bayesian reconstructions from emission tomography data using a modified em algorithm a novel method of reconstruction from single photon emission computerized tomography data is proposed this method builds on the expectation maximization em approach to maximum likelihood reconstruction from emission tomography data but aims instead at maximum posterior probability estimation which takes account of prior belief about smoothness in the isotope concentration a novel modification to the em algorithm yields a practical method the method is illustrated by an application to data from brain scans

convergence of em image reconstruction algorithms with gibbs smoothing p j green has defined an osl one step late algorithm that retains the e step of the em algorithm for image reconstruction in emission tomography but provides an approximate solution to the m step further modifications of the osl algorithm guarantee convergence to the unique maximum of the log posterior function convergence is proved under a specific set of sufficient conditions several of these conditions concern the potential function of the gibb s prior and a number of candidate potential functions are identified generalization of the osl algorithm to transmission tomography is also considered

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

artistic edge and corner enhancing smoothing two important visual properties of paintings and painting like images are the absence of texture details and the increased sharpness of edges as compared to photographic images painting like artistic effects can be achieved from photographic images by filters that smooth out texture details while preserving or enhancing edges and corners however not all edge preserving smoothers are suitable for this purpose we present a simple nonlinear local operator that generalizes both the well known kuwahara filter and the more general class of filters known in the literature as ldquocriterion and value filter structure rdquo this class of operators suffers from intrinsic theoretical limitations which give rise to a dramatic instability in presence of noise especially on shadowed areas such limitations are discussed in the paper and overcome by the proposed operator a large variety of experimental results shows that the output of the proposed operator is visually similar to a painting comparisons with existing techniques on a large set of natural images highlight conditions on which traditional edge preserving smoothers fail whereas our approach produces good results in particular unlike many other well established approaches the proposed operator is robust to degradations of the input image such as blurring and noise contamination

a greedy tree growing algorithm for the design of variable rate vector quantizers image compression a technique for directly designing a variable rate tree structured vector quantizer by growing the tree one node at a time rather than one layer at time is presented the technique is a natural extension of a tree growing method for decision trees when the tree is pruned with a generalized algorithm for optimally pruning trees improvement is measured in the signal to noise ratio at high rates over pruning a fixed rate tree structured vector quantizer of the same initial rate the growing algorithm can be interpreted as a constrained inverse of the pruning algorithm

a new method for parameter estimation of edge preserving regularization in image restoration in image restoration the so called edge preserving regularization method is used to solve an optimization problem whose objective function has a data fidelity term and a regularization term the two terms are balanced by a parameter l in some aspect the value of l determines the quality of images in this paper we establish a new model to estimate the parameter and propose an algorithm to solve the problem in order to improve the quality of images in our algorithm an image is divided into some blocks on each block a corresponding value of l has to be determined numerical experiments are reported which show efficiency of our method

a perturbative approach to novelty detection in autoregressive models we propose a new method to perform novelty detection in dynamical systems governed by linear autoregressive models the method is based on a perturbative expansion to a statistical test whose leading term is the classical f test and whose o 1 n correction can be approximated as a function of the number of training points and the model order alone the method can be justified as an approximation to an information theoretic test we demonstrate on several synthetic examples that the first correction to the f test can dramatically improve the control over the false positive rate of the system we also test the approach on some real time series data demonstrating that the method still retains a good accuracy in detecting novelties

a generalized gaussian image model for edge preserving map estimation the authors present a markov random field model which allows realistic edge modeling while providing stable maximum a posterior map solutions the model referred to as a generalized gaussian markov random field ggmrf is named for its similarity to the generalized gaussian distribution used in robust detection and estimation the model satisfies several desirable analytical and computational properties for map estimation including continuous dependence of the estimate on the data invariance of the character of solutions to scaling of data and a solution which lies at the unique global minimum of the a posteriori log likelihood function the ggmrf is demonstrated to be useful for image reconstruction in low dosage transmission tomography

on the equivalence of soft wavelet shrinkage total variation diffusion total variation regularization and sides soft wavelet shrinkage total variation tv diffusion tv regularization and a dynamical system called sides are four useful techniques for discontinuity preserving denoising of signals and images in this paper we investigate under which circumstances these methods are equivalent in the one dimensional case first we prove that haar wavelet shrinkage on a single scale is equivalent to a single step of space discrete tv diffusion or regularization of two pixel pairs in the translationally invariant case we show that applying cycle spinning to haar wavelet shrinkage on a single scale can be regarded as an absolutely stable explicit discretization of tv diffusion we prove that space discrete tv diffusion and tv regularization are identical and that they are also equivalent to the sides system when a specific force function is chosen afterwards we show that wavelet shrinkage on multiple scales can be regarded as a single step diffusion filtering or regularization of the laplacian pyramid of the signal we analyze possibilities to avoid gibbs like artifacts for multiscale haar wavelet shrinkage by scaling the thresholds finally we present experiments where hybrid methods are designed that combine the advantages of wavelets and pde variational approaches these methods are based on iterated shift invariant wavelet shrinkage at multiple scales with scaled thresholds

medical image noise reduction using the sylvester lyapunov equation multiplicative noise is often present in medical and biological imaging such as magnetic resonance imaging mri ultrasound positron emission tomography pet single photon emission computed tomography spect and fluorescence microscopy noise reduction in medical images is a difficult task in which linear filtering algorithms usually fail bayesian algorithms have been used with success but they are time consuming and computationally demanding in addition the increasing importance of the 3 d and 4 d medical image analysis in medical diagnosis procedures increases the amount of data that must be efficiently processed this paper presents a bayesian denoising algorithm which copes with additive white gaussian and multiplicative noise described by poisson and rayleigh distributions the algorithm is based on the maximum a posteriori map criterion and edge preserving priors which avoid the distortion of relevant anatomical details the main contribution of the paper is the unification of a set of bayesian denoising algorithms for additive and multiplicative noise using a well known mathematical framework the sylvester lyapunov equation developed in the context of the control theory

codeword distribution for frequency sensitive competitive learning with one dimensional input data we study the codeword distribution for a conscience type competitive learning algorithm frequency sensitive competitive learning fscl using one dimensional input data we prove that the asymptotic codeword density in the limit of large number of codewords is given by a power law of the form q x c spl middot p x sup spl alpha where p x is the input data density and spl alpha depends on the algorithm and the form of the distortion measure to be minimized we further show that the algorithm can be adjusted to minimize any l sub p distortion measure with p ranging in 0 2

neural tree density estimation for novelty detection in this paper a neural competitive learning tree is introduced as a computationally attractive scheme for adaptive density estimation and novelty detection the learning rule yields equiprobable quantization of the input space and provides an adaptive focusing mechanism capable of tracking time varying distributions it is shown by simulation that the neural tree performs reasonably well while being much faster than any of the other competitive learning algorithms

optimal edge detectors for ramp edges it is argued that the best way to model an edge is by assuming all ideal mathematical function passed through a low pass filter and and immersed in noise using techniques similar to those developed by j canny 1983 1986 and l a spacek 1986 optimal filters are derived for ramp edges of various slopes the optimal nonrecursive filter for ideal step edges is then derived as a limiting case of the filters for ramp edges because there are no step edges in images edge detection is improved when the ramp filter is used instead of the filters developed for step edges for practical purposes some convolution masks are given which can be used directly for edge detection without the need to go into the details of the subject

edge detectors based on nonlinear filters a class of edge detectors is proposed which is obtained from the difference of the outputs of two nonlinear filters the nonlinear filters used are based on nonlinear means which contain homomorphic filters or order statistic which contain median filters the performance of these edge detectors in the presence of noise is evaluated and is compared to the performance of well established edge detectors their computational requirements are described and some examples are presented

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

topographic map formation by maximizing unconditional entropy a plausible strategy for online unsupervised competitive learning and nonparametric density estimation an unsupervised competitive learning rule called the vectorial boundary adaptation rule vbar is introduced for topographic map formation since vbar is aimed at producing an equiprobable quantization of the input space it yields a nonparametric model of the input probability density function furthermore since equiprobable quantization is equivalent to unconditional entropy maximization we argue that this is a plausible strategy for maximizing mutual information shannon information rate in the case of online learning we use mutual information as a tool for comparing the performance of our rule with kohonen s self organizing feature map algorithm

adaptive determination of filter scales for edge detection the authors suggest a regularization method for determining scales for edge detection adaptively for each site in the image plane specifically they extend the optimal filter concept of t poggio et al 1984 and the scale space concept of a witkin 1983 to an adaptive scale parameter to avoid an ill posed feature synthesis problem the scheme automatically finds optimal scales adaptively for each pixel before detecting final edge maps the authors introduce an energy function defined as a functional over continuous scale space natural constraints for edge detection are incorporated into the energy function to obtain a set of optimal scales that can minimize the energy function a parallel relaxation algorithm is introduced experiments for synthetic and natural scenes show the advantages of the algorithm in particular it is shown that this system can detect both step and diffuse edges while drastically filtering out the random noise

on discontinuity adaptive smoothness priors in computer vision a variety of analytic and probabilistic models in connection with markov random fields mrfs have been proposed in the last decade for solving low level vision problems involving discontinuities this paper presents a systematic study of these models and defines a general discontinuity adaptive da mrf model by analyzing the euler equation associated with the energy minimization it shows that the fundamental difference between different models lies in the behavior of interaction between neighboring points which is determined by the a priori smoothness constraint encoded into the energy function an important necessary condition is derived for the interaction to be adaptive to discontinuities to avoid oversmoothing this forms the basis on which a class of adaptive interaction functions aifs is defined the da model is defined in terms of the euler equation constrained by this class of aifs its solution is c sup 1 continuous and allows arbitrarily large but bounded slopes in dealing with discontinuities because of the continuous nature it is stable to changes in parameters and data a good property for regularizing ill posed problems experimental results are shown

multiobjective algorithm parameter optimization using multivariate statistics in three dimensional electron microscopy reconstruction many algorithms require the tuning of parameters in order to achieve optimal performance usually the best values of these parameters depend on both the particular conditions under which the experimental data have been acquired and the kind of information that we aim to obtain the performance of an algorithm can be measured by means of numerical observers called figures of merit foms usually there are no analytical formulas expressing the dependence of the foms on the parameters but the nature of such dependence can be observed by the use of computational experiments this article proposes a methodology for assigning values to the algorithmic parameters in the presence of a high number of foms a multiobjective optimization framework is provided that identifies a set of optimal parameter values whose performance from several points of view based on the initial foms is statistically indistinguishable this methodology is illustrated by applying it to the three dimensional reconstruction using an algebraic reconstruction technique of single particles in electron microscopy

parameter estimation in markov random field contextual models using geometric models of objects we present a new scheme for the estimation of markov random field line process parameters which uses geometric cad models of the objects in the scene the models are used to generate synthetic images of the objects from random view points the edge maps computed from the synthesized images are used as training samples to estimate the line process parameters using a least squares method we show that this parameter estimation method is useful for detecting edges in range as well as intensity edges the main contributions of the paper are 1 use of cad models to obtain true edge labels which are otherwise not available and 2 use of canonical markov random field representation to reduce the number of parameters

close form solution and parameter selection for convex minimization based edge preserving smoothing this work presents a new approach for the analysis of convex minimization based edge preserving image smoothing and the parameter selection therein the global solution that is the response of a convex smoothing model to the ideal step edge is derived in close form by analyzing the close form solution insights are drawn into how the optimal solution responds to edges in the data and how the parameter values affect resultant edges in the solution based on this a scheme is proposed for selecting parameters to achieve desirable responses at edges the theoretic results are substantiated by experiments

uncovering fuzzy community structure in complex networks there has been an increasing interest in properties of complex networks such as small world property power law degree distribution and network transitivity which seem to be common to many real world networks in this study a useful community detection method based on non negative matrix factorization nmf technique is presented based on a popular modular function a proper feature matrix from diffusion kernel and nmf algorithm the presented method can detect an appropriate number of fuzzy communities in which a node may belong to more than one community the distinguished characteristic of the method is its capability of quantifying how much a node belongs to a community the quantification provides an absolute membership degree for each node to each community which can be employed to uncover fuzzy community structure the computational results of the method on artificial and real networks confirm its ability

adaptive filtering with binary reinforcement recently there has been increased interest in high speed adaptive filtering where the usual stochastic gradient or least mean square lms algorithm is replaced with the simpler algorithm where adaptation is guided only by the polarity of the error signal in this paper the convergence of this binary reinforcement br algorithm is proved under the usual independence assumption and the surprising observation is made that unlike the lms algorithm convergence occurs for any positive value of the step size parameter while the stochastic gradient algorithm attempts to minimize a mean square error cost function the binary reinforcement algorithm in fact attempts to minimize a mean absolute error cost function it is proved for the binary reinforcement algorithm that the tap weight vector converges in distribution to a random vector that is suitably concentrated about the optimal value based on a least mean absolute error cost function for a sufficiently small step size the expected cost of the asymptotic weight vector can be made as close as desired to thc minimum cost attain ed by the optimum weight vector

statistical independence and novelty detection with information preserving nonlinear maps according to barlow 1989 feature extraction can be understood as finding a statistically independent representation of the probability distribution underlying the measured signals the search for a statistically independent representation can be formulated by the criterion of minimal mutual information which reduces to decorrelation in the case of gaussian distributions if nongaussian distributions are to be considered minimal mutual information is the appropriate generalization of decorrelation as used in linear principal component analyses pca we also generalize to nonlinear transformations by only demanding perfect transmission of information this leads to a general class of nonlinear transformations namely symplectic maps conservation of information allows us to consider only the statistics of single coordinates the resulting factorial representation of the joint probability distribution gives a density estimation we apply this concept to the real world problem of electrical motor fault detection treated as a novelty detection task

neural gas network for vector quantization and its application to time series prediction a neural network algorithm based on a soft max adaptation rule is presented this algorithm exhibits good performance in reaching the optimum minimization of a cost function for vector quantization data compression the soft max rule employed is an extension of the standard k means clustering procedure and takes into account a neighborhood ranking of the reference weight vectors it is shown that the dynamics of the reference weight vectors during the input driven adaptation procedure are determined by the gradient of an energy function whose shape can be modulated through a neighborhood determining parameter and resemble the dynamics of brownian particles moving in a potential determined by the data point density the network is used to represent the attractor of the mackey glass equation and to predict the mackey glass time series with additional local linear mappings for generating output values the results obtained for the time series prediction compare favorably with the results achieved by backpropagation and radial basis function networks

a markov model for blind image separation by a mean field em algorithm this paper deals with blind separation of images from noisy linear mixtures with unknown coefficients formulated as a bayesian estimation problem this is a flexible framework where any kind of prior knowledge about the source images and the mixing matrix can be accounted for in particular we describe local correlation within the individual images through the use of markov random field mrf image models these are naturally suited to express the joint pdf of the sources in a factorized form so that the statistical independence requirements of most independent component analysis approaches to blind source separation are retained our model also includes edge variables to preserve intensity discontinuities mrf models have been proved to be very efficient in many visual reconstruction problems such as blind image restoration and allow separation and edge detection to be performed simultaneously we propose an expectation maximization algorithm with the mean field approximation to derive a procedure for estimating the mixing matrix the sources and their edge maps we tested this procedure on both synthetic and real images in the fully blind case i e no prior information on mixing is exploited and found that a source model accounting for local autocorrelation is able to increase robustness against noise even space variant furthermore when the model closely fits the source characteristics independence is no longer a strict requirement and cross correlated sources can be separated as well

on the canny edge detector abstract the canny edge detector is widely used in computer vision to locate sharp intensity changes and to find object boundaries in an image the canny edge detector classifies a pixel as an edge if the gradient magnitude of the pixel is larger than those of pixels at both its sides in the direction of maximum intensity change in this paper we will show that defining edges in this manner causes some obvious edges to be missed we will also show how to revise the canny edge detector to improve its detection accuracy

jump surface estimation edge detection and image restoration surface estimation is important in many applications when conventional smoothing procedures e g running averages local polynomial kernel smoothing procedures smoothing spline procedures are used for estimating jump surfaces from noisy data jumps are blurred at the same time when noise is removed in recent years new smoothing methodologies have been proposed in the statistical literature for detecting jumps in surfaces and for estimating jump surfaces with jumps preserved we provide a review of these methodologies because a monochrome image can be considered a jump surface of the image intensity function with jumps at the outlines of objects edge detection and image restoration problems in image processing are closely related to the jump surface estimation problem in statistics we also review major methodologies on edge detection and image restoration and discuss connections and differences among these methods and related methods in the statistical literature

stochastic nonlinear image restoration using the wavelet transform the dominant methodology for image restoration is to stabilize the problem by including a roughness penalty in addition to faithfulness to the data among various choices concave stabilizers stand out for their boundary detection capabilities but the resulting cost function to be minimized is generally multimodal although simulated annealing is theoretically optimal to take up this challenge standard stochastic algorithms suffer from two drawbacks i practical convergence difficulties are encountered with second order prior models and ii it remains computationally demanding to favor the formation of smooth contour lines by taking the discontinuity field explicitly into account this work shows that both weaknesses can be overcome in a multiresolution framework by means of the 2 d discrete wavelet transform dwt we first propose to improve convergence toward global minima by single site updating on the wavelet domain for this purpose a new restricted dwt space is introduced and a theoretically sound updating mechanism is constructed on this subspace next we suggest to incorporate the smoothness of the discontinuity field via an additional penalty term defined on the high frequency subbands the resulting increase in complexity is small and the approach requires the specification of a unique extra parameter for which an explicit selection formula is derived