the first nontrivial eigenvalue for a system of p laplacians with neumann and dirichlet boundary conditions we deal with the first eigenvalue for a system of two pp laplacians with dirichlet and neumann boundary conditions if pw div w p 2 w pw div w p 2 w stands for the pp laplacian and p q 1 we consider pu u 2u v in qv u v 2v in with mixed boundary conditions u 0 v q 2 v 0 on we show that there is a first non trivial eigenvalue that can be characterized by the variational minimization problem p q min u ppdx v qqdx u v dx u v ap q where ap q u v w01 p w1 q uv 0 and u v 2vdx 0 we also study the limit of p q as p q p q assuming that p 0 1 and qp q 0 as p q p q we find that this limit problem interpolates between the pure dirichlet and neumann cases for a single equation when we take q 1q 1 and the limits 1 1 and 0 0

understanding optimising and extending data compression with anisotropic diffusion galic et al journal of mathematical imaging and vision 31 255 269 2008 have shown that compression based on edge enhancing anisotropic diffusion eed can outperform the quality of jpeg for medium to high compression ratios when the interpolation points are chosen as vertices of an adaptive triangulation however the reasons for the good performance of eed remained unclear and they could not outperform the more advanced jpeg 2000 the goals of the present paper are threefold firstly we investigate the compression qualities of various partial differential equations this sheds light on the favourable properties of eed in the context of image compression secondly we demonstrate that it is even possible to beat the quality of jpeg 2000 with eed if one uses specific subdivisions on rectangles and several important optimisations these amendments include improved entropy coding brightness and diffusivity optimisation and interpolation swapping thirdly we demonstrate how to extend our approach to 3 d and shape data experiments on classical test images and 3 d medical data illustrate the high potential of our approach

euler s elastica and curvature based inpainting image inpainting is a special image restoration problem for which image prior models play a crucial role euler s elastica was first introduced to computer vision by mumford algebraic geometry and its applications springer verlag new york 1994 pp 491 506 as a curve prior model by functionalizing the elastica energy masnou and morel proceedings of the 5th ieee international conference image processing 3 1998 pp 259 263 proposed an elastica based variational inpainting model the current paper is intended to contribute to the development of its mathematical foundation and the study of its properties and connections to the earlier works of bertalmio sapiro caselles and ballester siggraph 2000 acm press new york 2000 and chan and shen j visual comm image rep 12 2001 pp 436 449 a computational scheme based on numerical pdes is presented which allows the automatic handling of topologically complex inpainting domains

polynomial modeling for time varying systems based on a particle swarm optimization algorithm in this paper an effective particle swarm optimization pso is proposed for polynomial models for time varying systems the basic operations of the proposed pso are similar to those of the classical pso except that elements of particles represent arithmetic operations and variables of time varying models the performance of the proposed pso is evaluated by polynomial modeling based on various sets of time invariant and time varying data results of polynomial modeling in time varying systems show that the proposed pso outperforms commonly used modeling methods which have been developed for solving dynamic optimization problems including genetic programming gp and dynamic gp an analysis of the diversity of individuals of populations in the proposed pso and gp reveals why the proposed pso obtains better results than those obtained by gp

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

geodesic matting a framework for fast interactive image and video segmentation and matting an interactive framework for soft segmentation and matting of natural images and videos is presented in this paper the proposed technique is based on the optimal linear time computation of weighted geodesic distances to user provided scribbles from which the whole data is automatically segmented the weights are based on spatial and or temporal gradients considering the statistics of the pixels scribbled by the user without explicit optical flow or any advanced and often computationally expensive feature detectors these could be naturally added to the proposed framework as well if desired in the form of weights in the geodesic distances an automatic localized refinement step follows this fast segmentation in order to further improve the results and accurately compute the corresponding matte function additional constraints into the distance definition permit to efficiently handle occlusions such as people or objects crossing each other in a video sequence the presentation of the framework is complemented with numerous and diverse examples including extraction of moving foreground from dynamic background in video natural and 3d medical images and comparisons with the recent literature

the infinity laplacian with a transport term abstract we consider the following problem given a bounded domain r n and a vector field r n find a solution to u d u 0 in u f on where is the 1 homogeneous infinity laplace operator that is formally given by u d 2 u d u d u d u d u and f a lipschitz boundary datum if we assume that is a continuous gradient vector field then we obtain the existence and uniqueness of a viscosity solution by an l p approximation procedure also we prove the stability of the unique solution with respect to in addition when is more regular lipschitz continuous but not necessarily a gradient using tug of war games we prove that this problem has a solution

smart nonlinear diffusion a probabilistic approach in this paper a stochastic interpretation of nonlinear diffusion equations used for image filtering is proposed this is achieved by relating the problem of evolving smoothing images to that of tracking the transition probability density functions of an underlying random process we show that such an interpretation of e g perona malik equation in turn allows additional insight and sufficient flexibility to further investigate some outstanding problems of nonlinear diffusion techniques in particular upon unraveling the limitations as well as the advantages of such an equation we are able to propose a new approach which is demonstrated to improve performance over existing approaches and more importantly to lift the longstanding problem of a stopping criterion for a nonlinear evolution equation with no data term constraint substantiating examples in image enhancement and segmentation are provided

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

scaling theorems for zero crossings we characterize some properties of the zero crossings of the laplacian of signals in particular images filtered with linear filters as a function of the scale of the filter extending recent work by witkin 16 we prove that in any dimension the only filter that does not create generic zero crossings as the scale increases is the gaussian this result can be generalized to apply to level crossings of any linear differential operator it applies in particular to ridges and ravines in the image intensity in the case of the second derivative along the gradient there is no filter that avoids creation of zero crossings unless the filtering is performed after the derivative is applied

infinity laplacian equation with strong absorptions abstract we study regularity properties of solutions to reaction diffusion equations ruled by the infinity laplacian operator we focus our analysis in models presenting plateaus i e regions where a non negative solution vanishes identically we obtain sharp geometric regularity estimates for solutions along the boundary of plateaus sets in particular we show that the n hausdorff measure of the plateaus boundary is finite for a universal number 0

on the impact of anisotropic diffusion on edge detection content aware edge preserving smoothing techniques have gained visibility in recent years however they have had a rather limited impact on the edge detection literature compared to content unaware linear techniques often based on gaussian filters in this work we focus on anisotropic diffusion covering its initial definition by perona and malik and subsequent extensions a visual case study is used to illustrate their features we perform a quantitative evaluation of the performance of the canny method for edge detection when substituting linear gaussian smoothing filters by anisotropic diffusion highlightsreviewing the main trends in anisotropic diffusion identifying the practical scenarios on which anisotropic diffusion fails quantifying the improvement of edge detection when anisitropic diffusion is applied

absolutely minimal lipschitz extension of tree valued mappings we prove that every lipschitz function from a subset of a locally compact length space to a metric tree has a unique absolutely minimal lipschitz extension amle we relate these extensions to a stochastic game called politics a generalization of a game called tug of war that has been used in peres et al j am math soc 22 1 167 210 2009 to study real valued amles

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

the behaviour of the p x laplacian eigenvalue problem as p x abstract in this paper we study the behaviour of the solutions to the eigenvalue problem corresponding to the p x laplacian operator div u p x 2 u p x u p x 2 u in u 0 on as p x we consider a sequence of functions p n x that goes to infinity uniformly in under adequate hypotheses on the sequence p n namely that the limits ln p n x x and p n n x q x exist we prove that the corresponding eigenvalues p n and eigenfunctions u p n verify that p n 1 n u p n u uniformly in where u is a nontrivial viscosity solution of the following problem min u u 2 log u u u q u q 0 in u 0 on

variable exponent linear growth functionals in image restoration we study a functional with variable exponent 1 leq p x leq 2 which provides a model for image denoising enhancement and restoration the diffusion resulting from the proposed model is a combination of total variation tv based regularization and gaussian smoothing the existence uniqueness and long time behavior of the proposed model are established experimental results illustrate the effectiveness of the model in image restoration

morphological filters part i their set theoretic analysis and relations to linear shift invariant filters this paper examines the set theoretic interpretation of morphological filters in the framework of mathematical morphology and introduces the representation of classical linear filters in terms of morphological correlations which involve supremum infimum operations and additions binary signals are classified as sets and multilevel signals as functions two set theoretic representations of signals are reviewed filters are classified as set processing sp or function processing fp conditions are provided for certain fp filters that pass binary signals to commute with signal thresholding because then they can be analyzed and implemented as sp filters the basic morphological operations of set erosion dilation opening and closing are related to minkowski set operations and are used to construct fp morphological filters emphasis is then given to analytically and geometrically quantifying the similarities and differences between morphological filtering of signals by sets and functions the latter case allows the definition of morphological convolutions and correlations toward this goal various properties of fp morphological filters are also examined linear shift invariant filters due to their translation invariance are uniquely characterized by their kernel which is a special collection of input signals increasing linear filters are represented as the supremum of erosions by their kernel functions if the filters are also discrete and have a finite extent impulse response they can be represented as the supremum of erosions only by their minimal with respect to a signal ordering kernel functions stable linear filters can be represented as the sum of at most two weighted suprema of erosions these results demonstrate the power of mathematical morphology as a unifying approach to both linear and nonlinear signal shaping strategies

an axiomatic approach to image interpolation we discuss possible algorithms for interpolating data given in a set of curves and or points in the plane we propose a set of basic assumptions to be satisfied by the interpolation algorithms which lead to a set of models in terms of possibly degenerate elliptic partial differential equations the absolute minimal lipschitz extension model amle is singled out and studied in more detail we show experiments suggesting a possible application the restoration of images with poor dynamic range

effect of perceptually irrelevant variance in head related transfer functions on principal component analysis the significant amount of variance in head related transfer functions hrtfs resulting from source location and subject dependencies have led researchers to use principal components analysis pca to approximate hrtfs with a small set of basis functions pca minimizes a mean square error and consequently may spend modeling effort on perceptually irrelevant properties to investigate the extent of this effect pca performance was studied before and after removal of perceptually irrelevant variance the results indicate that from the sixth pca component onward a substantial amount of perceptually irrelevant variance is being accounted for

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

on edge detection edge detection is the process that attempts to characterize the intensity changes in the image in terms of the physical processes that have originated them a critical intermediate goal of edge detection is the detection and characterization of significant intensity changes this paper discusses this part of the edge detection problem to characterize the types of intensity changes derivatives of different types and possibly different scales are needed thus we consider this part of edge detection as a problem in numerical differentiation we show that numerical differentiation of images is an ill posed problem in the sense of hadamard differentiation needs to be regularized by a regularizing filtering operation before differentiation this shows that this part of edge detection consists of two steps a filtering step and a differentiation step following this perspective the paper discusses in detail the following theoretical aspects of edge detection 1 the properties of different types of filters with minimal uncertainty with a bandpass spectrum and with limited support are derived minimal uncertainty filters optimize a tradeoff between computational efficiency and regularizing properties 2 relationships among several 2 d differential operators are established in particular we characterize the relation between the laplacian and the second directional derivative along the gradient zero crossings of the laplacian are not the only features computed in early vision 3 geometrical and topological properties of the zero crossings of differential operators are studied in terms of transversality and morse theory

the behavior of solutions to an elliptic equation involving a p laplacian and a q laplacian for large p in this paper we study the behavior as p of solutions up q to pu qu 0 in a bounded smooth domain with a lipschitz dirichlet boundary datum u g on we find that there is a uniform limit of a subsequence of solutions that is there is pj such that upj q u uniformly in and we prove that this limit u is a solution to a variational problem that when the lipschitz constant of the boundary datum is less than or equal to one is given by the minimization of the lq norm of the gradient with a pointwise constraint on the gradient in addition we show that the limit is a viscosity solution to a limit pde problem that involves the q laplacian and the laplacian

compression of head related transfer function using autoregressive moving average models and legendre polynomials head related transfer functions hrtfs are generally large datasets which can be an important constraint for embedded real time applications a method is proposed here to reduce redundancy and compress the datasets in this method hrtfs are first compressed by conversion into autoregressive moving average arma filters whose coefficients are calculated using prony s method such filters are specified by a few coefficients which can generate the full head related impulse responses hrirs next legendre polynomials lps are used to compress the arma filter coefficients lps are derived on the sphere and form an orthonormal basis set for spherical functions higher order lps capture increasingly fine spatial details the number of lps needed to represent an hrtf therefore is indicative of its spatial complexity the results indicate that compression ratios can exceed 98 while maintaining a spectral error of less than 4 db in the recovered hrtfs

how to choose interpolation data in images we introduce and discuss shape based models for finding the best interpolation data when reconstructing missing regions in images by means of solving the laplace equation the shape analysis is done in the framework of gamma convergence from two different points of view first we propose a continuous pde model and get pointwise information on the importance of each pixel by a topological asymptotic method second we introduce a finite dimensional setting into the continuous model based on fat pixels balls with positive radius and study by gamma convergence the asymptotics when the radius vanishes in this way we obtain relevant information about the optimal distribution of the best interpolation pixels we show that the resulting optimal data sets are identical to sets that can also be motivated using level set ideas and approximation theoretic considerations numerical computations are presented that confirm the usefulness of our theoretical findings for pde based image compression

perceptual color correction through variational techniques in this paper we present a discussion about perceptual based color correction of digital images in the framework of variational techniques we propose a novel image functional whose minimization produces a perceptually inspired color enhanced version of the original the variational formulation permits a more flexible local control of contrast adjustment and attachment to data we show that a numerical implementation of the gradient descent technique applied to this energy functional coincides with the equation of automatic color enhancement ace a particular perceptual based model of color enhancement moreover we prove that a numerical approximation of the euler lagrange equation reduces the computational complexity of ace from o n2 to o nlogn where n is the total number of pixels in the image

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

a new interpretation and improvement of the nonlinear anisotropic diffusion for image enhancement the purpose of the article is to give an analysis of the anisotropic diffusion ad and propose adaptive nonlinear filtering based on a judicious choice of the conductance function cf and the edgeness threshold a new undesirable effect which we call the pinhole effect may result when ad is introduced for the first time a robust solution to this effect is proposed and evaluated through experimental data the evolution of the diffused signal is analyzed through a physical model using the optical flow technique oft the overall strategy is evaluated through experimental results obtained on synthetic and actual images

a novel pde based image restoration convection diffusion equation for image denoising in this paper we present a convection diffusion equation for processing image denoising edge preservation and compression we compare it with a popular nonlinear diffusion model which has been widely implemented in image denoising for gaussian white noise here we show that this convection diffusion model effectively removes noise especially for the mixture of gaussian and salt and pepper noises we propose the modified streamline diffusion method y shih h c elman modified streamline diffusion schemes for convection diffusion problems comput methods appl mech eng 1998 for the discretization of this convection diffusion model to prevent internal layers because of the discontinuities while using the coarsening algorithm for the image compression numerical experiments have shown that our convection diffusion model for removing both gaussian and salt and pepper noises efficiently and reliably preserves edges quite satisfactorily

memetic multiobjective particle swarm optimization based radial basis function network for classification problems this paper presents a new multiobjective evolutionary algorithm applied to a radial basis function rbf network design based on multiobjective particle swarm optimization augmented with local search features the algorithm is named the memetic multiobjective particle swarm optimization rbf network mpson because it integrates the accuracy and structure of an rbf network the proposed algorithm is implemented on two class and multiclass pattern classification problems with one complex real problem the experimental results indicate that the proposed algorithm is viable and provides an effective means to design multiobjective rbf networks with good generalization capability and compact network structure the accuracy and complexity of the network obtained by the proposed algorithm are compared with the memetic non dominated sorting genetic algorithm based rbf network mgan through statistical tests this study shows that mpson generates rbf networks coming with an appropriate balance between accuracy and simplicity outperforming the other algorithms considered

color image enhancement via chromaticity diffusion a novel approach for color image denoising is proposed in this paper the algorithm is based on separating the color data into chromaticity and brightness and then processing each one of these components with partial differential equations or diffusion flows in the proposed algorithm each color pixel is considered as an n dimensional vector the vectors direction a unit vector gives the chromaticity while the magnitude represents the pixel brightness the chromaticity is processed with a system of coupled diffusion equations adapted from the theory of harmonic maps in liquid crystals this theory deals with the regularization of vectorial data while satisfying the intrinsic unit norm constraint of directional data such as chromaticity both isotropic and anisotropic diffusion flows are presented for this n dimensional chromaticity diffusion flow the brightness is processed by a scalar median filter or any of the popular and well established anisotropic diffusion flows for scalar image enhancement we present the underlying theory a number of examples and briefly compare with the current literature

reversible interpolation of vectorial images by an anisotropic diffusion projection pde in this paper a nonlinear model for the interpolation of vector valued images is proposed this model is based on an anisotropic diffusion pde and performs an interpolation that is reversible the interpolation solution is restricted to the subspace of functions that can recover the discrete input image after an appropriate smoothing and sampling the proposed nonlinear diffusion flow lies on this subspace while its strength and anisotropy adapt to the local variations and geometry of image structures the derived method effectively reconstructs the real image structures and yields a satisfactory interpolation result compared to classic and other existing pde based interpolation methods our proposed method seems to increase the accuracy of the result and to reduce the undesirable artifacts such as blurring ringing block effects and edge distortion we present extensive experimental results that demonstrate the potential of the method as applied to graylevel and color images

a global approach for solving evolutive heat transfer for image denoising and inpainting this paper proposes an alternative to partial differential equations pdes for solving problems in computer vision based on evolutive heat transfer traditionally the method for solving such physics based problems is to discretize and solve a pde by a purely mathematical process instead of using the pde we propose to use the global heat principle and to decompose it into basic laws we show that some of these laws admit an exact global version since they arise from conservative principles we also show that the assumptions made about the other basic laws can be made wisely taking into account knowledge about the problem and the domain the numerical scheme is derived in a straightforward way from the modeled problem thus providing a physical explanation for each step in the solution the advantage of such an approach is that it minimizes the approximations made during the whole process and it modularizes it allowing changing the application to a great number of problems we apply the scheme to two applications image denoising and inpainting which are modeled with heat transfer for denoising we propose a new approximation for the conductivity coefficient and we add thin lines to the features in order to block diffusion

increasing selective pressure towards the best compromise in evolutionary multiobjective optimization the extended nosga method most current approaches in the evolutionary multiobjective optimization literature concentrate on adapting an evolutionary algorithm to generate an approximation of the pareto frontier however finding this set does not solve the problem the decision maker still has to choose the best compromise solution out of that set here we introduce a new characterization of the best compromise solution of a multiobjective optimization problem by using a relational system of preferences based on a multicriteria decision aid way of thinking and an outranked based dominance generalization we derive some necessary and sufficient conditions which describe satisfactory approximations to the best compromise such conditions define a lexicographic minimum of a bi objective optimization problem which is a map of the original one the nosga ii method is a nsga ii inspired efficient way of solving the resulting mapped problem

a convergent difference scheme for the infinity laplacian construction of absolutely minimizing lipschitz extensions this article considers the problem of building absolutely minimizing lipschitz extensions to a given function these extensions can be characterized as being the solution of a degenerate elliptic partial differential equation the infinity laplacian for which there exist unique viscosity solutions a convergent difference scheme for the infinity laplacian equation is introduced which arises by minimizing the discrete lipschitz constant of the solution at every grid point existence and uniqueness of solutions to the scheme is shown directly solutions are also shown to satisfy a discrete comparison principle solutions are computed using an explicit iterative scheme which is equivalent to solving the parabolic version of the equation

fractional order anisotropic diffusion for image denoising this paper introduces a new class of fractional order anisotropic diffusion equations for noise removal these equations are euler lagrange equations of a cost functional which is an increasing function of the absolute value of the fractional derivative of the image intensity function so the proposed equations can be seen as generalizations of second order and fourth order anisotropic diffusion equations we use the discrete fourier transform to implement the numerical algorithm and give an iterative scheme in the frequency domain it is one important aspect of the algorithm that it considers the input image as a periodic image to overcome this problem we use a folded algorithm by extending the image symmetrically about its borders finally we list various numerical results on denoising real images experiments show that the proposed fractional order anisotropic diffusion equations yield good visual effects and better signal to noise ratio

locally monotonic diffusion anisotropic diffusion affords an efficient adaptive signal smoothing technique that can be used for signal enhancement signal segmentation and signal scale space creation this paper introduces a novel partial differential equation pde based diffusion method for generating locally monotonic signals unlike previous diffusion techniques that diverge or converge to trivial signals locally monotonic lomo diffusion converges rapidly to well defined lomo signals of the desired degree the property of local monotonicity allows both slow and rapid signal transitions ramp and step edges while excluding outliers due to noise in contrast with other diffusion methods lomo diffusion does not require an additional regularization step to process a noisy signal and uses no ad hoc thresholds or parameters in the paper we develop the lomo diffusion technique and provide several salient properties including stability and a characterization of the root signals the convergence of the algorithm is well behaved nonoscillatory and is independent of the signal length in contrast with the median filter a special case of lomo diffusion is identical to the optimal solution achieved via regression experimental results validate the claim that lomo diffusion can produce denoised lomo signals with low error using less computation than the median order statistic approach

a singular boundary value problem for a degenerate elliptic pde abstract we consider a singular boundary value problem associated with the laplacian and having nonseparable inhomogeneous term we establish the existence of ground state solutions to such a problem in bounded domains as well as in the whole euclidean space the investigation is based on subsolution and supersolution methods and existence of principal eigenfunctions to the eigenvalue problem of dirichlet type corresponding to the laplacian

on convergence of the multi objective particle swarm optimizers several variants of the particle swarm optimization pso algorithm have been proposed in recent past to tackle the multi objective optimization mo problems based on the concept of pareto optimality although a plethora of significant research articles have so far been published on analysis of the stability and convergence properties of pso as a single objective optimizer till date to the best of our knowledge no such analysis exists for the multi objective pso mopso algorithms this paper presents a first simple analysis of the general pareto based mopso and finds conditions on its most important control parameters the inertia factor and acceleration coefficients that govern the convergence behavior of the algorithm to the optimal pareto front in the objective function space computer simulations over benchmark mo problems have also been provided to substantiate the theoretical derivations

a perceptually motivated three component image model part ii applications to image compression for past i see ibid vol 4 no 4 p 405 1995 the use of the image model of part i is investigated in the context of image compression the model decomposes the image into a primary component that contains the strong edge information a smooth component that represents the background slow intensity variations and a texture component that contains the textures the primary component which is known to be perceptually important is encoded separately by encoding the intensity and geometric information of the strong edge brim contours two alternatives for coding the smooth and texture components are studied entropy coded adaptive dct and entropy coded subband coding it is shown via simulations that the proposed schemes which can be thought of as a hybrid of waveform coding and feature based coding techniques result in both subjective and objective performance improvements over several other image coding schemes and in particular over the jpeg continuous tone image compression standard these improvements are especially noticeable at low bit rates furthermore it is shown that a perceptual tuning based on the contrast sensitivity of the human visual system can be used in the dct based scheme which in conjunction with the three component model leads to additional subjective performance improvements

limits as p x of p x harmonic functions abstract in this note we study the limit as p x of solutions to p x u 0 in a domain with dirichlet boundary conditions our approach consists in considering sequences of variable exponents converging uniformly to and analyzing how the corresponding solutions of the problem converge and which equation is satisfied by the limit

adaptive smoothing via contextual and local discontinuities a novel adaptive smoothing approach is proposed for noise removal and feature preservation where two distinct measures are simultaneously adopted to detect discontinuities in an image inhomogeneity underlying an image is employed as a multiscale measure to detect contextual discontinuities for feature preservation and control of the smoothing speed while local spatial gradient is used for detection of variable local discontinuities during smoothing unlike previous adaptive smoothing approaches two discontinuity measures are combined in our algorithm for synergy in preserving nontrivial features which leads to a constrained anisotropic diffusion process that inhomogeneity offers intrinsic constraints for selective smoothing thanks to the use of intrinsic constraints our smoothing scheme is insensitive to termination times and the resultant images in a wide range of iterations are applicable to achieve nearly identical results for various early vision tasks our algorithm is formally analyzed and related to anisotropic diffusion comparative results indicate that our algorithm yields favorable smoothing results and its application in extraction of hydrographic objects demonstrates its usefulness as a tool for early vision

principal components analysis interpolation of head related transfer functions using locally chosen basis functions spatial interpolation between measured head related transfer functions hrtfs may be accomplished by using principal components analysis kistler and wightman 1992 the data set can be reduced by using only the most important basis functions bfs when reconstructing the magnitude spectrum of the hrtfs relatively good performance can be achieved by using a small fraction of the bfs required for an error free representation in this study a comparison is made between two methods for choosing which basis functions are included in the hrtf reconstruction for a given position the usual approach is to choose the subset of bfs which have the largest impact common variance on the global set of measured hrtfs this will be compared to a method in which the subset of bfs are chosen to have the largest impact on the measured hrtfs in the area local to the position being reconstructed advantages and disadvantages to the two methods are discussed work supported by nih dc00100

motion of level sets by mean curvature i we continue our investigation of the level set technique for describing the generalized evolution of hypersurfaces moving according to their mean curvature the principal assertion of this paper is a kind of reconciliation with the geometric measure theoretic approach pioneered by k brakke we prove that almost every level set of the solution to the mean curvature evolution pde is in fact aunit density varifold moving according to its mean curvature in particular a e level set is endowed with a kind of geometric structure the proof utilizes compensated compactness methods to pass to limits in various geometric expressions

on the evolution governed by the infinity laplacian we investigate the basic properties of the degenerate and singular evolution equation ut d 2 u du du du du which is a parabolic version of the increasingly popular infinity laplace equa tion we prove existence and uniqueness results for both dirichlet and cauchy problems establish interior and boundary lipschitz estimates and a harnack inequality and also provide numerous explicit solutions

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

uniqueness of lipschitz extensions minimizing the sup norm of the gradient in this paper we examine the problem of minimizing the sup norm of the gradient of a function with prescribed boundary values geometrically this can be interpreted as finding a minimal lipschitz extension due to the weak convexity of the functional associated to this problem solutions are generally nonunique by adopting g aronsson s notion of absolutely minimizing we are able to prove uniqueness by characterizing minimizers as the unique solutions of an associated partial differential equation in fact we actually prove a weak maximum principle for this partial differential equation which in some sense is the euler equation for the minimization problem this is significantly difficult because the partial differential equation is both fully nonlinear and has very degenerate ellipticity to overcome this difficulty we use the weak solutions of m g crandall and p l lions also known as viscosity solutions in conjunction with some arguments using integration by parts

the effect of median filtering on edge estimation and detection in this paper we consider the effect of median prefiltering on the subsequent estimation and detection of edges in digital images where possible a quantitative statistical comparison is made for a number of filters defined with two dimensional geometries in some cases one dimensional analyses are required to illustrate certain points noise images prefiltered by median filters defined with a variety of windowing geometries are used to support the analysis and it is found that median prefiltering improves the performance of both thresholding and zero crossing based edge detectors

pareto evolutionary neural networks for the purposes of forecasting or classification tasks neural networks nns are typically trained with respect to euclidean distance minimization this is commonly the case irrespective of any other end user preferences in a number of situations most notably time series forecasting users may have other objectives in addition to euclidean distance minimization recent studies in the nn domain have confronted this problem by propagating a linear sum of errors however this approach implicitly assumes a priori knowledge of the error surface defined by the problem which typically is not the case this study constructs a novel methodology for implementing multiobjective optimization within the evolutionary neural network enn domain this methodology enables the parallel evolution of a population of enn models which exhibit estimated pareto optimality with respect to multiple error measures a new method is derived from this framework the pareto evolutionary neural network pareto enn the pareto enn evolves a population of models that may be heterogeneous in their topologies inputs and degree of connectivity and maintains a set of the pareto optimal enns that it discovers new generalization methods to deal with the unique properties of multiobjective error minimization that are not apparent in the uni objective case are presented and compared on synthetic data with a novel method based on bootstrapping of the training data shown to significantly improve generalization ability finally experimental evidence is presented in this study demonstrating the general application potential of the framework by generating populations of enns for forecasting 37 different international stock indexes

a new image smoothing method based on a simple model of spatial processing in the early stages of human vision the difficulty of preserving edges is central to the problem of smoothing images the main problem is that of distinguishing between meaningful contours and noise so that the image can be smoothed without loss of details substantial efforts have been devoted to solving this difficult problem and a plethora of filtering methods have been proposed in the literature non linear filters have proved to be more efficient than their linear counterparts here a new nonlinear filter for noise smoothing is introduced this filter is based on the psychophysical phenomenon of human visual contrast sensitivity results on real images are presented to demonstrate the validity of our approach compared to other known filtering methods

learning simultaneous adaptive clustering and classification via moea clustering learning and classification learning are two major tasks in pattern recognition the traditional hybrid clustering and classification algorithms handle them in a sequential way rather than a simultaneous way fortunately multiobjective optimization provides a way to solve this problem in this paper an algorithm that learns simultaneous clustering and classification adaptively via multiobjective evolutionary algorithm is proposed the main idea of this paper is to optimize two objective functions which represent fuzzy cluster connectedness and classification error rate to achieve the goal of simultaneous learning firstly we adopt a graph based representation scheme to encode so that it can generate a set of solutions with different number of clusters in a single run then the relationship between clustering and classification is built via the bayesian theory during the optimization process the quality of clustering and classification is measured by the objective functions and the feedback drawn from both aspects is used to guide the mutation at last a set of nondominated solutions are generated from which the final pareto optimal solution is selected by using adjusted rand index the results on synthetic datasets and real life datasets demonstrate the rationality and effectiveness of the proposed algorithm furthermore we apply the proposed algorithm to image segmentation including texture images and synthetic aperture radar images the experimental results show the superiority of the proposed algorithm compared with other five algorithms highlightsa simultaneous adaptive clustering and classification learning via moea is proposed new clustering objective function is designed and two objective functions complement with each other the number of clusters can be determined adaptively during the learning process the drawback from clustering classification learning is used to guide the search we extend it to texture image and sar image segmentation to show its effectiveness

capso centripetal accelerated particle swarm optimization meta heuristic search algorithms are developed to solve optimization problems such algorithms are appropriate for global searches because of their global exploration and local exploitation abilities swarm intelligence si algorithms comprise a branch of meta heuristic algorithms that imitate the behavior of insects birds fishes and other natural phenomena to find solutions for complex optimization problems in this study an improved particle swarm optimization pso scheme combined with newton s laws of motion the centripetal accelerated particle swarm optimization capso scheme is introduced capso accelerates the learning and convergence of optimization problems in addition the binary mode of the proposed algorithm binary centripetal accelerated particle swarm optimization bcapso is introduced for binary search spaces these algorithms are evaluated using nonlinear benchmark functions and the results are compared with the gravitational search algorithm gsa and pso in both the real and the binary search spaces moreover the performance of capso in solving the functions is compared with some well known pso algorithms in the literature the experimental results showed that the proposed methods enhance the performance of pso in terms of convergence speed solution accuracy and global optimality

multiobjective evolutionary optimization of the size shape and position parameters of radial basis function networks for function approximation this paper presents a multiobjective evolutionary algorithm to optimize radial basis function neural networks rbfnns in order to approach target functions from a set of input output pairs the procedure allows the application of heuristics to improve the solution of the problem at hand by including some new genetic operators in the evolutionary process these new operators are based on two well known matrix transformations singular value decomposition svd and orthogonal least squares ols which have been used to define new mutation operators that produce local or global modifications in the radial basis functions rbfs of the networks the individuals in the population in the evolutionary procedure after analyzing the efficiency of the different operators we have shown that the global mutation operators yield an improved procedure to adjust the parameters of the rbfnns

asymptotic behavior of viscosity solutions for a degenerate parabolic equation associated with the infinity laplacian the asymptotic behavior of viscosity solutions to the cauchy dirichlet problem for the degenerate parabolic equation u t u in 0 where stands for the so called infinity laplacian is studied in three cases i omega mathbb r n and the initial data has a compact support ii is bounded and the boundary condition is zero iii is bounded and the boundary condition is non zero our method of proof is based on the comparison principle and barrier function arguments explicit representations of separable type and self similar type of solutions are also established moreover in case iii we propose another type of barrier function deeply related to a solution of delta infty phi 0

an axiomatic approach to scalar data interpolation on surfaces we discuss possible algorithms for interpolating data given on a set of curves in a surface of 3 we propose a set of basic assumptions to be satisfied by the interpolation algorithms which lead to a set of models in terms of possibly degenerate elliptic partial differential equations the absolutely minimizing lipschitz extension model amle is singled out and studied in more detail we study the correctness of our numerical approach and we show experiments illustrating the interpolation of data on some simple test surfaces like the sphere and the torus

principal eigenvalue of a very badly degenerate operator and applications abstract in this paper we define and investigate the properties of the principal eigenvalue of the singular infinity laplace operator u d 2 u d u d u d u d u this operator arises from the optimal lipschitz extension problem and it plays the same fundamental role in the calculus of variations of l functionals as the usual laplacian does in the calculus of variations of l 2 functionals our approach to the eigenvalue problem is based on the maximum principle and follows the outline of the celebrated work of berestycki nirenberg and varadhan h berestycki l nirenberg s r s varadhan the principal eigenvalue and maximum principle for second order elliptic operators in general domains comm pure appl math 47 1 1994 47 92 in the case of uniformly elliptic linear operators as an application we obtain existence and uniqueness results for certain related non homogeneous problems and decay estimates for the solutions of the evolution problem associated to the infinity laplacian

on the choice of the parameters for anisotropic diffusion in image processing anisotropic diffusion filtering is highly dependent on some crucial parameters such as the conductance function the gradient threshold parameter and the stopping time of the iterative process the various alternative options at each stage of the algorithm are examined and evaluated and the best choice is selected an automatic stopping criterion is proposed that takes into consideration the quality of the preserved edges as opposed to just the level of smoothing achieved the proposed scheme is evaluated with the help of real and simulated images and compared with other state of the art schemes using objective criteria

morse description and geometric encoding of digital elevation maps two complementary geometric structures for the topographic representation of an image are developed in this work the first one computes a description of the morse topological structure of the image while the second one computes a simplified version of its drainage structure the topographic significance of the morse and drainage structures of digital elevation maps dems suggests that they can been used as the basis of an efficient encoding scheme as an application we combine this geometric representation with an interpolation algorithm and lossless data compression schemes to develop a compression scheme for dems this algorithm achieves high compression while controlling the maximum error in the decoded elevation map a property that is necessary for the majority of applications dealing with dems we present the underlying theory and compression results for standard dem data

magnification of label maps with a topology preserving level set method image segmentation aims at partitioning an image into multiple segments the application of this procedure produces a label map also referred to as segmentation map that classifies the pixels of the original image in contrast to natural images label maps are nominal scale images typically represented as integer valued images nominal scaled label maps can also appear as a representation of the raw data in areas such as in geostatistics in some applications the original resolution of a label map does not suffice and a larger size map has to be generated in this paper we present a magnification algorithm for label maps and nominal images the main property of our method is that it preserves the topology during the magnification process which means that no isolated pixel vanishes to the best of our knowledge apart from nearest neighbor interpolation the problem of label map magnification has not previously been addressed in the literature the main idea of the proposed method is to accomplish a boundary refinement by smoothing the regions boundaries on a finer grid the method relies on well known methods namely the fundamental operations of morphological image processing erosion and dilation and the level set method the level set method is well suited for our purposes since it does not depend on a parametrization and it is numerically stable the topological flexibility of the level set method often found to be an advantage in applications is a drawback here since the topology of the original label map should be preserved however using the so called simple point criterion from digital topology one can adapt the conventional level set method so that the topology will not be modified throughout the magnification procedure

local variance controlled forward and backward diffusion for image enhancement and noise reduction in order to improve signal to noise ratio snr and contrast to noise ratio this paper introduces a local variance controlled forward and backward lvcfab diffusion algorithm for edge enhancement and noise reduction in our algorithm an alternative fab diffusion algorithm is proposed the results for the alternative fab algorithm show better algorithm behavior than other existing diffusion fab approaches furthermore two distinct discontinuity measures and the alternative fab diffusion are incorporated into a lvcfab diffusion algorithm where the joint use of the two measures leads to a complementary effect for preserving edge features in digital images this lvc mechanism adaptively modifies the degree of diffusion at any image location and is dependent on both local gradient and inhomogeneity qualitative experiments based on general digital images and magnetic resonance images show significant improvements when the lvcfab diffusion algorithm is used versus the existing anisotropic diffusion and the previous fab diffusion algorithms for enhancing edge features and improving image contrast quantitative analyses based on peak snr confirm the superiority of the proposed lvcfab diffusion algorithm

gradient field approximation application to registration in image processing we study a spline based approximation of vector fields in the conservative case the gradient vector field derives from a potential function we introduce a minimization problem on a hilbert space for which the existence and uniqueness of the solution is given we apply this approach to a registration process in image processing

mathematical models for local nontexture inpaintings dedicated to stanley osher on the occasion of his 60th birthday abstract inspired by the recent work of bertalmio et al on digital inpaintings siggraph 2000 we develop general mathematical models for local inpaintings of nontexture images on smooth regions inpaintings are connected to the harmonic and biharmonic extensions and inpainting orders are analyzed for inpaintings involving the recovery of edges we study a variational model that is closely connected to the classical total variation tv denoising model of rudin osher and fatemi phys d 60 1992 pp 259 268 other models are also discussed based on the mumford shah regularity comm pure appl math xlii 1989 pp 577 685 and curvature driven diffusions cdd of chan and shen j visual comm image rep 12 2001 the broad applications of the inpainting models are demonstrated through restoring scratched old photos disocclusion in vision analysis text removal digital zooming and edge based image coding