differential area profiles decomposition properties and efficient computation differential area profiles daps are point based multiscale descriptors used in pattern analysis and image segmentation they are defined through sets of size based connected morphological filters that constitute a joint area opening top hat and area closing bottom hat scale space of the input image the work presented in this paper explores the properties of this image decomposition through sets of area zones an area zone defines a single plane of the dap vector field and contains all the peak components of the input image whose size is between the zone s attribute extrema area zones can be computed efficiently from hierarchical image representation structures in a way similar to regular attribute filters operations on the dap vector field can then be computed without the need for exporting it first and an example with the leveling like convex concave segmentation scheme is given this is referred to as the one pass method and it is demonstrated on the max tree structure its computational performance is tested and compared against conventional means for computing differential profiles relying on iterative application of area openings and closings applications making use of the area zone decomposition are demonstrated in problems related to remote sensing and medical image analysis

effects of levy noise in aperiodic stochastic resonance we present a grunwald letnikov implicit finite difference method to solve the space fractional fokker planck equation with natural boundary condition then the properties of aperiodic stochastic resonance in the presence of levy noise are investigated in theory and tested by simulation it is shown that aperiodic stochastic resonance does occur in the presence of levy noise but is reduced by the lower levy index with the optimal system parameters the probability of detection error decreases with the decrease of therefore the performance of a bistable system is improved by the lower index of levy noise

small delay approximation of stochastic delay differential equations delay differential equations evolve in an infinite dimensional phase space in this paper we consider the effect of external fluctuations noise on delay differential equations involving one variable thus leading to univariate stochastic delay differential equations sdde s for small delays a univariate nondelayed stochastic differential equation approximating such a sdde is presented another approximation complementary to the first is also obtained using an average of the sdde s drift term over the delayed dynamical variable which defines a conditional average drift this second approximation is characterized by the fact that the diffusion term is identical to that of the original sdde for small delays our approach yields a steady state probability density and a conditional average drift which are in close agreement with numerical simulations of the original sdde we illustrate this scheme with the delayed linear langevin equation and a stochastic version of the delayed logistic equation the technique can be used with any type of noise and is easily generalized to multiple delays s1063 651x 99 08304 x

a comparison of algorithms for connected set openings and closings the implementation of morphological connected set operators for image filtering and pattern recognition is discussed two earlier algorithms based on priority queues and hierarchical queues respectively are compared to a more recent union find approach unlike the earlier algorithms which process regional extrema in the image sequentially the union find method allows simultaneous processing of extrema in the context of area openings closings and pattern spectra the union find algorithm outperforms the previous methods on almost all natural and synthetic images tested finally extensions to pattern spectra and the more general class of attribute operators are presented for all three algorithms and memory usages are compared

stationary states in langevin dynamics under asymmetric levy noises properties of systems driven by white non gaussian noises can be very different from these of systems driven by the white gaussian noise we investigate stationary probability densities for systems driven by ensuremath alpha stable l evy type noises which provide natural extension to the gaussian noise having however a new property namely a possibility of being asymmetric stationary probability densities are examined for a particle moving in parabolic quartic and in generic double well potential models subjected to the action of ensuremath alpha stable noises relevant solutions are constructed by methods of stochastic dynamics in situations where analytical results are known they are compared with numerical results furthermore the problem of estimation of the parameters of stationary densities is investigated

flat zones filtering connected operators and filters by reconstruction this correspondence deals with the notion of connected operators starting from the definition for operator acting on sets it is shown how to extend it to operators acting on function typically a connected operator acting on a function is a transformation that enlarges the partition of the space created by the flat zones of the functions it is shown that from any connected operator acting on sets one can construct a connected operator for functions however it is not the unique way of generating connected operators for functions moreover the concept of pyramid is introduced in a formal way it is shown that if a pyramid is based on connected operators the flat zones of the functions increase with the level of the pyramid in other words the flat zones are nested filters by reconstruction are defined and their main properties are presented finally some examples of application of connected operators and use of flat zones are described

hp multigrid as smoother algorithm for higher order discontinuous galerkin discretizations of advection dominated flows part ii optimization of the runge kutta smoother using a detailed multilevel analysis of the complete hp multigrid as smoother algorithm accurate predictions are obtained of the spectral radius and operator norms of the multigrid error transformation operator this multilevel analysis is used to optimize the coefficients in the semi implicit runge kutta smoother such that the spectral radius of the multigrid error transformation operator is minimal under properly chosen constraints the runge kutta coefficients for a wide range of cell reynolds numbers and a detailed analysis of the performance of the hp mgs algorithm are presented in addition the computational complexity of the hp mgs algorithm is investigated the hp mgs algorithm is tested on a fourth order accurate space time discontinuous galerkin finite element discretization of the advection diffusion equation for a number of model problems which include thin boundary layers and highly stretched meshes and a non constant advection velocity for all test cases excellent multigrid convergence is obtained

the mechanism of stochastic resonance it is shown that a dynamical system subject to both periodic forcing and random perturbation may show a resonance peak in the power spectrum which is absent when either the forcing or the perturbation is absent

theoretical aspects of gray level morphology after a brief discussion of the extension of mathematical morphology to complete lattices the space of gray level functions is considered and the concept of a threshold set is introduced it is shown how one can use binary morphological operators and thresholding techniques to build a large class of gray level morphological operators particular attention is given to the class of so called flat operators i e operators which commute with thresholding it is also shown how to define dilations and erosions with nonflat structuring elements if the gray level set is finite it is reported that mere truncation yields wrong results

face segmentation and tracking based on connected operators and partition projection abstract a new technique for segmenting and tracking human faces in video sequences is presented the algorithm relies on the concepts of connected operators and partition projection to tackle the problems of face segmentation and tracking respectively it uses a connected operator to extract the connected component that more likely belongs to a face such a connected operator is implemented by means of a binary partition tree a set of connected regions a node in the tree is selected maximizing the estimation of the likelihood of being part of a face this way a first estimate of the face is obtained final face segmentation is carried out by a face extraction step that applies the previous maximization in the partition space faces are tracked through the sequence based on the partition projection approach partition projection accommodates the partition of the previous image into the information of the current frame the current image is classified into face no face and uncertain regions by projecting the previous face partition therefore the projection yields the first estimate of the face the face core component is grown up to obtain the final face segmentation using the previous face extraction process the technique has been successfully assessed using several test sequences in raw format mpeg 4 database as well as in mpeg 1 format from the mpeg 7 database

a p multigrid discontinuous galerkin method for the euler equations on unstructured grids a p multigrid p polynomial degree discontinuous galerkin method is presented for the solution of the compressible euler equations on unstructured grids the method operates on a sequence of solution approximations of different polynomial orders a distinct feature of this p multigrid method is to use different time integration schemes on different approximation levels resulting in an accurate fast and low memory method that can be used to accelerate the convergence of the euler equations to a steady state for discontinuous galerkin methods the developed method is used to compute the compressible flows for a variety of test problems on unstructured grids the numerical results obtained strongly indicate the order independent property of this p multigrid method an overall speed up factor more than one order of magnitude for both second and third order solutions of all test cases in comparison with the explicit method is demonstrated

partition induced connections and operators for pattern analysis in this paper we present a generalization on the notion of image connectivity similar to that modeled by second generation connections the connected operators based on this new type of connection make use of image partitions aided by mask images to extract path wise connected regions that were previously treated as sets of singletons this leads to a redistribution of image power which affects texture descriptors these operators find applications in problems involving contraction based connectivities and we show how they can be used to counter the over segmentation problem of connected filters despite restrictions which prevent extensions to gray scale we present a method for gray scale spectral analysis of biomedical images characterized by filamentous details using connected pattern spectra as feature vectors to train a classifier we show that the new operators outperform the existing contraction based ones and that the classification performance competes with and in some cases outperforms methods based on the standard 4 or 8 connectivity finally combining the two methods we enrich the texture description and increase the overall classification rate

hyperconnected attribute filters based on k flat zones in this paper we present a new method for attribute filtering combining contrast and structural information using hyperconnectivity based on k flat zones we improve the ability of attribute filters to retain internal details in detected objects simultaneously we improve the suppression of small unwanted detail in the background we extend the theory of attribute filters to hyperconnectivity and provide a fast algorithm to implement the new method the new version is only marginally slower than the standard max tree algorithm for connected attribute filters and linear in the number of pixels or voxels it is two orders of magnitude faster than anisotropic diffusion the method is implemented in the form of a filtering rule suitable for handling both increasing size and nonincreasing shape attributes we test this new framework on nonincreasing shape filters on both 2d images from astronomy document processing and microscopy and 3d ct scans and show increased robustness to noise while maintaining the advantages of previous methods

fast p multigrid discontinuous galerkin method for compressible flows at all speeds ap multigrid wherep is the polynomial degree discontinuous galerkin method is presented for the solution of the compressible euler equations on unstructured grids the method operates on a sequence of solution approximations of different polynomial orders a distinct feature ofthisp multigrid method is the application of an explicit smoother on the higher level approximations p 0 and an implicit smoother on the lowest level approximation p 0 resulting in a fast and low storage method that can be efficiently used to accelerate the convergence to a steady state solution furthermore this p multigrid method can be naturally applied to compute the flows with discontinuities in which a monotonic limiting procedure is usually required for discontinuous galerkin methods an accurate representation of the boundary normals based on the definition of the geometries is used for imposing slip boundary conditions for curved geometries krivodonova l and berger m high order implementation of solid wall boundary conditions in curved geometries journal of computational physics vol 211 no 2 2006 pp 492 512 and luo h baum j d and lohner r on the computation of steady state compressible flows using a discontinuous galerkin method international journal for numerical methods in engineering vol 73 no 5 2008 pp 597 623 a variety of compressible flow problems for a wide range of flow conditions from low mach number to supersonic in both two dimensional and three dimensional configurations are computed to demonstrate the performance ofthisp multigrid method the numerical results obtained strongly indicate the order independent property of this p multigrid method and demonstrate that this method is orders of magnitude faster than its explicit counterpart the performance comparison with a finite volume method shows that using this p multigrid method the discontinuous galerkin method provides a viable attractive competitive and probably even superior alternative to the finite volume method for computing compressible flows at all speeds

levy flights in a steep potential well levy flights in steeper than harmonic potentials have been shown to exhibit finite variance and a critical time at which a bifurcation from an initial monomodal to a terminal bimodal distribution occurs chechkin et al phys rev e 67 010102 r 2003 in this paper we present a detailed study of levy flights in potentials of the type u x x c with c 2 apart from the bifurcation into bimodality we find the interesting result that for c 4 a trimodal transient exists due to the temporal overlap between the decay of the central peak around the initial condition and the building up of the two emerging side peaks which are characteristic for the stationary state thus for certain system parameters there exists a transient trimodal distribution of the levy flight these properties of levy flights in external potentials of the power law type can be represented by certain phase diagrams we also present details about the proof of multimodality and the numerical procedures to establish the probability distribution of the process

solving discontinuous galerkin formulations of poisson s equation using geometric and p multigrid methods for solving discontinuous galerkin formulations of the poisson equation by coupling p multigrid to geometric multigrid are investigated the simple approach of performing iterative relaxation on solution approximations of decreasing polynomial degree p down to p 0 and then applying geometric multigrid is ineffective the transition from p 1 top 0 causes the performance of the entire iteration to degrade because the long wavelength eigenfunctions of the p 1 discontinuous system are not represented well in thep 0 space a new approach is proposed that coarsens from thep 1 discontinuous space to thep 1 continuous space this approach eliminates the problems caused by the p 1 to p 0 transition furthermore the p 1 continuous space is a standard finite element space for which geometric multigrid is well defined in addition when the discontinuous galerkin equations are restricted to a continuous space one recovers the galerkin formulation of continuous finite elements thus applying geometric multigrid to this system is straightforward and effective numerical tests agree well with the analysis and confirm that the new approach gives rapid convergence rates that are grid independent and only weakly sensitive to the polynomial order

stochastic resonance in time delayed bistable systems driven by weak periodic signal abstract we study theoretically a bistable system with time delayed feedback driven by a weak periodic force the effective potential function and the steady state probability density are derived the delay time and the strength of its feedback can change the shapes of the potential wells in the adiabatic approximation the signal to noise ratio snr of the system with a weak periodic force is obtained the time delayed feedback modulates the magnitude of snr by changing the shape of the potential and the effective strength of the signal the maximum of snr decreases with increasing the feedback intensity when is negative or positive the time delay can suppress or promote the stochastic resonance phenomenon

object based image analysis using multiscale connectivity this paper introduces a novel approach for image analysis based on the notion of multiscale connectivity we use the proposed approach to design several novel tools for object based image representation and analysis which exploit the connectivity structure of images in a multiscale fashion more specifically we propose a nonlinear pyramidal image representation scheme which decomposes an image at different scales by means of multiscale grain filters these filters gradually remove connected components from an image that fail to satisfy a given criterion we also use the concept of multiscale connectivity to design a hierarchical data partitioning tool we employ this tool to construct another image representation scheme based on the concept of component trees which organizes partitions of an image in a hierarchical multiscale fashion in addition we propose a geometrically oriented hierarchical clustering algorithm which generalizes the classical single linkage algorithm finally we propose two object based multiscale image summaries reminiscent of the well known morphological pattern spectrum which can be useful in image analysis and image understanding applications

connected shape size pattern spectra for rotation and scale invariant classification of gray scale images in this paper we describe a multiscale and multishape morphological method for pattern based analysis and classification of gray scale images using connected operators compared with existing methods which use structuring elements our method has three advantages first in our method the time needed for computing pattern spectra does not depend on the number of scales or shapes used i e the computation time is independent of the dimensions of the pattern spectrum second size and strict shape attributes can be computed which we use for the construction of joint 2d shape size pattern spectra third our method is significantly less sensitive to noise and is rotation invariant although rotation invariance can also be approximated by methods using structuring elements at different angles this tends to be computationally intensive the classification performance of these methods is discussed using four image sets brodatz coil 20 coil 100 and diatoms the new method obtains better or equal classification performance to the best competitor with a 5 to 9 fold speed gain

scale space classification using area morphology we explore the application of area morphology to image classification from the input image a scale space is created by successive application of an area morphology operator the pixels within the scale space corresponding to the same image location form a scale space vector a scale space vector therefore contains the intensity of a particular pixel for a given set of scales determined in this approach by image granulometry using the standard k means algorithm or the fuzzy c means algorithm the image pixels can be classified by clustering the associated scale space vectors the scale space classifier presented here is rooted in the novel area open close and area close open scale spaces unlike other scale generating filters the area operators affect the image by removing connected components within the image level sets that do not satisfy the minimum area criterion to show that the area open close and area close open scale spaces provide an effective multiscale structure for image classification we demonstrate the fidelity causality and edge localization properties for the scale spaces the analysis also reveals that the area open close and area close open scale spaces improve classification by clustering members of similar objects more effectively than the fixed scale classifier experimental results are provided that demonstrate the reduction in intra region classification error and in overall classification error given by the scale space classifier for classification applications where object scale is important in both visual and objective comparisons the scale space approach outperforms the traditional fixed scale clustering algorithms and the parametric bayesian classifier for classification tasks that depend on object scale

hp multigrid as smoother algorithm for higher order discontinuous galerkin discretizations of advection dominated flows part i multilevel analysis the hp multigrid as smoother algorithm hp mgs for the solution of higher order accurate space time discontinuous galerkin discretizations of advection dominated flows is presented this algorithm combines p multigrid with h multigrid at all p levels where the h multigrid acts as smoother in the p multigrid the performance of the hp mgs algorithm is further improved using semi coarsening in combination with a new semi implicit runge kutta method as smoother a detailed multilevel analysis of the hp mgs algorithm is presented to obtain more insight into the theoretical performance of the algorithm as model problem a fourth order accurate space time discontinuous galerkin discretization of the advection diffusion equation is considered the multilevel analysis shows that the hp mgs algorithm has excellent convergence rates both for steady state and time dependent problems and low and high cell reynolds numbers including highly stretched meshes

some properties of interpolations using mathematical morphology the problem of interpolation between two images is defined as given two images one at time t 0 and another at t t one must estimate the series of intermediate images for all intermediate time steps this problem is not well posed in the sense that without further constraints there are many possible solutions the solution is thus usually dictated by the choice of the constraints assumptions which in turn relies on the domain of application in this article we follow the approach of obtaining a solution to the interpolation problem using the operators from mathematical morphology mm these operators have an advantage of preserving structures since the operators are defined on sets in this paper we explore the solutions obtained using mm and provide several results along with proofs which corroborates the validity of the assumptions provide links among existing methods and intuition about them we also summarize few possible extensions and prospective problems of current interest

how to tune the system parameters to realize stochastic resonance the paper presents a numerical method of realizing stochastic resonance sr by tuning system parameters firstly a simple and effective method of evaluating the system response speed 1 is introduced then the parameter induced sr problem can be reduced to the parameter optimization problem under the condition 1 const to solve this optimization problem we put forward the following techniques i compensate the deviation from the prescribed system response speed 1 at each step ii take the curve length increment on the parameter plane as the step size in searching the maximal signal to noise ratio snr gain finally a numerical simulation confirms the effectiveness of this method

levy flights transitions and meta stability we consider l vy flights of stability index 0 2 in a potential landscape in the limit of a small noise parameter we give a purely probabilistic description of the random dynamics on the basis of a special decomposition of the driving l vy processes into independent small jumps and compound poisson parts we prove that escape times from a potential well are exponentially distributed and their mean values increase as a power of the noise intensity this allows us to obtain meta stability results for a jump diffusion in a double well potential

fast fuzzy connected filter implementation using max tree updates connected filters are widely used filters in image processing and their implementation highly benefits from tree representations of images called max trees extending these filters to fuzzy sets which may be used to represent imprecision on gray levels in fuzzy gray level images requires frequent manipulations of these trees in this paper we propose efficient algorithms to update tree representations of fuzzy sets according to modifications of the membership values we show that any modification can be reduced to a series of simple changes where only one pixel is modified at each step

aperiodic stochastic resonance stochastic resonance sr is a phenomenon wherein the response of a nonlinear system to a weak periodic input signal is optimized by the presence of a particular level of noise recently we presented a method and theory for characterizing sr type behavior in excitable systems with aperiodic i e broadband input signals phys rev e 52 r3321 1995 we coined the term aperiodic stochastic resonance asr to describe this general type of behavior in that earlier study we demonstrated asr in the fitzhugh nagumo neuronal model here we demonstrate asr in three additional systems a bistable well system an integrate and fire neuronal model and the hodgkin huxley hh neuronal model we present computational and theoretical results for each system in the context of the hh model we develop a general theory for asr in excitable membranes this work clearly shows that sr type behavior is not limited to systems with periodic inputs thus in general noise can serve to enhance the response of a nonlinear system to a weak input signal regardless of whether the signal is periodic or aperiodic textcopyright 1996 the american physical society

evaluation of stochastic resonance based detectors of weak harmonic signals in additive white gaussian noise a thorough evaluation of stochastic resonance in the framework of statistical detection theory is presented both as a nonlinear signal preprocessor and as a detector the pertinent receiver operating characteristics are compared with those of the known statistically optimum detector using extensive monte carlo simulations parameter optimization and computational budget aspects are discussed

binary partition tree as an efficient representation for image processing segmentation and information retrieval this paper discusses the interest of binary partition trees as a region oriented image representation binary partition trees concentrate in a compact and structured representation a set of meaningful regions that can be extracted from an image they offer a multiscale representation of the image and define a translation invariant 2 connectivity rule among regions as shown in this paper this representation can be used for a large number of processing goals such as filtering segmentation information retrieval and visual browsing furthermore the processing of the tree representation leads to very efficient algorithms finally for some applications it may be interesting to compute the binary partition tree once and to store it for subsequent use for various applications in this context the paper shows that the amount of bits necessary to encode a binary partition tree remains moderate

mtos a tree of shapes for multivariate images the topographic map of a gray level image also called tree of shapes provides a high level hierarchical representation of the image contents this representation invariant to contrast changes and to contrast inversion has been proved very useful to achieve many image processing and pattern recognition tasks its definition relies on the total ordering of pixel values so this representation does not exist for color images or more generally multivariate images common workarounds such as marginal processing or imposing a total order on data are not satisfactory and yield many problems this paper presents a method to build a tree based representation of multivariate images which features marginally the same properties of the gray level tree of shapes briefly put we do not impose an arbitrary ordering on values but we only rely on the inclusion relationship between shapes in the image definition domain the interest of having a contrast invariant and self dual representation of multivariate image is illustrated through several applications filtering segmentation and object recognition on different types of data color natural images document images satellite hyperspectral imaging multimodal medical imaging and videos

directed connected operators asymmetric hierarchies for image filtering and segmentation connected operators provide well established solutions for digital image processing typically in conjunction with hierarchical schemes in graph based frameworks such operators basically rely on symmetric adjacency relations between pixels in this article we introduce a notion of directed connected operators for hierarchical image processing by also considering non symmetric adjacency relations the induced image representation models are no longer partition hierarchies i e trees but directed acyclic graphs that generalize standard morphological tree structures such as component trees binary partition trees or hierarchical watersheds we describe how to efficiently build and handle these richer data structures and we illustrate the versatility of the proposed framework in image filtering and image segmentation

characteristic multigrid method application to solve the euler equations with unstructured and unnested grids abstract a new multigrid method for the solution of hyperbolic systems of conservation laws such as the euler equations of comprehensive inviscid flows combined with higher order upwind approximation is constructed the novelty of the method lies in the introduction of an upwind transfer operator between two successive grids first the efficiency of the method is investigated for a scalar linear advection equation in one dimension of space using fourier analysis an extension to an unstructured multigrid method is then proposed numerical results for two dimensional flow computations including hypersonic flow simulation are presented

data adaptive algorithms for signal detection in sub gaussian impulsive interference we address the problem of coherent detection of a signal embedded in heavy tailed noise modeled as a sub gaussian alpha stable process we assume that the signal is a complex valued vector of length l known only within a multiplicative constant while the dependence structure of the noise i e the underlying matrix of the sub gaussian process is not known we implement a generalized likelihood ratio detector that employs robust estimates of the unknown noise underlying matrix and the unknown signal strength the performance of the proposed adaptive detector is compared with that of an adaptive matched filter that uses gaussian estimates of the noise underlying matrix and the signal strength and is found to be clearly superior the proposed new algorithms are theoretically analyzed and illustrated in a monte carlo simulation

effects of small time delay on a bistable system subject to levy stable noise l vy stable noise is often used to describe impulsive noise bursting in communication systems this paper investigates the effects of small time delay on a bistable system driven by an aperiodic bipolar pulse signal and l vy stable noise we obtain the dynamical probability density of the system response by solving the approximated time delayed fractional fokker planck equation ffpe via an implicit finite difference method a new approach to evaluate the system response time is presented the bit error rate ber is employed to measure the performance of the bistable system in detecting binary signals the theoretical ber is validated by the monte carlo simulation we find that the existence of time delay can change both the drift term and the diffusion coefficient in time delayed ffpe for small noise intensity the time delay extends the system response time and thus reduces the detection performance however effects of this kind will fade away with the increase of noise intensity

morphological grayscale reconstruction in image analysis applications and efficient algorithms two different formal definitions of gray scale reconstruction are presented the use of gray scale reconstruction in various image processing applications discussed to illustrate the usefulness of this transformation for image filtering and segmentation tasks the standard parallel and sequential approaches to reconstruction are reviewed it is shown that their common drawback is their inefficiency on conventional computers to improve this situation an algorithm that is based on the notion of regional maxima and makes use of breadth first image scannings implemented using a queue of pixels is introduced its combination with the sequential technique results in a hybrid gray scale reconstruction algorithm which is an order of magnitude faster than any previously known algorithm

shape representation and recognition through morphological curvature scale spaces a multiscale morphological method for the purpose of shape based object recognition is presented a connected operator similar to the morphological hat transform is defined and two scale space representations are built using the curvature function as the underlying one dimensional signal each peak and valley of the curvature is extracted and described by its maximum and average heights and by its extent and represents an entry in the top or bottom hat transform scale spaces we demonstrate object recognition based on hat transform scale spaces for three large data sets a set of diatom contours the set of silhouettes from the mpeg 7 database and the set of two dimensional views of three dimensional objects from the coil 20 database our approach outperforms other methods for which comparative results exist

bifurcation bimodality and finite variance in confined levy flights we investigate the statistical behavior of levy flights confined in a symmetric quartic potential well u x proportional variant x 4 at stationarity the probability density function features a distinct bimodal shape and decays with power law tails which are steep enough to give rise to a finite variance in contrast to free levy flights from a delta initial condition a bifurcation of the unimodal state is observed at t c 0 the nonlinear oscillator with potential u x ax 2 2 bx 4 4 a b 0 shows a crossover from unimodal to bimodal behavior at stationarity depending on the ratio a b

connected filtering based on multivalued component trees in recent papers a new notion of component graph was introduced it extends the classical notion of component tree initially proposed in mathematical morphology to model the structure of gray level images component graphs can indeed model the structure of any gray level or multivalued images we now extend the anti extensive filtering scheme based on component trees to make it tractable in the framework of component graphs more precisely we provide solutions for building a component graph reducing it based on selection criteria and reconstructing a filtered image from a reduced component graph in this paper we first consider the cases where component graphs still have a tree structure they are then called multivalued component trees the relevance and usefulness of such multivalued component trees are illustrated by applicative examples on hierarchically classified remote sensing images

shape based invariant texture indexing this paper introduces a new texture analysis scheme which is invariant to local geometric and radiometric changes the proposed methodology relies on the topographic map of images obtained from the connected components of level sets this morphological tool providing a multi scale and contrast invariant representation of images is shown to be well suited to texture analysis we first make use of invariant moments to extract geometrical information from the topographic map this yields features that are invariant to local similarities or local affine transformations these features are invariant to any local contrast change we then relax this invariance by computing additional features that are invariant to local affine contrast changes and investigate the resulting analysis scheme by performing classification and retrieval experiments on three texture databases the obtained experimental results outperform the current state of the art in locally invariant texture analysis

dynamics of two competing species in the presence of levy noise sources we consider a lotka volterra system of two competing species subject to multiplicative stable levy noise the interaction parameter between the species is a random process which obeys a stochastic differential equation with a generalized bistable potential in the presence both of a periodic driving term and an additive stable levy noise we study the species dynamics which is characterized by two different regimes exclusion of one species and coexistence of both we find quasiperiodic oscillations and stochastic resonance phenomenon in the dynamics of the competing species analyzing the role of the levy noise sources

stochastic resonance in a bistable system subject to multi time delayed feedback and aperiodic signal we discuss in detail the effects of the multi time delayed feedback driven by an aperiodic signal on the output of a stochastic resonance sr system the effective potential function and dynamical probability density function pdf are derived to measure the performance of the sr system in the presence of a binary random signal the bit error rate ber defined by the dynamical pdf is employed as is commonly used in digital communications we find that the delay time strength of the feedback and number of time delayed terms can change the effective potential function and the effective amplitude of the signal and then affect the ber of the sr system the numerical simulations strongly support the theoretical results the goal of this investigation is to explore the effects of the multi time delayed feedback on sr and give a guidance to nonlinear systems in the application of information processing

isophotes selection and reaction diffusion model for object boundaries estimation this paper investigates generic region based segmentation schemes using area minimization constraint and background modeling and develops a computationally efficient framework based on level lines selection coupled with biased anisotropic diffusion a common approach to image segmentation is to construct a cost function whose minima yield the segmented image this is generally achieved by competition of two terms in the cost function one that punishes deviations from the original image and another that acts as a regularization term we propose a variational framework for characterizing global minimizers of a particular segmentation energy that can generates irregular object boundaries in image segmentation our motivation comes from the observation that energy functionals are traditionally complex for which it is usually difficult to precise global minimizers corresponding to best segmentations in this paper we prove that the set of curves that minimizes the basic energy model under concern is a subset of level lines or isophotes i e the boundaries of image level sets the connections of our approach with region growing techniques snakes and geodesic active contours are also discussed moreover it is absolutely necessary to regularize isophotes delimiting object boundaries and to determine piecewise smooth or constant approximations of the image data inside the objects boundaries for vizualization and pattern recognition purposes thus we have constructed a reaction diffusion process based on the perona malik anisotropic diffusion equation in particular a reaction term has been added to force the solution to remain close to the data inside object boundaries and to be constant in non informative regions that is the background region in the overall approach diffusion requires the design of the background and foreground regions obtained by segmentation and segmentation of the adaptively smoothed image is performed after each iteration of the diffusion process from an application point of view the sound initialization free algorithm is shown to perform well in a variety of imaging contexts with variable texture noise and lighting conditions including optical imaging medical imaging and meteorological imaging depending on the context it yields either a reliable segmentation or a good pre segmentation that can be used as initialization for more sophisticated application dependent segmentation models

coupling p multigrid to geometric multigrid for discontinuous galerkin formulations of the convection diffusion equation an improved p multigrid algorithm for discontinuous galerkin dg discretizations of convection diffusion problems is presented the general p multigrid algorithm for dg discretizations involves a restriction from the p 1 to p 0 discontinuous polynomial solution spaces this restriction is problematic and has limited the efficiency of the p multigrid method for purely diffusive problems helenbrook and atkins have demonstrated rapid convergence using a method that restricts from a discontinuous to continuous polynomial solution space at p 1 it is shown that this method is not directly applicable to the convection diffusion cd equation because it results in a central difference discretization for the convective term to remedy this ideas from the streamwise upwind petrov galerkin supg formulation are used to devise a transition from the discontinuous to continuous space at p 1 that yields an upwind discretization the results show that the new method converges rapidly for all peclet numbers

acceleration for microflow simulations of high order moment models by using lower order model correction we study the acceleration of steady state computation for microflow which is modeled by the high order moment models derived recently from the steady state boltzmann equation with bgk type collision term by using the lower order model correction a novel nonlinear multi level moment solver is developed numerical examples verify that the resulting solver improves the convergence significantly thus is able to accelerate the steady state computation greatly the behavior of the solver is also numerically investigated it is shown that the convergence rate increases indicating the solver would be more efficient as the total levels increases three order reduction strategies of the solver are considered numerical results show that the most efficient order reduction strategy would be ml1 ml 2

dispersion and dissipation properties of the 1d spectral volume method and application to a p multigrid algorithm in this article the wave propagation properties of the 1d spectral volume method are studied through analysis of the fourier footprint of the schemes a p multigrid algorithm for the spectral volume method is implemented restriction and prolongation operators are discussed and the efficiency of the smoothing operators is analyzed the results are verified for simple 1d advection problems and for a quasi 1d euler flow it is shown that a significant decrease in computational effort is possible with the p multigrid algorithm

building the component tree in quasi linear time the level sets of a map are the sets of points with level above a given threshold the connected components of the level sets thanks to the inclusion relation can be organized in a tree structure that is called the component tree this tree under several variations has been used in numerous applications various algorithms have been proposed in the literature for computing the component tree the fastest ones considering the worst case complexity have been proven to run in o nln n in this paper we propose a simple to implement quasi linear algorithm for computing the component tree on symmetric graphs based on tarjan s union find procedure we also propose an algorithm that computes the n most significant lobes of a map

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

binary partition tree construction from multiple features for image segmentation in the context of digital image processing and analysis the binary partition tree bpt is a classical data structure for the hierarchical modelling of images at different scales bpts belong both to the families of graph based models and morphological hierarchies they constitute an efficient way to define sets of nested partitions of image support that further provide knowledge guided reduced research spaces for optimization based segmentation procedures basically a bpt is built in a mono feature way i e for one given image and one given metric by merging pairs of connected image regions that are similar in the induced feature space we propose in this work a generalization of the bpt construction framework allowing to embed multiple features the cornerstone of our approach relies on a collaborative strategy enabling to establish a consensus between different metrics thus allowing to obtain a unified hierarchical segmentation space in particular this provides alternatives to the complex issue of arbitrary metric construction from several possibly non comparable features to reach that goal we first revisit the bpt construction algorithm to describe it in a fully graph based formalism then we present the structural and algorithmic evolutions and impacts when embedding multiple features in bpt construction we also discuss different ways to tackle the induced memory and time complexity issues raised by this generalized framework final experiments illustrate how this multi feature framework can be used to build bpts from multiple metrics computed through the potentially multiple image content s in particular in the context of remote sensing

application of p multigrid to discontinuous galerkin formulations of the poisson equation we investigate p multigrid as a solution method for several different discontinuous galerkin dg formulations of the poisson equation different combinations of relaxation schemes and basis sets have been combined with the dg formulations to find the best performing combination the damping factors of the schemes have been determined using fourier analysis for both one and two dimensional problems one important finding is that when using dg formulations the standard approach of forming the coarse p matrices separately for each level of multigrid is often unstable to ensure stability the coarse p matrices must be constructed from the fine grid matrices using algebraic multigrid techniques of the relaxation schemes we find that the combination of jacobi relaxation with the spectral element basis is fairly effective the results using this combination are p sensitive in both one and two dimensions but reasonable convergence rates can still be achieved for moderate values of p and isotropic meshes a competitive alternative is a block gauss seidel relaxation this actually out performs a more expensive line relaxation when the mesh is isotropic when the mesh becomes highly anisotropic the implicit line method and the gauss seidel implicit line method are the only effective schemes adding the gauss seidel terms to the implicit line method gives a significant improvement over the line relaxation method

hyperconnections and hierarchical representations for grayscale and multiband image processing connections in image processing are an important notion that describes how pixels can be grouped together according to their spatial relationships and or their gray level values in recent years several works were devoted to the development of new theories of connections among which hyperconnection h connection is a very promising notion this paper addresses two major issues of this theory first we propose a new axiomatic that ensures that every h connection generates decompositions that are consistent for image processing and more precisely for the design of h connected filters second we develop a general framework to represent the decomposition of an image into h connections as a tree that corresponds to the generalization of the connected component tree such trees are indeed an efficient and intuitive way to design attribute filters or to perform detection tasks based on qualitative or quantitative attributes these theoretical developments are applied to a particular fuzzy h connection and we test this new framework on several classical applications in image processing i e segmentation connected filtering and document image binarization the experiments confirm the suitability of the proposed approach it is robust to noise and it provides an efficient framework to design selective filters

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100