complete discrete 2 d gabor transforms by neural networks for image analysis and compression a three layered neural network is described for transforming two dimensional discrete signals into generalized nonorthogonal 2 d gabor representations for image analysis segmentation and compression these transforms are conjoint spatial spectral representations which provide a complete image description in terms of locally windowed 2 d spectral coordinates embedded within global 2 d spatial coordinates in the present neural network approach based on interlaminar interactions involving two layers with fixed weights and one layer with adjustable weights the network finds coefficients for complete conjoint 2 d gabor transforms without restrictive conditions in wavelet expansions based on a biologically inspired log polar ensemble of dilations rotations and translations of a single underlying 2 d gabor wavelet template image compression is illustrated with ratios up to 20 1 also demonstrated is image segmentation based on the clustering of coefficients in the complete 2 d gabor transform

autocorrelation driven diffusion filtering in this paper we present a novel scheme for anisotropic diffusion driven by the image autocorrelation function we show the equivalence of this scheme to a special case of iterated adaptive filtering by determining the diffusion tensor field from an autocorrelation estimate we obtain an evolution equation that is computed from a scalar product of diffusion tensor and the image hessian we propose further a set of filters to approximate the hessian on a minimized spatial support on standard benchmarks the resulting method performs favorable in many cases in particular at low noise levels in a gpu implementation video real time performance is easily achieved

explicit simplicial discretization of distributed parameter port hamiltonian systems simplicial dirac structures as finite analogues of the canonical stokes dirac structure capturing the topological laws of the system are defined on simplicial manifolds in terms of primal and dual cochains related by the coboundary operators these finite dimensional dirac structures offer a framework for the formulation of standard input output finite dimensional port hamiltonian systems that emulate the behavior of distributed parameter port hamiltonian systems this paper elaborates on the matrix representations of simplicial dirac structures and the resulting port hamiltonian systems on simplicial manifolds employing these representations we consider the existence of structural invariants and demonstrate how they pertain to the energy shaping of port hamiltonian systems on simplicial manifolds

interconnection and damping assignment passivity based control of port controlled hamiltonian systems passivity based control pbc is a well established technique that has shown to be very powerful to design robust controllers for physical systems described by euler lagrange el equations of motion for regulation problems of mechanical systems which can be stabilized shaping only the potential energy pbc preserves the el structure and furthermore assigns a closed loop energy function equal to the difference between the energy of the system and the energy supplied by the controller thus we say that stabilization is achieved via energy balancing unfortunately these nice properties of el pbc are lost when used in other applications which require shaping of the total energy for instance in electrical or electromechanical systems or even some underactuated mechanical devices our main objective in this paper is to develop a new pbc theory which extends to a broader class of systems the aforementioned energy balancing stabilization mechanism and the structure invariance towards this end we depart from the el description of the systems and consider instead port controlled hamiltonian models which result from the network modelling of energy conserving lumped parameter physical systems with independent storage elements and strictly contain the class of el models

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

on the synthesis of boundary control laws for distributed port hamiltonian systems this paper is concerned with the energy shaping of 1 d linear boundary controlled port hamiltonian systems the energy casimir method is first proposed to deal with power preserving systems it is shown how to use finite dimensional dynamic boundary controllers and closed loop structural invariants to partially shape the closed loop energy function and how such controller finally reduces to a state feedback when dissipative port hamiltonian systems are considered the casimir functions do not exist anymore dissipation obstacle and the immersion via a dynamic controller reduction through invariants method cannot be applied the main contribution of this paper is to show how to use the same ideas and state functions to shape the closed loop energy function of dissipative systems through direct state feedback i e without relying on a dynamic controller and a reduction step in both cases the existence of solution and the asymptotic stability by additional damping injection of the closed loop system are proven the general theory and achievable closed loop performances are illustrated with the help of a concluding example the boundary stabilization of a longitudinal beam vibrations

chinchilla middle ear transmission matrix model and middle ear flexibility the function of the middle ear me in transforming me acoustic inputs and outputs sound pressures and volume velocities can be described with an acoustic two port transmission matrix this description is independent of the load on the me cochlea or ear canal and holds in either direction forward from ear canal to cochlea or reverse from cochlea to ear canal a transmission matrix describing me function in chinchilla an animal commonly used in auditory research is presented computed from measurements of forward me function input admittance ytm me pressure gain gmep me velocity transfer function hv and cochlear input admittance yc in the same set of ears ravicz and rosowski 2012b j acoust soc am 132 2437 2454 2013a j acoust soc am 133 2208 2223 2013b j acoust soc am 134 2852 2865 unlike previous estimates these computations require no assumptions about the state of the inner ear effectiveness of me manipulations or measurements of sound transmission in the reverse direction these element values are generally consistent with physical constraints and the anatomical me transformer ratio differences from a previous estimate in chinchilla songer and rosowski 2007 j acoust soc am 122 932 942 may be due to a difference in me flexibility between the two subject groups

weak form of stokes dirac structures and geometric discretization of port hamiltonian systems we present the mixed galerkin discretization of distributed parameter port hamiltonian systems due to the inherent definition of boundary interconnection ports this system representation is particularly useful for the modeling of interconnected multi physics systems and control at the prototypical example of a system of two conservation laws in arbitrary spatial dimension we derive the main contributions i a weak formulation of the underlying geometric stokes dirac structure ii its geometric approximation by a finite dimensional dirac structure using a mixed galerkin approach and power preserving maps on the space of discrete power variables and iii the approximation of the hamiltonian to obtain finite dimensional port hamiltonian state space models the power preserving maps on the discrete bond space offer design degrees of freedom for the discretization which is illustrated at the example whitney finite elements on a 2d simplicial triangulation the resulting schemes can be considered as trade offs between centered approximations and upwinding

a fast and stable well balanced scheme with hydrostatic reconstruction for shallow water flows we consider the saint venant system for shallow water flows with nonflat bottom it is a hyperbolic system of conservation laws that approximately describes various geophysical flows such as rivers coastal areas and oceans when completed with a coriolis term or granular flows when completed with friction numerical approximate solutions to this system may be generated using conservative finite volume methods which are known to properly handle shocks and contact discontinuities however in general these schemes are known to be quite inaccurate for near steady states as the structure of their numerical truncation errors is generally not compatible with exact physical steady state conditions this difficulty can be overcome by using the so called well balanced schemes we describe a general strategy based on a local hydrostatic reconstruction that allows us to derive a well balanced scheme from any given numerical flux for the homogeneous problem whenever the initial solver satisfies some classical stability properties it yields a simple and fast well balanced scheme that preserves the nonnegativity of the water height and satisfies a semidiscrete entropy inequality

effects of ear canal standing waves on measurements of distortion product otoacoustic emissions at frequencies above 3 khz standing waves in the ear canal complicate calibration of stimulus sound pressure levels spls for measurements of distortion product otoacoustic emissions dpoaes in the literature two stimulus presentation strategies have been used for dpoae measurements in the in the ear adjustment strategy the voltage command to the speakers is adjusted to maintain a constant stimulus spl across frequency at the dpoae measurement microphone in the iso voltage strategy the voltage presented to the speakers is held constant across frequency on the basis of the assumption that the frequency response of the speakers is approximately flat at the eardrum in the average human ear canal because of standing wave effects there are large systematic but idiosyncratic differences of stimulus spl between the two strategies dpoae versus frequency functions dpoae audiograms obtained using both stimulus presentation strategies in the same ears are presented the differences of sti

a well balanced flux vector splitting scheme designed for hyperbolic systems of conservation laws with source terms abstract we propose a way to construct robust numerical schemes for the computations of numerical solutions of one and two dimensional hyperbolic systems of balance laws in order to reduce the computational cost we selected the family of flux vector splitting schemes we reformulate the source terms as nonconservative products and treat them directly in the definition of the numerical fluxes by means of generalized jump relations this is applied to a 1d shallow water system with topography and to a 2d simplified model of two phase flows with damping effects numerical results and comparisons with a classical centered discretizations scheme are supplied

nonlinear resonance for quasilinear hyperbolic equation the purpose of this paper is to study the wave behavior of hyperbolic conservation laws with a moving source resonance occurs when the speed of the source is too close to one of the characteristic speeds of the system for the nonlinear system characteristic speeds depend on the basic dependence variables and resonance gives rise to nonlinear interactions which lead to rich wave phenomena motivated by physical examples a scalar model is proposed and analyzed to describe the qualitative behavior of waves for a general system in resonance with the source analytical understanding is used to design a numerical scheme based on the random choice method an important physical example is transonic gas flow through a nozzle this analysis provides a transparent and revealing qualitative understanding of wave behavior of gas flow including such phenomena as nonlinear stability instability and changing types of waves

an isohazard function for impulse noise existing criteria for safe exposure to impulse noise do not consider the frequency spectrum of an impulse as a variable in the evaluation of the hazards to the auditory system this study was designed to determine the relative potential that impulsive energy concentrated at different frequencies has in causing auditory system trauma one hundred and thirty 130 chinchillas divided into 22 groups of 5 to 7 animals were used pre and postexposure audiograms were measured on each animal using avoidance conditioning procedures quantitative histology was used to determine the extent and pattern of the sensory cell damage cochleograms noise exposure employed seven different computer generated narrow band impulses approximately 400 hz bandwidth having center frequencies located at 0 260 0 775 1 025 1 350 2 075 2 450 and 3 550 khz presented at two to four different intensities an isohazard weighting function derived from the audiometric and histological data demonstrates that equivalent amounts

middle ear function in the chinchilla circuit models and comparison with other mammalian species the middle ear efficiently transmits sound from the ear canal into the inner ear through a broad range of frequencies thus understanding middle ear transmission characteristics is essential in the study of hearing mechanics two models of the chinchilla middle ear are presented in the first model the middle ear is modeled as a lumped parameter system with elements that represent the ossicular chain and the middle ear cavity parameters of this model are fit using available experimental data of two port transmission matrix parameters in an effort to improve agreement between model simulations and the phase of published experimental measurements for the forward pressure transfer function at high frequencies a second model in which a lossless transmission line model of the tympanic membrane is appended to the original model is proposed two port transmission matrix parameter results from this second model were compared with results from previously developed models of the guinea pig cat and human middle ears model results and published experimental data for the two port transmission matrix parameters are found to be qualitatively similar between species quantitative differences in the two port transmission matrix parameters suggest that the ossicular chains of chinchillas cats and guinea pigs are less flexible than in humans

coherence enhancing diffusion filtering the completion of interrupted lines or the enhancement of flow like structures is a challenging task in computer vision human vision and image processing we address this problem by presenting a multiscale method in which a nonlinear diffusion filter is steered by the so called interest operator second moment matrix structure tensor an m dimensional formulation of this method is analysed with respect to its well posedness and scale space properties an efficient scheme is presented which uses a stabilization by a semi implicit additive operator splitting aos and the scale space behaviour of this method is illustrated by applying it to both 2 d and 3 d images

equilibrium schemes for scalar conservation laws with stiff sources we consider a simple model case of stiff source terms in hyperbolic conservation laws namely the case of scalar conservation laws with a zeroth order source with low regularity it is well known that a direct treatment of the source term by finite volume schemes gives unsatisfactory results for both the reduced cfl condition and refined meshes required because of the lack of accuracy on equilibrium states the source term should be taken into account in the upwinding and discretized at the nodes of the grid in order to solve numerically the problem we introduce a so called equilibrium schemes with the properties that i the maximum principle holds true ii discrete entropy inequalities are satisfied iii steady state solutions of the problem are maintained one of the difficulties in studying the convergence is that there are no bv estimates for this problem we therefore introduce a kinetic interpretation of upwinding taking into account the source terms based on the kinetic formulation we give a new convergence proof that only uses property ii in order to ensure desired compactness framework for a family of approximate solutions and that relies on minimal assumptions the computational efficiency of our equilibrium schemes is demonstrated by numerical tests that show that in comparison with an usual upwind scheme the corresponding equilibrium version is far more accurate furthermore numerical computations show that equilibrium schemes enable us to treat efficiently the sources with singularities and oscillating coefficients

ear canal acoustic distortion at 2f1 f2 from human ears relation to other emissions and perceived combination tones two aspects of the intermodulation distortion product at 2f1 f2 generated by normal human ears and measured acoustically in the ear canal were studied 1 its relation to tone evoked and spontaneous otoacoustic emissions and 2 its relation to the perceived combination tone at the same frequency with regard to 1 substantial differences among ears in the detectability of emissions were observed ears tended to exhibit all or none of the emission types that were sought within ears possessing emissions the magnitudes of tone evoked emissions and acoustic distortion showed a similar dependence on frequency with regard to 2 a three primary tone stimulus was employed to ask whether the ear canal acoustic distortion tone is canceled under the same stimulus conditions that produce perceptual cancellation simultaneous cancellation of perceptual and acoustic distortion was produced rarely results are interpreted qualitatively with a model in which primary tones produce distortion at their interaction

space time discontinuous galerkin finite element method for shallow water flows a space time discontinuous galerkin dg finite element method is presented for the shallow water equations over varying bottom topography the method results in nonlinear equations per element which are solved locally by establishing the element communication with a numerical hllc flux to deal with spurious oscillations around discontinuities we employ a dissipation operator only around discontinuities using krivodonova s discontinuity detector the numerical scheme is verified by comparing numerical and exact solutions and validated against a laboratory experiment involving flow through a contraction we conclude that the method is second order accurate in both space and time for linear polynomials

space time discontinuous galerkin finite element method with dynamic grid motion for inviscid compressible flows i general formulation a new space time discontinuous galerkin finite element method for the solution of the euler equations of gas dynamics in time dependent flow domains is presented the discontinuous galerkin discretization results in an efficient elementwise conservative upwind finite element method which is particularly well suited for local mesh refinement the upwind scheme uses a formulation of the hllc flux applicable to moving meshes and several formulations for the stabilization operator to ensure that monotone solutions around discontinuities are investigated the non linear equations of the space time discretization are solved using a multigrid accelerated pseudo time integration technique with an optimized runge kutta method the linear stability of the pseudo time integration method is investigated for the linear advection equation the numerical scheme is demonstrated with simulations of the flow field in a shock tube a channel with a bump and an oscillating naca 0012 airfoil these simulations show that using the data at the superconvergence points the accuracy of the numerical discretization is o h5 2 in space for smooth subsonic flows both on structured and on locally refined meshes and that the space time adaptation can significantly improve the accuracy and efficiency of the numerical method

first and second order error estimates for the upwind source at interface method the upwind source at interface method for hyperbolic conservation laws with source term introduced in b perthame c simeoni convergence of the upwind interface source method for hyperbolic conservation laws hyperbolic problems theory numerics applications t hou and e tadmor eds springer 2003 is essentially first order accurate under appropriate hypotheses of consistency on the finite volume discretization of the source term we prove l p error estimates 1 le p infty in the case of a uniform spatial mesh for which an optimal result can be obtained we thus conclude that the same convergence rates hold as for the corresponding homogeneous problem to improve the numerical accuracy we develop two different approaches of dealing with the source term and we discuss the question of deriving second order error estimates numerical evidence shows that those techniques produce high resolution schemes compatible with the upwind source at interface method

distortion product otoacoustic emission 2 f1 f2 amplitude as a function of f2 f1 frequency ratio and primary tone level separation in human adults and neonates distortion product otoacoustic emission dpoae 2 f1 f2 amplitude is dependent upon both the frequency ratio and level separation of the eliciting primary tones in adults it has been established that on average a f2 f1 ratio of 1 22 is optimal for evoking the most robust dpoae dpoae amplitude is systematically reduced when f2 f1 ratio is either increased or decreased thus forming a bandpass function harris et al 1989 the frequency ratio function dpoae amplitude f2 f1 ratio is thought to reflect the filtering properties of the cochlea allen and fahey 1993 brown et al 1993 primary tone level separation also influences dpoae amplitude with a 10 to 15 db level difference between the primary tones l1 l2 typically generating largest amplitude in adults equivalent studies have not been conducted in neonates the present study evoked the 2 f1 f2 dpoae in adults term and premature neonates to define the optimal f2 f1 ratio and l1 l2 level separation and to investigate the filtering prope

port hamiltonian discretization for open channel flows a finite dimensional port hamiltonian formulation for the dynamics of smooth open channel flows is presented a numerical scheme based on this formulation is developed for both the linear and nonlinear shallow water equations the scheme is verified against exact solutions and has the advantage of conservation of mass and energy to the discrete level

a level set method for anisotropic geometric diffusion in 3d image processing a new morphological multiscale method in three dimensional 3d image processing is presented which combines the image processing methodology based on nonlinear diffusion equations and the theory of geometric evolution problems its aim is to smooth the level sets of a 3d image while simultaneously preserving geometric features such as edges and corners on the level sets this is obtained by an anisotropic curvature evolution where time serves as the multiscale parameter thereby the diffusion tensor depends on a regularized shape operator of the evolving level sets as one suitable regularization local l2 projection onto quadratic polynomials is considered the method is compared to a related parametric surface approach and a geometric interpretation of the evolution and its invariance properties is given a spatial finite element discretization on hexahedral meshes and a semi implicit regularized backward euler discretization in time are the building blocks of the easy to code algorithm different a

middle ear phenomenology the view from the three windows to provide a common ground for the comparison between theory and experiment this paper presents a framework for the phenomenological description of middle ear mechanics the framework defines those measurements sufficient to characterize the transduction properties of the middle ear and its components phenomenological equations are represented in the form of an equivalent electrical circuit that can be used to deduce testable relations among measurable quantities two applications are then discussed first the classical concept of the middle ear transformer ratio is generalized to include any effects of eardrum flexion or nonrotational ossicular motion middle ear models predict that the resulting transformer ratios vary considerably with frequency second the conditions under which the topology of existing circuit analogs satisfactorily approximates middle ear mechanics are given most middle ear models cannot be used to correctly predict the absolute pressures in the cochlea

localized measurement of emergent image frequencies by gabor wavelets the authors derive implement and demonstrate a computational approach for the measurement of emergent image frequencies measuring emergent signal frequencies requires spectral measurements accurate in both frequency and time or space conflicting requirements that are shown to be balanced by a generalized uncertainty relationship such spectral measurements can be obtained from the responses of multiple wavelet like channel filters that sample the signal spectrum and that yield a locus of possible solutions for each locally emergent frequency it is shown analytically that this locus of solutions is maximally localized in both space and frequency if the channel filters used are gabor wavelets a constrained solution is obtained by imposing a stabilizing term that develops naturally from the assumptions on the signal the measurement of frequencies is then cast as an ill posed extremum problem regularized by the stabilizing term leading to an iterative constraint propagation algorithm the technique is demonstrated by application to a variety of 2 d textured images

the behavior of the acoustic distortion product 2f1 f2 from the human ear and its relation to auditory sensitivity the acoustic intermodulation distortion product 2f1 f2 adp was measured in human subjects to investigate 1 the dependence of adp level on stimulus parameters and 2 the relationship between adp level and auditory sensitivity the frequency ratio f2 f1 at which adp level is maximal varies only slightly across frequency and subjects the average optimal ratio is 1 225 beyond the maximum the adp level declines with increasing f2 f1 ratio at rates of up to 250 db oct as the level of one stimulus is increased relative to the other the adp grows saturates and in most cases shows a bendover maximum distortion is generated when l 1 exceeds l 2 growth rate and saturation point are dependent on which stimulus is incremented and on the level of the stationary stimulus with optimal stimulus parameters levels below 60 db spl l 1 greater than l 2 by 15 db f2 f1 1 225 adp levels are commonly 30 db below l 2 patterns of adp level across frequency vary between subjects but are repeatable within each subject as the frequency of one or both of the stimuli is varied changes in adp level exhibit a broadly featured pattern with a fine structure superimposed upon it this fine structure was compared with the features in the stimulus frequency emission spectrum in one subject with appropriate stimulus parameters half of our subjects show a statistically significant correlation across frequency between adp level and auditory sensitivity at the corresponding f1 frequency our results suggest that with low levels of stimulation adp measurements could form the basis of an objective measure of cochlear function in human subjects

space time discontinuous galerkin discretization of rotating shallow water equations a space time discontinuous galerkin dg discretization is presented for the rotating shallow water equations over varying topography we formulate the space time dg finite element discretization in an efficient and conservative discretization the hllc flux is used as numerical flux through the finite element boundaries when discontinuities are present we locally apply dissipation around these discontinuities with the help of krivodonova s discontinuity indicator such that spurious oscillations are suppressed the non linear algebraic system resulting from the discretization is solved using a pseudo time integration with a second order five stage runge kutta method a thorough verification of the space time dg finite element method is undertaken by comparing numerical and exact solutions we also carry out a discrete fourier analysis of the one dimensional linear rotating shallow water equations to show that the method is unconditionally stable with minimal dispersion and dissipation error the numerical scheme is validated in a novel way by considering various simulations of bore vortex interactions in combination with a qualitative analysis of pv generation by non uniform bores finally the space time dg method is particularly suited for problems where dynamic grid motion is required to demonstrate this we simulate waves generated by a wave maker and verify these for low amplitude waves where linear theory is approximately valid

dirac structures on hilbert spaces and boundary control of distributed port hamiltonian systems abstract aim of this paper is to show how the dirac structure properties can be exploited in the development of energy based boundary control laws for distributed port hamiltonian systems usually stabilization of non zero equilibria has been achieved by looking at or generating a set of structural invariants namely casimir functions in closed loop since this approach fails when an infinite amount of energy is required at the equilibrium dissipation obstacle this paper illustrates a novel approach that enlarges the class of stabilizing controllers the starting point is the parametrization of the dynamics provided by the image representation of the dirac structure that is able to show the effects of the boundary inputs on the state evolution in this way energy balancing and control by state modulated source methodologies are extended to the distributed parameter scenario and a geometric interpretation of these control techniques is provided the theoretical results are discussed with the help of a simple but illustrative example i e a transmission line with an rlc load in both serial and parallel configurations in the latter case energy balancing controllers are not able to stabilize non zero equilibria because of the dissipation obstacle the problem is solved thanks to a boundary state modulated source

on representations and integrability of mathematical structures in energy conserving physical systems in the present paper we elaborate on the underlying hamiltonian structure of interconnected energy conserving physical systems it is shown that a power conserving interconnection of port controlled generalized hamiltonian systems leads to an implicit generalized hamiltonian system and a power conserving partial interconnection to an implicit port controlled hamiltonian system the crucial concept is the notion of a generalized dirac structure defined on the space of energy variables or on the product of the space of energy variables and the space of flow variables in the port controlled case three natural representations of generalized dirac structures are treated necessary and sufficient conditions for closedness or integrability of dirac structures in all three representations are obtained the theory is applied to implicit port controlled generalized hamiltonian systems and it is shown that the closedness condition for the dirac structure leads to strong conditions on the input vector fields

robust processing of optical flow of fluids this paper proposes a new approach coupling physical models and image estimation techniques for modelling the movement of fluids the fluid flow is characterized by turbulent movement and dynamically changing patterns which poses challenges to existing optical flow estimation methods the proposed methodology which relies on navier stokes equations is used for processing fluid optical flow by using a succession of stages such as advection diffusion and mass conservation a robust diffusion step jointly considering the local data geometry and its statistics is embedded in the proposed framework the diffusion kernel is gaussian with the covariance matrix defined by the local second derivatives such an anisotropic kernel is able to implicitly detect changes in the vector field orientation and to diffuse accordingly a new approach is developed for detecting fluid flow structures such as vortices the proposed methodology is applied on artificially generated vector fields as well as on various image sequences

an anisotropic fourth order diffusion filter for image noise removal fourth order nonlinear diffusion filters used for image noise removal are mainly isotropic filters it means that the spatially varying diffusivity determined by a diffusion function is applied on the image regardless of the orientation of its local features however the optimal choice of parameters in the numerical solver of these filters for having a minimal distortion of the image features results in forming speckle noise on the denoised image and a very slow convergence rate especially when the noise level is moderately high in this paper a new fourth order nonlinear diffusion filter is introduced which has an anisotropic behavior on the image features in the proposed filter it is shown that a suitable choice for a set of diffusivity functions to unevenly control the strength of the diffusion on the directions of the level set and gradient leads to a good edge preservation capability compared to the other diffusion or regularization filters the comparison of the results obtained by the proposed filter with those of the other second and fourth order filters shows that the proposed method produces a noticeable improvement in the quality of denoised images evaluated subjectively and quantitatively

adaptive smoothing respecting feature directions accurate extraction of the image feature directions is essential to image smoothing and other image processing tasks we show that the gradient based feature direction extraction method can be very erroneous the gradient is too local and it cannot detect oscillations we have developed two new methods the hessian method an approach using higher order differentiations and the gabor 1946 method an approach using space frequency analysis

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

stability and passivity preserving petrov galerkin approximation of linear infinite dimensional systems this contribution presents two approximation methods for linear infinite dimensional systems that ensure the preservation of stability and passivity the first approach allows one to approximate internal source free infinite dimensional systems such that the resulting approximation is a port controlled hamiltonian system with dissipation the second method deals with the class of systems that are not required to have conjugated outputs but only a dissipative system operator it yields approximations with a dissipative system matrix for which bounds of their stability margin are provided both approaches are based on a state space formulation of the infinite dimensional system this makes it possible to use the petrov galerkin approximation whose free parameters are partly used for achieving the structure preservation since still free parameters remain further application specific objectives such as e g moment matching can be achieved both approaches are applied to the approximation of an euler bernoulli beam

a well balanced scheme for the numerical processing of source terms in hyperbolic equations in a variety of physical problems one encounters source terms that are balanced by internal forces and this balance supports multiple steady state solutions that are stable typical of these are gravity driven flows such as those described by the shallow water equations over a nonuniform ocean bottom 1 10 qquad h t hu x 0 text and hu t left hu 2 frac gh 2 2 right x ga x x h 0 many classic numerical schemes cannot maintain these steady solutions or achieve them in the long time limit with an acceptable level of accuracy because they do not preserve the proper balance between the source terms and internal forces we propose here a numerical scheme adapted to a scalar conservation law that preserves this balance and that can it is hoped be extended to more general hyperbolic systems the proof of convergence of this scheme toward the entropy solution is given and some numerical tests are reported

space time discontinuous galerkin method for nonlinear water waves a space time discontinuous galerkin dg finite element method for nonlinear water waves in an inviscid and incompressible fluid is presented the space time dg method results in a conservative numerical discretization on time dependent deforming meshes which follow the free surface evolution the algorithm is higher order accurate both in space and time and closely related to an arbitrary lagrangian eulerian ale approach a detailed derivation of the numerical algorithm is given including an efficient procedure to solve the nonlinear algebraic equations resulting from the space time discretization numerical examples are shown on a series of model problems to demonstrate the accuracy and capabilities of the method

cortical responses to the 2f1 f2 combination tone measured indirectly using magnetoencephalography the simultaneous presentation of two tones with frequencies f1 and f2 causes the perception of several combination tones in addition to the original tones the most prominent of these are at frequencies f2 f1 and 2f1 f2 this study measured human physiological responses to the 2f1 f2 combination tone at 500hz caused by tones of 750 and 1000hz with intensities of 65 and 55db spl respectively responses were measured from the cochlea using the distortion product otoacoustic emission dpoae and from the auditory cortex using the 40 hz steady state magnetoencephalographic meg response the perceptual response was assessed by having the participant adjust a probe tone to cause maximal beating best beats with the perceived combination tone the cortical response to the combination tone was evaluated in two ways first by presenting a probe tone with a frequency of 460hz at the perceptual best beats level resulting in a 40 hz response because of interaction with the combination tone at 500hz and secon

robust scale space filter using second order partial differential equations this paper describes a robust scale space filter that adaptively changes the amount of flux according to the local topology of the neighborhood in a manner similar to modeling heat or temperature flow in physics the robust scale space filter is derived by coupling fick s law with a generalized continuity equation in which the source or sink is modeled via a specific heat capacity the filter plays an essential part in two aspects first an evolution step size is adaptively scaled according to the local structure enabling the proposed filter to be numerically stable second the influence of outliers is reduced by adaptively compensating for the incoming flux we show that classical diffusion methods represent special cases of the proposed filter by analyzing the stability condition of the proposed filter we also verify that its evolution step size in an explicit scheme is larger than that of the diffusion methods the proposed filter also satisfies the maximum principle in the same manner as the diffusion our experimental results show that the proposed filter is less sensitive to the evolution step size as well as more robust to various outliers such as gaussian noise impulsive noise or a combination of the two

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

a port hamiltonian formulation of the navier stokes equations for reactive flows abstract we consider the problem of finding an energy based formulation of the navier stokes equations for reactive flows these equations occur in various applications e g in combustion engines or chemical reactors after modeling discretization and model reduction important system properties as the energy conservation are usually lost which may lead to unphysical simulation results in this paper we introduce a port hamiltonian formulation of the one dimensional navier stokes equations for reactive flows the port hamiltonian structure is directly associated with an energy balance which ensures that a temporal change of the total energy is only due to energy flows through the boundary furthermore the boundary ports may be used for control purposes

variational space time dis continuous galerkin method for nonlinear free surface water waves a new variational finite element method is developed for nonlinear free surface gravity water waves using the potential flow approximation this method also handles waves generated by a wave maker its formulation stems from miles variational principle for water waves together with a finite element discretization that is continuous in space and discontinuous in time one novel feature of this variational finite element approach is that the free surface evolution is variationally dependent on the mesh deformation vis a vis the mesh deformation being geometrically dependent on free surface evolution another key feature is the use of a variational dis continuous galerkin finite element discretization in time moreover in the absence of a wave maker it is shown to be equivalent to the second order symplectic stormer verlet time stepping scheme for the free surface degrees of freedom these key features add to the stability of the numerical method finally the resulting numerical scheme is verified against nonlinear analytical solutions with long time simulations and validated against experimental measurements of driven wave solutions in a wave basin of the maritime research institute netherlands

a discontinuous galerkin algorithm for the two dimensional shallow water equations a new high resolution finite element scheme is introduced for solving the two dimensional 2d depth integrated shallow water equations swe via local plane approximations to the unknowns bed topography data are locally approximated in the same way as the flow variables to render an instinctive well balanced scheme a finite volume fv wetting and drying technique that reconstructs the riemann states by ensuring non negative water depth and maintaining well balanced solution is adjusted and implemented in the current finite element framework meanwhile a local slope limiting process is applied and those troubled slope components are restricted by the minmod fv slope limiter the inter cell fluxes are upwinded using the hllc approximate riemann solver friction forces are separately evaluated via stable implicit discretization to the finite element approximating coefficients boundary conditions are derived and reported in details the present model is validated against several test cases including dam break flows on regular and irregular domains with flooding and drying

sources of distortion product otoacoustic emissions revealed by suppression experiments and inverse fast fourier transforms in normal ears primary and secondary sources combine to produce the 2f1 f2 distortion product otoacoustic emission dpoae measured in the ear canals of humans dpoaes were obtained in nine normal hearing subjects using a fixed f2 paradigm in which f1 was varied the f2 was 2 or 4 khz and absolute and relative primary levels were varied data were obtained with and without a third tone f3 placed 15 6 hz below 2f1 f2 the level of f3 was varied in order to suppress the stimulus frequency otoacoustic emission sfoae coming from the 2f1 f2 place these data were converted from the complex frequency domain into an equivalent time representation using an inverse fast fourier transform ifft iffts of unsuppressed dpoae data were characterized by two or more peaks relative amplitudes of these peaks depended on overall primary level and on primary level differences the suppressor eliminated later peaks but early peaks remained relatively unaltered results are interpreted to mean that the dpoae measured in humans includes components from the f2 place intermodulation distortion and dp place in the form of a sfoae these findings build on previous work by providing evidence that multiple peaks in the ifft are due to a secondary source at the dp place

a regularized curvature flow designed for a selective shape restoration among all filtering techniques those based exclusively on image level sets geometric flows have proven to be the less sensitive to the nature of noise and the most contrast preserving a common feature to existent curvature flows is that they penalize high curvature regardless of the curve regularity this constitutes a major drawback since curvature extreme values are standard descriptors of the contour geometry we argue that an operator designed with shape recovery purposes should include a term penalizing irregularity in the curvature rather than its magnitude to this purpose we present a novel geometric flow that includes a function that measures the degree of local irregularity present in the curve a main advantage is that it achieves nontrivial steady states representing a smooth model of level curves in a noisy image performance of our approach is compared to classical filtering techniques in terms of quality in the restored image shape and asymptotic behavior we empirically prove that our approach is the technique that achieves the best compromise between image quality and evolution stabilization

space time discontinuous galerkin finite element method for two fluid flows a novel numerical method for two fluid flow computations is presented which combines the space time discontinuous galerkin finite element discretization with the level set method and cut cell based interface tracking the space time discontinuous galerkin stdg finite element method offers high accuracy an inherent ability to handle discontinuities and a very local stencil making it relatively easy to combine with local hp refinement the front tracking is incorporated via cut cell mesh refinement to ensure a sharp interface between the fluids to compute the interface dynamics the level set method lsm is used because of its ability to deal with merging and breakup also the lsm is easy to extend to higher dimensions small cells arising from the cut cell refinement are merged to improve the stability and performance the interface conditions are incorporated in the numerical flux at the interface and the stdg discretization ensures that the scheme is conservative as long as the numerical fluxes are conservative the numerical method is applied to one and two dimensional two fluid test problems using the euler equations

energy shaping of distributed parameter port hamiltonian systems based on finite element approximation the main contribution of this paper is a procedure for the control by energy shaping via casimir generation of infinite dimensional port hamiltonian systems based on a particular finite element approximation the proposed approach is justified by the fact that the adopted spatial discretization technique is able to preserve casimir functions in the closed loop system when going from the distributed to the approximated lumped parameter system besides the intrinsic difficulties related to the large number of state variables the finite element model is generally given in terms of a dirac structure and is completely a causal which implies that the plant dynamics is not given in standard input state output form but as a set of daes consequently the classical energy casimir method has to be extended in order to deal with dynamical systems with constraints usually appearing in the form of lagrangian multipliers the general methodology is illustrated with the help of an example in which the distributed parameter system is a lossless transmission line

convergence of the 2 2 godunov method for a general resonant nonlinear balance law we introduce a generalized solution of the riemann problem for a general resonant nonlinear balance law and we prove the convergence of the 2 x 2 godunov numerical method based on these solutions in particular we obtain generic conditions that guarantee a canonical structure for the elementary waves in the solution of the riemann problem and an interesting multiplicity of time asymptotic wave patterns is observed and characterized

the effect of stimulus frequency ratio on distortion product otoacoustic emission components a detailed measurement of distortion product otoacoustic emission dpoae fine structure was used to extract estimates of the two major components believed to contribute to the overall dpoae level in the ear canal a fixed ratio paradigm was used to record dpoae fine structure from three normal hearing ears over a range of 400 hz for 12 different stimulus frequency ratios between 1 053 and 1 36 and stimulus levels between 45 and 75 db spl inverse fourier transforms of the amplitude and phase data were filtered to extract the early component from the generator region of maximum stimulus overlap and the later component reflected from the characteristic frequency region of the dpoae after filtering the data were returned to the frequency domain to evaluate the impact of the stimulus frequency ratio and stimulus level on the relative levels of the components although there were significant differences between data from different ears some consistent patterns could be detected the component from the overlap region of the stimulus tones exhibits a bandpass shape with the maximum occurring at a ratio of 1 2 the mean data from the dpoae characteristic frequency region also exhibits a bandpass shape but is less sharply tuned and exhibits greater variety across ears and stimulus levels the component from the dpoae characteristic frequency region is dominant at ratios narrower than approximately 1 1 the transition varies between ears the relative levels of the two components are highly variable at ratios greater than 1 3 and highly dependent on the stimulus level the reflection component is larger at all ratios at the lowest stimulus level tested 45 45 db spl we discuss the factors shaping dpoae component behavior and some cursory implications for the choice of stimulus parameters to be used in clinical protocols

spectral shapes of forward and reverse transfer functions between ear canal and cochlea estimated using dpoae input output functions it is widely assumed that the distortion characteristics of the cochlea are uniform across its length or at least across some portion of its length for each distortion product otoacoustic emission dpoae input output i o function across frequency there is a corresponding cochlear i o function defined over the cochlear source region an assumption of distortion invariance is adopted such that these cochlear i o functions are identical across tonotopic place which is testable in the sense that a single nonlinear function should adequately describe the set of dpoae i o functions across frequency if so the differences in measured dpoae i o functions across frequency are produced by differences in the forward stimulus transmission to the generation site and reverse dp transmission back to the ear canal the absolute transfer function magnitude is not determined by this technique but the spectral shapes across frequency and between ears are determined the role of middle ear functioning is implicit in the i o functions because of its controlling influence on these transfer functions results have been obtained using the average dpoae i o functions measured in a population of healthy ears gorga et al j acoust soc am 107 2128 2135 2000 and support the hypothesis of cochlear distortion invariance the measured forward and reverse transfer functions have a general bandpass characteristic and a more narrow band structure with similarities to the behavioral threshold curve

on structure preserving model reduction for damped wave propagation in transport networks we consider the discretization and subsequent model reduction of a system of partial differential algebraic equations describing the propagation of pressure waves in a pipeline network important properties like conservation of mass dissipation of energy passivity existence of steady states and exponential stability can be preserved by an appropriate semidiscretization in space via a mixed finite element method and also during the further dimension reduction by structure preserving galerkin projection which is the main focus of this paper krylov subspace methods are employed for the construction of the reduced models and we discuss certain modifications needed to satisfy some algebraic compatibility conditions which are required to ensure the well posedness of the reduced models and the preservation of the key properties our arguments are based on a careful analysis of the underlying infinite dimensional problem and its galerkin approximations the proposed algorithms therefore have a direct inte

discontinuous galerkin finite element methods for hyperbolic nonconservative partial differential equations we present space and space time discontinuous galerkin finite element dgfem formulations for systems containing nonconservative products such as occur in dispersed multiphase flow equations the main criterium we pose on the weak formulation is that if the system of nonconservative partial differential equations can be transformed into conservative form then the formulation must reduce to that for conservative systems standard dgfem formulations cannot be applied to nonconservative systems of partial differential equations we therefore introduce the theory of weak solutions for nonconservative products into the dgfem formulation leading to the new question how to define the path connecting left and right states across a discontinuity the effect of different paths on the numerical solution is investigated and found to be small we also introduce a new numerical flux that is able to deal with nonconservative products our scheme is applied to two different systems of partial differential equations first we consider the shallow water equations where topography leads to nonconservative products in which the known possibly discontinuous topography is formally taken as an unknown in the system second we consider a simplification of a depth averaged two phase flow model which contains more intrinsic nonconservative products

hamiltonian discretization of boundary control systems a fundamental problem in the simulation and control of complex physical systems containing distributed parameter components concerns finite dimensional approximation numerical methods for partial differential equations pdes usually assume the boundary conditions to be given while more often than not the interaction of the distributed parameter components with the other components takes place precisely via the boundary on the other hand finite dimensional approximation methods for infinite dimensional input output systems e g in semi group format are not easily relatable to numerical techniques for solving pdes and are mainly confined to linear pdes in this paper we take a new view on this problem by proposing a method for spatial discretization of boundary control systems based on a particular type of mixed finite elements resulting in a finite dimensional input output system the approach is based on formulating the distributed parameter component as an infinite dimensional port hamiltonian system and exploiting the geometric structure of this representation for the choice of appropriate mixed finite elements the spatially discretized system is again a port hamiltonian system which can be treated as an approximating lumped parameter physical system of the same type in the current paper this program is carried out for the case of an ideal transmission line described by the telegrapher s equations and for the two dimensional wave equation

discontinuous galerkin finite element method for shallow two phase flows we present a discontinuous galerkin finite element method for two depth averaged two phase flow models one of these models contains nonconservative products for which we developed a discontinuous galerkin finite element formulation in rhebergen et al 2008 j comput phys 227 1887 1922 the other model is a new depth averaged two phase flow model we introduce for shallow two phase flows that does not contain nonconservative products we will compare numerical results of both models and qualitatively validate the models against a laboratory experiment furthermore because of spurious oscillations that may occur near discontinuities a weno slope limiter is applied in conjunction with a discontinuity detector to detect regions where spurious oscillations appear

the effects of frequency region and bandwidth on the temporal modulation transfer function temporal modulation transfer functions tmtfs were measured using narrow band am and qfm noises with upper spectral edges from 0 6 to 4 8 khz and spectrum levels of 10 and 40 db spl the cutoff frequency of the tmtf increases as the upper spectral edge is increased up to 4 8 khz at low levels and is constant at higher levels sensitivity increases with bandwidth if frequency region is constant in a second experiment these results were compared to predictions of a model incorporating peripheral and central limitations to modulation detection to obtain an estimate of peripheral filtering frequency selectivity was measured using the notched noise method with probe frequencies and levels chosen to parallel those in the first experiment the tmtf data were then predicted using the model predicted cutoff frequencies as a function of the upper spectral edge of the test stimulus were lower than but parallel to those of the subjects at the lower stimulus level the model predicted only a slight increase in cutoff frequency with level and thus predicted an increase in cutoff frequency with frequency region at the higher level as well in contrast to the measured data these results suggest that there are peripheral and central limitations to temporal resolution but the psychoacoustically derived auditory filter may be only an indirect measure of peripheral filtering and or a more complex model may be needed

an entropy stable nodal discontinuous galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry we design an arbitrary high order accurate nodal discontinuous galerkin spectral element approximation for the non linear two dimensional shallow water equations with non constant possibly discontinuous bathymetry on unstructured possibly curved quadrilateral meshes the scheme is derived from an equivalent flux differencing formulation of the split form of the equations we prove that this discretization exactly preserves the local mass and momentum furthermore combined with a special numerical interface flux function the method exactly preserves the mathematical entropy which is the total energy for the shallow water equations by adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme that is the numerical scheme discretely satisfies the second law of thermodynamics finally with a particular discretization of the bathymetry source term we prove that the numerical approximation is well balanced we provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem

noise removal using smoothed normals and surface fitting in this work we use partial differential equation techniques to remove noise from digital images the removal is done in two steps we first use a total variation filter to smooth the normal vectors of the level curves of a noise image after this we try to find a surface to fit the smoothed normal vectors for each of these two stages the problem is reduced to a nonlinear partial differential equation finite difference schemes are used to solve these equations a broad range of numerical examples are given in the paper

a velocity divergence constraint for large eddy simulation of low mach flows the velocity divergence rate of fluid volumetric expansion is a flow field quantity of fundamental importance in low mach flows it directly affects the local mass density and therefore the local temperature through the equation of state in this paper starting from the conservative form of the sensible enthalpy transport equation we derive a discrete divergence constraint for use in large eddy simulation les of low mach flows the result accounts for numerical transport of mass and energy which is difficult to eliminate in relatively coarse engineering les calculations when total variation diminishing tvd scalar transport schemes are employed without the correction terms derived here unresolved numerical mixing of gas species with different heat capacities or molecular weights may lead to erroneous mixture temperatures and ultimately to an imbalance in the energy budget the new formulation is implemented in a publicly available les code called the fire dynamics simulator fds accuracy of the flow solver for transport is demonstrated using the method of manufactured solutions the conservation properties of the present scheme are demonstrated on two simple energy budget test cases one involving a small fire in a compartment with natural ventilation and another involving mixing of two gases with different thermal properties

a conservative high order discontinuous galerkin method for the shallow water equations with arbitrary topography a conservative high order godunov type scheme is presented for solving the balance laws of the 1d shallow water equations swe the scheme adopts a finite element runge kutta rk discontinuous galerkin dg framework based on an overall third order accurate formulation the model is referred to as rkdg3 treatment of topographic source term is built in the dg approximation simplified formulae for initializing bed data at a discrete level are derived by assuming a local linear bed function to ease practical flow simulations owing to the adverse effects caused by using an uncontrolled global limiting process in an rkdg3 scheme rkdg3 gl a new conservative rkdg3 scheme with user parameter free local limiting method rkdg3 ll is designed to gain better accuracy and conservativeness the advantages of the new rkdg3 ll model are demonstrated by applying to several steady and transient benchmark flow tests with irregular either differentiable or non differentiable topography copyright 2010 john wiley sons ltd