ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

blur identification by the method of generalized cross validation the point spread function psf of a blurred image is often unknown a priori the blur must first be identified from the degraded image data before restoring the image generalized cross validation gcv is introduced to address the blur identification problem the gcv criterion identifies model parameters for the blur the image and the regularization parameter providing all the information necessary to restore the image experiments are presented which show that gvc is capable of yielding good identification results a comparison of the gcv criterion with maximum likelihood ml estimation shows the gcv often outperforms ml in identifying the blur and image model parameters

estimation of the mean of a multivariate normal distribution estimation of the means of independent normal random variables is considered using sum of squared errors as loss an unbiased estimate of risk is obtained for an arbitrary estimate and certain special classes of estimates are then discussed the results are applied to smoothing by use of moving averages and to trimmed analogs of the james stein estimate a suggestion is made for calculating approximate confidence sets for the mean vector centered at an arbitrary estimate

blind deconvolution using a variational approach to parameter image and blur estimation following the hierarchical bayesian framework for blind deconvolution problems in this paper we propose the use of simultaneous autoregressions as prior distributions for both the image and blur and gamma distributions for the unknown parameters hyperparameters of the priors and the image formation noise we show how the gamma distributions on the unknown hyperparameters can be used to prevent the proposed blind deconvolution method from converging to undesirable image and blur estimates and also how these distributions can be inferred in realistic situations we apply variational methods to approximate the posterior probability of the unknown image blur and hyperparameters and propose two different approximations of the posterior distribution one of these approximations coincides with a classical blind deconvolution method the proposed algorithms are tested experimentally and compared with existing blind deconvolution methods

a new sure approach to image denoising interscale orthonormal wavelet thresholding this paper introduces a new approach to orthonormal wavelet image denoising instead of postulating a statistical model for the wavelet coefficients we directly parametrize the denoising process as a sum of elementary nonlinear processes with unknown weights we then minimize an estimate of the mean square error between the clean image and the denoised one the key point is that we have at our disposal a very accurate statistically unbiased mse estimate stein s unbiased risk estimate that depends on the noisy image alone not on the clean one like the mse this estimate is quadratic in the unknown weights and its minimization amounts to solving a linear system of equations the existence of this a priori estimate makes it unnecessary to devise a specific statistical model for the wavelet coefficients instead and contrary to the custom in the literature these coefficients are not considered random any more we describe an interscale orthonormal wavelet thresholding algorithm based on this new approach and show its near optimal performance both regarding quality and cpu requirement by comparing it with the results of three state of the art nonredundant denoising algorithms on a large set of test images an interesting fallout of this study is the development of a new group delay based parent child prediction in a wavelet dyadic tree

a nonlinear stein based estimator for multichannel image denoising the use of multicomponent images has become widespread with the improvement of multisensor systems having increased spatial and spectral resolutions however the observed images are often corrupted by an additive gaussian noise in this paper we are interested in multichannel image denoising based on a multiscale representation of the images a multivariate statistical approach is adopted to take into account both the spatial and the intercomponent correlations existing between the different wavelet subbands more precisely we propose a new parametric nonlinear estimator which generalizes many reported denoising methods the derivation of the optimal parameters is achieved by applying stein s principle in the multivariate case experiments performed on multispectral remote sensing images clearly indicate that our method outperforms conventional wavelet denoising techniques

a soft double regularization approach to parametric blind image deconvolution this paper proposes a blind image deconvolution scheme based on soft integration of parametric blur structures conventional blind image deconvolution methods encounter a difficult dilemma of either imposing stringent and inflexible preconditions on the problem formulation or experiencing poor restoration results due to lack of information this paper attempts to address this issue by assessing the relevance of parametric blur information and incorporating the knowledge into the parametric double regularization pdr scheme the pdr method assumes that the actual blur satisfies up to a certain degree of parametric structure as there are many well known parametric blurs in practical applications further it can be tailored flexibly to include other blur types if some prior parametric knowledge of the blur is available a manifold soft parametric modeling technique is proposed to generate the blur manifolds and estimate the fuzzy blur structure the pdr scheme involves the development of the meaningful cost function the estimation of blur support and structure and the optimization of the cost function experimental results show that it is effective in restoring degraded images under different environments

the sure let approach to image denoising we propose a new approach to image denoising based on the image domain minimization of an estimate of the mean squared error stein s unbiased risk estimate sure unlike most existing denoising algorithms using the sure makes it needless to hypothesize a statistical model for the noiseless image a key point of our approach is that although the nonlinear processing is performed in a transformed domain typically an undecimated discrete wavelet transform but we also address nonorthonormal transforms this minimization is performed in the image domain indeed we demonstrate that when the transform is a ldquotightrdquo frame an undecimated wavelet transform using orthonormal filters separate subband minimization yields substantially worse results in order for our approach to be viable we add another principle that the denoising process can be expressed as a linear combination of elementary denoising processes linear expansion of thresholds let armed with the sure and let principles we show that a denoising algorithm merely amounts to solving a linear system of equations which is obviously fast and efficient quite remarkably the very competitive results obtained by performing a simple threshold image domain sure optimized on the undecimated haar wavelet coefficients show that the sure let principle has a huge potential

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

blind deblurring and denoising of images corrupted by unidirectional object motion blur and sensor noise low light photography suffers from blur and noise in this paper we propose a novel method to recover a dense estimate of spatially varying blur kernel as well as a denoised and deblurred image from a single noisy and object motion blurred image a proposed method takes the advantage of the sparse representation of double discrete wavelet transform a generative model of image blur that simplifies the wavelet analysis of a blurred image and the bayesian perspective of modeling the prior distribution of the latent sharp wavelet coefficient and the likelihood function that makes the noise handling explicit we demonstrate the effectiveness of the proposed method on moderate noise and severely blurred images using simulated and real camera data

hyperspectral super resolution of locally low rank images from complementary multisource data remote sensing hyperspectral images hsis are quite often low rank in the sense that the data belong to a low dimensional subspace manifold this has been recently exploited for the fusion of low spatial resolution hsi with high spatial resolution multispectral images in order to obtain super resolution hsi most approaches adopt an unmixing or a matrix factorization perspective the derived methods have led to state of the art results when the spectral information lies in a low dimensional subspace manifold however if the subspace manifold dimensionality spanned by the complete data set is large i e larger than the number of multispectral bands the performance of these methods mainly decreases because the underlying sparse regression problem is severely ill posed in this paper we propose a local approach to cope with this difficulty fundamentally we exploit the fact that real world hsis are locally low rank that is pixels acquired from a given spatial neighborhood span a very low dimensional subspace manifold i e lower or equal than the number of multispectral bands thus we propose to partition the image into patches and solve the data fusion problem independently for each patch this way in each patch the subspace manifold dimensionality is low enough such that the problem is not ill posed anymore we propose two alternative approaches to define the hyperspectral super resolution through local dictionary learning using endmember induction algorithms we also explore two alternatives to define the local regions using sliding windows and binary partition trees the effectiveness of the proposed approaches is illustrated with synthetic and semi real data

blind deconvolution of medical ultrasound images a parametric inverse filtering approach the problem of reconstruction of ultrasound images by means of blind deconvolution has long been recognized as one of the central problems in medical ultrasound imaging in this paper this problem is addressed via proposing a blind deconvolution method which is innovative in several ways in particular the method is based on parametric inverse filtering whose parameters are optimized using two stage processing at the first stage some partial information on the point spread function is recovered subsequently this information is used to explicitly constrain the spectral shape of the inverse filter from this perspective the proposed methodology can be viewed as a ldquohybridizationrdquo of two standard strategies in blind deconvolution which are based on either concurrent or successive estimation of the point spread function and the image of interest moreover evidence is provided that the ldquohybridrdquo approach can outperform the standard ones in a number of important practical cases additionally the present study introduces a different approach to parameterizing the inverse filter specifically we propose to model the inverse transfer function as a member of a principal shift invariant subspace it is shown that such a parameterization results in considerably more stable reconstructions as compared to standard parameterization methods finally it is shown how the inverse filters designed in this way can be used to deconvolve the images in a nonblind manner so as to further improve their quality the usefulness and practicability of all the introduced innovations are proven in a series of both in silico and in vivo experiments finally it is shown that the proposed deconvolution algorithms are capable of improving the resolution of ultrasound images by factors of 2 24 or 6 52 as judged by the autocorrelation criterion depending on the type of regularization method used

wavelet shrinkage using cross validation summary wavelets are orthonormal basis functions with special properties that show potential in many areas of mathematics and statistics this paper concentrates on the estimation of functions and images from noisy data by using wavelet shrinkage a modified form of twofold cross validation is introduced to choose a threshold for wavelet shrinkage estimators operating on data sets of length a power of 2 the cross validation algorithm is then extended to data sets of any length and to multidimensional data sets the algorithms are compared with established threshold choosers by using simulation an application to a real data set arising from anaesthesia is presented

hierarchical classification of permutation classes in multistage interconnection networks this paper explores a new hierarchy among different permutation classes that has many applications in multistage interconnection networks the well known lc linear complement class is shown to be merely a subset of the closure set of the bp bit permute class known as the bpcl bit permute closure class the closure is obtained by applying certain group transformation rules on the bp permutations it indicates that for every permutation p of the lc class there exists a permutation pi in the bp class such that the conflict graphs of p and p are isomorphic for n stage min s this obviates the practice of treating the lc class as a special case the existing algorithm for optimal routing of bpc class in an n stage min can take care of optimal routing of the lc class as well finally the relationships of bpcl with other classes of permutations e g lie linear input equivalence bpie bit permute input equivalence bpoe bit permute output equivalence are also exposed apart from lending better understanding and an integral view of the universe of permutations these results are found to be useful in accelerating routability in n stage min s as well as in 2n 1 stage benes and shuffle exchange networks

motion blur identification in noisy images using mathematical models and statistical measures motion blur is one of the most common blurs that degrades images restoration of such images is highly dependent on estimation of motion blur parameters since 1976 many researchers have developed algorithms to estimate linear motion blur parameters these algorithms are different in their performance time complexity precision and robustness in noisy environments in this paper we have presented a novel algorithm to estimate linear motion blur parameters such as direction and length we used radon transform to find direction and bispectrum modeling to find the length of motion our algorithm is based on the combination of spatial and frequency domain analysis the great benefit of our algorithm is its robustness and precision in noisy images we used statistical measures to prove goodness of our model our method was tested on 80 standard images that were degraded with different directions and motion lengths with additive gaussian noise the error tolerance average of the estimated parameters was 0 9 o in direction and 0 95 pixel in length and the standard deviations were 0 69 and 0 85 respectively

general techniques for analyzing recursive algorithms with applications the complexity of divide and conquer algorithms is often described by recurrences of various forms in this paper we develop general techniques and master theorems for solving several kinds of recurrences and we give several applications of our results in particular almost all of the earlier work on solving the recurrences considered here is subsumed by our work in the process of solving such recurrences we establish interesting connections between some elegant mathematics and analysis of recurrences using our results and improved bipartite matching algorithms we also improve existing bounds in the literature for several problems viz associative commutative ac matching of linear terms associative matching of linear terms rooted subtree isomorphism and rooted subgraph homeomorphism for trees

generalized sure for exponential families applications to regularization stein s unbiased risk estimate sure was proposed by stein for the independent identically distributed i i d gaussian model in order to derive estimates that dominate least squares ls recently the sure criterion has been employed in a variety of denoising problems for choosing regularization parameters that minimize an estimate of the mean squared error mse however its use has been limited to the i i d case which precludes many important applications in this paper we begin by deriving a sure counterpart for general not necessarily i i d distributions from the exponential family this enables extending the sure design technique to a much broader class of problems based on this generalization we suggest a new method for choosing regularization parameters in penalized ls estimators we then demonstrate its superior performance over the conventional generalized cross validation and discrepancy approaches in the context of image deblurring and deconvolution the sure technique can also be used to design estimates without predefining their structure however allowing for too many free parameters impairs the estimate s performance to address this inherent tradeoff we propose a regularized sure objective and demonstrate its use in the context of wavelet denoising

a novel sure based criterion for parametric psf estimation we propose an unbiased estimate of a filtered version of the mean squared error the blur sure stein s unbiased risk estimate as a novel criterion for estimating an unknown point spread function psf from the degraded image only the psf is obtained by minimizing this new objective functional over a family of wiener processings based on this estimated blur kernel we then perform nonblind deconvolution using our recently developed algorithm the sure based framework is exemplified with a number of parametric psf involving a scaling factor that controls the blur size a typical example of such parametrization is the gaussian kernel the experimental results demonstrate that minimizing the blur sure yields highly accurate estimates of the psf parameters which also result in a restoration quality that is very similar to the one obtained with the exact psf when plugged into our recent multi wiener sure let deconvolution algorithm the highly competitive results obtained outline the great potential of developing more powerful blind deconvolution algorithms based on sure like estimates

a sure approach for digital signal image deconvolution problems in this paper we are interested in the classical problem of restoring data degraded by a convolution and the addition of a white gaussian noise the originality of the proposed approach is twofold first we formulate the restoration problem as a nonlinear estimation problem leading to the minimization of a criterion derived from stein s unbiased quadratic risk estimate secondly the deconvolution procedure is performed using any analysis and synthesis frames that can be overcomplete or not new theoretical results concerning the calculation of the variance of the stein s risk estimate are also provided in this work simulations carried out on natural images show the good performance of our method with respect to conventional wavelet based restoration methods

blind image deconvolution using machine learning for three dimensional microscopy in this work we propose a novel method for the regularization of blind deconvolution algorithms the proposed method employs example based machine learning techniques for modeling the space of point spread functions during an iterative blind deconvolution process a prior term attracts the point spread function estimates to the learned point spread function space we demonstrate the usage of this regularizer within a bayesian blind deconvolution framework and also integrate into the latter a method for noise reduction thus creating a complete blind deconvolution method the application of the proposed algorithm is demonstrated on synthetic and real world three dimensional images acquired by a wide field fluorescence microscope where the need for blind deconvolution algorithms is indispensable yielding excellent results

parametric blur estimation for blind restoration of natural images linear motion and out of focus this paper presents a new method to estimate the parameters of two types of blurs linear uniform motion approximated by a line characterized by angle and length and out of focus modeled as a uniform disk characterized by its radius for blind restoration of natural images the method is based on the spectrum of the blurred images and is supported on a weak assumption which is valid for the most natural images the power spectrum is approximately isotropic and has a power law decay with the spatial frequency we introduce two modifications to the radon transform which allow the identification of the blur spectrum pattern of the two types of blurs above mentioned the blur parameters are identified by fitting an appropriate function that accounts separately for the natural image spectrum and the blur frequency response the accuracy of the proposed method is validated by simulations and the effectiveness of the proposed method is assessed by testing the algorithm on real natural blurred images and comparing it with state of the art blind deconvolution methods

direct blind deconvolution blind deconvolution seeks to deblur an image without knowing the cause of the blur iterative methods are commonly applied to that problem but the iterative process is slow uncertain and often ill behaved this paper considers a significant but limited class of blurs that can be expressed as convolutions of two dimensional symmetric levy stable probability density functions this class includes and generalizes gaussian and lorentzian distributions for such blurs methods are developed that can detect the point spread function from one dimensional fourier analysis of the blurred image a separate image deblurring technique uses this detected point spread function to deblur the image each of these two steps uses direct noniterative methods and requires interactive tuning of parameters as a result blind deblurring of 512 512 images can be accomplished in minutes of cpu time on current desktop workstations numerous blind experiments on synthetic data show that for a given blurred image several di

block threshold rules for curve estimation using kernel and wavelet methods motivated by recently developed threshold rules for wavelet estimators we suggest threshold methods for general kernel density estimators including those of classical rosenblatt parzen type thresholding makes kernel methods competitive in terms of their adaptivity to a wide variety of aberrations in complex signals it is argued that term by term thresholding does not always produce optimal performance since individual coefficients cannot be estimated sufficiently accurately for reliable decisions to be made therefore we suggest grouping coefficients into blocks and making simultaneous threshold decisions about all coefficients within a given block it is argued that block thresholding has a number of advantages including that it produces adaptive estimators which achieve minimax optimal convergence rates without the logarithmic penalty that is sometimes associated with term by term thresholding more than this the convergence rates are achieved over large classes of functions with discontinuities indeed with a number of discontinuities that diverges polynomially fast with sample size these results are also established for block thresholded wavelet estimators which although they can be interpreted within the kernel framework are often most conveniently constructed in a slightly different way

single image refocusing and defocusing in this paper we present a postprocessing method to tackle the single image refocusing and defocusing problem the proposed method can accomplish the tasks of focus map estimation and image refocusing and defocusing given an image with a mixture of focused and defocused objects we first detect the edges and then estimate the focus map based on the edge blurriness which is depicted explicitly by a parametric model the image refocusing problem is addressed in a blind deconvolution framework where the image prior is modeled by using both global and local constraints in particular we correct the defocused blurry edges to sharp ones with the aid of the parametric edge model and then render this cue as a local prior to ensure the sharpness of the refocused image experimental results demonstrate that the proposed method performs well in producing visually plausible images with different focus effects from a single input

multiple depth layers and all in focus image generations by blurring and deblurring operations the depth map and all in focus generations from a single image are proposed the depth map bases on the characteristic curve of coc vs the depth characteristic curve of a camera all in focus image generation is from the estimated depth map a joint deblurring process is proposed to generate an all in focus image in this work we propose novel methods for the generation of multiple depth layers and all in focus images multiple depth layers are produced by applying a sequence of blurring and deblurring operations to determine the depth the proposed method makes no assumptions with regard to the properties of the scene in resolving depth ambiguity in complex images we also developed a method by which to generate all in focus images in which the sharpness is preserved and instabilities imposed by conventional deblurring operations largely eliminated this method involves updating outliers for which depth was over estimated while compensating for errors in the estimation of depth imposed by deblurring

a self routing benes network and parallel permutation algorithms a benes permutation network capable of setting its own switches dynamically is presented the total switch setting and delay time for the n input utput self routing network is o log n it is shown that the network is capable of performing a rich class of permutations the self routing scheme leads to efficient o log n parallel algorithms to perform the same class of permutations on cube connected and perfect shuffle computers

self routing technique in perfect shuffle networks using control tags the self routing technique using control tags on multiple pass perfect shuffle networks is generalized in particular they show that bit permute complement permutations can be realized and unscrambled in 2n 1 passes or less where n log sub 2 n n being the number of terminals on either side they also show that most of the frequently used permutations are in the intersection of omega realizing and inverse omega realizing sets and can be realized and unscrambled in n passes

linear and nonlinear image deblurring a documented study nonlinear image deblurring procedures based on probabilistic considerations are widely believed to outperform conventional linear methods this paper is exclusively concerned with nonsmooth images such as those that occur in biomedical imaging where reconstruction of high frequency detail is of prime interest and where avoidance of a priori smoothness constraints is a major concern the theoretical basis behind each of the following nonlinear procedures is examined the lucy richardson method the maximum likelihood e m algorithm the poisson maximum a posteriori method and the nunez llacer version of the maximum entropy method a linear iterative method vancittert s iteration is also studied it is shown that each of the first three methods as well as vancittert s method lack a necessary ingredient for successful solution of the ill posed deblurring problem while in the maximum entropy method the enforced smoothness may have adverse consequences in medical imaging a direct linear method the slow evolution from the continuation boundary secb method designed specifically for nonsmooth images is also considered that method is stabilized by constraining the blurring operator as well as the solution and does not require smoothness constraints it is shown that useful error estimates can be obtained in the secb method while this is impossible in tikhonov s method without a priori bounds on derivatives of the unknown solution reconstruction experiments on low noise synthetic mri data show that thousands of iterations are necessary to achieve sufficient resolution in the iterative procedures however the secb method provides higher resolution at considerable savings in computer time at high noise levels the iterative algorithms are shown to diverge at these same noise levels the secb method produces reconstructions comparable in quality to those that would be obtained in the iterative methods were one able to terminate the divergent algorithm at that iteration which best approximates the true solution in the l1 norm

an analysis of a good algorithm for the subtree problem correlated it is shown that the proof of the main result in reyner s paper similarly titled is incorrect interestingly by combining a simple modification of the algorithm with tighter analysis one can obtain the original result with a minor improvement

time invariant orthonormal wavelet representations a simple construction of an orthonormal basis starting with a so called mother wavelet together with an efficient implementation gained the wavelet decomposition easy acceptance and generated a great research interest in its applications an orthonormal basis may not however always be a suitable representation of a signal particularly when time or space invariance is a required property the conventional way around this problem is to use a redundant decomposition we address the time invariance problem for orthonormal wavelet transforms and propose an extension to wavelet packet decompositions we show that it is possible to achieve time invariance and preserve the orthonormality we subsequently propose an efficient approach to obtain such a decomposition we demonstrate the importance of our method by considering some application examples in signal reconstruction and time delay estimation

multi wiener sure let deconvolution in this paper we propose a novel deconvolution algorithm based on the minimization of a regularized stein s unbiased risk estimate sure which is a good estimate of the mean squared error we linearly parametrize the deconvolution process by using multiple wiener filters as elementary functions followed by undecimated haar wavelet thresholding due to the quadratic nature of sure and the linear parametrization the deconvolution problem finally boils down to solving a linear system of equations which is very fast and exact the linear coefficients i e the solution of the linear system of equations constitute the best approximation of the optimal processing on the wiener haar threshold basis that we consider in addition the proposed multi wiener sure let approach is applicable for both periodic and symmetric boundary conditions and can thus be used in various practical scenarios the very competitive both in computation time and quality results show that the proposed algorithm which can be interpreted as a kind of nonlinear wiener processing can be used as a basic tool for building more sophisticated deconvolution algorithms

an empirical identification method of gaussian blur parameter for image deblurring in this paper we propose an empirical identification method of the gaussian blur parameter for image deblurring the parameter estimate is chosen from a collection of candidate parameters the blurred image is restored by these candidate parameters under the assumption that the candidate is equal to the true value the estimate is selected to be at the maximum point of the differential coefficients of restored image laplacian l1 norm curve experimental results are presented to demonstrate the performance of the proposed method

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

an easily controlled network for frequently used permutations a network which is a concatenation of 2 networks 2 along with a simple control algorithm is proposed this network is capable of performing all network realizable permutations and the bit permute complement bpc class of permutations 5 in 0 log n time the control algorithm is actually a multiple pass control algorithm on the network which is more general than pease s lu decomposition method 6 and lenfant s decomposition method 4

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

a taxonomy of problems with fast parallel algorithms the class nc consists of problems solvable very fast in time polynomial in log n in parallel with a feasible polynomial number of processors many natural problems in nc are known in this paper an attempt is made to identify important subclasses of nc and give interesting examples in each subclass the notion of nc 1 reducibility is introduced and used throughout problem r is nc 1 reducible to problem s if r can be solved with uniform log depth circuits using oracles for s problems complete with respect to this reducibility are given for many of the subclasses of nc a general technique the parallel greedy algorithm is identified and used to show that finding a minimum spanning forest of a graph is reducible to the graph accessibility problem and hence is in nc 2 solvable by uniform boolean circuits of depth o log 2 n and polynomial size the class logcfl is given a new characterization in terms of circuit families the class det of problems reducible to integer determinants is defined and many examples given a new problem complete for deterministic polynomial time is given namely finding the lexicographically first maximal clique in a graph this paper is a revised version of s a cook 1983 in proceedings 1983 intl found comut sci conf lecture notes in computer science vol 158 pp 78 93 springer verlag berlin new york

recognition of images degraded by gaussian blur in this paper we propose a new theory of invariants to gaussian blur we introduce a notion of a primordial image as a canonical form of all gaussian blur equivalent images the primordial image is defined in spectral domain by means of projection operators we prove that the moments of the primordial image are invariant to gaussian blur and we derive recursive formulas for their direct computation without actually constructing the primordial image itself we show how to extend their invariance also to image rotation the application of these invariants is in blur invariant image comparison and recognition in the experimental part we perform an exhaustive comparison with two main competitors 1 the zhang distance and 2 the local phase quantization

blind deconvolution using generalized cross validation approach to regularization parameter estimation in this paper we propose and present an algorithm for total variation tv based blind deconvolution both the unknown image and blur can be estimated within an alternating minimization framework with the generalized cross validation gcv method the regularization parameters associated with the unknown image and blur can be updated in alternating minimization steps experimental results confirm that the performance of the proposed algorithm is better than variational bayesian blind deconvolution algorithms with student s t priors or a total variation prior

tight complexity bounds for term matching problems abstract in this paper we study the sequential and parallel complexity of various important term matching problems these problems occur frequently in applications such as term rewriting functional programming and logic programming first we obtain non trivial lower bounds on the parallel complexity of the uninterpreted term matching problem we also establish the tightness of these bounds for some representations and several models we then characterize completely the sequential complexity of associative and commutative matching when the number of occurrences of variables is varied specifically we show that even if each variable is restricted to at most two occurrences in the terms both associative matching and commutative matching are np complete interestingly for the important restriction of boolean terms we show that commutative matching is np complete whereas associative matching has a linear time sequential algorithm for linear terms we significantly improve the existing upper bound for associative commutative matching and present a new algorithm for associative matching designing direct parallel algorithms for associative commutative matching of linear terms appears to be a difficult task despite this we have been able to resolve questions about the parallel complexity of these problems using complexity theoretic techniques finally an interesting consequence of the research reported here is the demonstration of a tighter relationship between associative commutative matching for linear terms and bipartite matching on both sequential and parallel models

realization of permutations on generalized indra networks abstract the realization of permutations of data on a class of redundant path interconnection networks called generalized indra networks is studied this class of networks is constructed by combining l layers copies of subnetworks in parallel preceded by a distribution stage the subnetwork chosen being a delta network constructed from r r switching elements redundant links are provided on the input side of the network so that failures in the distribution stage could be sustained the problem of realizing an arbitrary permutation on such networks has a one to one correspondence with the problem of performing the same permutation in multiple passes on a delta network this problem is reduced to that of finding a vertex coloring for the conflict graph of the permutation although the general problem of finding optimal colorings for graphs of arbitrary permutations is unsolved classes of permutations with some regularity can be mapped optimally we illustrate this with the bpc class of permutations conflicts in a permutation in the bpc class are described by means of conflict cubes and these cubes are used to obtain an optimal mapping of the permutation on the network using a minimum number of layers several examples are provided to illustrate the underlying concepts of our work

a geometric approach to shape from defocus we introduce a novel approach to shape from defocus i e the problem of inferring the three dimensional 3d geometry of a scene from a collection of defocused images typically in shape from defocus the task of extracting geometry also requires deblurring the given images a common approach to bypass this task relies on approximating the scene locally by a plane parallel to the image the so called equifocal assumption we show that this approximation is indeed not necessary as one can estimate 3d geometry while avoiding deblurring without strong assumptions on the scene solving the problem of shape from defocus requires modeling how light interacts with the optics before reaching the imaging surface this interaction is described by the so called point spread function psf when the form of the psf is known we propose an optimal method to infer 3d geometry from defocused images that involves computing orthogonal operators which are regularized via functional singular value decomposition when the form of the psf is unknown we propose a simple and efficient method that first learns a set of projection operators from blurred images and then uses these operators to estimate the 3d geometry of the scene from novel blurred images our experiments on both real and synthetic images show that the performance of the algorithm is relatively insensitive to the form of the psf our general approach is to minimize the euclidean norm of the difference between the estimated images and the observed images the method is geometric in that we reduce the minimization to performing projections onto linear subspaces by using inner product structures on both infinite and finite dimensional hilbert spaces both proposed algorithms involve only simple matrix vector multiplications which can be implemented in real time