3 d image denoising by local smoothing and nonparametric regression three dimensional 3 d images are becoming increasingly popular in image applications such as magnetic resonance imaging mri functional mri fmri and other image applications observed 3 d images often contain noise that should be removed beforehand for improving the reliability of subsequent image analyses in the literature most existing image denoising methods are for 2 d images their direct extensions to 3 d cases generally cannot handle 3 d images efficiently because the structure of 3 d images is often substantially more complicated than that of 2 d images for instance edge locations are surfaces in 3 d cases which are much more challenging to handle compared to edge curves in 2 d cases in this article we propose a novel 3 d image denoising procedure based on nonparametric estimation of a 3 d jump surface from noisy data one important feature of this method is its ability to preserve edges and major edge structures such as intersections of two edge surfaces pyramids pointed corn

kernelization and parameterized algorithms for covering a tree by a set of stars or paths two restricted versions of the subforest isomorphism problem the covering a tree by a set of stars ctss and the covering a tree by a set of paths ctsp problems are studied both problems are np complete the problems are closely related to a number of well studied problems including the problems subgraph isomorphism tree editing and graph packing it is shown that the problems ctss and ctsp are fixed parameter tractable thorough development of parameterized algorithms and kernelization algorithms for these problems are presented

comments with reply on fast convolution with laplacian of gaussian masks by j s chen et al in a recent paper by j s chen et al ibid vol pami 9 p 584 90 july 1987 the authors presented a means of decomposing the laplacian of gaussian log kernel into the product of a gaussian and a smaller log mask they then proceeded to develop a fast algorithm for convolution which exploits the spatial frequency properties of these operators to allow the image to be decimated subsampled although this approach is both novel and interesting it is contended that the exposition suffers from some inconsistencies and minor errors the commenters clarify matters for those who wish to implement this technique the original authors acknowledge two of the three points raised and provide further clarification of the other one namely the claim that the masks gaussian and log are too small

improved estimates of partial volume coefficients from noisy brain mri using spatial context this paper addresses the problem of accurate voxel level estimation of tissue proportions in the human brain magnetic resonance imaging mri due to the finite resolution of acquisition systems mri voxels can contain contributions from more than a single tissue type the voxel level estimation of this fractional content is known as partial volume coefficient estimation in the present work two new methods to calculate the partial volume coefficients under noisy conditions are introduced and compared with current similar methods concretely a novel markov random field model allowing sharp transitions between partial volume coefficients of neighbouring voxels and an advanced non local means filtering technique are proposed to reduce the errors due to random noise in the partial volume coefficient estimation in addition a comparison was made to find out how the different methodologies affect the measurement of the brain tissue type volumes based on the obtained results the main conclusions are that 1 both markov random field modelling and non local means filtering improved the partial volume coefficient estimation results and 2 non local means filtering was the better of the two strategies for partial volume coefficient estimation

diffusions for global optimizations we seek a global minimum of u 0 1 n to r the solution to d dt x t nabla u x t will find local minima the solution to dx t nabla u x t dt sqrt 2t dw t where w is standard n dimensional brownian motion and the boundaries are reflecting will concentrate near the global minima of u at least when temperature t is small the equilibrium distribution for x t is gibbs with density pi t x alpha exp u x t this suggests setting t t t downarrow 0 to find the global minima of u we give conditions on u x and t t such that the solution to dx t nabla u x t dt sqrt 2t dw t converges weakly to a distribution concentrated on the global minima of u

adaptive relaxation labeling current implementation of probabilistic relaxation labeling prl is based on stationary compatibility coefficients scc s such labeling frequently diverges from an achieved minimum labeling error in this correspondence it is shown that by having nonstationary compatibility coefficients nscc s the prl stabilizes about the minimum error which is obtained during the early iterations also a noniterative labeling algorithm which uses nscc and has a performance similar to that of the modified prl is suggested

confidence and conflict in multivariate calibration summary multivariate calibration involves using an estimated relationship between a multivariate response y and an explanatory vector x to predict unknown x in future from further observed responses in controlled calibration with multivariate normal errors the profile likelihood function for the unknown x denoted 4 displays a term which measures the mutual inconsistency of the given response vector denoted z in predicting 4 this inconsistency diagnostic fundamentally differentiates the behaviour of likelihood based and bayes confidence regions from those of the unconditional sampling approach in addition the diagnostic serves to pinpoint an inadequate response vector z

restoration of severely blurred high range images using stochastic and deterministic relaxation algorithms in compound gauss markov random fields abstract over the last few years a growing number of researchers from varied disciplines have been utilizing markov random fields mrf models for developing optimal robust algorithms for various problems such as texture analysis image synthesis classification and segmentation surface reconstruction integration of several low level vision modules sensor fusion and image restoration however no much work has been reported on the use of simulated annealing sa and iterative conditional mode icm algorithms for maximum a posteriori estimation in image restoration problems when severe blurring is present in this paper we examine the use of compound gauss markov random fields cgmrf to restore severely blurred high range images for this deblurring problem the convergence of the sa and icm algorithms has not been established we propose two new iterative restoration algorithms which can be considered as extensions of the classical sa and icm approaches and whose convergence is established finally they are tested on real and synthetic images and the results compared with the restorations obtained by other iterative schemes

motion estimation methods for overlapped block motion compensation an extension of conventional block motion compensation bmc overlapped block motion compensation obmc has been shown to reduce residual errors and blocking effects in motion compensated video however the overlap creates a noncausal spatial dependence between blocks and complicates motion estimation me for obmc iterative methods have traditionally been employed for overlapped block motion estimation obme for compression the rate for the motion vector field mvf may also be constrained this work considers several rate constrained obme algorithms both iterative and noniterative experiments demonstrate that a simple raster scan algorithm is effective as a suboptimal noniterative solution with comparable or better rate distortion performance and computational complexity than iterative obme algorithms depending on the application either this method or a simple block matching algorithm plus iteration are the most attractive of the tested obme schemes

acceleration operators in the value iteration algorithms for markov decision processes we study the general approach to accelerating the convergence of the most widely used solution method of markov decision processes mdps with the total expected discounted reward inspired by the monotone behavior of the contraction mappings in the feasible set of the linear programming problem equivalent to the mdp we establish a class of operators that can be used in combination with a contraction mapping operator in the standard value iteration algorithm and its variants we then propose two such operators which can be easily implemented as part of the value iteration algorithm and its variants numerical studies show that the computational savings can be significant especially when the discount factor approaches one and the transition probability matrix becomes dense in which the standard value iteration algorithm and its variants suffer from slow convergence

partial volume bayesian classification of material mixtures in mr volume data using voxel histograms the authors present a new algorithm for identifying the distribution of different material types in volumetric datasets such as those produced with magnetic resonance imaging mri or computed tomography ct because the authors allow for mixtures of materials and treat voxels as regions their technique reduces errors that other classification techniques can create along boundaries between materials and is particularly useful for creating accurate geometric models and renderings from volume data it also has the potential to make volume measurements more accurately and classifies noisy low resolution data well there are two unusual aspects to the authors approach first they assume that due to partial volume effects or blurring voxels can contain more than one material e g both muscle and fat the authors compute the relative proportion of each material in the voxels second they incorporate information from neighboring voxels into the classification process by reconstructing a continuous function spl rho x from the samples and then looking at the distribution of values that spl rho x takes on within the region of a voxel this distribution of values is represented by a histogram taken over the region of the voxel the mixture of materials that those values measure is identified within the voxel using a probabilistic bayesian approach that matches the histogram by finding the mixture of materials within each voxel most likely to have created the histogram the size of regions that the authors classify is chosen to match the sparing of the samples because the spacing is intrinsically related to the minimum feature size that the reconstructed continuous function can represent

grouped coordinate ascent algorithms for penalized likelihood transmission image reconstruction presents a new class of algorithms for penalized likelihood reconstruction of attenuation maps from low count transmission scans we derive the algorithms by applying to the transmission log likelihood a version of the convexity technique developed by de pierro for emission tomography the new class includes the single coordinate ascent sca algorithm and lange s convex algorithm for transmission tomography as special cases the new grouped coordinate ascent gca algorithms in the class overcome several limitations associated with previous algorithms 1 fewer exponentiations are required than in the transmission maximum likelihood expectation maximization ml em algorithm or in the sca algorithm 2 the algorithms intrinsically accommodate nonnegativity constraints unlike many gradient based methods 3 the algorithms are easily parallelizable unlike the sca algorithm and perhaps line search algorithms we show that the gca algorithms converge faster than the sca algorithm even on conventional workstations an example from a low count positron emission tomography pet transmission scan illustrates the method

algorithms for parameterized maximum agreement forest problem on multiple trees the maximum agreement forest problem maf asks for a largest common subforest of a collection of phylogenetic trees the maf problem on two binary phylogenetic trees has been studied extensively in the literature in this paper we present a group of fixed parameter tractable algorithms for the maf problem on multiple i e two or more binary phylogenetic trees our techniques work fine for the problem for both rooted trees and unrooted trees the computational complexity of our algorithms is comparable with that of the known algorithms for two trees and is independent of the number of phylogenetic trees for which a maximum agreement forest is constructed

triplet markov fields for the classification of complex structure data we address the issue of classifying complex data we focus on three main sources of complexity namely the high dimensionality of the observed data the dependencies between these observations and the general nature of the noise model underlying their distribution we investigate the recent triplet markov fields and propose new models in this class designed for such data and in particular allowing very general noise models in addition our models can handle the inclusion of a learning step in a consistent way so that they can be used in a supervised framework one advantage of our models is that whatever the initial complexity of the noise model parameter estimation can be carried out using state of the art bayesian clustering techniques under the usual simplifying assumptions as generative models they can be seen as an alternative in the supervised case to discriminative conditional random fields identifiability issues underlying the models in the nonsupervised case are discussed while the models performance is illustrated on simulated and real data exhibiting the mentioned various sources of complexity

spatial classification using fuzzy membership models in the usual statistical approach to spatial classification it is assumed that each pixel belongs to precisely one of a small number of known groups this framework is extended to include mixed pixel data then only a proportion of each pixel belongs to each group two models based on multivariate gaussian random fields are proposed to model this fuzzy membership process the problems of predicting the group membership and estimating the parameters are discussed some simulations are presented to study the properties of this approach and an example is given using landsat remote sensing data

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

comments on application of the conditional population mixture model to image segmentation in the above correspondence1 a maximum likelihood method is proposed for estimating class memberships and underlying statistical parameters within the context of distribution mixtures in the present comment it is pointed out that biases are incurred in parameter estimation that the class memberships and parameters are conceptually different and therefore that the so called standard mixture likelihood is to be preferred also in the correspondence 1 akaike s information criterion aic is used to choose the number of classes in the mixture here a brief theoretical caveat is issued

automated 3 d extraction and evaluation of the inner and outer cortical surfaces using a laplacian map and partial volume effect classification accurate reconstruction of the inner and outer cortical surfaces of the human cerebrum is a critical objective for a wide variety of neuroimaging analysis purposes including visualization morphometry and brain mapping the anatomic segmentation using proximity asp algorithm previously developed by our group provides a topology preserving cortical surface deformation method that has been extensively used for the aforementioned purposes however constraints in the algorithm to ensure topology preservation occasionally produce incorrect thickness measurements due to a restriction in the range of allowable distances between the gray and white matter surfaces this problem is particularly prominent in pediatric brain images with tightly folded gyri this paper presents a novel method for improving the conventional asp algorithm by making use of partial volume information through probabilistic classification in order to allow for topology preservation across a less restricted range of cortical thickness values the new algorithm also corrects the classification of the insular cortex by masking out subcortical tissues for 70 pediatric brains validation experiments for the modified algorithm constrained laplacian asp clasp were performed by three methods i volume matching between surface masked gray matter gm and conventional tissue classified gm ii surface matching between simulated and clasp extracted surfaces and iii repeatability of the surface reconstruction among 16 mri scans of the same subject in the volume based evaluation the volume enclosed by the clasp wm and gm surfaces matched the classified gm volume 13 more accurately than using conventional asp in the surface based evaluation using synthesized thick cortex the average difference between simulated and extracted surfaces was 4 6 t 1 4 mm for conventional asp and 0 5 t 0 4 mm for clasp in a repeatability study clasp produced a 30 lower rms error for the gm surface and a 8 lower rms error for the

fast and robust parameter estimation for statistical partial volume models in brain mri due to the finite spatial resolution of imaging devices a single voxel in a medical image may be composed of mixture of tissue types an effect known as partial volume effect pve partial volume estimation that is the estimation of the amount of each tissue type within each voxel has received considerable interest in recent years much of this work has been focused on the mixel model a statistical model of pve we propose a novel trimmed minimum covariance determinant tmcd method for the estimation of the parameters of the mixel pve model in this method each voxel is first labeled according to the most dominant tissue type voxels that are prone to pve are removed from this labeled set following which robust location estimators with high breakdown points are used to estimate the mean and the covariance of each tissue class comparisons between different methods for parameter estimation based on classified images as well as expectation maximization like em like procedure for simultaneous parameter and partial volume estimation are reported the robust estimators based on a pruned classification as presented here are shown to perform well even if the initial classification is of poor quality the results obtained are comparable to those obtained using the em like procedure but require considerably less computation time segmentation results of real data based on partial volume estimation are also reported in addition to considering the parameter estimation problem we discuss differences between different approximations to the complete mixel model in summary the proposed tmcd method allows for the accurate robust and efficient estimation of partial volume model parameters which is crucial to a variety of brain mri data analysis procedures such as the accurate estimation of tissue volumes and the accurate delineation of the cortical surface

maximum likelihood reconstruction for emission tomography previous models for emission tomography et do not distinguish the physics of et from that of transmission tomography we give a more accurate general mathematical model for et where an unknown emission density x y z generates and is to be reconstructed from the number of counts n d in each of d detector units d within the model we give an algorithm for determining an estimate of which maximizes the probability p n of observing the actual detector count data n over all possible densities let independent poisson variables n b with unknown means b b 1 b represent the number of unobserved emissions in each of b boxes pixels partitioning an object containing an emitter suppose each emission in box b is detected in detector unit d with probability p b d d 1 d with p b d a one step transition matrix assumed known we observe the total number n n d of emissions in each detector unit d and want to estimate the unknown b b 1 b for each the observed data n has probability or likelihood p n the em algorithm of mathematical statistics starts with an initial estimate 0 and gives the following simple iterative procedure for obtaining a new estimate new from an old estimate old to obtain k k 1 2 new b old b dd 1 n d p b d old b p b d b 1 b

inhomogeneous prior models for image reconstruction abstract over recent years the use of homogeneous gibbs prior models in image processing has become widely accepted there has been however much discussion over precisely which models are most appropriate for most applications the simplest gaussian model tends to oversmooth reconstructions so it has been rejected in favor of various edge preserving alternatives we claim that the problem is not with the gaussian family but rather with the assumption of homogeneity in this article we propose an inhomogeneous gaussian random field as a general prior model for many image processing applications the simplicity of the gaussian model allows rapid calculation and the flexibility of the spatially varying prior parameter allows varying degrees of spatial smoothing this approach is in the spirit of adaptive kernel density methods where only the choice of the variable window width is important the analysis of real single photon emission computed tomography data is used to illustrate the methods and simu

turbo segmentation of textured images we consider the problem of semi supervised segmentation of textured images existing model based approaches model the intensity field of textured images as a gauss markov random field to take into account the local spatial dependencies between the pixels classical bayesian segmentation consists of also modeling the label field as a markov random field to ensure that neighboring pixels correspond to the same texture class with high probability well known relaxation techniques are available which find the optimal label field with respect to the maximum a posteriori or the maximum posterior mode criterion but these techniques are usually computationally intensive because they require a large number of iterations to converge in this paper we propose a new bayesian framework by modeling two dimensional textured images as the concatenation of two one dimensional hidden markov autoregressive models for the lines and the columns respectively a segmentation algorithm which is similar to turbo decoding in the context of error correcting codes is obtained based on a factor graph approach the proposed method estimates the unknown parameters using the expectation maximization algorithm

technical communique policy set iteration for markov decision processes this communique presents an algorithm called policy set iteration psi for solving infinite horizon discounted markov decision processes with finite state and action spaces as a simple generalization of policy iteration pi psi generates a monotonically improving sequence of stationary markovian policies p k based on a set manipulation as opposed to pi s single policy manipulation at each iteration k when the set involved with psi at k contains n independently generated sample policies from a given distribution d the probability that the expected value of any sampled policy from d with respect to an initial state distribution is greater than that of p k converges to zero with o n k rate moreover psi converges to an optimal policy no slower than pi in terms of the number of iterations for any d

rank based inference in the proportional hazards model for interval censored data summary a marginal likelihood approach to fitting the proportional hazards model to interval censored or grouped data is proposed this approach maximises a likelihood that is the sum over all rankings of the data that are consistent with the observed censoring intervals as in the usual proportional hazards model the method does not require specification of the baseline hazard function the score equations determining the maximum marginal likelihood estimator can be written as the expected value of the score of the usual proportional hazards model with respect to a certain distribution of rankings a gibbs sampling scheme is given to generate rankings from this distribution and stochastic approximation is used to solve the score equations simulation results under various censoring schemes give point estimates that are close to estimates obtained using actual failure times

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

bayes smoothing algorithms for segmentation of binary images modeled by markov random fields a new image segmentation algorithm is presented based on recursive bayes smoothing of images modeled by markov random fields and corrupted by independent additive noise the bayes smoothing algorithm yields the a posteriori distribution of the scene value at each pixel given the total noisy image in a recursive way the a posteriori distribution together with a criterion of optimality then determine a bayes estimate of the scene the algorithm presented is an extension of a 1 d bayes smoothing algorithm to 2 d and it gives the optimum bayes estimate for the scene value at each pixel computational concerns in 2 d however necessitate certain simplifying assumptions on the model and approximations on the implementation of the algorithm in particular the scene noiseless image is modeled as a markov mesh random field a special class of markov random fields and the bayes smoothing algorithm is applied on overlapping strips horizontal vertical of the image consisting of several rows columns it is assumed that the signal scene values vector sequence along the strip is a vector markov chain since signal correlation in one of the dimensions is not fully used along the edges of the strip estimates are generated only along the middle sections of the strips the overlapping strips are chosen such that the union of the middle sections of the strips gives the whole image the bayes smoothing algorithm presented here is valid for scene random fields consisting of multilevel discrete or continuous random variables

robust voxel similarity metrics for the registration of dissimilar single and multimodal images in this paper we develop data driven registration algorithms relying on pixel similarity metrics that enable an accurate subpixel rigid registration of dissimilar single or multimodal 2d 3d images gross dissimilarities are handled by considering similarity measures related to robust m estimators in particular a novel robust similarity metric is proposed for comparing multimodal images the proposed robust similarity metrics are compared to the most popular standard similarity metrics on synthetic as well as on real world image pairs showing gross dissimilarities three case studies are considered the registration of single modal and multimodal 3d medical images the matching of multispectral remotely sensed images and the registration of intensity and range images the proposed robust similarity measures compare favourably with the standard non robust techniques

accelerating procedures of the value iteration algorithm for discounted markov decision processes based on a one step lookahead analysis accelerating procedures for solving discounted markov decision processes problems are developed based on a one step lookahead analysis of the value iteration algorithm we apply the criteria of minimum difference and minimum variance to obtain good adaptive relaxation factors that speed up the convergence of the algorithm several problems including howard s automobile replacement are tested and a preliminary numerical evaluation reveals considerable reductions in computation time when compared to existing value iteration schemes

on the foundations of relaxation labeling processes a large class of problems can be formulated in terms of the assignment of labels to objects frequently processes are needed which reduce ambiguity and noise and select the best label among several possible choices relaxation labeling processes are just such a class of algorithms they are based on the parallel use of local constraints between labels this paper develops a theory to characterize the goal of relaxation labeling the theory is founded on a definition of con sistency in labelings extending the notion of constraint satisfaction in certain restricted circumstances an explicit functional exists that can be maximized to guide the search for consistent labelings this functional is used to derive a new relaxation labeling operator when the restrictions are not satisfied the theory relies on variational cal culus it is shown that the problem of finding consistent labelings is equivalent to solving a variational inequality a procedure nearly identical to the relaxation operator derived under restricted circum stances serves in the more general setting further a local convergence result is established for this operator the standard relaxation labeling formulas are shown to approximate our new operator which leads us to conjecture that successful applications of the standard methods are explainable by the theory developed here observations about con vergence and generalizations to higher order compatibility relations are described

markov random field texture models we consider a texture to be a stochastic possibly periodic two dimensional image field a texture model is a mathematical procedure capable of producing and describing a textured image we explore the use of markov random fields as texture models the binomial model where each point in the texture has a binomial distribution with parameter controlled by its neighbors and number of tries equal to the number of gray levels was taken to be the basic model for the analysis a method of generating samples from the binomial model is given followed by a theoretical and practical analysis of the method s convergence examples show how the parameters of the markov random field control the strength and direction of the clustering in the image the power of the binomial model to produce blurry sharp line like and blob like textures is demonstrated natural texture samples were digitized and their parameters were estimated under the markov random field model a hypothesis test was used for an objective assessment of goodness of fit under the markov random field model overall microtextures fit the model well the estimated parameters of the natural textures were used as input to the generation procedure the synthetic microtextures closely resembled their real counterparts while the regular and inhomogeneous textures did not

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

compound gauss markov random fields for image estimation algorithms for obtaining approximations to statistically optimal estimates for images modeled as compound gauss markov random fields are discussed the authors consider both the maximum a posteriori probability map estimate and the minimum mean squared error mmse estimate for image estimation and image restoration compound image models consist of several submodels having different characteristics along with an underlying structure model which govern transitions between these image submodels two different compound random field models are employed the doubly stochastic gaussian dsg random field and a compound gauss markov cgm random field the authors present map estimators for dsg and cgm random fields using simulated annealing a fast converging algorithm called deterministic relaxation which however converges to only a locally optimal map estimate is also presented as an alternative for reducing computational loading on sequential machines for comparison purposes the authors include results on the fixed lag smoothing mmse estimator for the dsg field and its suboptimal m algorithm approximation

image reconstruction and restoration overview of common estimation structures and problems developments in the theory of image reconstruction and restoration over the past 20 or 30 years are outlined particular attention is paid to common estimation structures and to practical problems not properly solved yet the problem of image reconstruction and restoration is first formulated some of the current regularization approaches used to solve the problem are then described the concepts of a priori information and compound criterion are introduced a bayesian interpretation of the regularization techniques is given which clarifies the role of the tuning parameters and indicates how they could be estimated the practical aspects of computing the solution first when the hyperparameters are known and second when they must be estimated are then considered conclusions are drawn and points that still need to be investigated are outlined

segmentation registration and measurement of shape variation via image object shape a model of object shape by nets of medial and boundary primitives is justified as richly capturing multiple aspects of shape and yet requiring representation space and image analysis work proportional to the number of primitives metrics are described that compute an object representation s prior probability of local geometry by reflecting variabilities in the net s node and link parameter values and that compute a likelihood function measuring the degree of match of an image to that object representation a paradigm for image analysis of deforming such a model to optimize a posteriori probability is described and this paradigm is shown to be usable as a uniform approach for object definition object based registration between images of the same or different imaging modalities and measurement of shape variation of an abnormal anatomical object compared with a normal anatomical object examples of applications of these methods in radiotherapy surgery and psychiatry are given

maximum likelihood discriminant analysis on the plane using a markovian model of spatial context abstract a method is presented for utilising spatial information in performing discriminant analysis on multivariate data at each point on a regular lattice as for example with landsat the spatial information is modelled as a particularly simple markov random field the discriminant analysis is based on the maximum likelihood method the results are compared with alternatives by monte carlo simulation and seem to be encouraging

parameter estimation and tissue segmentation from multispectral mr images a statistical method is developed to classify tissue types and to segment the corresponding tissue regions from relaxation time t sub 1 t sub 2 and proton density p sub d weighted magnetic resonance images the method assumes that the distribution of image intensities associated with each tissue type can be expressed as a multivariate likelihood function of three weighted signal intensity values t sub 1 t sub 2 p sub d at each location within that tissue regions the method further assumes that the underlying tissue regions are piecewise contiguous and can be characterized by a markov random field prior in classifying the tissue types the method models the likelihood of realizing the images as a finite multivariate mixture function the class parameters associated with the tissue types i e the weighted intensity means variances and correlation coefficients of the multivariate function as well as the number of voxels within regions of the tissue types of are estimated by maximum likelihood the estimation fits the class parameters to the image data via the expectation maximization algorithm the number of classes associated with the tissue types is determined by the information criterion of minimum description length the method segments the tissue regions given the estimated class parameters by maximum a posteriori probability the prior is constructed by the tissue region membership of the first and second order neighborhood the method is tested by a few sets of t sub 1 t sub 2 and p sub d weighted images of the brain acquired with a 1 5 tesla whole body scanner the number of classes and the associated class parameters are automatically estimated the regions of different brain tissues are satisfactorily segmented

graphical and recursive models for contingency tables summary we discuss two classes of models for contingency tables graphical and recursive models both of which arise from restrictions that are expressible as conditional independencies of variable pairs the first of these is a subclass of hierarchical log linear models each of its models can be represented by an undirected graph in the second class each model corresponds to a particular kind of a directed graph instead and can be characterized by a nontrivial factorization of the joint distribution in terms of response variables we derive decomposable or multiplicative models as the intersecting class this result has useful consequences for exploratory types of analysis as well as for the model interpretation we can give an aid for detecting well fitting decomposable models in a transformation of the observed contingency table and each decomposable model may be interpreted with the help of an undirected or directed graph

probabilistic segmentation of brain tissue in mr imaging a new method has been developed for probabilistic segmentation of five different types of brain structures white matter gray matter cerebro spinal fluid without ventricles ventricles and white matter lesion in cranial mr imaging the algorithm is based on information from t1 weighted t1 w inversion recovery ir proton density weighted pd t2 weighted t2 w and fluid attenuation inversion recovery flair scans it uses the k nearest neighbor classification technique that builds a feature space from spatial information and voxel intensities the technique generates for each tissue type an image representing the probability per voxel being part of it by application of thresholds on these probability maps binary segmentations can be obtained a similarity index si and a probabilistic si psi were calculated for quantitative evaluation of the results the influence of each image type on the performance was investigated by alternately leaving out one of the five scan types this procedure showed that the incorporation of the t1 w pd or t2 w did not significantly improve the segmentation results further investigation indicated that the combination of ir and flair was optimal for segmentation of the five brain tissue types evaluation with respect to the gold standard showed that the si values for all tissues exceeded 0 8 and all psi values exceeded 0 7 implying an excellent agreement

interval estimation in discrimination the multivariate normal equal covariance case summary a general approach to discrimination problems is described which emphasizes the viewpoint of individual cases and expresses the uncertainty with which individual decisions are made it is applied to the particular case of two multivariate normal distributions with a common covariance matrix an affine transformation to which the key quantities are invariant simplifies discussion of the distribution of the estimated log odds ratio and suggests a practically useful plot which generalizes the usual display of discriminant scores and has several attractive features an illustration is given two approximate interval estimation techniques for the true log odds ratio are described and evaluated in a range of practical situations by a simulation study some further applications of our general approach are briefly indicated

maximum agreement subtree in a set of evolutionary trees metrics and efficient algorithms the maximum agreement subtree approach is one method of reconciling different evolutionary trees for the same set of species an agreement subtree enables choosing a subset of the species for whom the restricted subtree is equivalent under a suitable definition in all given evolutionary trees recently dynamic programming ideas were used to provide polynomial time algorithms for finding a maximum homeomorphic agreement subtree of two trees generalizing these methods to sets of more than two trees yields algorithms that are exponential in the number of trees unfortunately it turns out that in reality one is usually presented with more than two trees sometimes as many as thousands of trees in this paper we prove that the maximum homeomorphic agreement subtree problem is cal np complete for three trees with unbounded degrees we then show an approximation algorithm of time o kn5 for choosing the species that are not in a maximum agreement subtree of a set of k trees our approximation is guaranteed to provide a set that is no more than 4 times the optimum solution while the set of evolutionary trees may be large in practice the trees usually have very small degrees typically no larger than three we develop a new method for finding a maximum agreement subtree of k trees of which one has degree bounded by d this new method enables us to find a maximum agreement subtree in time o knd 1 n2d

on the covariance of two noncentral f random variables and the variance of the estimated liner discriminant function summary the covariance of two noncentral f random variables with a common covariance matrix is obtained from which the variance of their difference follows easily an application of this latter result in discriminant analysis is then given

generalized polynomial approximations in markovian decision processes abstract fitting the value function in a markovian decision process by a linear superposition of m basis functions reduces the problem dimensionality from the number of states down to m with good accuracy retained if the value function is a smooth function of its argument the state vector this paper provides for both the discounted and undiscounted cases three algorithms for computing the coefficients in the linear superposition linear programming policy iteration and least squares

a relative value iteration algorithm for nondegenerate controlled diffusions the ergodic control problem for a nondegenerate diffusion controlled through its drift is considered under a uniform stability condition that ensures the well posedness of the associated hamilton jacobi bellman hjb equation a nonlinear parabolic evolution equation is then proposed as a continuous time continuous state space analogue of white s relative value iteration algorithm for solving the ergodic dynamic programming equation for the finite state finite action case its convergence to the solution of the hjb equation is established using the theory of monotone dynamical systems and also alternatively by using the theory of reverse martingales

a markov random field model based approach to image interpretation an image is segmented into a collection of disjoint regions that form the nodes of an adjacency graph and image interpretation is achieved through assigning object labels or interpretations to the segmented regions or nodes using domain knowledge extracted feature measurements and spatial relationships between the various regions the interpretation labels are modeled as a markov random field mrf on the corresponding adjacency graph and the image interpretation problem is then formulated as a maximum a posteriori map estimation rule given domain knowledge and region based measurements simulated annealing is used to find this best realization or optimal map interpretation this approach also provides a systematic method for organizing and representing domain knowledge through appropriate design of the clique functions describing the gibbs distribution representing the pdf of the underlying mrf a general methodology is provided for the design of the clique functions results of image interpretation experiments on synthetic and real world images are described

matching hierarchical structures using association graphs it is well known that the problem of matching two relational structures can be posed as an equivalent problem of finding a maximal clique in a derived association graph however it is not clear how to apply this approach to computer vision problems where the graphs are hierarchically organized i e are trees since maximal cliques are not constrained to preserve the partial order we provide a solution to the problem of matching two trees by constructing the association graph using the graph theoretic concept of connectivity we prove that in the new formulation there is a one to one correspondence between maximal cliques and maximal subtree isomorphisms this allows us to cast the tree matching problem as an indefinite quadratic program using the motzkin straus theorem and we use replicator dynamical systems developed in theoretical biology to solve it such continuous solutions to discrete problems are attractive because they can motivate analog and biological implementations the framework is also extended to the matching of attributed trees by using weighted association graphs we illustrate the power of the approach by matching articulated and deformed shapes described by shock trees

analysis of field experiments by least squares smoothing summary assuming a smooth trend plus independent error model for the environmental effects in the yields of a field plot experiment least squares smoothing methods are developed to estimate both the treatment effects and the unknown trend treatment estimates are closely related to those resulting from a generalized least squares analysis in which the covariance structure for the environmental effects has a particular form however the main emphases are on the accuracy of treatment estimates under a fixed smooth trend plus error model and the exploratory power of the basic method to isolate trend effects of unknown form although the detailed development is for the one dimensional case generalizations of the smoothness concept and extensions to two dimensions are also discussed application of the basic method is illustrated on three data sets and the results compared with other analyses

object based estimation of dense motion fields motion estimation belongs to key techniques in image sequence processing segmentation of the motion fields such that ideally each independently moving object uniquely corresponds to one region is one of the essential elements in object based image processing this paper is concerned with unsupervised simultaneous estimation of dense motion fields and their segmentations it is based on a stochastic model relating image intensities to motion information based on the analysis of natural images a region based model of motion compensated prediction error is proposed in each region the error is modeled by a white stationary generalized gaussian random process the motion field and its segmentation are themselves modeled by a compound gibbs markov random field accounting for statistical bindings in spatial direction and along the direction of motion trajectories the a posteriori distribution of the motion field for a given image sequence is formulated as an objective function such that its maximization results in the map estimate a deterministic multiscale relaxation technique with regular structure is employed for optimization of the objective function simulation results are in a good agreement with human perception for both the motion fields and their segmentations

image segmentation by iterated region merging with localized graph cuts this paper presents an iterated region merging based graph cuts algorithm which is a novel extension of the standard graph cuts algorithm graph cuts addresses segmentation in an optimization framework and finds a globally optimal solution to a wide class of energy functions however the extraction of objects in a complex background often requires a lot of user interaction the proposed algorithm starts from the user labeled sub graph and works iteratively to label the surrounding un segmented regions in each iteration only the local neighboring regions to the labeled regions are involved in the optimization so that much interference from the far unknown regions can be significantly reduced meanwhile the data models of the object and background are updated iteratively based on high confident labeled regions the sub graph requires less user guidance for segmentation and thus better results can be obtained under the same amount of user interaction experiments on benchmark datasets validated that our method yields much better segmentation results than the standard graph cuts and the grabcut methods in either qualitative or quantitative evaluation

quantification of mr brain images by mixture density and partial volume modeling the problem of automatic quantification of brain tissue by utilizing single valued single echo magnetic resonance imaging mri brain scans is addressed it is shown that this problem can be solved without classification or segmentation a method that may be particularly useful in quantifying white matter lesions where the range of values associated with the lesions and the white matter may heavily overlap the general technique utilizes a statistical model of the noise and partial volume effect together with a finite mixture density description of the tissues the quantification is then formulated as a minimization problem of high order with up to six separate densities as part of the mixture this problem is solved by tree annealing with and without partial volume utilized the results compared and the sensitivity of the tree annealing algorithm to various parameters is exhibited the actual quantification is performed by two methods a classification based method called bayes quantification and parameter estimation results from each method are presented for synthetic and actual data

3 d contextual bayesian classifiers we extend a series of multivariate bayesian two dimensional 2 d contextual classifiers to three dimensional 3 d by specifying a simultaneous gaussian distribution for the feature vectors as well as a prior distribution of the class variables of a pixel and its six nearest 3 d neighbors

simple fast algorithms for the editing distance between trees and related problems ordered labeled trees are trees in which the left to right order among siblings is significant the distance between two ordered trees is considered to be the weighted number of edit operations insert delete and modify to transform one tree to another the problem of approximate tree matching is also considered specifically algorithms are designed to answer the following kinds of questions 1 what is the distance between two trees 2 what is the minimum distance between t 1 and t 2 when zero or more subtrees can be removed from t 2 3 let the pruning of a tree at node n mean removing all the descendants of node n the analogous question for prunings as for subtrees is answered a dynamic programming algorithm is presented to solve the three questions in sequential time o t 1 times t 2 times min textit depth t 1 textit leaves t 1 times min textit depth t 2 textit leaves t 2 and space o t 1 times t 2 compared with o t 1 times t 2 t

a survey on tree edit distance and related problems we survey the problem of comparing labeled trees based on simple local operations of deleting inserting and relabeling nodes these operations lead to the tree edit distance alignment distance and inclusion problem for each problem we review the results available and present in detail one or more of the central algorithms for solving the problem

segmentation based on fusion of range and intensity images using robust trimmed methods abstract this paper proposes a segmentation algorithm based on fusion of range and intensity images using robust trimmed methods based on the bayesian theory a priori knowledge is represented using the markov random field mrf a maximum a posteriori map estimator is constructed using the edge features extracted from both range and intensity images objects are represented by a number of local planar surfaces in range images and the parametric space for surface representation is constructed with the surface parameters estimated pixel by pixel based on the least trimmed squares lts method whereas in intensity images the trimmed variance is adopted as the feature for edge extraction a final edge map is obtained by the map estimator that is constructed using the likelihood functions based on the edge information obtained from range and intensity images finally an image is segmented using the fused edge map computer simulation results show that our new segmentation algorithm effectively segments test images independent of shadow noise and lighting environment

a tree structured markov random field model for bayesian image segmentation we present a new image segmentation algorithm based on a tree structured binary mrf model the image is recursively segmented in smaller and smaller regions until a stopping condition local to each region is met each elementary binary segmentation is obtained as the solution of a map estimation problem with the region prior modeled as an mrf since only binary fields are used and thanks to the tree structure the algorithm is quite fast and allows one to address the cluster validation problem in a seamless way in addition all field parameters are estimated locally allowing for some spatial adaptivity to improve segmentation accuracy a split and merge procedure is also developed and a spatially adaptive mrf model is used numerical experiments on multispectral images show that the proposed algorithm is much faster than a similar reference algorithm based on flat mrf models and its performance in terms of segmentation accuracy and map smoothness is comparable or even superior

the linear programming approach to approximate dynamic programming the curse of dimensionality gives rise to prohibitive computational requirements that render infeasible the exact solution of large scale stochastic control problems we study an efficient method based on linear programming for approximating solutions to such problems the approach fits a linear combination of pre selected basis functions to the dynamic programming cost to go function we develop error bounds that offer performance guarantees and also guide the selection of both basis functions and state relevance weights that influence quality of the approximation experimental results in the domain of queueing network control provide empirical support for the methodology

a statistical model for positron emission tomography abstract positron emission tomography pet still in its research stages is a technique that promises to open new medical frontiers by enabling physicians to study the metabolic activity of the body in a pictorial manner much as in x ray transmission tomography and other modes of computerized tomography the quality of the reconstructed image in pet is very sensitive to the mathematical algorithm to be used for reconstruction in this article we tailor a mathematical model to the physics of positron emissions and we use the model to describe the basic image reconstruction problem of pet as a standard problem in statistical estimation from incomplete data we describe various estimation procedures such as the maximum likelihood ml method using the em algorithm the method of moments and the least squares method a computer simulation of a pet experiment is then used to demonstrate the ml and the least squares reconstructions the main purposes of this article are to report on what we believe is an

statistical approach to segmentation of single channel cerebral mr images a statistical model is presented that represents the distributions of major tissue classes in single channel magnetic resonance mr cerebral images using the model cerebral images are segmented into gray matter white matter and cerebrospinal fluid csf the model accounts for random noise magnetic field inhomogeneities and biological variations of the tissues intensity measurements are modeled by a finite gaussian mixture smoothness and piecewise contiguous nature of the tissue regions are modeled by a three dimensional 3 d markov random field mrf a segmentation algorithm based on the statistical model approximately finds the maximum a posteriori map estimation of the segmentation and estimates the model parameters from the image data the proposed scheme for segmentation is based on the iterative conditional modes icm algorithm in which measurement model parameters are estimated using local information at each site and the prior model parameters are estimated using the segmentation after each cycle of iterations application of the algorithm to a sample of clinical mr brain scans comparisons of the algorithm with other statistical methods and a validation study with a phantom are presented the algorithm constitutes a significant step toward a complete data driven unsupervised approach to segmentation of mr images in the presence of the random noise and intensity inhomogeneities

magnetic resonance image tissue classification using a partial volume model abstract we describe a sequence of low level operations to isolate and classify brain tissue within t1 weighted magnetic resonance images mri our method first removes nonbrain tissue using a combination of anisotropic diffusion filtering edge detection and mathematical morphology we compensate for image nonuniformities due to magnetic field inhomogeneities by fitting a tricubic b spline gain field to local estimates of the image nonuniformity spaced throughout the mri volume the local estimates are computed by fitting a partial volume tissue measurement model to histograms of neighborhoods about each estimate point the measurement model uses mean tissue intensity and noise variance values computed from the global image and a multiplicative bias parameter that is estimated for each region during the histogram fit voxels in the intensity normalized image are then classified into six tissue types using a maximum a posteriori classifier this classifier combines the partial volume tissue measurement model with a gibbs prior that models the spatial properties of the brain we validate each stage of our algorithm on real and phantom data using data from the 20 normal mri brain data sets of the internet brain segmentation repository our method achieved average indices of 0 746 0 114 for gray matter gm and 0 798 0 089 for white matter wm compared to expert labeled data our method achieved average indices 0 893 0 041 for gm and 0 928 0 039 for wm compared to the ground truth labeling on 12 volumes from the montreal neurological institute s brainweb phantom