeling tumor growth by stokes equation in this paper we investigate regularity of solutions to a free boundary problem modeling tumor growth in fluid like tissues the model equations include a quasi stationary diffusion equation for the nutrient concentration and a stokes equation with a source representing the proliferation density of the tumor cells subject to a boundary condition with stress tensor effected by surface tension this problem is a fully nonlinear problem involving nonlocal terms based on the employment of the functional analytic method and the theory of maximal regularity we prove that the free boundary of this problem is real analytic in temporal and spatial variables for initial data of less regularity

existence of analytic solutions for the classical stefan problem we prove that under mild regularity assumptions on the initial data the two phase classical stefan problem admits a unique solution that is analytic in space and time

fast computation of the difference of low pass transform this paper defines the difference of low pass dolp transform and describes a fast algorithm for its computation the dolp is a reversible transform which converts an image into a set of bandpass images a dolp transform is shown to require o n2 multiplies and produce o n log n samples from an n sample image when gaussian low pass filters are used the result is a set of images which have been convolved with difference of gaussian dog filters from an exponential set of sizes a fast computation technique based on resampling is described and shown to reduce the dolp transform complexity to o n log n multiplies and o n storage locations a second technique cascaded convolution with expansion is then defined and also shown to reduce the computational cost to o n log n multiplies combining these two techniques yields an algorithm for a dolp transform that requires o n storage cells and requires o n multiplies

no triple point of planar brownian motion is accessible burdzy s research supported in part by nsf grant dms 9322689 and ams centennial research fellowship werner s research supported by an eec hcm leibniz fellowship

the heat equation shrinks embedded plane curves to round points soit c 0 s 1 r 2 une courbe lisse plongee dans le plan alors c s 1 0 t r 2 existe en satisfaisant c t k n ou k est la courbure de c et n est son vecteur unite normal entrant c t est lisse pour tout t il converge vers un point quand t t et sa forme limite quand t t est un cercle rond avec convergence dans norme c

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

curve shortening and the topology of closed geodesics on surfaces we study flat knot types of geodesics on compact surfaces m2 for every flat knot type and any riemannian metric g we introduce a conley index associated with the curve shortening flow on the space of immersed curves on m2 we conclude existence of closed geodesics with prescribed flat knot types provided the associated conley index is nontrivial

image filtering using multiresolution representations it is shown how multiresolution representations can be used for filter design and implementation these representations provide a coarse frequency decomposition of the image which forms the basis for two filtering techniques the first method based on image pyramids is used for approximating the convolution of an image with a given mask in this technique a filter is designed using a least squares procedure based on filters synthesized from the basic pyramid equivalent filters the second method is an adaptive noise reduction algorithm an optimally filtered image is synthesized from the multiresolution levels which in this case are maintained at the original sampling density individual pixels of the image representation are linearly combined under a minimum mean square error criterion this uses a local signal to noise ratio estimate to provide the best compromise between noise removal and resolution loss

symmetry groups and separation of variables of a class of nonlinear diffusion convection equations in this paper a class of nonlinear diffusion convection equations ut d u uxn x p u ux which has quite a large number of physical applications is analysed by using symmetry group methods which include the classical method the potential symmetry method and the generalized conditional symmetry method a complete classification of the functional forms of the diffusion and convection coefficients is presented when the equation admits lie s point symmetry groups and potential symmetry groups the separation of variables for the equation is investigated using the generalized conditional symmetry approach for some interesting cases exact solutions using the method of separation of variables are discussed in detail

parabolic equations for curves on surfaces part i curves with p integrable curvature this is the first of a two part paper in which we develop a theory of parabolic equations for curves on surfaces which can be applied to the so called curve shortening of flow by mean curvature problem as well as to a number of models for phase transitions in two dimensions we introduce a class of equations for which the initial value problem is solvable for initial data with p integrable curvature and we also give estimates for the rate at which the p norms of the curvature must blow up if the curve becomes singular in finite time a detailed discussion of the way in which solutions can become singular and a method for continuing the solution through a singularity will be the subject of the second part

the heat equation shrinking convex plane curves soient m et m des varietes de riemann et f m m une application reguliere si m est une courbe convexe plongee dans le plan r 2 l equation de la chaleur contracte m a un point

holder domains and the boundary harnack principle the constant c depends on l only through the constant cl defined in 1 below of course c also depends on d v and k the above result shows that the boundary harnack principle holds in all holder domains it was first proven for the range 1 2 1 by bass and burdzy 1990a theorems 3 5 and 4 5 it was subsequently extended by banuelos unpublished to the full range of provided the domain also satisfies a uniform capacity condition on the boundary in banuelos 1990 a class of domains called uniformly holder domains of order was introduced a boundary harnack principle may be obtained for such domains for all 0 1 by a variation of the proof of theorem 1 in order to make this note compact we refer

evolution of plane curves driven by a nonlinear function of curvature and anisotropy in this paper we study evolution of plane curves satisfying a geometric equation v beta k nu where v is the normal velocity and k and nu are the curvature and tangential angle of a plane curve gamma we follow the direct approach and we analyze the so called intrinsic heat equation governing the motion of plane curves obeying such a geometric equation the intrinsic heat equation is modified to include an appropriate nontrivial tangential velocity functional alpha we show how the presence of a nontrivial tangential velocity can prevent numerical solutions from forming various instabilities from an analytical point of view we present some new results on short time existence of a regular family of evolving curves in the degenerate case when beta k nu gamma nu k m 0 m le 2 and the governing system of equations includes a nontrivial tangential velocity functional

the hermite transform theory the author introduces a scheme for the local processing of visual information called the hermite transform the problem is addressed from the point of view of image coding and therefore the scheme is presented as an analysis resynthesis system the objectives of the present work however are not restricted to coding the analysis part is designed so that it can also serve applications in the area of computer vision indeed derivatives of gaussians which have found widespread application in feature detection over the past few years play a central role in the hermite analysis it is also argued that the proposed processing scheme is in close agreement with current insight into the image processing that is carried out by the human visual system in particular it is demonstrated that the hermite transform is in better agreement with human visual modeling than gabor expansions

symmetries and invariant solutions for the geometric heat flows we study lie symmetries and invariant solutions of the geometric heat flows the basic similarity reductions for the ghe are performed reduced equations and exact solutions associated with the symmetries are obtained group invariant solutions and reductions for the affine case are also discussed in a special case

finite time singularities for lagrangian mean curvature flow given any embedded lagrangian on a four dimensional compact calabi yau we find another lagrangian in the same hamiltonian isotopy class that develops a finite time singularity under mean curvature flow this contradicts a weaker version of the thomas yau conjecture regarding long time existence and convergence of lagrangian mean curvature flow

a boundary harnack principle in twisted holder domains the boundary harnack principle for the ratio of positive harmonic functions is shown to hold in twisted holder domains of order a for a e 1 2 1 for each a e 0 1 2 there exists a twisted h6lder domain of order a for which the boundary harnack principle fails extensions are given to l harmonic

on optimal infinite impulse response edge detection filters the authors outline the design of an optimal computationally efficient infinite impulse response edge detection filter the optimal filter is computed based on canny s high signal to noise ratio good localization criteria and a criterion on the spurious response of the filter to noise an expression for the width of the filter which is appropriate for infinite length filters is incorporated directly in the expression for spurious responses the three criteria are maximized using the variational method and nonlinear constrained optimization the optimal filter parameters are tabulated for various values of the filter performance criteria a complete methodology for implementing the optimal filter using approximating recursive digital filtering is presented the approximating recursive digital filter is separable into two linear filters operating in two orthogonal directions the implementation is very simple and computationally efficient has a constant time of execution for different sizes of the operator and is readily amenable to real time hardware implementation

homogenization limit of a parabolic equation with nonlinear boundary conditions abstract consider the parabolic equation e u t a u x u x x f u x 1 x 1 t 0 with nonlinear boundary conditions u x 1 t g u 1 t e nbc u x 1 t g u 1 t e where e 0 is a parameter g is a function which takes values near its supremum frequently each almost periodic function is a special example of g we consider a time global solution u e of e nbc and show that its homogenization limit as e 0 is the solution of e with linear boundary conditions lbc x 1 t sup g x 1 t sup g provided moves upward monotonically when g is almost periodic lou preprint 21 obtained the unique almost periodic traveling wave u e of e nbc this paper proves that the homogenization limit of u e is a classical traveling wave of e lbc

sparse representation for coarse and fine object recognition this paper offers a sparse multiscale representation of objects it captures the object appearance by selection from a very large dictionary of gaussian differential basis functions the learning procedure results from the matching pursuit algorithm while the recognition is based on polynomial approximation to the bases turning image matching into a problem of polynomial evaluation the method is suited for coarse recognition between objects and by adding more bases also for fine recognition of the object pose the advantages over the common representation using pca include storing sampled points for recognition is not required adding new objects to an existing data set is trivial because retraining other object models is not needed and significantly in the important case where one has to scan an image over multiple locations in search for an object the new representation is readily available as opposed to pca projection at each location the experimental result on the coil 100 data set demonstrates high recognition accuracy with real time performance