proportional hazards estimate of the conditional survival function summary we introduce a new estimator of the conditional survival function given some subset of the covariate values under a proportional hazards regression the new estimate does not require estimating the base line cumulative hazard function an estimate of the variance is given and is easy to compute involving only those quantities that are routinely calculated in a cox model analysis the asymptotic normality of the new estimate is shown by using a central limit theorem for kaplan meier integrals we indicate the straightforward extension of the estimation procedure under models with multiplicative relative risks including non proportional hazards and to stratified and frailty models the estimator is applied to a gastric cancer study where it is of interest to predict patients survival based only on measurements obtained before surgery the time at which the most important prognostic variable stage becomes known

relations between auditory functions in impaired hearing relations between auditory functions as expressed by coefficients of correlation were studied for a group of 22 sensorineurally hearing impaired subjects with moderate losses in addition to the audiogram we measured frequency resolution temporal resolution and speech reception in quiet and in noise frequency resolution was derived from masking with comb filtered noise and from the psychophysical tuning curve for both paradigms in simultaneous and in nonsimultaneous masking the critical ratio was also determined temporal resolution was determined with intensity modulated noise and from backward and forward masking all tests were performed at 1000 hz correlations among tests were gathered in a matrix and subjected to a principal components analysis it turned out that tests on frequency resolution form a cluster and are approximately independent of audiometric loss furthermore hearing loss for speech in noise is closely allied to frequency resolution whereas hearing loss for speech in quiet is governed by audiometric loss

pixelwise adaptive blind optical flow assuming nonstationary statistics we address some of the major issues in optical flow within a new framework assuming nonstationary statistics for the motion field and for the errors problems addressed include the preservation of discontinuities model data errors outliers confidence measures and performance evaluation in solving these problems we assume that the statistics of the motion field and the errors are not only spatially varying but also unknown we thus derive a blind adaptive technique based on generalized cross validation for estimating an independent regularization parameter for each pixel our formulation is pixelwise and combines existing first and second order constraints with a new second order temporal constraint we derive a new confidence measure for an adaptive rejection of erroneous and outlying motion vectors and compare our results to other techniques in the literature a new performance measure is also derived for estimating the signal to noise ratio for real sequences when the ground truth is unknown

on the unification of line processes outlier rejection and robust statistics with applications in early vision the modeling of spatial discontinuities for problems such as surface recovery segmentation image reconstruction and optical flow has been intensely studied in computer vision while line process models of discontinuities have received a great deal of attention there has been recent interest in the use of robust statistical techniques to account for discontinuities this paper unifies the two approaches to achieve this we generalize the notion of a line process to that of an analog outlier process and show how a problem formulated in terms of outlier processes can be viewed in terms of robust statistics we also characterize a class of robust statistical problems for which an equivalent outlier process formulation exists and give a straightforward method for converting a robust estimation problem into an outlier process formulation we show how prior assumptions about the spatial structure of outliers can be expressed as constraints on the recovered analog outlier processes and how traditional continuation methods can be extended to the explicit outlier process formulation these results indicate that the outlier process approach provides a general framework which subsumes the traditional line process approaches as well as a wide class of robust estimation problems examples in surface reconstruction image segmentation and optical flow are presented to illustrate the use of outlier processes and to show how the relationship between outlier processes and robust statistics can be exploited an appendix provides a catalog of common robust error norms and their equivalent outlier process formulations

short term temporal integration evidence for the influence of peripheral compression thresholds for a 6 5 khz sinusoidal signal temporally centered in a 400 ms broadband noise masker were measured as a function of signal duration for normally hearing listeners and listeners with cochlear hearing loss over a range of masker levels for the normally hearing listeners the slope of the function relating signal threshold to signal duration integration function was steeper at medium masker levels than at low or high levels by a factor of nearly 2 for signal durations between 2 and 10 ms while no significant effect of level was found for signal durations of 20 ms and more no effect of stimulus level was found for the hearing impaired listeners at any signal duration for signal durations greater than 10 ms consistent with many previous studies the slope of the integration function was shallower for the hearing impaired listeners than for the normally hearing listeners however for shorter durations there was no significant difference in slope between the results from the hearing impaired listeners and those from the normally hearing listeners in the high and low level masker conditions a model incorporating a compressive nonlinearity representing the effect of basilar membrane bm compression and a short term temporal integrator postulated to be a more central process can account well for changes in the short term integration function with level if it is assumed that the compression is greater at medium levels than at low or high levels by a factor of about 4 this is in reasonable agreement with physiological measurements of bm compression and with previous psychophysical estimates

density estimation under random censorship and order restrictions from asymptotic to small samples do a random censorship and or order restrictions e g nonnegativity monotonicity convexity affect estimation of a smooth density under mean integrated squared error mise under mild assumptions the known asymptotic results which are concerned only with rates answer no this answer especially for censored data contradicts practical experience and statistical intuition so what can be said about constants of mise convergence it is shown that asymptotically a censorship does affect the constant and this allows one to find a relationship between sample sizes of directly observed and censored datasets that implies the same precision of estimation and b an order restriction does not affect the constant and thus no isotonic estimation is needed intensive monte carlo simulations show that the lessons of the sharp asymptotics are valuable for small sample sizes also the estimator developed is illustrated both on simulated data and a dataset of lifetimes of conveyer blades used at wastewate

adaptive grid refinement procedures for efficient optical flow computation two approaches are described that improve the efficiency of optical flow computation without incurring loss of accuracy the first approach segments images into regions of moving objects the method is based on a previously defined galerkin finite element method on a triangular mesh combined with a multiresolution segmentation approach for object flow computation images are automatically segmented into subdomains of moving objects by an algorithm that employs a hierarchy of mesh coarseness for the flow computation and these subdomains are reconstructed over a finer mesh on which to recompute flow more accurately the second approach uses an adaptive mesh in which the resolution increases where motion is found to occur optical flow is computed over a reasonably coarse mesh and this is used to construct an optimal adaptive mesh in a way that is different from the gradient methods reported in the literature the finite element mesh facilitates a reduction in computational effort by enabling processing to focus on particular objects of interest in a scene i e those areas where motion is detected the proposed methods were tested on real and synthetic image sequences and promising results are reported

robust optical flow estimation based on a sparse motion trajectory set this paper presents an approach to the problem of estimating a dense optical flow field the approach is based on a multiframe irregularly spaced motion trajectory set where each trajectory describes the motion of a given point as a function of time from this motion trajectory set a dense flow field is estimated using a process of interpolation a set of localized motion models are estimated with each pixel labeled as belonging to one of the motion models a markov random field framework is adopted allowing the incorporation of contextual constraints to encourage region like structures the approach is compared with a number of conventional optical flow estimation algorithms taken over a number of real and synthetic sequences results indicate that the method produces more accurate results for sequences with known ground truth flow also applying the method to real sequences with unknown flow results in lower dfd for all of the sequences tested

relations between intelligibility of narrow band speech and auditory functions both in the 1 khz frequency region relations between perception of suprathreshold speech and auditory functions were examined in 24 hearing impaired listeners and 12 normal hearing listeners the speech intelligibility index sii was used to account for audibility the auditory functions included detection efficiency temporal and spectral resolution temporal and spectral integration and discrimination of intensity frequency rhythm and spectro temporal shape all auditory functions were measured at 1 khz speech intelligibility was assessed with the speech reception threshold srt in quiet and in noise and with the speech reception bandwidth threshold srbt previously developed for investigating speech perception in a limited frequency region around 1 khz the results showed that the elevated srt in quiet could be explained on the basis of audibility audibility could only partly account for the elevated srt values in noise and the deviant srbt values suggesting that suprathreshold deficits affected intelligibility in these conditions sii predictions for the srbt improved significantly by including the individually measured upward spread of masking in the sii model reduced spectral resolution reduced temporal resolution and reduced frequency discrimination appeared to be related to speech perception deficits loss of peripheral compression appeared to have the smallest effect on the intelligibility of suprathreshold speech

spectral and temporal integration of brief tones both spectral and temporal integration of tones have been explored in detail but integration of tones varying across both dimensions has received little attention this study explores temporal integration of tone pulses that vary over a range of frequencies baseline thresholds were obtained for both spectral and temporal integration with the same signals and compared with prior research the signals were then varied on both dimensions in several ways with equivalent spectral and temporal step sizes different spectral and temporal step sizes and a random pattern of frequency presentation the data were also analyzed by spectral step size temporal step size frequency range direction and slope of frequency change and predictability the spectral and temporal integration conditions showed that the current procedures and signals yielded the same improvement in detection thresholds as prior studies the spectrotemporal integration conditions showed the improvement for overall detection of the signals to be limited by spectral integration with improvement related primarily to the number of tones regardless of timing and frequency surprisingly trial by trial random presentation of signal frequencies did not negatively influence detection these results support the multiple looks hypothesis viemeister n f and wakefield g h 1991 temporal integration and multiple looks j acoust soc am 90 858 865 as applied to spectrotemporal integration

detection and intensity discrimination of gaussian shaped tone pulses as a function of duration j acoust soc am 105 3425 3435 1999 proposed that the auditory system partitions the spectro temporal domain into frequency time f t windows and that the characteristics of these windows could be explored by measuring intensity discrimination for gaussian shaped tone pulses presented just above their detection threshold in noise they reasoned that for a long duration tone pulse the auditory representation would be maximally compact in the frequency domain but would spread across several f t windows in the time domain for a very short duration tone pulse the auditory representation would be maximally compact in the time domain but would spread across several f t windows in the frequency domain there should be some intermediate duration at which the auditory representation is compact in both the time and frequency domains and for which intensity discrimination performance should worsen due to the limited opportunity for multiple looks their data for signal frequencies of 1 and 4 khz were consistent with this expectation intensity discrimination was poorest at a duration of about 3 5 ms at 1 khz and 1 ms at 4 khz durations are specified between 6 8 db down points on the envelope this experiment attempted to replicate those results and to extend them to a wider range of frequencies and levels intensity discrimination of gaussian shaped tone pulses was measured at three levels 10 db above absolute threshold or above masked threshold in a pink noise with a spectrum level of either 15 or 40 db at 1 khz the signal frequency was 0 25 khz durations from 2 to 320 ms 1 khz durations from 0 5 to 80 ms or 4 khz durations from 0 1 to 20 ms three normally hearing subjects were tested at 1 and 4 khz performance was poorest overall for the 15 db pink noise level and thresholds showed a peak at intermediate durations about 3 5 ms at 1 khz and 1 ms at 4 khz such peaks were still apparent but smaller in the no noise condition and were almost absent at the higher noise level for the 0 25 khz signal frequency peaks were not observed consistently at any level although two subjects showed small peaks for durations around 10 ms an explanation is offered for the results in terms of the level and frequency dependence of basilar membrane input output functions

effects of degradation of intensity time or frequency content on speech intelligibility for normal hearing and hearing impaired listeners many hearing impaired listeners suffer from distorted auditory processing capabilities this study examines which aspects of auditory coding i e intensity time or frequency are distorted and how this affects speech perception the distortion sensitivity model is used the effect of distorted auditory coding of a speech signal is simulated by an artificial distortion and the sensitivity of speech intelligibility to this artificial distortion is compared for normal hearing and hearing impaired listeners stimuli speech plus noise are wavelet coded using a complex sinusoidal carrier with a gaussian envelope 14 octave bandwidth intensity information is distorted by multiplying the modulus of each wavelet coefficient by a random factor temporal and spectral information are distorted by randomly shifting the wavelet positions along the temporal or spectral axis respectively measured were 1 detection thresholds for each type of distortion and 2 speech reception thresholds for various degrees

cooperative robust estimation using layers of support we present an approach to the problem of representing images that contain multiple objects or surfaces rather than using an edge based approach to represent the segmentation of a scene we propose a multilayer estimation framework which uses support maps to represent the segmentation of the image into homogeneous chunks this support based approach can represent objects that are split into disjoint regions or have surfaces that are transparently interleaved our framework is based on an extension of robust estimation methods that provide a theoretical basis for support based estimation we use a selection criteria derived from the minimum description length principle to decide how many support maps to use in describing an image our method has been applied to a number of different domains including the decomposition of range images into constituent objects the segmentation of image sequences into homogeneous higher order motion fields and the separation of tracked motion features into distinct rigid body motions

relations between frequency selectivity temporal fine structure processing and speech reception in impaired hearing frequency selectivity temporal fine structure tfs processing and speech reception were assessed for six normal hearing nh listeners ten sensorineurally hearing impaired hi listeners with similar high frequency losses and two listeners with an obscure dysfunction od tfs processing was investigated at low frequencies in regions of normal hearing through measurements of binaural masked detection tone lateralization and monaural frequency modulation fm detection lateralization and fm detection thresholds were measured in quiet and in background noise speech reception thresholds were obtained for full spectrum and lowpass filtered sentences with different interferers both the hi listeners and the od listeners showed poorer performance than the nh listeners in terms of frequency selectivity tfs processing and speech reception while a correlation was observed between the monaural and binaural tfs processing deficits in the hi listeners no relation was found between tfs processing and frequency selectivity the effect of noise on tfs processing was not larger for the hi listeners than for the nh listeners finally tfs processing performance was correlated with speech reception in a two talker background and lateralized noise but not in amplitude modulated noise the results provide constraints for future models of impaired auditory signal processing

nonparametric estimation of transition probabilities for a general progressive multi state model under cross sectional sampling nonparametric estimation of the transition probability matrix of a progressive multi state model is considered under cross sectional sampling two different estimators adapted to possibly right censored and left truncated data are proposed the estimators require full retrospective information before the truncation time which when exploited increases efficiency they are obtained as differences between two survival functions constructed for sub samples of subjects occupying specific states at a certain time point both estimators correct the oversampling of relatively large survival times by using the left truncation times associated with the cross sectional observation asymptotic results are established and finite sample performance is investigated through simulations one of the proposed estimators performs better when there is no censoring while the second one is strongly recommended with censored data the new estimators are applied to data on patients in intensive care units icus

speech reception in quiet and in noisy conditions by individuals with noise induced hearing loss in relation to their tone audiogram tone thresholds and speech reception thresholds were measured in 200 individuals 400 ears with noise induced hearing loss the speech reception thresholds were measured in a quiet condition and in noise with a speech spectrum at levels of 35 50 65 and 80 dba the tone audiograms could be described by three principal components hearing loss in the regions above 3 khz from 1 to 3 khz and below 1 khz the speech thresholds could be described by two components speech reception in quiet and speech reception in noise at 50 80 dba hearing loss above 1 khz was related to speech reception in noise hearing loss at and below 1 khz to speech reception in quiet the correlation between the speech thresholds in quiet and in noise was only r 0 45 an adequate predictor of the speech threshold in noise the primary factor in the hearing handicap was the pure tone average at 2 and 4 khz pta2 4 r 0 72 the minimum value of the prediction error for any tone audiometric predictor of this speech threshold was 1 2 db standard deviation the prediction could not be improved by taking into account the critical ratio for low frequency noise nor by its upward spread of masking the prediction error is due to measurement error and to a factor common to both ears the latter factor is ascribed to cognitive skill in speech reception hearing loss above 10 to 15 db hl hearing level already shows an effect on the speech threshold in noise a noticeable handicap is found at pta2 4 30 db hl

modeling speech intelligibility in quiet and noise in listeners with normal and impaired hearing the speech intelligibility index sii is an often used calculation method for estimating the proportion of audible speech in noise for speech reception thresholds srts measured in normally hearing listeners using various types of stationary noise this model predicts a fairly constant speech proportion of about 0 33 necessary for dutch sentence intelligibility however when the sii model is applied for srts in quiet the estimated speech proportions are often higher and show a larger inter subject variability than found for speech in noise near normal speech levels 65 db sound pressure level spl the present model attempts to alleviate this problem by including cochlear compression it is based on a loudness model for normally hearing and hearing impaired listeners of moore and glasberg 2004 hear res 188 70 88 it estimates internal excitation levels for speech and noise and then calculates the proportion of speech above noise and threshold using similar spectral weighting as used in the sii the present model and the standard sii were used to predict sii values in quiet and in stationary noise for normally hearing and hearing impaired listeners the present model predicted siis for three listener types normal hearing noise induced and age induced hearing loss with markedly less variability than the standard sii

scene segmentation from visual motion using global optimization this paper presents results from computer experiments with an algorithm to perform scene disposition and motion segmentation from visual motion or optic flow the maximum a posteriori map criterion is used to formulate what the best segmentation or interpretation of the scene should be where the scene is assumed to be made up of some fixed number of moving planar surface patches the bayesian approach requires first specification of prior expectations for the optic flow field which here is modeled as spatial and temporal markov random fields and secondly a way of measuring how well the segmentation predicts the measured flow field the markov random fields incorporate the physical constraints that objects and their images are probably spatially continuous and that their images are likely to move quite smoothly across the image plane to compute the flow predicted by the segmentation a recent method for reconstructing the motion and orientation of planar surface facets is used the search for the globally optimal segmentation is performed using simulated annealing

efficient across frequency integration in short signal detection a series of experiments was performed on the influence of bandwidth on the masked threshold of brief deterministic signals in continuous broadband noise the signal bandwidth is quantified by the number n of constituent 1 3 oct bands for n increasing from 1 to typically 9 the masked threshold level in the constituent 1 3 oct bands is found to decrease by 8 log n this integration rule is obtained when each of the 1 3 oct bands covered by the signal equally contributes to detection i e that for each of these 1 3 oct bands the difference between signal level and the individual masked threshold level is the same it was found that this integration rule also applies to noncontiguous signal spectra and that it remains intact over a broad range of masker levels commonly the masked threshold of compound signals for instance n frequency components with a spacing of typically 1 3 oct relative to the masked threshold of single component signals has been described by a 5 log n integration rule however this rule was obtained for signal durations of typically 100 ms or more for the present brief signals typically 10 ms or less the across frequency integration is found to be more effective

additivity of auditory masking using gaussian shaped tones both temporal and spectral masking have been studied extensively in the literature mostly they have been regarded as separate phenomena very little is known about the interaction between these two effects i e masking in the time frequency domain data on the time frequency spread of masking evoked by a single gaussian shaped tone pulse are presented in an accompanying study at the same conference necciari et al the current study gathers data on the additivity of masking by up to four approximately equally effective gaussian maskers erb 600 hz separated either along the time or the frequency axis for temporal separation the amount of masking increases with the number of maskers with excess masking exceeding linear additivity of up to 25 db for frequency separation preliminary data excess masking amounts up to 15 db and the higher frequency masker relative to the target contributes more to the additivity than the lower frequency maskers experiments with multiple maskers combining both temporal and frequency separation are underway combined with the single maker data these data may serve as a basis for modeling time frequency masking effects in complex signals work partly supported by oead wtz project amadeus and anr

additivity of masking in normally hearing and hearing impaired subjects the effects of combining two equally effective maskers were studied in normally hearing and elderly hearing impaired subjects the additivity of nonsimultaneous masking was investigated by measuring thresholds for a brief 4 khz signal in the presence of a broadband noise forward masker a backward masker and a combination of both for the normally hearing subjects combining two equally effective nonsimultaneous maskers resulted in up to a 15 db greater increase in threshold than the 3 db predicted by an energy summation model excess masking however the hearing impaired subjects showed little or no excess masking the difference between the two groups is consistent with a theory linking excess masking to the compressive transfer function measured on the basilar membrane bm in the hearing impaired subjects the transfer function is more linear accounting for the lack of excess masking the additivity of simultaneous masking was investigated by measuring thresholds for a 100 ms 4 khz signal in the presence of either a 400 ms broadband noise masker or a 400 ms sinusoidal masker at the same frequency as the signal and then combining two equally effective maskers a noise and a tone the maximum amount of excess masking 3 to 4 db was similar across the two groups of subjects consistent with an explanation based on the use of different detection cues for the tonal and noise maskers it is argued that while peripheral compression may underlie excess masking for pairs of nonsimultaneous maskers it is unlikely that in simultaneous masking where the maskers are close in frequency to the signal the two maskers are compressed individually before their effects are combined it is further suggested that bm nonlinearity may underlie the effects of the upward spread of masking and the nonlinear growth of forward masking as well as accounting for the additivity of simultaneous masking when the masker frequencies are well below that of the signal

functional limit laws for the increments of kaplan meier product limit processes and applications we prove functional limit laws for the increment functions of empirical processes based upon randomly right censored data the increment sizes we consider are classified into different classes covering the whole possible spectrum we apply these results to obtain a description of the strong limiting behavior of a series of estimators of local functionals of lifetime distributions in particular we treat the case of kernel density and hazard rate estimators

bayesian estimation of motion vector fields a stochastic approach to the estimation of 2d motion vector fields from time varying images is presented the formulation involves the specification of a deterministic structural model along with stochastic observation and motion field models two motion models are proposed a globally smooth model based on vector markov random fields and a piecewise smooth model derived from coupled vector binary markov random fields two estimation criteria are studied in the maximum a posteriori probability map estimation the a posteriori probability of motion given data is maximized whereas in the minimum expected cost mec estimation the expectation of a certain cost function is minimized both algorithms generate sample fields by means of stochastic relaxation implemented via the gibbs sampler two versions are developed one for a discrete state space and the other for a continuous state space the map estimation is incorporated into a hierarchical environment to deal efficiently with large displacements

on the empirical choice of the time window for restricted mean survival time the t year mean survival or restricted mean survival time rmst has been used as an appealing summary of the survival distribution within a time window 0 t rmst is the patient s life expectancy until time t and can be estimated nonparametrically by the area under the kaplan meier curve up to t in a comparative study the difference or ratio of two rmsts has been utilized to quantify the between group difference as a clinically interpretable alternative summary to the hazard ratio the choice of the time window 0 t may be prespecified at the design stage of the study based on clinical considerations on the other hand after the survival data have been collected the choice of time point t could be data dependent the standard inferential procedures for the corresponding rmst which is also data dependent ignore this subtle yet important issue in this paper we clarify how to make inference about a random parameter moreover we demonstrate that under a rather mild condition on the censoring distribution one can make inference about the rmst up to t where t is less than or even equal to the largest follow up time either observed or censored in the study this finding reduces the subjectivity of the choice of t empirically the proposal is illustrated with the survival data from a primary biliary cirrhosis study and its finite sample properties are investigated via an extensive simulation study

intensity discrimination of gaussian windowed tones indications for the shape of the auditory frequency time window the just noticeable difference in intensity jnd i was measured for 1 khz tones with a gaussian shaped envelope as a function of their spectro temporal shape the stimuli with constant energy and a constant product of bandwidth and duration ranged from a long duration narrow band tone to a short duration broadband click the jnd i was measured in three normal hearing listeners at sensation levels of 0 10 20 and 30 db in 35 db a spl pink noise at intermediate sensation levels jnd i depends on the spectro temporal shape at the extreme shapes tones and clicks intensity discrimination performance is best whereas at intermediate shapes the jnd i is larger similar results are observed at a higher overall sound level and at a higher carrier frequency the maximum jnd i is observed for stimuli with an effective bandwidth of about 1 3 octave and an effective duration of 4 ms at 1 khz 1 ms at 4 khz a generalized multiple window model is proposed that assumes that the spectro temporal domain is partitioned into internal auditory frequency time windows the model predicts that intensity discrimination thresholds depend upon the number of windows excited by a signal jnd i is largest for stimuli covering one window

intensity discrimination determined with two paradigms in normal and hearing impaired subjects the literature on auditory intensity jnd s is ambiguous with respect to the relationship between the jnd s measured with gated and continuous pedestals and with respect to changes in this relationship in the presence of loudness recruitment accompanying cochlear pathology in an attempt to clarify these issues and to lay a foundation for systematic investigations of the dependence on the jnd s on loudness functions the jnd s for pure tones with gated and continuous pedestal paradigms of two groups of subjects one with normal hearing and one with hearing loss of cochlear origin were measured the experiments were performed at 0 5 2 and 6 khz and at a wide range of sensation levels sls by means of an adaptive two alternative forced choice 2ifc procedure the jnd s obtained with the continuous pedestal method were smaller than those obtained with the gated pedestal method for both groups of subjects they also had smaller intersubject standard deviations when jnd s of the two groups were compared on the basis of equal sls the group with hearing loss showed smaller jnd values than the group with normal hearing for both pedestal paradigms when the comparisons were made on the basis of equal sound pressure levels spls both groups showed similar values for moderate and high spls at relatively low spls the group with hearing loss tended to have somewhat higher values

asymptotics for a censored generalized linear model with unknown link function for censored response variable against projected co variable a generalized linear model with an unknown link function can cover almost all existing models under censorship its special cases include the accelerated failure time model with censored data such a model in the uncensored case is called the single index model in econometrics in this paper we systematically study the asymptotic properties we derive the central limit theorem and the law of the iterated logarithm for an estimator of the direction parameter we also obtain the optimal convergence rate of an estimator of the unknown link function in the model

the application of mean field theory to image motion estimation previously markov random field mrf model based techniques have been proposed for image motion estimation since motion estimation is usually an ill posed problem various constraints are needed to obtain a unique and stable solution the main advantage of the mrf approach is its capacity to incorporate such constraints for instance motion continuity within an object and motion discontinuity at the boundaries between objects in the mrf approach motion estimation is often formulated as an optimization problem and two frequently used optimization methods are simulated annealing sa and iterative conditional mode icm although the sa is theoretically optimal in the sense of finding the global optimum it usually takes many iterations to converge the icm on the other hand converges quickly but its results are often unsatisfactory due to its hard decision nature previously the authors have applied the mean field theory to image segmentation and image restoration problems it provides results nearly as good as sa but with much faster convergence the present paper shows how the mean field theory can be applied to mrf model based motion estimation this approach is demonstrated on both synthetic and real world images where it produced good motion estimates

dense motion estimation using regularization constraints on local parametric models this paper presents a method for dense optical flow estimation in which the motion field within patches that result from an initial intensity segmentation is parametrized with models of different order we propose a novel formulation which introduces regularization constraints between the model parameters of neighboring patches in this way we provide the additional constraints for very small patches and for patches whose intensity variation cannot sufficiently constrain the estimation of their motion parameters in order to preserve motion discontinuities we use robust functions as a regularization mean we adopt a three frame approach and control the balance between the backward and forward constraints by a real valued direction field on which regularization constraints are applied an iterative deterministic relaxation method is employed in order to solve the corresponding optimization problem experimental results show that the proposed method deals successfully with motions large in magnitude motion discontinuities and produces accurate piecewise smooth motion fields

the jackknife estimate of variance of a kaplan meier integral let f n be the kaplan meier estimator of a distribution function f computed from randomly censored data it is known that under certain integrability assumptions on a function the kaplan meier integral df n when properly standardized is asymptotically normal in this paper it is shown that with probability 1 the jackknife estimate of variance consistently estimates the limit variance

auditory temporal integration and the power function model the auditory temporal integration function was studied with the objective of improving both its quantitative description and the specification of its principle independent variable stimulus duration in sec i temporal integration data from 20 studies were subjected to uniform analyses using standardized definitions of duration and two models of temporal integration analyses revealed that these data were best described by a power function model used in conjunction with a definition of duration termed assigned duration that de emphasized the rise fall portions of the stimuli there was a strong effect of stimulus frequency and in general the slope of the temporal integration function was less than 10 db per decade of duration i e a power function exponent less than 1 0 in sec ii an experimental study was performed to further evaluate the models and definitions detection thresholds were measured in 11 normal hearing human subjects using a total of 24 single burst and multiple burst acoustic stimuli of 3 125 khz the issues addressed are the quantitative description of the temporal integration function the definition of stimulus duration the similarity of the integration processes for single burst and multiple burst stimuli and the contribution of rise fall time to the integration process a power function in conjunction with the assigned duration definition was again most effective in describing the data single and multiple burst stimuli both seemed to be integrated by the same central mechanism with data for each type of stimulus being described by a power function exponent of approximately 0 6 at 3 125 khz it was concluded that the contribution of the rise fall portions of the stimuli can be factored out from the rest of the temporal integration process in sec iii the conclusions that emerged from the review of published work and the present experimental work suggested that auditory temporal integration is best described by a power function in conjunction with the assigned duration definition the exponent for the power function is typically less than 1 0 and varies with frequency and hearing level second a means of empirically assaying the contribution of the rise fall portions of the stimuli is presented and evaluated finally properties of a central auditory integrator are hypothesized abstract truncated at 250 words

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

multi threshold accelerated failure time model a two stage procedure for simultaneously detecting multiple thresholds and achieving model selection in the segmented accelerated failure time aft model is developed in this paper in the first stage we formulate the threshold problem as a group model selection problem so that a concave 2 norm group selection method can be applied in the second stage the thresholds are finalized via a refining method we establish the strong consistency of the threshold estimates and regression coefficient estimates under some mild technical conditions the proposed procedure performs satisfactorily in our simulation studies its real world applicability is demonstrated via analyzing a follicular lymphoma data

psychoacoustic and phonetic temporal processing in normal and hearing impaired listeners four measures of auditory temporal processing were obtained from 16 normals and 16 individuals with a hearing loss of heterogeneous origin these measures were 1 temporal integration the difference in detection thresholds between signals of 10 and 1000 ms duration which was determined to provide an estimate of the ability to integrate energy over time 2 gap detection the shortest duration of silence between two noise bursts that can be discriminated from an uninterrupted noise 3 temporal difference limen the increment in duration necessary to detect a difference in the duration of a noise burst 4 gap difference limen the increment in duration necessary to detect a difference in the duration of a silent interval between two noise bursts each measure was obtained for stimuli centered both at 500 and at 4000 hz using a three alternative forced choice procedure in addition measures of identification and discrimination were obtained for two sets of synthetic speech syllables varying chiefly in a temporal parameter voice onset time from ba to pa and from bi to pi finally speech identification in noise was measured with the faaf test most of the hearing impaired listeners displayed poorer temporal analysis than the normals on all of the psychoacoustical tasks regardless of whether the two groups were compared at similar sound pressure levels or at similar sensation levels although the hearing impaired listeners displayed a reduction in the ability to discriminate subphonemic cues for the voiced voiceless distinction their identification of that distinction in stop consonants appeared to be normal the hearing impaired group made about twice as many errors as did the normals on each of the consonant features of place manner and voicing when identifying speech in noise increased temporal difference limen and longer gap detection thresholds were found to correlate significantly with reduced speech intelligibility in noise even when the effects of the pure tone threshold loss were partialed out

the effect of intensity perturbations on speech intelligibility for normal hearing and hearing impaired listeners hearing impaired listeners are known to suffer from reduced speech intelligibility in noise even if sounds are above their hearing thresholds this study examined the possible contribution of reduced acuity of intensity coding to this problem the distortion sensitivity model was used the effect of reduced acuity of auditory intensity coding on intelligibility was mimicked by an artificial distortion of the speech intensity coding and the sensitivity to this distortion for hearing impaired listeners was compared with that for normal hearing listeners stimuli speech plus noise were wavelet coded using a gaussian wavelet 1 4 octave bandwidth the intensity coding was distorted by multiplying the modulus of each wavelet coefficient by a random factor speech reception thresholds srts were measured for various degrees of intensity perturbation hearing impaired listeners were classified as suffering from suprathreshold deficits if intelligibility of undistorted speech was worse than predicted from audibility by the speech intelligibility index model ansi ansi s3 5 1997 1997 hearing impaired listeners without suprathreshold deficits were as sensitive to the intensity distortion as the normal hearing listeners hearing impaired listeners with suprathreshold deficits appeared to be less sensitive results indicate that reduced acuity of auditory intensity coding may be a factor underlying reduced speech intelligibility in noise for the hearing impaired hearing impaired listeners are known to suffer from reduced speech intelligibility in noise even if sounds are above their hearing thresholds this study examined the possible contribution of reduced acuity of intensity coding to this problem the distortion sensitivity model was used the effect of reduced acuity of auditory intensity coding on intelligibility was mimicked by an artificial distortion of the speech intensity coding and the sensitivity to this distortion for hearing impaired listeners was compared with that for normal hearing listeners stimuli speech plus noise were wavelet coded using a gaussian wavelet 1 4 octave bandwidth the intensity coding was distorted by multiplying the modulus of each wavelet coefficient by a random factor speech reception thresholds srts were measured for various degrees of intensity perturbation hearing impaired listeners were classified as suffering from suprathreshold deficits if intelligibility of undistorted speech was worse than predicted from

robust adaptive scale parametric model estimation for computer vision robust model fitting essentially requires the application of two estimators the first is an estimator for the values of the model parameters the second is an estimator for the scale of the noise in the inlier data indeed we propose two novel robust techniques the two step scale estimator tsse and the adaptive scale sample consensus assc estimator tsse applies nonparametric density estimation and density gradient estimation techniques to robustly estimate the scale of the inliers the assc estimator combines random sample consensus ransac and tsse using a modified objective function that depends upon both the number of inliers and the corresponding scale assc is very robust to discontinuous signals and data with multiple structures being able to tolerate more than 80 percent outliers the main advantage of assc over ransac is that prior knowledge about the scale of inliers is not needed assc can simultaneously estimate the parameters of a model and the scale of the inliers belonging to that model experiments on synthetic data show that assc has better robustness to heavily corrupted data than least median squares lmeds residual consensus resc and adaptive least kth order squares alks we also apply assc to two fundamental computer vision tasks range image segmentation and robust fundamental matrix estimation experiments show very promising results

the central limit theorem under random censorship let f n be the kaplan meier estimator of a distribution function f computed from randomly censored data we show that under optimal integrability assumptions on a function the kaplan meier integral df n when properly standardized is asymptotically normal

measuring the threshold for speech reception by adaptive variation of the signal bandwidth ii hearing impaired listeners in a previous study noordhoek et al j acoust soc am 105 2895 2902 1999 an adaptive test was developed to determine the speech reception bandwidth threshold srbt i e the width of a speech band around 1 khz required for a 50 intelligibility score in this test the band filtered speech is presented in complementary bandstop filtered noise in the present study the performance of 34 hearing impaired listeners was measured on this srbt test and on more common srt speech reception threshold tests namely the srt in quiet the standard srt in noise standard speech spectrum and the spectrally adapted srt in noise fitted to the individual s dynamic range the aim was to investigate to what extent the performance on these tests could be explained simply from audibility as estimated with the sii speech intelligibility index model or require the assumption of suprathreshold deficits for most listeners an elevated srt in quiet or an elevated standard srt in noise could be explained on the basis of audibility for the spectrally adapted srt in noise and especially for the srbt the data of most listeners could not be explained from audibility suggesting that the effects of suprathreshold deficits may be present possibly such a deficit is an increased downward spread of masking

image flow segmentation and estimation by constraint line clustering image flow is the velocity field in the image plane caused by the motion of the observer objects in the scene or apparent motion and can contain discontinuities due to object occlusion in the scene an algorithm that can estimate the image flow velocity field when there are discontinuities due to occlusions is described the constraint line clustering algorithm uses a statistical test to estimate the image flow velocity field in the presence of step discontinuities in the image irradiance or velocity field particular emphasis is placed on motion estimation and segmentation in situations such as random dot patterns where motion is the only cue to segmentation experimental results on a demanding synthetic test case and a real image are presented a smoothing algorithm for improving the velocity field estimate is also described the smoothing algorithm constructs a smooth estimate of the velocity field by approximating a surface between step discontinuities it is noted that the velocity field estimate can be improved using surface reconstruction between velocity field boundaries

image registration using wavelet based motion model an image registration algorithm is developed to estimate dense motion vectors between two images using the coarse to fine wavelet based motion model this motion model is described by a linear combination of hierarchical basis functions proposed by cai and wang siam numer anal 33 3 937 970 1996 the coarser scale basis function has larger support while the finer scale basis function has smaller support with these variable supports in full resolution the basis functions serve as large to small windows so that the global and local information can be incorporated concurrently for image matching especially for recovering motion vectors containing large displacements to evaluate the accuracy of the wavelet based method two sets of test images were experimented using both the wavelet based method and a leading pyramid spline based method by szeliski et al international journal of computer vision 22 3 199 218 1996 one set of test images taken from barron et al international journal of computer vision 12 43 77 1994 contains small displacements the other set exhibits low texture or spatial aliasing after image blurring and contains large displacements the experimental results showed that our wavelet based method produced better motion estimates with error distributions having a smaller mean and smaller standard deviation

efficient across frequency integration evidence from psychometric functions across frequency integration of complex signals was investigated by measuring psychometric functions log d versus signal level in db spl for detection of brief and long signals presented in broadband noise the signals were tones at 630 1600 and 4000 hz and a nine tone complex with components spaced at one third octave frequencies between 630 and 4000 hz the phase relationship of the components in the complex was varied such that adjacent components were in phase at 0 degrees 90 or 180 degrees out of phase signal durations defined in terms of the number of cycles between the half amplitude points of the gaussian envelopes of 4 7 and 150 cycles were tested results for six normal hearing listeners showed that the slopes of the psychometric functions were steeper for the brief than for the long signals and steeper for the tone complexes than for the tones particularly for the brief signals this suggests that the transformation from signal intensity to decision variable may be different fo

the deterioration of hearing with age frequency selectivity the critical ratio the audiogram and speech threshold the frequency selectivity of the auditory system was measured by masking a sinusoidal signal 0 5 2 0 or 4 0 khz or a filtered speech signal with a wideband noise having a notch or stopband centered on the signal as the notch was widened performance improved for both types of signal but the rate of improvement decreased as the age of the 16 listeners increased from 23 to 75 years indicating a loss in frequency selectivity with age auditory filter shapes derived from the tone in noise data show a that the passband of the filter broadens progressively with age and b that the dynamic range of the filter ages like the audiogram that is the range changes little with age before 55 but beyond this point there is an accelerating rate of loss the speech experiment shows comparable but smaller effects the filter width measurements show that the critical ratio is a poor estimator of frequency selectivity because it confounds the tuning of the system with the efficiency of the signal detection and speech processing mechanisms that follow the filter an alternative one point measure of frequency selectivity which is both sensitive and reliable is developed via the filter shape model of masking

a semiparametric estimate of treatment effects with censored data summary a semiparametric estimate of an average regression effect with right censored failure time data has recently been proposed under the cox type model where the regression effect t is allowed to vary with time in this article we derive a simple algebraic relationship between this average regression effect and a measurement of group differences in k sample transformation models when the random error belongs to the gp family of harrington and fleming 1982 biometrika69 553 566 the latter being equivalent to the conditional regression effect in a gamma frailty model the models considered here are suitable for the attenuating hazard ratios that often arise in practice the results reveal an interesting connection among the above three classes of models as alternatives to the proportional hazards assumption and add to our understanding of the behavior of the partial likelihood estimate under nonproportional hazards the algebraic relationship provides a simple estimator under the transformation model we develop a variance estimator based on the empirical influence function that is much easier to compute than the previously suggested resampling methods when there is truncation in the right tail of the failure times we propose a method of bias correction to improve the coverage properties of the confidence intervals the estimate its estimated variance and the bias correction term can all be calculated with minor modifications to standard software for proportional hazards regression

detection of time and bandlimited increments and decrements in a random level noise the purpose of this study was to compare detection of increments and decrements occurring over limited regions of time and frequency within a 500 ms broadband 0 6000 hz noise three listeners tracked detection thresholds adaptively in a two interval two alternative forced choice task thresholds were measured for both increments and decrements in level l 10 log10 1 n0 n0 db where n0 is the spectral power density of the noise as a function of signal duration t 30 500 ms for a range of signal bandwidths w 62 6000 hz that were logarithmically centered around 2500 hz listeners were forced to rely on temporal and spectral profile cues for detection due to randomization of overall presentation level from interval to interval which rendered overall energy an inconsistent cue increments were detectable for all combinations of w and t whereas decrements were not consistently detectable for w 500 hz narrow band decrements were not detectable due to spread of excitation from the spectral edges of

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

a computational framework and an algorithm for the measurement of visual the robust measurement of visual motion from digitized image sequences has been an important but difficult problem in computer vision this paper describes a hierarchical computational framework for the determination of dense displacement fields from a pair of images and an algorithm consist ent with that framework our framework is based on the separation of the image intensity information as well as the process of measuring motion according to scale the large scale intensity information is first used to obtain rough estimates of image motion which are then refined by using intensity information at smaller scales the estimates are in the form of displacement or velocity vectors for pixels and are accompanied by a direction dependent confidence measure a smoothness constraint is employed to propagate the measurements with high confidence to their neigboring areas where the confidences are low at all levels the computations are pixel parallel uniform across the image and based on information from a small neighborhood of a pixel for our algorithm the local displacement vectors are determind by mini mizing the sum of squared differences ssd of intensities the confidence measures are derived from the shape of the ssd surface and the smoothness constraint is cast in the form of energy minimization results of applying our algorithm to pairs of real images are included in addition to our own

estimating piecewise smooth optical flow with global matching and graduated optimization this paper presents a new method for estimating piecewise smooth optical flow we propose a global optimization formulation with three frame matching and local variation and develop an efficient technique to minimize the resultant global energy this technique takes advantage of local gradient global gradient and global matching methods and alleviates their limitations experiments on various synthetic and real data show that this method achieves highly competitive accuracy

lucas kanade meets horn schunck combining local and global optic flow methods differential methods belong to the most widely used techniques for optic flow computation in image sequences they can be classified into local methods such as the lucas kanade technique or bigun s structure tensor method and into global methods such as the horn schunck approach and its extensions often local methods are more robust under noise while global techniques yield dense flow fields the goal of this paper is to contribute to a better understanding and the design of novel differential methods in four ways i we juxtapose the role of smoothing regularisation processes that are required in local and global differential methods for optic flow computation ii this discussion motivates us to describe and evaluate a novel method that combines important advantages of local and global approaches it yields dense flow fields that are robust against noise iii spatiotemporal and nonlinear extensions as well as multiresolution frameworks are presented for this hybrid method iv we propose a simple confidence measure for optic flow methods that minimise energy functionals it allows to sparsify a dense flow field gradually depending on the reliability required for the resulting flow comparisons with experiments from the literature demonstrate the favourable performance of the proposed methods and the confidence measure

robust optical flow computation based on least median of squares regression an optical flow estimation technique is presented which is based on the least median of squares lmeds robust regression algorithm enabling more accurate flow estimates to be computed in the vicinity of motion discontinuities the flow is computed in a blockwise fashion using an affine model through the use of overlapping blocks coupled with a block shifting strategy redundancy is introduced into the computation of the flow this eliminates blocking effects common in most other techniques based on blockwise processing and also allows flow to be accurately computed in regions containing three distinct motions a multiresolution version of the technique is also presented again based on lmeds regression which enables image sequences containing large motions to be effectively handled an extensive set of quantitative comparisons with a wide range of previously published methods are carried out using synthetic realistic computer generated images of natural scenes with known flow and natural images both angular and absolute flow errors are calculated for those sequences with known optical flow displaced frame difference error used extensively in video compression is used for those natural scenes with unknown flow in all of the sequences tested a comparison with those methods that result in a dense flow field greater than 80 spatial coverage show that the lmeds technique produces the least error irrespective of the error measure used

computation of component image velocity from local phase information we present a technique for the computation of 2d component velocity from image sequences initially the image sequence is represented by a family of spatiotemporal velocity tuned linear filters component velocity computed from spatiotemporal responses of identically tuned filters is expressed in terms of the local first order behavior of surfaces of constant phase justification for this definition is discussed from the perspectives of both 2d image translation and deviations from translation that are typical in perspective projections of 3d scenes the resulting technique is predominantly linear efficient and suitable for parallel processing moreover it is local in space time robust with respect to noise and permits multiple estimates within a single neighborhood promising quantiative results are reported from experiments with realistic image sequences including cases with sizeable perspective deformation

multimodal estimation of discontinuous optical flow using markov random fields the estimation of dense velocity fields from image sequences is basically an ill posed problem primarily because the data only partially constrain the solution it is rendered especially difficult by the presence of motion boundaries and occlusion regions which are not taken into account by standard regularization approaches in this paper the authors present a multimodal approach to the problem of motion estimation in which the computation of visual motion is based on several complementary constraints it is shown that multiple constraints can provide more accurate flow estimation in a wide range of circumstances the theoretical framework relies on bayesian estimation associated with global statistical models namely markov random fields the constraints introduced here aim to address the following issues optical flow estimation while preserving motion boundaries processing of occlusion regions fusion between gradient and feature based motion constraint equations deterministic relaxation algorithms are used to merge information and to provide a solution to the maximum a posteriori estimation of the unknown dense motion field the algorithm is well suited to a multiresolution implementation which brings an appreciable speed up as well as a significant improvement of estimation when large displacements are present in the scene experiments on synthetic and real world image sequences are reported

error analysis of robust optical flow estimation by least median of squares methods for the varying illumination model the apparent pixel motion in an image sequence called optical flow is a useful primitive for automatic scene analysis and various other applications of computer vision in general however the optical flow estimation suffers from two significant problems the problem of illumination that varies with time and the problem of motion discontinuities induced by objects moving with respect to either other objects or with respect to the background various integrated approaches for solving these two problems simultaneously have been proposed of these those that are based on the lmeds least median of squares appear to be the most robust the goal of this paper is to carry out an error analysis of two different lmeds based approaches one based on the standard lmeds regression and the other using a modification thereof as proposed by us recently while it is to be expected that the estimation accuracy of any approach would decrease with increasing levels of noise for lmeds like methods it is not always clear as to how much of that decrease in performance can be attributed to the fact that only a small number of randomly selected samples is used for forming temporary solutions to answer this question our study here includes a baseline implementation in which all of the image data is used for forming motion estimates we then compare the estimation errors of the two lmeds based methods with the baseline implementation our error analysis demonstrates that for the case of gaussian noise our modified lmeds approach yields better estimates at moderate levels of noise but is outperformed by the standard lmeds method as the level of noise increases for the case of salt and pepper noise the modified lmeds method consistently performs better than the standard lmeds method

level discrimination of tones as a function of duration difference limens for level ls db 20 log p p p where p is the pressure were measured as a function of duration for tones at 250 500 and 8000 hz stimulus durations ranged from 2 ms to 2 s and the stimulus power was held constant rise and fall times were 1 ms the interstimulus interval was 250 ms at each frequency three levels were tested 85 65 and approximately 40 db spl an adaptive two alternative forced choice procedure with feedback was used for three normal listeners ls decreased as duration increased up to at least 2 s except at 250 hz at 250 hz l stopped decreasing at durations between 0 5 and 1 s in a double logarithmic plot of l versus duration the rate of decrease is generally well fitted by a sloping line the average slope is 0 28 it is steeper at high levels than at low levels because the average slope is shallower than the 0 5 slope predicted for an optimum detector it may be that fast adaptation of auditory nerve activity and or memory effects interfere w

psychometric functions for level discrimination to determine the form of psychometric functions for 2i 2afc level discrimination ten increment levels were presented in random order within blocks of 100 trials stimuli were chosen to encompass a wide range of conditions and difference limens eight 10 ms tones had frequencies of 0 25 1 8 or 14 khz and levels of 30 60 or 90 db spl two 500 ms stimuli also were tested a 1 khz tone at 90 db spl and a white noise at 63 db spl for each condition at least 20 blocks were presented in mixed order results for three normal listeners show that the sensitivity d is nearly proportional to l 20 log p p p where p is pressure over the entire range of difference limens when d is plotted against weber fractions for pressure p p or intensity i i exponents of the best fitting power functions decrease with increasing difference limens and are less than one for large difference limens these results indicate that the transformation from stimulus intensity to decision variable may be approximately lo

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