vertical normal modes of human ears individual variation and frequency estimation from pinna anthropometry beyond the first peak of head related transfer functions or pinna related transfer functions prtfs human pinnae are known to have two normal modes with vertical resonance patterns involving two or three pressure anti nodes in cavum cymba and fossa however little is known about individual variations in these modes and there is no established model for estimating their center frequencies from anthropometry here with geometries of 38 pinnae measured prtfs were calculated and vertical modes visualized by numerical simulation most pinnae were found to have both cavum fossa and cavum cymba modes with opposite phase anti nodes in cavum and either fossa or cymba respectively nevertheless in both modes fossa involvement varied substantially across pinnae dependent on scaphoid fossa depth and cymba shallowness linear regression models were evaluated in mode frequency estimation with 3322 measures derived from 31 pinna landmarks the cavum fossa normal mode frequency was best estimated correlat

a steerable complex wavelet construction and its application to image denoising this work addresses the design of a novel complex steerable wavelet construction the generation of transform space feature measurements associated with corner and edge presence and orientation properties and the application of these measurements directly to image denoising the decomposition uses pairs of bandpass filters that display symmetry and antisymmetry about a steerable axis of orientation while the angular characterization of the bandpass filters is similar to those previously described the radial characteristic is new as is the manner of constructing the interpolation functions for steering the complex filters have been engineered into a multirate system providing a synthesis and analysis subband filtering system with good reconstruction properties although the performance of our proposed denoising strategy is currently below that of recently reported state of the art techniques in denoising it does compare favorably with wavelet coring approaches employing global thresholds and with an oracle shrinkage technique and presents a very promising avenue for exploring structure based denoising in the wavelet domain

mechanism for generating peaks and notches of head related transfer functions in the median plane it has been suggested that the first spectral peak and the first two spectral notches of head related transfer functions hrtfs are cues for sound localization in the median plane therefore to examine the mechanism for generating spectral peaks and notches hrtfs were calculated from four head shapes using the finite difference time domain method the comparison between hrtfs calculated from the whole head and the pinna related transfer functions calculated from the segmented pinna indicated that the pinna determines the basic peak notch pattern of the hrtfs an analysis of the distribution patterns of pressure nodes and anti nodes on the pinna computed in the steady state for sinusoidal excitations confirmed that the first three peaks correspond to the first three normal modes of the pinna the analysis also revealed that at the first spectral notch frequencies one or two anti nodes appeared in the cymba and the triangular fossa and a node developed in the concha furthermore according to changes in the instantaneous pressure distribution patterns on the pinna three types of mechanisms were hypothesized for inducing the node in the concha depending on the source elevation angle

binary restoration of thin objects in multidimensional imagery we present a method for restoration of noisy tomographic images for detecting thin objects such as explosives use of a weighted mean square estimate optimizes the solution to place emphasis on the infrequent but significant local structure associated with thin objects experimental results show successful restoration at very high noise levels

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

virtual localization improved by scaling nonindividualized external ear transfer functions in frequency this study examined virtual sound localization in three conditions that differed according to the directional transfer functions dtfs that were used to synthesize the virtual targets the own ear and other ear conditions used dtfs measured from listeners own ears and those measured from other subjects respectively the scaled ear condition employed other ear dtfs that were scaled in frequency to minimize the mismatch between spectral features in the listener s and the other subject s dtfs all measures of localization error typically were lowest in the own ear condition in other ear conditions all error measures tended to increase in proportion to the inter subject differences in dtfs when spectral features in an other ear set of dtfs fell systematically lower in frequency than in a listener s own dtfs low frontal targets typically were reported as low in the rear and high rear targets were reported as high in front when spectral features in a set of dtfs fell systematically higher in frequency than in a listener s own dtfs elevation judgements showed an upward bias in the scaled ear condition all measures of performance tended to improve relative to the other ear condition in the majority of cases frequency scaling more than halved the penalty for use of another subject s dtfs

individual differences in external ear transfer functions reduced by scaling in frequency this study examined inter subject differences in the transfer functions from the free field to the human ear canal which are commonly know as head related transfer functions the directional components of such transfer functions are referred here to as directional transfer functions dtfs the dtfs of 45 subjects varied systematically among subjects in regard to the frequencies of spectral features such as peaks and notches inter subject spectral differences in dtfs were quantified between 3 7 and 12 9 khz for sound source directions throughout the coordinate sphere for each pair of subjects an optimal frequency scale factor aligned spectral features between subjects and thus minimized inter subject spectral differences frequency scaling of dtfs reduced spectral differences by a median value of 15 5 across all pairs of subjects and by more than half in 9 5 of subject pairs optimal scale factors showed a median value of 1 061 and a maximum of 1 38 the optimal scale factor between any pair of subjects correlated highly with the ratios of subjects maximum interaural delays sizes of their external ears and widths of their heads

design of multiparameter steerable functions using cascade basis reduction an efficient method of computing the least squares optimal basis functions to steer any function locally is presented the method combines the lie group theoretic and the singular value decomposition approaches its efficiency is demonstrated with the design of basis functions to steer a gabor function under the four parameter linear transformation group

approximating filtered scale variant signals we develop theorems that place limits on the point wise approximation of the responses of filters both linear shift invariant lsi and linear shift variant lsv to input signals and images that are lsv in the following sense they can be expressed as the outputs of systems with lsv impulse responses where the shift variance is with respect to the filter scale of a single prototype filter the approximations take the form of lsi approximations to the responses we develop tight bounds on the approximation errors expressed in terms of filter durations and derivative sobolev norms finally we find application of the developed theory to defoveation of images deblurring of shift variant blurs and shift variant edge detection

a comparative study of interaural time delay estimation methods the interaural time delay itd is an important binaural cue for sound source localization calculations of itd values are obtained either from measured time domain head related impulse responses hrirs or from their frequency transform head related transfer functions hrtfs numerous methods exist in current literature based on a variety of definitions and assumptions of the nature of the itd as an acoustic cue this work presents a thorough comparative study of the degree of variability between some of the most common methods for calculating the itd from measured data thirty two different calculations or variations are compared for positions on the horizontal plane for the hrtf measured on both a kemar mannequin and a rigid sphere specifically the spatial variations of the methods are investigated included is a discussion of the primary potential causes of these differences such as the existence of multiple peaks in the hrir of the contra lateral ear for azimuths near the inter aural axis due to multipath propagation and head pinnae shadowing

invertible apertured orientation filters in image analysis a unitary approach for locally apertured orientation analysis of 2d and 3d scalar images is proposed the size of the local aperture the scale needed for the orientation representation induces in general a lost of spatial acuity or blur our construction permits a compensation of the blur by a reconstruction procedure for this purpose a special scale dependent orientation bundle map of the visual space into function of both position and orientation is build from the local gaussian derivatives jet of a scalar image in this construction there is an invertible relation between the orientation bundle and the original image this invertible transformation is used to regain the original acuity in the spatial domain after analyzing orientation features at any given scale the approach turns out to be highly effective for the detection of elongated structures and for removal of elongated artifacts in 2d images

fast multipole boundary element method to calculate head related transfer functions for a wide frequency range head related transfer functions hrtfs play an important role in spatial sound localization the boundary element method bem can be applied to calculate hrtfs from non contact visual scans because of high computational complexity hrtf simulations with bem for the whole head and pinnae have only been performed for frequencies below 10khz in this study the fast multipole method fmm is coupled with bem to simulate hrtfs for a wide frequency range the basic approach of the fmm and its implementation are described a mesh with over 70 000 elements was used to calculate hrtfs for one subject with this mesh the method allowed to calculate hrtfs for frequencies up to 35khz comparison to acoustically measured hrtfs has been performed for frequencies up to 16khz showing a good congruence below 7khz simulations with an additional shoulder mesh improved the congruence in the vertical direction reduction in the mesh size by 5 resulted in a substantially worse representation of spectral cues the effec

spherical harmonics singular value decomposition and the head related transfer function abstract the singular value decomposition svd can be used to analyze the matrix of green functions relating the acoustic pressure at a number of field points to the strengths of a number of point sources on the surface of a body which radiates or scatters sound the left and right singular vectors of the resulting decomposition yield at a given frequency two sets of orthogonal basis functions describing field mode shapes and source mode shapes respectively this paper attempts to make the connection between this decomposition and the basis functions of classical acoustics in particular it is found that for a spherical co ordinate system when the source points and field points are chosen in order to sample the source and field appropriately then the matrices of left and right singular vectors are related to the sampled spherical harmonics by a unitary transformation preliminary investigations are presented of the sensitivity of this relationship to the manner in which the source and field are sampled in addition the great utility of the method is illustrated with some new results of numerical analysis of the scattering of sound by the outer ear pinna resonances and their associated mode shapes are identified at certain frequencies where high values of the dominant singular values indicate a strong coupling between source and field

fast approximations of shift variant blur image deblurring is essential in high resolution imaging e g astronomy microscopy or computational photography shift invariant blur is fully characterized by a single point spread function psf blurring is then modeled by a convolution leading to efficient algorithms for blur simulation and removal that rely on fast fourier transforms however in many different contexts blur cannot be considered constant throughout the field of view and thus necessitates to model variations of the psf with the location these models must achieve a trade off between the accuracy that can be reached with their flexibility and their computational efficiency several fast approximations of blur have been proposed in the literature we give a unified presentation of these methods in the light of matrix decompositions of the blurring operator we establish the connection between different computational tricks that can be found in the literature and the physical sense of corresponding approximations in terms of equivalent psfs physically based approximations being preferable we derive an improved approximation that preserves the same desirable low complexity as other fast algorithms while reaching a minimal approximation error comparison of theoretical properties and empirical performances of each blur approximation suggests that the proposed general model is preferable for approximation and inversion of a known shift variant blur

approximate orientation steerability based on angular gaussians junctions are significant features in images with intensity variation that exhibits multiple orientations this makes the detection and characterization of junctions a challenging problem the characterization of junctions would ideally be given by the response of a filter at every orientation this can be achieved by the principle of steerability that enables the decomposition of a filter into a linear combination of basis functions however current steerability approaches suffer from the consequences of the uncertainty principle in order to achieve high resolution in orientation they need a large number of basis filters increasing thus the computational complexity furthermore these functions have usually a wide support which only accentuates the computational burden we propose a novel alternative to current steerability approaches it is based on utilizing a set of polar separable filters with small support to sample orientation information the orientation signature is then obtained by interpolating orientation samples using gaussian functions with small support compared with current steerability techniques our approach achieves a higher orientation resolution with a lower complexity in addition we build a polar pyramid to characterize junctions of arbitrary inherent orientation scales

finite difference computation of head related transfer function for human hearing modeling the head related transfer function hrtf is a key to many applications in spatial audio to understand and predict the effects of head geometry and the surrounding environment on the hrtf a three dimensional finite difference time domain model 3d fdtd has been developed to simulate acoustic wave interaction with a human head a perfectly matched layer pml is used to absorb outgoing waves at the truncated boundary of an unbounded medium an external source is utilized to reduce the computational domain size through the scattered field total field formulation this numerical model has been validated by analytical solutions for a spherical head model the 3d fdtd code is then used as a computational tool to predict the hrtf for various scenarios in particular a simplified spherical head model is compared to a realistic head model up to about 7 khz the hrtf is also computed for a realistic head model in the presence of a wall it is demonstrated that this 3d fdtd model can be a useful tool for spatial audio applications

sequential convolution techniques for image filtering sequentially convolving images with small size operators is a promising idea for performing image filtering various classes of two dimensional finite impulse response fir filters that can be implemented with such techniques are studied design procedures are presented for each of the classes they are based upon minimizing l2and l criteria results are assessed in an image processing context

suggested formulae for calculating auditory filter bandwidths and excitation patterns recent estimates of auditory filter shape are used to derive a simple formula relating the equivalent rectangular bandwidth erb of the auditory filter to center frequency the value of the auditory filter bandwidth continues to decrease as center frequency decreases below 500 hz a formula is also given relating erb rate to frequency finally a method is described for calculating excitation patterns from filter shapes

trace inference curvature consistency and curve detection an approach is described for curve inference that is based on curvature information the inference procedure is divided into two stages a trace inference stage which is the subject of the present work and a curve synthesis stage it is shown that recovery of the trace of a curve requires estimating local models for the curve at the same time and that tangent and curvature information are sufficient these make it possible to specify powerful constraints between estimated tangents to a curve in terms of a neighborhood relationship called cocircularity and between curvature estimates in terms of a curvature consistency relation because all curve information is quantized special care must be taken to obtain accurate estimates of trace points tangents and curvatures this issue is addressed specifically to the introduction of a smoothness constraint and a maximum curvature constraint the procedure is applied to two types of images artificial images designed to evaluate curvature and noise sensitivity and natural images

the radiation modes of baffled finite plates the modal style approach for representing the exterior radiation characteristics of structures generally seeks to find a set of orthogonal functions or radiation modes that diagonalize a discretized radiation operator in the exterior domain of the structure the choice of basis functions for the modal representation is arbitrary though use of the structural modes of vibration tends to provide some physical insight the radiation modes are found through an eigenanalysis or singular value decomposition analysis of the radiation operator the eigenvalue or singular value associated with a given radiation mode is directly proportional to the radiation efficiency of that radiation mode in this paper the dependency of the radiation efficiencies and radiation mode shapes on the number of degrees of freedom permitted in the derivation of the radiation operator is investigated for a baffled finite rectangular plate the accuracy of the acoustic modal representation depends on the number of degrees of freedom in the radiation operator with the least efficient radiation modes converging slowest further the rate of convergence is dependent on the particular basis function selection the convergence behavior has significant impact on those applications of the exterior acoustic modal approach that seek to exploit the least efficient radiation modes

dyadic scale space in this paper we first approximate the gaussian function with any scale by the linear finite combination of gaussian functions with dyadic scale consequently the scale space can be constructed much more efficiently we only perform smoothing at these dyadic scales and the smoothed signals at other scales can be found by calculating linear combinations of these discrete scale signals we show that the approximation error is so small that our approach can be used in most of the computer vision fields we analyse the behavior of zero crossing zc across scales and show that features at any scale can be found efficiently by tracking from the dyadic scales thus we show that the new representation is necessary and complete in the case that the derivatives are calculated by a special multiscale filter we show that all the derivative signals can be treated in the same way

reducing individual differences in the external ear transfer functions of the mongolian gerbil this study examines individual differences in the directional transfer functions dtfs the directional components of head related transfer functions of gerbils and seeks a method for reducing these differences the difference between the dtfs of a given animal pair was quantified by the intersubject spectral difference issd which is the variance in the difference spectra of dtfs for frequencies between 5 and 45khz and for 361 source directions an attempt was made to reduce the issd by scaling the dtfs of one animal in frequency and or rotating the dtfs along the source coordinate sphere the issd was reduced by a median of 12 after optimal frequency scaling alone by a median of 19 after optimal spatial rotation alone and by a median of 36 after simultaneous frequency scaling and spatial rotation the optimal scaling factor osf and the optimal coordinate rotation ocr correlated strongly with differences in head width and pinna angles i e pinna inclination around the vertical and front ba

a geometric method for detecting chaotic dynamics a new method of detection of chaos in dynamical systems generated by time periodic nonautonomous differential equations is presented it is based on the existence of some sets called periodic isolating segments in the extended phase space satisfying some topological conditions by chaos we mean the existence of a compact invariant set such that the poincare map is semiconjugated to the shift on two symbols and the counterimage by the semiconjugacy of any periodic point in the shift contains a periodic point of the poincare map as an application we prove that the planar equationz 1 ei t z 2 zgenerates chaotic dynamics provided 0 1 288

the design and use of steerable filters the authors present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters allowing one to adaptively steer a filter to any orientation and to determine analytically the filter output as a function of orientation steerable filters may be designed in quadrature pairs to allow adaptive control over phase as well as orientation the authors show how to design and steer the filters and present examples of their use in the analysis of orientation and phase angularly adaptive filtering edge detection and shape from shading one can also build a self similar steerable pyramid representation the same concepts can be generalized to the design of 3 d steerable filters

orientation diffusions diffusions are useful for image processing and computer vision because they provide a convenient way of smoothing noisy data analyzing images at multiple scales and enhancing discontinuities a number of diffusions of image brightness have been defined and studied so far they may be applied to scalar and vector valued quantities that are naturally associated with intervals of either the real line or other flat manifolds some quantities of interest in computer vision and other areas of engineering that deal with images are defined on curved manifolds typical examples are orientation and hue that are defined on the circle generalizing brightness diffusions to orientation is not straightforward especially in the case where a discrete implementation is sought an example of what may go wrong is presented a method is proposed to define diffusions of orientation like quantities first a definition in the continuum is discussed then a discrete orientation diffusion is proposed the behavior of such diffusions is explored both analytically and experimentally it is shown how such orientation diffusions contain a nonlinearity that is reminiscent of edge process and anisotropic diffusion a number of open questions are proposed

new families of fourier eigenfunctions for steerable filtering a new diadic family of eigenfunctions of the 2 d fourier transform has been discovered specifically new wavelets are derived by steering the elongated hermite gauss filters with respect to rotations thus obtaining a natural generalization of the laguerre gauss harmonics interestingly these functions are also proportional to their 2 d fourier transform their analytical expression is provided in a compact and treatable form by means of a new ad hoc matrix notation in which the cases of even and odd orders of the hermite polynomials are unified moreover these functions can be efficiently implemented by means of a recursive formula that is derived in this paper the proposed filters are applied to the problem of gradient estimation to improve the theoretical canny tradeoff of position accuracy versus noise rejection that occurs in edge detection experimental results show considerable improvements in using the new wavelets over both isotropic gaussian derivatives and other elongated steerable filters more recently introduced finally being the proposed wavelets a set of fourier eigenfunctions they can be of interest in other fields of science such as optics and quantum mechanics

isolating segments fixed point index and symbolic dynamics abstract an extension of the recently introduced srzednicki wojcik method for detecting chaotic dynamics in periodically forced ordinary differential equations is presented as an application of the method we construct a topological model for the planar equation z 1 e i t z 2 z z c 1 and we show by a continuation argument that the symbolic dynamics on three symbols for the topological model continues to eq 1 for 0

frequency and amplitude estimation of the first peak of head related transfer functions from individual pinna anthropometry the first lowest peak of head related transfer functions hrtfs is known to be a concha depth resonance and a spectral cue in human sound localization however there is still no established model to estimate its center frequency f1 and amplitude a1 from pinna anthropometry here with geometries of 38 pinnae measured and their median plane hrtfs calculated by numerical simulation linear regression models were evaluated in estimating f1 and a1 from 25 concha depth and aperture measurements f1 was best estimated correlation coefficient r 0 84 mean absolute error mae 118 hz by lateral distances from the base of the posterior cavum concha to the outer surface of the antitragus and antihelix longest measures of concha depth a1 was best estimated r 0 83 mae 0 84 db by the lateral distance from the ear canal entrance to the side of the cheek near the anterior notch shortest measure of concha depth and by the equivalent diameter of the concha aperture these results suggest that the first resonance s quarter wavelength corresponds to the longest lateral extent of the concha and that its energy lost to the surrounding air depends on the concha aperture and the cavum concha s shortest lateral depth

duality of log polar image representations in the space and spatial frequency domains in this paper we study the result of applying a lowpass variant filtering using scaling rotating kernels to both the spatial and spatial frequency representations of a two dimensional 2 d signal image it is shown that if we apply this transformation to a fourier pair the two resulting signals can also form a fourier pair when the filters used in each domain maintain a dual relationship for a large class of self dual filters a perfect symmetry exists so that the lowpass scaling rotating variant filtering srvf is the same in both domains thus commuting with the fourier transform operator the lowpass srvf of an image is often referred to as a foveated image whereas its fourier pair the lowpass srvf of its spectrum can be realized as a local spectrum estimation around the point of attention this lowpass srvf is equivalent to a log polar warping of the image representation followed by a lowpass invariant filtering and the corresponding inverse warping the use of the log polar warped representation allows us to extend the one dimensional 1 d scale transform to higher dimensions in particular to images for which we have defined a scale rotation invariant representation we also present an efficient implementation using steerable filters to compute both the foveated image and the local spectrum

computing steerable principal components of a large set of images and their rotations we present here an efficient algorithm to compute the principal component analysis pca of a large image set consisting of images and for each image the set of its uniform rotations in the plane we do this by pointing out the block circulant structure of the covariance matrix and utilizing that structure to compute its eigenvectors we also demonstrate the advantages of this algorithm over similar ones with numerical experiments although it is useful in many settings we illustrate the specific application of the algorithm to the problem of cryo electron microscopy

the relationship of singular value decomposition to wave vector filtering in sound radiation problems singular value decomposition svd has recently been suggested as a filtering tool to analyze acoustic radiation the relationship between this filtering technique and the more familiar wave vector filtering is examined for a geometry with a preferred axis the source modes are found to consist approximately of a single wave number and the accompanying radiation modes are thus beams some simple examples are worked out to illustrate the general behavior of the filtering and some of the properties of the beams are given

optical flow using spatiotemporal filters a model is presented consonant with current views regarding the neurophysiology and psychophysics of motion perception that combines the outputs of a set of spatiotemporal motion energy filters to estimate image velocity a parallel implementation computes a distributed representation of image velocity a measure of image flow uncertainty is formulated preliminary results indicate that this uncertainty measure may be used to recognize ambiguity due to the aperture problem the model appears to deal with the aperture problem as well as the human visual system since it extracts the correct velocity for some patterns that have large differences in contrast at different spatial orientations

steerable weighted median filters a filter is steerable if transformed i e rotated scaled etc versions of its impulse response can be expressed as linear combinations of a fixed set of basis functions steerability is important for numerous image processing applications however it is a property presently shared only by a specific class of linear filters on the other hand several classes of nonlinear filters such as weighted median filters wmfs may offer certain advantages over linear filters such as robustness and edge preserving capabilities in this paper the concept of steerability is extended to encompass wmfs it will be shown that in general a steerable wmf design technique needs to be capable of handling negative weights although methods that allow the design of wmfs admitting negative weights have already been proposed such methods do not necessarily produce filters that are steerable as opposed to the approach presented in this work experimental results illustrate the applicability of steerable wmfs in two applications namely edge detection and orientation analysis

on the variation of interaural time differences with frequency interaural time difference itd is a major cue to sound localization in humans and animals for a given subject and position in space itd depends on frequency this variation is analyzed here using a head related transfer functions hrtfs database collected from the literature and comprising human hrtfs from 130 subjects and animal hrtfs from six specimens of different species for humans the itd is found to vary with frequency in a way that shows consistent differences with respect to a spherical head model maximal itd values were found to be about 800 s in low frequencies and 600 s in high frequencies the itd variation with frequency up to 200 s for some positions occurs within the frequency range where itd is used to judge the lateral position of a sound source in addition itd varies substantially within the bandwidth of a single auditory filter leading to systematic differences between envelope and fine structure itds because the frequency dependent pattern of itd does not display spherical symmetries it potentially provides cues to elevation and resolves front back confusion the fact that the relation between position and itds strongly depends on the sound s spectrum in turn suggests that humans and animals make use of this relationship for the localization of sounds

complex derivative filters steerable filters are a valuable tool for various low level vision tasks in this paper we argue for the use of complex analysis in the context of 2 d steerable filters in particular we recommend the use of complex partial derivatives as a computational basis complex derivatives have a major advantage in comparison to real derivatives they show a canonical rotation behavior namely a rotation affects the derivative just by a multiplication with a complex unit number so the complex derivatives can be steered in a more elegant way and above that they are less expensive to compute we present several analytical formulas for common and new filter kernels in terms of complex derivatives further we relate the complex derivatives of a gaussian with the gauss laguerre transform and show that the gauss laguerre functions provide an optimal signal representation for local and smooth images we discuss various finite difference schemes for the realization of the derivatives and use them in practice in a first experiment we use a newly introduced filter kernel for anisotropic blurring the complex formalism offers an elegant way to locally adapt the shape and orientation of the kernel second we use the proposed filters as matched filters to detect vessels in retinal images

median plane sound localization as a function of the number of spectral channels using a channel vocoder using a vocoder median plane sound localization performance was measured in eight normal hearing listeners as a function of the number of spectral channels the channels were contiguous and logarithmically spaced in the range from 0 3 to 16 khz acutely testing vocoded stimuli showed significantly worse localization compared to noises and 100 pulses click trains both of which were tested after feedback training however localization for the vocoded stimuli was better than chance a second experiment was performed using two different 12 channel spacings for the vocoded stimuli now including feedback training one spacing was from experiment 1 the second spacing called the speech localization spacing assigned more channels to the frequency range associated with speech there was no significant difference in localization between the two spacings however even with training localizing 12 channel vocoded stimuli remained worse than localizing virtual wideband noises by 4 8 degrees in local root mean square error and 5 2 in quadrant error rate speech understanding for the speech localization spacing was not significantly different from that for a typical spacing used by cochlear implant users these experiments suggest that current cochlear implants have a sufficient number of spectral channels for some vertical plane sound localization capabilities albeit worse than normal hearing listeners without loss of speech understanding

modeling individual differences in ferret external ear transfer functions individual variations in head and outer ear size as well as growth of these structures during development can markedly alter the values of the binaural and monaural cues which form the basis for auditory localization this study investigated individual differences in the directional component of the head related transfer function of both adult and juvenile ferrets in line with previous studies in humans and cats intersubject spectral differences were found to be reduced by scaling one of the directional transfer functions on a log frequency axis the optimal scale factor correlated most highly with pinna cavity height optimal frequency scaling reduced interear spectral difference equally well for adult juvenile comparisons as for comparisons between pairs of adult ears this illustrates that the developmental changes in localization cue values should be at least partly predictable on the basis of the expected growth rate of the outer ear structures predictions of interaural time differences itds were also derived from the physical dimensions of the head itds were found to be poorly fitted by the spherical head model while much better predictions could be derived from a model based on von mises spherical basis functions together these findings show how more accurate estimates of spatial cue values can be made from knowledge of the dimensions of the head and outer ears and may facilitate the generation of virtual acoustic space stimuli in the absence of acoustical measurements from individual subjects

observations on a principal components analysis of head related transfer functions a recent principal components analysis kistler and wightman 1992 has shown that the transfer functions of the human external ear for a wide range of source locations can be expressed as weighted sums of a small number of basis vectors directional transfer functions obtained in this laboratory using substantially different measurement techniques yielded principal component basis vectors that are remarkably similar to those reported by kistler and wightman when this subject population was divided in half according to the overall physical sizes of subjects basis vectors computed for the subpopulation of smaller subjects were shifted systematically to higher frequencies relative to those computed for the subpopulation of larger subjects

wavelet steerability and the higher order riesz transform our main goal in this paper is to set the foundations of a general continuous domain framework for designing steerable reversible signal transformations a k a frames in multiple dimensions d 2 to that end we introduce a self reversible nth order extension of the riesz transform we prove that this generalized transform has the following remarkable properties shift invariance scale invariance inner product preservation and steerability the pleasing consequence is that the transform maps any primary wavelet frame or basis of l 2 bbr d into another steerable wavelet frame while preserving the frame bounds the concept provides a functional counterpart to simoncelli s steerable pyramid whose construction was primarily based on filterbank design the proposed mechanism allows for the specification of wavelets with any order of steerability in any number of dimensions it also yields a perfect reconstruction filterbank algorithm we illustrate the method with the design of a novel family of multidimensional riesz laplace wavelets that essentially behave like the n th order partial derivatives of an isotropic gaussian kernel

scale space properties of quadratic feature detectors we consider the scale space properties of quadratic feature detectors and in particular investigate whether like linear detectors they permit a scale selection scheme with the causality property which guarantees that features are never created as the scale is coarsened we concentrate on the design of one dimensional detectors with two constituent filters with the scale selection implemented as convolution and a scaling function we consider two special cases of interest the constituent filter pairs related by the hilbert transform and by the first spatial derivative we show that under reasonable assumptions hilbert pair quadratic detectors cannot have the causality property in the case of derivative pair detectors we describe a family of scaling functions related to fractional derivatives of the gaussian that are necessary and sufficient for causality in addition we report experiments that show the effects of these properties in practice we thus demonstrate that at least one class of quadratic feature detectors has the same desirable scaling property as the more familiar detectors based on linear filtering

adaptive morphological filters based on a multiple orientation vector field dependent on image local features this paper addresses the formulation of adaptive morphological filters based on spatially variant structuring elements the adaptivity of these filters is achieved by modifying the shape and orientation of the structuring elements according to a multiple orientation vector field this vector field is provided by means of a bank of directional openings which can take into account the possible multiple orientations of the contours in the image after reviewing and formalizing the definition of the spatially variant dilation erosion opening and closing the proposed structuring elements are described these spatially variant structuring elements are based on ellipses which vary over the image domain adapting locally their orientation according to the multiple orientation vector field and their shape the eccentricity of the ellipses according to the distance to relevant contours of the objects the proposed adaptive morphological filters are used on gray level images and are compared with spatially invariant filters with spatially variant filters based on a single orientation vector field and with adaptive morphological bilateral filters results show that the morphological filters based on a multiple orientation vector field are more adept at enhancing and preserving structures which contains more than one orientation

the principal components of natural images revisited this paper investigates the principal components pcs of natural gray and color images a horizontal and vertical typology of pcs is found which leads to the identification of groups of basis functions for steerable bandpass filters using this system the contribution of spatio chromatic structure to the total variance can be quantified for selected spatial frequencies

multidimensional orientation estimation with applications to texture analysis and optical flow the problem of detection of orientation in finite dimensional euclidean spaces is solved in the least squares sense the theory is developed for the case when such orientation computations are necessary at all local neighborhoods of the n dimensional euclidean space detection of orientation is shown to correspond to fitting an axis or a plane to the fourier transform of an n dimensional structure the solution of this problem is related to the solution of a well known matrix eigenvalue problem the computations can be performed in the spatial domain without actually doing a fourier transformation along with the orientation estimate a certainty measure based on the error of the fit is proposed two applications in image analysis are considered texture segmentation and optical flow the theory is verified by experiments which confirm accurate orientation estimates and reliable certainty measures in the presence of noise the comparative results indicate that the theory produces algorithms computing robust texture features as well as optical flow

numerical modelling of the spatial acoustic response of the human pinna abstract this paper is concerned with the spatial acoustic response of the human pinna modelled with the boundary element method bem accurate geometric models of five pinnae are captured by using state of the art 3 d laser scanners and digitisers these computer models are converted to valid bem models and analysed acoustically up to 20 khz using baffled pinnae models we first repeat and validate numerically the normal concha modes as measured in the classical experiments made by e a g shaw in the 1970s we then study the spatial mode shapes of a baffled cylinder as a simplified model of the concha and accurate pinnae by applying the singular value decomposition svd technique the method is used to analyse at discrete frequencies a matrix of green functions relating the acoustic pressure at field points and source points in space we demonstrate how the singular vectors which appear as spatial mode shapes couple to the singular vectors of the sound field the relationship between these basis functions found with the svd and the normal concha mode shapes is demonstrated the method is also used in producing reduced order transfer functions by taking into account only the most dominant features of the singular vectors for the cases of a baffled cylinder and accurate baffled pinnae

equivariant holomorphic filters for contour denoising and rapid object detection it is well known that linear filters are not powerful enough for many low level image processing tasks however it is also very difficult to design robust nonlinear filters that respond exclusively to features of interest and that are at the same time equivariant with respect to translation and rotation this paper proposes a new class of rotation equivariant nonlinear filters that is based on the principle of group integration these filters become efficiently computable by an iterative scheme based on repeated differentiation of products and summations of intermediate results the relations of the proposed approach to volterra filters and steerable filters are shown in the context of detection problems the filter may be interpreted as some kind of generalized hough transform the experiments show that the new filter can be used for enhancing noisy contours and rapid object detection in microscopical images in the detection context our experiments show that the proposed filter is definitely superior to alternative approaches when high localization accuracy is required

interpretations on principal components analysis of head related impulse responses in the median plane a principal components analysis of the median plane head related impulse responses hrirs in the cipic hrtf database reveals that the individual hrirs can be reconstructed by a linear combination of 12 principal components pcs within 5 of error in the least squares sense the pcs include the intersubject and interelevation variations in the median plane hrirs each pc provides sound cues for the front back discrimination and or the vertical perception there exist common systematic elevation dependencies in the weights of lower numbered pcs which contribute to the pinna head diffractions whereas the elevation dependencies in the weights of higher numbered pcs are different from subject to subject

a hybrid algorithm for selecting head related transfer function based on similarity of anthropometric structures abstract as the basic data for virtual auditory technology head related transfer function hrtf has many applications in the areas of room acoustic modeling spatial hearing and multimedia how to individualize hrtf fast and effectively has become an opening problem at present based on the similarity and relativity of anthropometric structures a hybrid hrtf customization algorithm which has combined the method of principal component analysis pca multiple linear regression mlr and database matching dm has been presented in this paper the hrtfs selected by both the best match and the worst match have been applied into obtaining binaurally auralized sounds which are then used for subjective listening experiments and the results are compared for the area in the horizontal plane the localization results have shown that the selection of hrtfs can enhance the localization accuracy and can also abate the problem of front back confusion

recognition without correspondence using multidimensionalreceptive field histograms the appearance of an object is composed of local structure this local structure can be described and characterized by a vector of local features measured by local operators such as gaussian derivatives or gabor filters this article presents a technique where appearances of objects are represented by the joint statistics of such local neighborhood operators as such this represents a new class of appearance based techniques for computer vision based on joint statistics the paper develops techniques for the identification of multiple objects at arbitrary positions and orientations in a cluttered scene experiments show that these techniques can identify over 100 objects in the presence of major occlusions most remarkably the techniques have low complexity and therefore run in real time

radial projection an efficient update rule for relaxation labeling relaxation labeling uses contextual information for finding consistent labelings of graphs although relaxation labeling is parallel and iterative the complexity of updating with standard rules is too costly for practical implementation a description is given of a computationally more efficient updating rule that utilizes radial projection instead of normal projection to avoid the complexities incurred by previous update rules when boundaries to the labeling space are encountered this reduction in complexity is achieved by first restricting support vectors to the positive quadrant and then using radial projection onto the constraint instead of normal projection crucial order information is conserved through smooth convergence towards the optimum and a rate of convergence proportional to the magnitudes of the support functions

design and use of linear models for image motion analysis linear parameterized models of optical flow particularly affine models have become widespread in image motion analysis the linear model coefficients are straightforward to estimate and they provide reliable estimates of the optical flow of smooth surfaces here we explore the use of parameterized motion models that represent much more varied and complex motions our goals are threefold to construct linear bases for complex motion phenomenas to estimate the coefficients of these linear modelss and to recognize or classify image motions from the estimated coefficients we consider two broad classes of motions i generic motion features such as motion discontinuities and moving barss and ii non rigid object specific motions such as the motion of human mouths for motion features we construct a basis of steerable flow fields that approximate the motion features for object specific motions we construct basis flow fields from example motions using principal component analysis in both cases the model coefficients can be estimated directly from spatiotemporal image derivatives with a robust multi resolution scheme finally we show how these model coefficients can be use to detect and recognize specific motions such as occlusion boundaries and facial expressions

characterization of external ear impulse responses using golay codes this report explains the use of a complementary series golay codes for probing the impulse response of the external ear the codes are used to measure both the resonance of the human ear canal using a sealed sound delivery system and to measure the transfer function of the pinna using a free field source with two series of 512 binary numbers the improvement in signal to noise ratio over a single impulse approaches the theoretical value of 30 1 db 10 log 2 512 this technique has many of the same properties as maximal length sequences m r schroeder j acoust soc am 66 497 500 1979 but it has the added advantage that the sequence length is an integer power of two and is therefore particularly convenient to use with modern fourier transform techniques

optimal approximation of uniformly rotated images relationship between karhunen loeve expansion and discrete cosine transform we present the concept that for uniformly rotated images the optimal approximation of the images can be obtained by computing the basis vectors for the discrete cosine transform dct of the original image in polar coordinates and that the images can be represented as linear combinations of the basis vectors

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

efficient deformable filter banks this article describes efficient schemes for the computation of a large number of differently scaled oriented filtered versions of an image we generalize the well known steerable scalable deformable filter bank structure by imposing x y separability on the basis filters the resulting systems designed by an iterative projections technique achieve substantial reduction of the computational cost to reduce the memory requirement we adopt a multirate implementation due to the inner sampling rate alteration the resulting structure is not shift invariant we introduce a design criterion for multirate deformable structures that jointly controls the approximation error and the shift variance

a new adaptive framework for unbiased orientation estimation in textured images this paper focuses on directional texture analysis we propose a new approach for orientation estimation this approach hinges on two classes of convolution masks i e the gradient and the valleyness operators we provide a framework for their optimization regarding bias reduction and noise robustness as the gradient and the valleyness operators are complementary we propose a combination named gv joe this combination consists in using the gradient on inflexion pixels the valleyness on crests and valleys and a linear mixture of both elsewhere we implement an adaptive selection of the size of our operators in order to take into account the variations of the texture scale in the image we apply our approach both on synthetic and natural textures these experiments show that when used separately both classes of operators are more accurate than classical derivative approaches in noisy cases the gv joe implementation improves the robustness of our operators without affecting their accuracy moreover compared to well known orientation estimators it gives the best estimates in the most difficult cases i e for high frequency textures and low snr

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

shiftable multiscale transforms one of the major drawbacks of orthogonal wavelet transforms is their lack of translation invariance the content of wavelet subbands is unstable under translations of the input signal wavelet transforms are also unstable with respect to dilations of the input signal and in two dimensions rotations of the input signal the authors formalize these problems by defining a type of translation invariance called shiftability in the spatial domain shiftability corresponds to a lack of aliasing thus the conditions under which the property holds are specified by the sampling theorem shiftability may also be applied in the context of other domains particularly orientation and scale jointly shiftable transforms that are simultaneously shiftable in more than one domain are explored two examples of jointly shiftable transforms are designed and implemented a 1 d transform that is jointly shiftable in position and scale and a 2 d transform that is jointly shiftable in position and orientation the usefulness of these image representations for scale space analysis stereo disparity measurement and image enhancement is demonstrated

design of steerable filters for feature detection using canny like criteria we propose a general approach for the design of 2d feature detectors from a class of steerable functions based on the optimization of a canny like criterion in contrast with previous computational designs our approach is truly 2d and provides filters that have closed form expressions it also yields operators that have a better orientation selectivity than the classical gradient or hessian based detectors we illustrate the method with the design of operators for edge and ridge detection we present some experimental results that demonstrate the performance improvement of these new feature detectors we propose computationally efficient local optimization algorithms for the estimation of feature orientation we also introduce the notion of shape adaptable feature detection and use it for the detection of image corners

deformable kernels for early vision early vision algorithms often have a first stage of linear filtering that extracts from the image information at multiple scales of resolution and multiple orientations a common difficulty in the design and implementation of such schemes is that one feels compelled to discretize coarsely the space of scales and orientations in order to reduce computation and storage costs a technique is presented that allows 1 computing the best approximation of a given family using linear combinations of a small number of basis functions and 2 describing all finite dimensional families i e the families of filters for which a finite dimensional representation is possible with no error the technique is based on singular value decomposition and may be applied to generating filters in arbitrary dimensions and subject to arbitrary deformations the relevant functional analysis results are reviewed and precise conditions for the decomposition to be feasible are stated experimental results are presented that demonstrate the applicability of the technique to generating multiorientation multi scale 2d edge detection kernels the implementation issues are also discussed

isolating chains and chaotic dynamics in planar nonautonomous odes abstract we present a topological method for detecting complicated dynamics in nonautonomous periodic ode s the method is based on the notion of isolating chain as an application we show the chaotic behaviour of processes generated by the equations in the complex plane z z k e i t z where k 3 is an even number and is close to 0

boundary element method calculation of individual head related transfer function ii impedance effects and comparisons to real measurements following previous work by the author involving the calculation of an individual head related transfer function hrtf using a boundary element method bem approach impedance conditions are now included to take account of the acoustic properties of human hair in addition comparisons are made here between calculations and measured values for the hrtf of a specific individual numerous works have been published regarding the measurement of hrtfs but rarely are several methods compared for the same individual the results presented in the work compare two different measurement techniques and a computational bem for acquiring an individual hrtf impedance effects have been incorporated in the bem model for hair based on measured data providing a final set for comparison measurement results show significant variations for the same individual computational results show good agreement within the range of experimental variations definite trends are observed for many directions while the limitations of the methods are also highlighted for others the effects of incorporating hair impedance are shown to provide an improvement in the correlation of computational results indicating an affect of hair impedance on the hrtf

on periodic solutions inside isolating chains abstract we develop a geometric approach to problems concerning the existence of t periodic solutions of a non autonomous time t periodic ordinary differential equation we consider isolating segments subsets of the extended phase space of the equation which in some ways resemble isolating blocks from the theory of isolated invariant sets the union of several contiguous isolating segments is called an isolating chain isolating segments determine some homomorphisms in reduced singular homologies the main theorem asserts that the lefschetz number of the composition of the homomorphisms determined by segments such that their union is a periodic isolating chain is equal to the fixed point index of the poincare map of the equation in the set of initial values of t periodic solutions contained inside the chain we give some applications of the theorem to planar polynomial equations in particular we prove that the equation z z 5 sin 2 t z has four nonzero periodic solutions provided 0 336

two dimensional sound localization by human listeners this study measured the ability of subjects to localize broadband sound sources that varied in both horizontal and vertical location brief 150 ms sounds were presented in a free field and subjects reported the apparent stimulus location by turning to face the sound source head orientation was measured electromagnetically localization of continuous sounds also was tested to estimate errors in the motor act of orienting with the head localization performance was excellent for brief sounds presented in front of the subject the smallest errors averaged across subjects were about 2 and 3 5 in the horizontal and vertical dimensions respectively the sizes of errors increased for more peripheral stimulus locations to maxima of about 20 localization performance was better in the horizontal than in the vertical dimension for stimuli located on or near the frontal midline but the opposite was true for most stimuli located further peripheral front back confusions occurred in 6 of trials the characteristics of those responses suggest that subjects derived horizontal localization information principally from interaural difference cues the generally high level of performance obtained with the head orientation technique argues for its utility in continuing studies of sound localization

a differential model of the complex cell the receptive fields of simple cells in the visual cortex can be understood as linear filters these filters can be modeled by gabor functions or gaussian derivatives gabor functions can also be combined in an energy model of the complex cell response this letter proposes an alternative model of the complex cell based on gaussian derivatives it is most important to account for the insensitivity of the complex response to small shifts of the image the new model uses a linear combination of the first few derivative filters at a single position to approximate the first derivative filter at a series of adjacent positions the maximum response over all positions gives a signal that is insensitive to small shifts of the image this model unlike previous approaches is based on the scale space theory of visual processing in particular the complex cell is built from filters that respond to the 2d differential structure of the image the computational aspects of the new model are studied in one and two dimensions using the steerability of the gaussian derivatives the response of the model to basic images such as edges and gratings is derived formally the response to natural images is also evaluated using statistical measures of shift insensitivity the neural implementation and predictions of the model are discussed

boundary detection by contextual non linear smoothing abstract in this paper we present a two step boundary detection algorithm the first step is a nonlinear smoothing algorithm which is based on an orientation sensitive probability measure by incorporating geometrical constraints through the coupling structure we obtain a robust nonlinear smoothing algorithm where many nonlinear algorithms can be derived as special cases even when noise is substantial the proposed smoothing algorithm can still preserve salient boundaries compared with anisotropic diffusion approaches the proposed nonlinear algorithm not only performs better in preserving boundaries but also has a non uniform stable state whereby reliable results are available within a fixed number of iterations independent of images the second step is simply a sobel edge detection algorithm without non maximum suppression and hysteresis tracking due to the proposed nonlinear smoothing salient boundaries are extracted effectively experimental results using synthetic and real images are provided

evaluation of interest point detectors many different low level feature detectors exist and it is widely agreed that the evaluation of detectors is important in this paper we introduce two evaluation criteria for interest points repeatability rate and information content repeatability rate evaluates the geometric stability under different transformations information content measures the distinctiveness of features different interest point detectors are compared using these two criteria we determine which detector gives the best results and show that it satisfies the criteria well

individual differences in external ear transfer functions of cats knowledge of the direction dependent filter characteristics of the external ears is useful for the study of spatial hearing in experimental animals the present study examined individual differences in the directional components of external ear transfer functions directional transfer functions dtfs among 24 anesthetized cats ears were fixed in a frontal position inter cat differences in dtfs were quantified across a mid frequency range from 8 to 16 khz and across 30 locations in the horizontal plane and vertical midline across cats dtfs showed similar direction dependence but tended to differ in regard to the center frequencies of spectral features such as spectral peaks and notches certain mid frequency notches for instance varied in frequency across cats by nearly a factor of 2 scaling of dtfs in frequency could reduce the overall differences between pairs of cats scale factors that minimized inter cat differences ranged as high as 1 57 and correlated moderately with cats body weights nevertheless appreciable individual differences remained after frequency scaling inter cat differences in dtfs were substantially larger than differences that resulted from variability in positioning the ears the results suggest some guidelines regarding the conditions under which it is acceptable to apply dtf measurements from one cat to another

efficient steerable circular harmonic functions two dimensional 2d filtering and pattern matching applications often involve processing of images using a set sf which includes several transformed e g rotated scaled warped versions of the same 2d function f depending on the application f may correspond to a filter kernel or a pattern in general image processing using all functions in sf poses a computational burden steerability offers a solution to the problem specifically each function in sf can be exactly expressed or closely approximated by a linear combination of a few basis or steering functions in such cases processing images by employing steering functions and obtaining linear combinations of the associated responses may be preferable over utilizing all functions in sf however employing the steering functions is still a computationally expensive process this paper presents a method to significantly improve the computational efficiency of circular harmonic functions which are the steering functions when rotation is the transformation of interest the method is presented mainly in the context of image filtering yet 2d pattern matching is also discussed the advantages of the proposed technique in relation to other techniques are presented and its efficiency is demonstrated in terms of execution time and number of operations an extension of the technique to more general cases where sf includes rotated but also otherwise transformed versions of f is also discussed highlightsvery efficient circular harmonic function chf steerable filter technique presented chf implementation several times faster than direct convolution and fft conditionally technique provides exact results as direct convolution comparisons presented for pattern matching orientation analysis and denoising

the gray code filter kernels in this paper we introduce a family of filter kernels the gray code kernels gck and demonstrate their use in image analysis filtering an image with a sequence of gray code kernels is highly efficient and requires only two operations per pixel for each filter kernel independent of the size or dimension of the kernel we show that the family of kernels is large and includes the walsh hadamard kernels among others the gck can be used to approximate any desired kernel and as such forms a complete representation the efficiency of computation using a sequence of gck filters can be exploited for various real time applications such as pattern detection feature extraction texture analysis texture synthesis and more

subjective surfaces a geometric model for boundary completion we present a geometric model and a computational method for segmentation of images with missing boundaries in many situations the human visual system fills in missing gaps in edges and boundaries building and completing information that is not present boundary completion presents a considerable challenge in computer vision since most algorithms attempt to exploit existing data a large body of work concerns completion models which postulate how to construct missing datas these models are often trained and specific to particular images in this paper we take the following alternative perspective we consider a given reference point within the image and then develop an algorithm which tries to build missing information on the basis of the given point of view and the available information as boundary data to the algorithm starting from this point of view a surface is constructed it is then evolved with the mean curvature flow in the metric induced by the image until a piecewise constant solution is reached we test the computational model on modal completion amodal completion and texture segmentation we extend the geometric model and the algorithm to 3d in order to extract shapes from low signal noise ratio ultrasound image volumes results in 3d echocardiography and 3d fetal echography are also presented

recovery of individual head related transfer functions from a small set of measurementsa head related transfer functions hrtfs vary with individuals and in practice measuring hrtfs with high directional resolution for each individual is tiresome based on a basis functions representation of hrtfs the present work proposes a method for recovering individual hrtfs from a small set of measurements the hrtfs are represented by a combination of a small set of spatial basis functions sbfs with frequency and individual dependent weights the sbfs are derived by applying spatial principal component analysis to a baseline hrtf dataset with high directional resolution the individual weights for any subject outside the dataset are estimated from measurements at a few source directions and then the hrtfs with high directional resolution are recovered by combining the sbfs and the individual weights in an illustrative case the sbfs derived from a baseline dataset that includes 20 subjects are used to recover the hrtf magnitudes for six subjects outside the baseline dataset results show that individual hrtf magnitudes can be recovered from measurements at 73 directions with a mean signal to distortion ratio of 19 db the proposed method is also applicable to recovering head related impulse responses the results of psychoacoustic experiments indicate that in most cases the recovered and measured hrtfs are indistinguishable