an mrf model based approach to simultaneous recovery of depth and restoration from defocused images in this paper we propose a map markov random field mrf based scheme for recovering the depth and the focused image of a scene from two defocused images the space variant blur parameter and the focused image of the scene are both modeled as mrfs and their map estimates are obtained using simulated annealing the scheme is amenable to the incorporation of smoothness constraints on the spatial variations of the blur parameter as well as the scene intensity it also allows for inclusion of line fields to preserve discontinuities the performance of the proposed scheme is tested on synthetic as well as real data and the estimates of the depth are found to be better than that of the existing window based depth from defocus technique the quality of the space variant restored image of the scene is quite good even under severe space varying blurring conditions

a stochastic approximation algorithm with markov chain monte carlo method for incomplete data estimation problems we propose a general procedure for solving incomplete data estimation problems the procedure can be used to find the maximum likelihood estimate or to solve estimating equations in difficult cases such as estimation with the censored or truncated regression model the nonlinear structural measurement error model and the random effects model the procedure is based on the general principle of stochastic approximation and the markov chain monte carlo method applying the theory on adaptive algorithms we derive conditions under which the proposed procedure converges simulation studies also indicate that the proposed procedure consistently converges to the maximum likelihood estimate for the structural measurement error logistic regression model

performance analysis of maximum likelihood estimator for recovery of depth from defocused images and optimal selection ofcamera parameters the recovery of depth from defocused images involves calculating the depth of various points in a scene by modeling the effect that the focal parameters of the camera have on images acquired with a small depth of field in the existing methods on depth from defocus dfd two defocused images of a scene are obtained by capturing the scene with different sets of camera parameters although the dfd technique is computationally simple the accuracy is somewhat limited compared to the stereo algorithms further an arbitrary selection of the camera settings can result in observed images whose relative blurring is insufficient to yield a good estimate of the depth in this paper we address the dfd problem as a maximum likelihood ml based blur identification problem we carry out performance analysis of the ml estimator and study the effect of the degree of relative blurring on the accuracy of the estimate of the depth we propose a criterion for optimal selection of camera parameters to obtain an improved estimate of the depth the optimality criterion is based on the cramer rao bound of the variance of the error in the estimate of blur a number of simulations as well as experimental results on real images are presented to substantiate our claims

fusing images with different focuses using support vector machines many vision related processing tasks such as edge detection image segmentation and stereo matching can be performed more easily when all objects in the scene are in good focus however in practice this may not be always feasible as optical lenses especially those with long focal lengths only have a limited depth of field one common approach to recover an everywhere in focus image is to use wavelet based image fusion first several source images with different focuses of the same scene are taken and processed with the discrete wavelet transform dwt among these wavelet decompositions the wavelet coefficient with the largest magnitude is selected at each pixel location finally the fused image can be recovered by performing the inverse dwt in this paper we improve this fusion procedure by applying the discrete wavelet frame transform dwft and the support vector machines svm unlike dwt dwft yields a translation invariant signal representation using features extracted from the dwft coefficients a svm is trained to select the source image that has the best focus at each pixel location and the corresponding dwft coefficients are then incorporated into the composite wavelet representation experimental results show that the proposed method outperforms the traditional approach both visually and quantitatively

lattice boltzmann simulations on irregular grids introduction of the natrium library the lattice boltzmann method is a modern approach to simulate fluid flow in its original formulation it is restricted to regular grids second order discretizations and a unity cfl number this paper describes our new off lattice boltzmann solver natrium an extensible and parallel c code to perform lattice boltzmann simulations on irregular grids natrium also allows high order spatial discretizations and non unity cfl numbers to be used we demonstrate how these features can efficiently decrease the number of grid points required in a simulation and thus reduce the computational time compared to the standard lattice boltzmann method we detail the implementation of a recently proposed semi lagrangian lattice boltzmann method and prove its efficiency in comparisons to other state of the art off lattice boltzmann schemes

nonuniform sampling and antialiasing in image representation a unified approach to the representation and processing of a class of images which are not bandlimited but belong to the space of locally bandlimited signals is presented a nonuniform sampling theorem clark et al 1985 for functions belonging to this space is extended and a class of nonstationary stochastic processes is considered the space of locally bandlimited signals is shown to be a reproducing kernel space a generalized projection theorem can therefore be applied yielding either a continuous or a discrete projection filter the former can be used for image conditioning prior to nonuniform sampling while the latter provides a general tool for image representation by nonuniform sampling schemes the problem of finding the local bandwidth of a given signal in order to generate an optimal sampling scheme is addressed in the context of signal representation in the combined position frequency space the stochastic estimation of parameters which characterize the local bandwidth is discussed bounds on the error resulting from the utilization of nonexact position varying signal parameters are derived

linear systems in gabor time frequency space a new approach for the description and operation of linear time varying systems is presented the proposed formalism implements the superposition integral describing a general linear operation in gabor time frequency space enabling the use of its joint properties the method is based on transforming both the input and the time varying impulse response function into the gabor space the 2 and 4 d arrays corresponding to the gabor spectra of the input signal and the impulse response respectively are multiplied yielding a 2 d array corresponding to the output gabor spectrum from which the output time signal is subsequently reconstructed unlike other time varying operation methods carried out in different mixed time frequency spaces e g wigner space the suggested approach when employing the critically sampled gabor expansion generates a legal output spectrum and eliminates the need to resort to cumbersome and numerically taxing approximate synthesis techniques the proposed formalism can be implemented in the areas of time variant filtering speech scrambling and any other linear operations that vary their characterizations in time

shape from focus using multilayer feedforward neural networks the conventional shape from focus sff methods have inaccuracies because of piecewise constant approximation of the focused image surface fis we propose a scheme for sff based on representation of three dimensional 3 d fis in terms of neural network weights the neural networks are trained to learn the shape of the fis that maximizes the focus measure

numerical simulation of sound generated by vortex pairing in a mixing layer a numerical code solving the filtered navier stokes equations is developed using special techniques of computational aeroacoustics this approach allows a direct determination of the compressible field on a computational domain including the acoustic far field a two dimensional mixing layer between two flows at m 1 0 12 and m 2 0 48 is simulated the reynolds number built up from the initial vorticity thickness and the velocity difference across the mixing layer is re 1 28 x 10 4 an appropriate forcing of the mixing layer is defined to have only one pairing in the computational domain at a fixed location the sound generation pattern for a single pairing displays a double spiral structure corresponding to the rotating quadrupole associated to two corotative vortices successive pairings produce an acoustic radiation at the frequency of this mechanism the directly computed far field sound is then compared to the prediction of lighthill s acoustic analogy lighthill m j on sound generated aerodynamically i general theory proceedings of the royal society of london vol 211 series a 1107 1952 pp 564 587 based on the aerodynamic fluctuations provided by the large eddy simulation code two integral formulations of the analogy based on spatial derivatives and time derivatives respectively are tested results are in good qualitative agreement with the results of direct simulation the accuracy is however greater with the formulation using time derivatives instead of spatial derivatives

defocus map estimation from a single image based on two parameter defocus model defocus map estimation dme is highly important in many computer vision applications nearly all existing approaches for dme from a single image are based on a one parameter defocus model which does not allow for the variation of depth over edges in this paper a novel two parameter model of defocused edges is proposed for dme from a single image we can estimate the defocus amounts for each side of the edges through this proposed model and the confidence that the edge is a pattern edge where the depth remains the same over the edge can be generated then we modify the tv l1 algorithm for structure texture decomposition by taking advantage of this confidence to eliminate pattern edges while preserving structural ones finally the defocus amounts estimated at the edge positions are used as initial values and the structure component is employed as a guidance in the following laplacian matting procedure to avoid the influence of pattern edges on the final defocus map experiment results show that the proposed method can effectively eliminate the influence of pattern edges compared with the state of art method furthermore the estimated defocus map is feasible in applications of depth estimation and foreground background segmentation

image reconstruction from projections under wavelet constraints first the authors discuss how the wavelet transform can be used to perform spatially varying filtering of an image suppressing noise locally in smooth regions of the image and discuss detection of such regions in a noise corrupted image second they show how to compute the minimum mean square estimate of an image given 1 noisy projections of the image 2 statistics of additive noise in the projections and 3 constraints on wavelet coefficients of the image examples illustrate the resulting procedure

ascent based monte carlo expectation maximization summary the expectation maximization em algorithm is a popular tool for maximizing likelihood functions in the presence of missing data unfortunately em often requires the evaluation of analytically intractable and high dimensional integrals the monte carlo em mcem algorithm is the natural extension of em that employs monte carlo methods to estimate the relevant integrals typically a very large monte carlo sample size is required to estimate these integrals within an acceptable tolerance when the algorithm is near convergence even if this sample size were known at the onset of implementation of mcem its use throughout all iterations is wasteful especially when accurate starting values are not available we propose a data driven strategy for controlling monte carlo resources in mcem the algorithm proposed improves on similar existing methods by recovering em s ascent i e likelihood increasing property with high probability being more robust to the effect of user defined inputs and handling classical monte carlo and markov chain monte carlo methods within a common framework because of the first of these properties we refer to the algorithm as ascent based mcem we apply ascent based mcem to a variety of examples including one where it is used to accelerate the convergence of deterministic em dramatically

time frequency distribution inversion of the radon transform image reconstruction in using filtered backprojection to compute the inverse radon transform the ramp filter amplifies noise spatially invariant noise filters reduce resolution it is desirable to filter noise where projections have no local high frequency components using the short time fourier transform the authors apply a time frequency mask filter that zeroes out projections where local signal energy is below a threshold results show improvement over reconstructions using spatially invariant smoothing filters

optimal filtering in fractional fourier domains for time invariant degradation models and stationary signals and noise the classical fourier domain wiener filter which can be implemented in o n log n time gives the minimum mean square error estimate of the original undistorted signal for time varying degradations and nonstationary processes however the optimal linear estimate requires o n sup 2 time for implementation we consider filtering in fractional fourier domains which enables significant reduction of the error compared with ordinary fourier domain filtering for certain types of degradation and noise especially of chirped nature while requiring only o n log n implementation time thus improved performance is achieved at no additional cost expressions for the optimal filter functions in fractional domains are derived and several illustrative examples are given in which significant reduction of the error by a factor of 50 is obtained

edge and depth from focus this paper proposes a novel method to obtain the reliable edge and depth information by integrating a set of multi focus images i e a sequence of images taken by systematically varying a camera parameter focus in previous work on depth measurement using focusing or defocusing the accuracy depends upon the size and location of local windows where the amount of blur is measured in contrast no windowing is needed in our method the blur is evaluated from the intensity change along corresponding pixels in the multi focus images such a blur analysis enables us not only to detect the edge points without using spatial differentiation but also to estimate the depth with high accuracy in addition the analysis result is stable because the proposed method involves integral computations such as summation and least square model fitting this paper first discusses the fundamental properties of multi focus images based on a step edge model then two algorithms are presented edge detection using an accumulated defocus image which represents the spatial distribution of blur and depth estimation using a spatio focal image which represents the intensity distribution along focus axis the experimental results demonstrate that the highly precise measurement has been achieved 0 5 pixel position fluctuation in edge detection and 0 2 error at 2 4 m in depth estimation

an investigation of methods for determining depth from focus the concept of depth from focus involves calculating distances to points in an observed scene by modeling the effect that the camera s focal parameters have on images acquired with a small depth of field this technique is passive and requires only a single camera the most difficult segment of calculating depth from focus is deconvolving the defocus operator from the scene and modeling it most current methods for determining the defocus operator employ inverse filtering the authors reveal some fundamental problems with inverse filtering inaccuracies in finding the frequency domain representation windowing effects and border effects a general matrix based method using regularization is presented which eliminates these problems the new method is confirmed experimentally with the results showing an rms error of 1 3

a spectral difference lattice boltzmann method for solution of inviscid compressible flows on structured grids in this work a spectral difference lattice boltzmann method sdlbm is developed and applied for an accurate simulation of two dimensional inviscid compressible flows on structured grids the compressible form of the discrete boltzmann bgk equation is used in which multiple particle speeds have to be employed to correctly model the compressibility in a thermal fluid here the 2d compressible lattice boltzmann lb model proposed by watari is applied the spectral difference sd method is implemented for the solution of the lb equation in which the particle distribution function is stored at the solution points while the fluxes are computed at the flux points for calculating the particle distribution function for time accurate solutions the fourth order runge kutta scheme is used to discretize the temporal term in the lb equation note that the procedure of implementing the sd method to solve the lb equation is nearly the same as that procedure developed in the literature for the solution of the euler equations the accuracy and robustness of the present solution methodology are demonstrated by simulating different benchmark compressible flow problems a sensitivity study is also conducted to evaluate the effects of the numerical parameters and the grid size distribution on the accuracy and performance of the solution at first three inviscid compressible flow problems namely the stationary isentropic vortex the shock tube and the shock vortex interaction are solved by using the sdlbm to demonstrate the accuracy and robustness of the present solution methodology results computed for these test cases are in good agreement with the analytical and the available numerical solutions to more assess the accuracy and robustness of the sdlbm a third order finite volume lbm fvlbm is also developed and the solutions obtained by these two methods for the test cases simulated are thoroughly compared with each other it is demonstrated that the sdlbm is more accurate and robust compressible inviscid flow solver that can be used for evaluating the other compressible lb based flow solvers as the final problem the supersonic flow past a bump is simulated to demonstrate the accuracy and robustness of the sdlbm in reaching to a steady state solution

spatially varying spectral filtering of signals on the unit sphere this paper presents a general framework for spatially varying spectral filtering of signals defined on the unit sphere as an analogy to joint time frequency filtering for this purpose we first map spherical signals from spatial domain into joint spatio spectral domain where a spatio spectral signal transformation or modification is introduced for mapping spatial signals into joint spatio spectral domain we use the spatially localized spherical harmonic transform slsht from the literature we then propose a suitable scheme to transform the modified signal from the spatio spectral domain back to an admissible signal in the spatial domain using the least squares approach we also show that the overall action of the slsht and spatio spectral signal modification can be described through a single transformation matrix which is useful in practice finally we discuss two specific and useful instances of spatially varying spectral filtering defined through multiplicative and convolutive modification of the slsht distribution and show through numerical examples their effectiveness in selective spectral filtering of different spatial regions of the signal

time variant filtering of signals in the mixed time frequency domain a new approach to the problem of time variant filtering is presented this approach is based upon the generation of the mixed time frequency representation mtfr of a signal multiplication of that representation by a time frequency function h t and obtaining a filtered output by an inverse operation the resultant filter is linear if the time frequency representation used is the complex spectrogram in contrast the filter is nonlinear if the wigner distribution function is used not every function of two variables is an allowed mtfr of a signal some conditions must be satisfied if the function produced by the product of the signal mtfr and the filter function is not an allowed mtfr an approximation based on projection onto the space of allowed mtfr functions is investigated this approximation yields a filtered function whose mtfr is as close as possible in the least squared sense to the desired

the hyperbolic class of quadratic time frequency representations ii subclasses intersection with the affine and power classes regularity and unitarity for pt i see ibid vol 41 p 3425 444 1993 part i introduced the hyperbolic class hc of quadratic bilinear time frequency representations qtfrs the present paper defines and studies four subclasses of the hc 1 the focalized kernel subclass of the hc is related to a time frequency concentration property of qtfrs it is analogous to the localized kernel subclass of the affine qtfr class 2 the affine subclass of the hc affine hc consists of all hc qtfrs that satisfy the conventional time shift covariance property it forms the intersection of the hc with the affine qtfr class 3 the power subclasses of the hc consist of all hc qtfrs that satisfy a power time shift covariance property they form the intersection of the hc with the recently introduced power classes 4 the power warp subclass of the hc consists of all hc qtfrs that satisfy a covariance to power law frequency warpings it is the hc counterpart of the shift scale covariant subclass of cohen s class all of these subclasses are characterized by 1d kernel functions the affine hc is contained in both the localized kernel hyperbolic subclass and the localized kernel affine subclass and that any affine hc qtfr can be derived from the bertrand unitary po distribution by a convolution we furthermore consider the properties of regularity and unitarity in the hc the calculus of inverse kernels is developed and important implications of regularity and unitarity are summarized the results comprise a general method for least squares signal synthesis and new relations for the altes marinovich q distribution

monocular extraction of 2 1d sketch using constrained convex optimization this paper presents an approach to estimating the 2 1d sketch from monocular low level visual cues we use a low level segmenter to partition the image into regions and then estimate their 2 1d sketch subject to figure ground and similarity constraints between neighboring regions the 2 1d sketch assigns a depth ordering to image regions which are expected to correspond to objects and surfaces in the scene this is cast as a constrained convex optimization problem and solved within the optimization transfer framework the optimization objective takes into account the curvature and convexity of parts of region boundaries appearance and spatial layout properties of regions our new optimization transfer algorithm admits a closed form expression of the duality gap and thus allows explicit computation of the achieved accuracy the algorithm is efficient with quadratic complexity in the number of constraints between image regions quantitative and qualitative results on challenging real world images of berkeley segmentation geometric context and stanford make3d datasets demonstrate our high accuracy efficiency and robustness

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

focused image recovery from two defocused images recorded with different camera settings two new methods are presented for recovering the focused image of an object from only two blurred images recorded with different camera parameter settings the camera parameters include lens position focal length and aperture diameter first a blur parameter 0 is estimated using one of our two recently proposed depth from defocus methods then one of the two blurred images is deconvolved to recover the focused image the first method is based on a recently proposed spatial domain convolutioddeconvolution transform this method requires only the knowledge of 7 of the camera s point spread function psf it does not require information about the actual form of the camera s psf the second method in contrast to the first requires full knowledge of the form of the psf as part of the second method we present a calibration procedure for estimating the camera s psf for different values of the blur parameter 0 in the second method the focused image is obtained through deconvolution in the fourier domain using the wiener filter for both methods results of experiments on actual defocused images recorded by a ccd camera are given the first method requires much less computation than the second method the first method gives satisfactory results for up to medium levels of blur and the second method gives good results for up to relatively high levels of blur

reconstruction from projections under time frequency constraints low pass filtering computed tomography ct images to reduce noise may smooth or modify image features which are very important to the physician image features are often more easily identified and processed in the time frequency plane the authors use time frequency distributions for spatially varying filtering of noisy ct images constraining time frequency representation coefficients of the projection data or of the reconstructed image to be zero in certain regions of the time frequency plane the authors consider two different applications 1 filtering the projection data and then performing image reconstruction and 2 filtering the reconstructed image directly criteria minimized subject to constraints may be either a deterministic minimum weighted perturbation of the given projection data or a stochastic minimum mean square error in colored gaussian noise results show improvement over processing the image with a linear spatially invariant filter

improving estimates of genetic maps a maximum likelihood approach as a result of previous large multipoint linkage studies there is a substantial amount of existing marker data due to the increased sample size genetic maps estimated from these data could be more accurate than publicly available maps however current methods for map estimation are restricted to data sets containing pedigrees with a small number of individuals or cannot make full use of marker data that are observed at several loci on members of large extended pedigrees in this article a maximum likelihood ml method for map estimation that can make full use of the marker data in a large multipoint linkage study is described the method is applied to replicate sets of simulated marker data involving seven linked loci and pedigree structures based on the real multipoint linkage study of abkevich et al 2003 american journal of human genetics 73 1271 1281 the variance of the ml estimate is accurately estimated and tests of both simple and composite null hypotheses are performed an efficient procedure for combining map estimates over data sets is also suggested

real time focus range sensor structures of dynamic scenes can only be recovered using a real time range sensor depth from defocus offers an effective solution to fast and dense range estimation however accurate depth estimation requires theoretical and practical solutions to a variety of problems including recovery of textureless surfaces precise blur estimation and magnification variations caused by defocusing both textured and textureless surfaces are recovered using an illumination pattern that is projected via the same optical path used to acquire images the illumination pattern is optimized to maximize accuracy and spatial resolution in computed depth the relative blurring in two images is computed using a narrow band linear operator that is designed by considering all the optical sensing and computational elements of the depth from defocus system defocus invariant magnification is achieved by the use of an additional aperture in the imaging optics a prototype focus range sensor has been developed that has a workspace of 1 cubic foot and produces up to 512 spl times 480 depth estimates at 30 hz with an average rms error of 0 2 several experimental results are included to demonstrate the performance of the sensor

numerical simulation of sound generation in a mixing layer by the finite difference lattice boltzmann method we simulated aerodynamic sound in a two dimensional mixing layer using the finite difference lattice boltzmann method fdlbm we introduced a finite difference scheme called the dispersion relation preserving drp scheme into the fdlbm to carry out an accurate simulation of aerodynamic problems the scheme is designed such that the dispersion relation of the finite difference scheme is the same as that of the original partial differential equations and is useful for acoustic simulations a turbulent flow field was simulated by large eddy simulation les using the smagorinsky model and the results were compared with those from a direct simulation based on the navier stokes equations to confirm the usefulness of this method the combination of the fdlbm and the drp scheme was shown to be very effective for direct simulations of aerodynamic sound

the wigner distribution of linear time variant systems the wigner distribution relation between the two input and output time varying spectra of the linear time variant system is derived this mathematical relationship can show how a time variant system modifies the time varying spectrum of the input to determine that of the output and this result will be very useful for time variant filtering in the mixed time frequency domain a linear time variant digital filtering example is used to show the effect of time variant filtering by using the wigner distribution

reconstructing arbitrarily focused images from two differently focused images using linear filters we present a novel filtering method for reconstructing an all in focus image or an arbitrarily focused image from two images that are focused differently the method can arbitrarily manipulate the degree of blur of the objects using linear filters without segmentation the filters are uniquely determined from a linear imaging model in the fourier domain an effective and accurate blur estimation method is developed the simulation results show that the accuracy and computational time of the proposed method are improved compared with the previous iterative method and that the effects of blur estimation error on the quality of the reconstructed image are very small the method performs well for real images acquired without visible artifacts

analysis and filtering using the optimally smoothed wigner distribution the authors consider the analysis and filtering of a deterministic signal with slowly time varying spectra using the optimally smoothed wigner distribution oswd they compare this mixed time frequency representation mtfr to other mtfrs such as the spectrogram the short time fourier transform stft and the wigner and pseudo wigner distributions the authors propose an approach to designing linear time varying filters for slowly time varying signals which is based on the concept of local nonstationarity cancellation and show that it is equivalent to masking the optimal stft the performance of the filter in suppressing white noise and in decomposing a slowly time varying signal into its components is studied and compared to the performance of the techniques based on the stft

a variational approach to recovering depth from defocused images in this paper we propose a regularized solution to the depth from defocus dfd problem using the space frequency representation sfr framework a smoothness constraint is imposed on the estimates of the blur parameter and a variational approach to the dfd problem is developed among the numerous sfrs we study the applicability of the complex spectrogram and the wigner distribution in particular for depth recovery the performance of the proposed variational method is tested on both synthetic and real images the method yields good results and the quality of the estimates is significantly better than that obtained without the smoothness constraint on the blur parameter