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

the einstein equation for signature type changing spacetimes we give a local existence and uniqueness theorem for solutions of einstein s equations with dust energy momentum tensor in the class of m dimensional analytic transverse signature type changing spacetimes where the initial condi tions are given on the hypersurface of signature type change we also prove a similar theorem in the case that the energy momentum tensor represents a scalar field

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

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

rigidity of proper holomorphic maps between bounded symmetric domains our first main result gives assumptions guaranteeing that proper holomorphic maps between cartan type i bounded symmetric domains have simple block matrix shape answering positively a question of mok the proof is based on the second main result establishing similar phenomenon for local cr maps between arbitrary boundary components of two bounded symmetric domains of the above type since boundary components other than shilov boundaries are levi degenerate our analysis is based on their 2 nondegeneracy combining levi forms with higher order tensors

transverse type changing pseudo riemannian metrics and the extendability of geodesics we study the geodesics and pre geodesics of a smooth manifold with smooth pseudo riemannian metric which changes bilinear type i e the signature changes on a hypersurface we classify all geodesics and pre geodesics that cross the hypersurface of type change transversely we then apply these results to the eikonal partial differential equation to find geometric conditions for the local existence or non existence of smooth transverse solutions

partial rigidity of degenerate cr embeddings into spheres abstract in this paper we study degenerate cr embeddings f of a strictly pseudoconvex hypersurface m c n 1 into a sphere s in a higher dimensional complex space c n 1 the degeneracy of the mapping f will be characterized in terms of the ranks of the cr second fundamental form and its covariant derivatives in 2004 the author together with x huang and d zaitsev established a rigidity result for cr embeddings f into spheres in low codimensions a key step in the proof of this result was to show that degenerate mappings are necessarily contained in a complex plane section of the target sphere partial rigidity in the 2004 paper it was shown that if the total rank d of the second fundamental form and all of its covariant derivatives is n here n is the cr dimension of m then f m is contained in a complex plane of dimension n d 1 the converse of this statement is also true as is easy to see when the total rank d exceeds n it is no longer true in general that f m is contained in a complex plane of dimension n d 1 as can be seen by examples in this paper we carry out a systematic study of degenerate cr mappings into spheres we show that when the ranks of the second fundamental form and its covariant derivatives exceed the cr dimension n then partial rigidity may still persist but there is a defect k that arises from the ranks exceeding n such that f m is only contained in a complex plane of dimension n d k 1 moreover this defect occurs in general as is illustrated by examples

robust classification of blurred imagery we present two novel approaches for the classification of blurry images it is assumed that the blur is linear and space invariant but that the exact blurring function is unknown the proposed fusion based approaches attempt to perform the simultaneous tasks of blind image restoration and classification we call such a problem blind image fusion the techniques are implemented using the nonnegativity and support constraints recursive inverse filtering nas rif algorithm for blind image restoration and the markov random field rirf based fusion method for classification by schistad solberg et al see ieee trans geosci remote sensing vol 32 p 768 78 1994 simulation results on synthetic and real photographic data demonstrate the potential of the approaches the algorithms are compared with one another and to situations in which blind blur removal is not attempted

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

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

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

inference for clustered data using the independence loglikelihood we use the properties of independence estimating equations to adjust the independence loglikelihood function in the presence of clustering the proposed adjustment relies on the robust sandwich estimator of the parameter covariance matrix which is easily calculated the methodology competes favourably with established techniques based on independence estimating equations we provide some insight as to why this is so the adjustment is applied to examples relating to the modelling of wind speed in europe and annual maximum temperatures in the u k

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

the equivalence problem and rigidity for hypersurfaces embedded into hyperquadrics we consider the class of levi nondegenerate hypersurfaces m in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i that admit a local cr transversal embedding near a point p e m into a standard nondegenerate hyperquadric in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i with codimension k n n small compared to the cr dimension n of m we show that for hypersurfaces in this class there is a normal form which is closely related to the embedding such that any local equivalence between two hypersurfaces in normal form must be an automorphism of the associated tangent hyperquadric we also show that if the signature of m and that of the standard hyperquadric in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i are the same then the embedding is rigid in the sense that any other embedding must be the original embedding composed with an automorphism of the quadric

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

holomorphic mappings between hyperquadrics with small signature difference in this paper we study holomorphic mappings sending a hyperquadric of signature ell in bbb c n into a hyperquadric of signature ell in bbb c n we show theorem 1 1 that if the signature difference ell ell is not too large then the mapping can be normalized by automorphisms of the target hyperquadric to a particularly simple form and in particular the image of the mapping is contained in a complex plane of a dimension that depends only on ell and ell and not on the target dimension n we also prove a hopf lemma type result theorem 1 3 for such mappings

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

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

classification based adaptive filtering for multiframe blind image restoration in this paper the blind restoration of a scene is investigated when multiple degraded blurred and noisy acquisitions are available an adaptive filtering technique is proposed where the distorted images are filtered classified and then fused based upon the classification decisions finite normal density mixture fnm models are used to model the filtered outputs at each iteration for simplicity fixed number of gaussian components classes is initially considered for each degraded frame and the selection of the optimal number of classes is performed according to the global relative entropy criterion however there exist cases where dynamically varying fnm models should be considered where the optimal number of classes is selected according to the akaike information criterion the iterative application of classification and fusion followed by optimal adaptive filtering converges to a global enhanced representation of the original scene in only a few iterations the proposed restoration method does not require knowledge of the point spread function support size or exact alignment of the acquired frames simulation results on synthetic and real data using both fixed and dynamically varying fnm models demonstrate its efficiency under both noisy and noise free conditions

regularity of mappings into classical domains we study the regularity and algebraicity for mappings into classical domains among other things we establish everywhere regularity and algebraicity results for c 2 cr maps into the set of smooth boundary points of a classical domain where the codimension can be arbitrarily large

d angelo conjecture in the third gap interval we show that the d angelo conjecture holds in the third gap interval more precisely we prove that the degree of any rational proper holomorphic map from mathbb b n to mathbb b 4n 6 with n ge 7 is not more than 3

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

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

super rigidity for cr embeddings of real hypersurfaces into hyperquadrics we consider holomorphic mappings sending a given levi nondegenerate pseudoconcave hypersurface m in into a nondegenerate hyperquadric of the same signature in and show that if m is sufficiently close to a hyperquadric in a certain sense then any two such mappings differ only by an automorphism of the hyperquadric

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

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

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

mixed type surfaces with bounded gaussian curvature in three dimensional lorentzian manifolds abstract a mixed type surface is a connected regular surface in a lorentzian 3 manifold with non empty spacelike and timelike point sets the induced metric of a mixed type surface is a signature changing metric and their lightlike points may be regarded as singular points of such metrics in this paper we investigate the behavior of gaussian curvature at a non degenerate lightlike point of a mixed type surface to characterize the boundedness of gaussian curvature at a non degenerate lightlike points we introduce several fundamental invariants along non degenerate lightlike points such as the lightlike singular curvature and the lightlike normal curvature moreover using the results by pelletier and steller we obtain the gauss bonnet type formula for mixed type surfaces with bounded gaussian curvature

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

embedding strictly pseudoconvex domains into balls every relatively compact strictly pseudocc nvex domain d with c2 boundary in a stein manifold can be embedded as a closed complex submanifold of a finite dimensional ball however for each n 2 there exist bounded strictly pseudoconvex domains d in cn with real analytic boundary such that no proper holomorphic map from d into any finite dimensional ball extends smoothly to d 0 introduction in this paper we study the representations of bounded strictly pseudoconvex domains d c cn if the boundary of d is of class ck k e 2 3 oo then by a theorem of fornaess 8 and khenkin 13 d can be mapped biholomorphically onto the intersection xn q of a bounded strictly convex domain q c cn with ck boundary and a closed complex submanifold x defirxed in a neighborhood of q in cn x intersecting the boundary of q transversally moreover the map f d x n q extends to a holomorphic map on a neighborhood of d the convex domain q depends on d hence a natural question is whether a similar result holds with q replaced by the unit ball b z z1l zn e cn z 2 e zjl2 n that intersects bbn transversally such that d is biholomorphically equivalent to xn e3ff this question has been mentioned by lempert 14 pinduk 20 bedford 2 and others our main result is that the answer to this question is negative in general if d is as above then every biholomorphism of d onto xne3n extends smoothly to d according to 3 however we will show that not all such domains d admit a proper holomorphic map into a finite dimensional ball that is smooth on d theorem 1 1 a similar local result was obtained independently by faran 7 we shall show that the answer to the question q is positive if we allow the intersections of complex submanifolds with strictly convex domains q c cn with real analytic boundaries theorem 1 2 thetheoremsoffornaess 8 andkhenkin 13 onlygiveanqwith smooth boundary received by the editors april 4t 1985 1980 mathematics subject classification primary 32h05 1research supported by a fellowship from the alfred p sloan foundation t 1986 american mathematical society 0002 9947 86 1 00 25 per page

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

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

a novel blind deconvolution scheme for image restoration using recursive filtering we present a novel blind deconvolution technique for the restoration of linearly degraded images without explicit knowledge of either the original image or the point spread function the technique applies to situations in which the scene consists of a finite support object against a uniformly black grey or white background this occurs in certain types of astronomical imaging medical imaging and one dimensional 1 d gamma ray spectra processing among others the only information required are the nonnegativity of the true image and the support size of the original object the restoration procedure involves recursive filtering of the blurred image to minimize a convex cost function we prove convexity of the cost function establish sufficient conditions to guarantee a unique solution and examine the performance of the technique in the presence of noise the new approach is experimentally shown to be more reliable and to have faster convergence than existing nonparametric finite support blind deconvolution methods for situations in which the exact object support is unknown we propose a novel support finding algorithm

testing mutual independence between two discrete valued spatial processes a correction to pearson chi squared a common feature of data collected in environmental and earth sciences is that they typically exhibit spatial autocorrelation violating the assumption of independent observations can have dramatic effects on inferences derived from standard statistical methods in this article we examine the consequences of spatial autocorrelation on pearson s chi squared test of mutual independence between two categorical responses with a general number of classes correspondingly we suggest a simple modification to the standard test statistic that allows for spatial autocorrelation our modified statistic is based on a first order correction factor and thus provides only an approximate test however we show by monte carlo simulation that this approximation results in satisfactory inferences in several situations of practical interest the usefulness of the method is displayed through an application to categorical data arising in the study of the relationship between the distribution pattern of plant species and woodland age in a forest in northern belgium

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

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

boundary characterization of holomorphic isometric embeddings between indefinite hyperbolic spaces abstract we provide in this paper a boundary characterization in terms of the boundary cr invariants or pseudo hermitian invariants for holomorphic isometric embeddings between indefinite hyperbolic spaces of general codimensions

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

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

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