component selection and smoothing in multivariate nonparametric regression we propose a new method for model selection and model fitting in multivariate nonparametric regression models in the framework of smoothing spline anova the cosso is a method of regularization with the penalty functional being the sum of component norms instead of the squared norm employed in the traditional smoothing spline method the cosso provides a unified framework for several recent proposals for model selection in linear models and smoothing spline anova models theoretical properties such as the existence and the rate of convergence of the cosso estimator are studied in the special case of a tensor product design with periodic functions a detailed analysis reveals that the cosso does model selection by applying a novel soft thresholding type operation to the function components we give an equivalent formulation of the cosso estimator which leads naturally to an iterative algorithm we compare the cosso with mars a popular method that builds functional anova models in simulations and real examples the cosso method can be extended to classification problems and we compare its performance with those of a number of machine learning algorithms on real datasets the cosso gives very competitive performance in these studies

multivariate locally weighted least squares regression nonparametric regression using locally weighted least squares was first discussed by stone and by cleveland recently it was shown by fan and by fan and gijbels that the local linear kernel weighted least squares regression estimator has asymptotic properties making it superior in certain senses to the nadaraya watson and gasser muller kernel estimators in this paper we extend their results on asymptotic bias and variance to the case of multivariate predictor variables we are able to derive the leading bias and variance terms for general multivariate kernel weights using weighted least squares matrix theory this approach is especially convenient when analysing the asymptotic conditional bias and variance of the estimator at points near the boundary of the support of the predictors we also investigate the asymptotic properties of the multivariate local quadratic least squares regression estimator discussed by cleveland and devlin and in the univariate case higher order polynomial fits and derivative estimation

estimates for the bar partial neumann problem in pseudoconvex domains of finite type in c2problem in pseudoconvex domains of finite type in c2

iterative voting for inference of structural saliency and characterization of subcellular events saliency is an important perceptual cue that occurs at different levels of resolution important attributes of saliency are symmetry continuity and closure detection of these attributes is often hindered by noise variation in scale and incomplete information this paper introduces the iterative voting method which uses oriented kernels for inferring saliency as it relates to symmetry a unique aspect of the technique is the kernel topography which is refined and reoriented iteratively the technique can cluster and group nonconvex perceptual circular symmetries along the radial line of an object s shape it has an excellent noise immunity and is shown to be tolerant to perturbation in scale the application of this technique to images obtained through various modes of microscopy is demonstrated furthermore as a case example the method has been applied to quantify kinetics of nuclear foci formation that are formed by phosphorylation of histone gammah2ax following ionizing radiation iterative voting has been implemented in both 2 d and 3 d for multi image analysis

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

a multiphase level set framework for image segmentation using the mumford and shah model we propose a new multiphase level set framework for image segmentation using the mumford and shah model for piecewise constant and piecewise smooth optimal approximations the proposed method is also a generalization of an active contour model without edges based 2 phase segmentation developed by the authors earlier in t chan and l vese 1999 in scale space 99 m nilsen et al eds lncs vol 1682 pp 141 151 and t chan and l vese 2001 ieee ip 10 2 266 277 the multiphase level set formulation is new and of interest on its own by construction it automatically avoids the problems of vacuum and overlaps it needs only log n level set functions for n phases in the piecewise constant cases it can represent boundaries with complex topologies including triple junctionss in the piecewise smooth case only two level set functions formally suffice to represent any partition based on the four color theorem finally we validate the proposed models by numerical results for signal and image denoising and segmentation implemented using the osher and sethian level set method

fractional oscillator driven by a gaussian noise abstract the time dependent response is studied of a fractional oscillator driven by a gaussian white noise applying the method of characteristic functionals combined with the technique of integral transforms we derive explicit formulas for the variances of position and velocity and the asymptotic power spectrum of the oscillator the effects of the order of fractional derivative on statistical characteristics of the oscillator are analyzed numerically

a new stochastic renormalization approach to random processes with very long memory fractal time as a process with almost complete connections an attempt is made to apply the mathematical theory of random jump processes with complete connections to the physically oriented description of very long memory effects a new stochastic renormalization approach is introduced starting from a stochastic process with infinite memory the author attaches to each step a very small probability that the memory is lost as a result of this change the memory acts over a variable number of steps forming blocks of different sizes this renormalization procedure leads to the self similarity of the probability of the number of steps over which the memory is kept the model yields a new explanation for the fractal time

a variational model for segmentation of overlapping objects with additive intensity value we propose a variant of the mumford shah model for the segmentation of a pair of overlapping objects with additive intensity value unlike standard segmentation models it does not only determine distinct objects in the image but also recover the possibly multiple membership of the pixels to accomplish this some a priori knowledge about the smoothness of the object boundary is integrated into the model additivity is imposed through a soft constraint which allows the user to control the degree of additivity and is more robust than the hard constraint we also show analytically that the additivity parameter can be chosen to achieve some stability conditions to solve the optimization problem involving geometric quantities efficiently we apply a multiphase level set method segmentation results on synthetic and real images validate the good performance of our model and demonstrate the model s applicability to images with multiple channels and multiple objects

convergence index filter for vector fields this paper proposes a unique fitter called an iris filter which evaluates the degree of convergence of the gradient vectors within its region of support toward a pixel of interest the degree of convergence is related to the distribution of the directions of the gradient vectors and not to their magnitudes the convergence index of a gradient vector at a given pixel is defined as the cosine of its orientation with respect to the line connecting the pixel and the pixel of interest the output of the iris filter is the average of the convergence indices within its region of support and lies within the range 1 1 the region of support of the iris filter changes so that the degree of convergence of the gradient vectors in it becomes a maximum i e the size and shape of the region of support at each pixel of interest changes adaptively according to the distribution pattern of the gradient vectors around it theoretical analysis using models of a rounded convex region and a semi cylindrical one is given these show that rounded convex regions are generally enhanced even if the contrast to their background is weak and also that elongated objects are suppressed the filter output is 1 spl pi at the boundaries of rounded convex regions and semi cylindrical ones this value does not depend on the contrast to their background this indicates that boundaries of rounded or slender objects with weak contrast to their background are enhanced by the iris filter and that the absolute value of 1 spl pi can be used to detect the boundaries of these objects these theoretical characteristics are confirmed by experiments using x ray images

segmentation inference and classification of partially overlapping nanoparticles this paper presents a method that enables automated morphology analysis of partially overlapping nanoparticles in electron micrographs in the undertaking of morphology analysis three tasks appear necessary separate individual particles from an agglomerate of overlapping nano objects infer the particle s missing contours and ultimately classify the particles by shape based on their complete contours our specific method adopts a two stage approach the first stage executes the task of particle separation and the second stage conducts simultaneously the tasks of contour inference and shape classification for the first stage a modified ultimate erosion process is developed for decomposing a mixture of particles into markers and then an edge to marker association method is proposed to identify the set of evidences that eventually delineate individual objects we also provided theoretical justification regarding the separation capability of the first stage in the second stage the set of evidences become inputs to a gaussian mixture model on b splines the solution of which leads to the joint learning of the missing contour and the particle shape using twelve real electron micrographs of overlapping nanoparticles we compare the proposed method with seven state of the art methods the results show the superiority of the proposed method in terms of particle recognition rate

better subset regression using the nonnegative garrote a new method called the nonnegative nn garrote is proposed for doing subset regression it both shrinks and zeroes coefficients in tests on real and simulated data it produces lower prediction error than ordinary subset selection it is also compared to ridge regression if the regression equations generated by a procedure do not change drastically with small changes in the data the procedure is called stable subset selection is unstable ridge is very stable and the nn garrote is intermediate simulation results illustrate the effects of instability on prediction error

maximum entropy formalism fractals scaling phenomena and 1 f noise a tale of tails in this report on examples of distribution functions with long tails we a show that the derivation of distributions with inverse power tails from a maximum entropy formalism would be a consequence only of an unconventional auxilliary condition that involves the specification of the average value of a complicated logarithmic function b review several models that yield log normal distributions c show that log normal distributions may mimic 1 f noise over a certain range and d present an amplification model to show how log normal personal income distributions are transformed into inverse power pareto distributions in the high income range

simple incorporation of interactions into additive models summary often the functional form of covariate effects in an additive model varies across groups defined by levels of a categorical variable this structure represents a factor by curve interaction this article presents penalized spline models that incorporate factor by curve interactions into additive models a mixed model formulation for penalized splines allows for straightforward model fitting and smoothing parameter selection we illustrate the proposed model by applying it to pollen ragweed data in which seasonal trends vary by year

selecting variables in non parametric regression models for binary response an application to the computerized detection of breast cancer in many biomedical applications interest lies in being able to distinguish between two possible states of a given response variable depending on the values of certain continuous predictors if the number of predictors p is high or if there is redundancy among them it then becomes important to decide on the selection of the best subset of predictors that will be able to obtain the models with greatest discrimination capacity with this aim in mind logistic generalized additive models were considered and receiver operating characteristic roc curves were applied in order to determine and compare the discriminatory capacity of such models this study sought to develop bootstrap based tests that allow for the following to be ascertained a the optimal number q or p of predictors and b the model or models including q predictors which display the largest auc area under the roc curve a simulation study was conducted to verify the behaviour of these tests finally the proposed method was applied to a computer aided diagnostic system dedicated to early detection of breast cancer

boundary regularity for on q pseudoconvex wedges of cn for a wedge of c n we refine the notion of weak q pseudoconvexity of g zampieri solvabil

characteristic functional approach to multiplicative fractal noise with application to environmental fluctuations in nonlinear chemical systems far from equilibrium a temporal analog of anderson localization abstract we compute the characteristic functional of a nonlinear transformation of a set of random variables the equation is applied to the study of fractal stochastic processes with multiplicative noise for illustration we investigate two types of chemical systems subjected to environmental fluctuations we analyze the interaction between the intrinsic chemical fluctuations and environmental noise and evaluate the stochastic properties of the system in the presence of multiplicative noise for an autocatalytic reaction subjected to external noise and with gaussian and generally non markovian multiplicative external noise the averaged joint probability density of concentrations displays long tails of the negative power law type which are independent of the detailed properties of the noise we also study the influence of multiplicative noise on a nonlinear chemical system with a stable limit cycle in the presence of multiplicative noise the limit cycle collapses and the average trajectory in the composition space becomes a spiral this effect is a temporal analog of anderson localization we evaluate the damping factors and localization times for different types of noise ranging from noise with infinite memory static disorder and noise with long memory dynamic disorder with fractal noise to markovian noise dynamic disorder with short memory

accurate cervical cell segmentation from overlapping clumps in pap smear images accurate segmentation of cervical cells in pap smear images is an important step in automatic pre cancer identification in the uterine cervix one of the major segmentation challenges is overlapping of cytoplasm which has not been well addressed in previous studies to tackle the overlapping issue this paper proposes a learning based method with robust shape priors to segment individual cell in pap smear images to support automatic monitoring of changes in cells which is a vital prerequisite of early detection of cervical cancer we define this splitting problem as a discrete labeling task for multiple cells with a suitable cost function the labeling results are then fed into our dynamic multi template deformation model for further boundary refinement multi scale deep convolutional networks are adopted to learn the diverse cell appearance features we also incorporated high level shape information to guide segmentation where cell boundary might be weak or lost due to cell overlapping an evaluation carried out using two different datasets demonstrates the superiority of our proposed method over the state of the art methods in terms of segmentation accuracy

combining predictors for classification using the area under the receiver operating characteristic curve no single biomarker for cancer is considered adequately sensitive and specific for cancer screening it is expected that the results of multiple markers will need to be combined in order to yield adequately accurate classification typically the objective function that is optimized for combining markers is the likelihood function in this article we consider an alternative objective function the area under the empirical receiver operating characteristic curve auc we note that it yields consistent estimates of parameters in a generalized linear model for the risk score but does not require specifying the link function like logistic regression it yields consistent estimation with case control or cohort data simulation studies suggest that auc based classification scores have performance comparable with logistic likelihood based scores when the logistic regression model holds analysis of data from a proteomics biomarker study shows that performance can be far superior to logistic regression derived scores when the logistic regression model does not hold model fitting by maximizing the auc rather than the likelihood should be considered when the goal is to derive a marker combination score for classification or prediction

splitting touching cells based on concave points and ellipse fitting a new touching cells splitting algorithm based on concave points and ellipse fitting is proposed in this paper the algorithm includes two parts contour pre processing and ellipse processing the purpose of contour pre processing is to smooth fluctuations of the contour find concave points of the contour and divide the contour into different segments via the concave points the purpose of ellipse processing is to process the different segments of the contour into possible single cells by using the properties of the fitted ellipses because concave points divide the whole contour of touching cells into different segments and different segments of one single cell have similar properties the ellipse processing can separate the touching cells through ellipse fitting this paper demonstrates a new way of using ellipse fitting to split the binary contour of touching cells experimental results show that our algorithm is efficient

functional characterization of linear delay langevin equations we present an exact functional characterization of linear delay langevin equations driven by any noise structure defined through its characteristic functional this method relies on the possibility of finding an explicitly analytical expression for each realization of the delayed stochastic process in terms of those of the driving noise general properties of the transient dissipative dynamics are analyzed the corresponding interplay with a color gaussian noise is presented as a full application of our functional method we study a model for population growth with non gaussian fluctuations the gompertz model driven by multiplicative white shot noise

sobolev estimates for the bar partial neumann operator on domains inc n admitting a defining function that is plurisubharmonic on the boundary neumann operator on domains inc n admitting a defining function that is plurisubharmonic on the boundary

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

the digital morphological sampling theorem morphological sampling reduces processing time and cost and yet produces results sufficiently close to the result of full processing a morphological sampling theorem is described which states 1 how a digital image must be morphologically filtered before sampling in order to preserve the relevant information after sampling 2 to what precision an appropriate morphologically filtered image can be reconstructed after sampling and 3 the relationship between morphologically operating before sampling and the more computationally efficient scheme of morphologically operating on the sampled image with a sampled structuring element the digital sampling theorem is developed first for the case of binary morphology and then it is extended to gray scale morphology through the use of the umbra homomorphism theorems

overestimation of the receiver operating characteristic curve for logistic regression logistic regression is often used to find a linear combination of covariates which best discriminates between two groups or populations the roc receiver operating characteristic curve is a good way of assessing the performance of the resulting score but using the same data both to fit the score and to calculate its roc leads to an over optimistic estimate of the performance which the score would give if it were to be validated on a sample of future cases the paper studies the extent of this overestimation and suggests a shrinkage correction for the roc curve itself and for the area under the curve the correction is consistent with efron s formula for the bias in the error rate of a binary prediction rule two medical examples are discussed

analogs of renormalization group transformations in random processes abstract we review the properties of a real space renormalization group transformation of the free energy including the existence of oscillatory terms multiplying the non analytic part of the free energy we then construct stochastic processes which incorporate into probability distributions the features of the free energy scaling equation the essential information is obtainable from the scaling equation and a direct solution for a probability is not necessary these random processes are shown to be generated directly from cantor sets in a spatial representation the ensuing random process exhibits a transition between gaussian and fractal behavior in the fractal regime the trajectories will in an average sense form self similar clusters in a temporal representation the random process exhibits a transition between an asymptotically constant renewal rate and fractal behavior the fractal regime represents a frozen state with only transient effects allowed and is related to charge transport in glasses

thin plate regression splines discuss the production of low rank smoothers for d greater than or equal to 1 dimensional data which can be fitted by regression or penalized regression methods the smoothers are constructed by a simple transformation and truncation of the basis that arises from the solution of the thin plate spline smoothing problem and are optimal in the sense that the truncation is designed to result in the minimum possible perturbation of the thin plate spline smoothing problem given the dimension of the basis used to construct the smoother by making use of lanczos iteration the basis change and truncation are computationally efficient the smoothers allow the use of approximate thin plate spline models with large data sets avoid the problems that are associated with knot placement that usually complicate modelling with regression splines or penalized regression splines provide a sensible way of modelling interaction terms in generalized additive models provide low rank approximations to generalized smoothing spline models appropriate for use with large data sets provide a means for incorporating smooth functions of more than one variable into non linear models and improve the computational efficiency of penalized likelihood models incorporating thin plate splines given that the approach produces spline like models with a sparse basis it also provides a natural way of incorporating unpenalized spline like terms in linear and generalized linear models and these can be treated just like any other model terms from the point of view of model selection inference and diagnostics

behavior of the bergman projection on the diederich fornaess worm w 1 introduction in this paper we show that the bergman projection operator for certain smooth bounded pseudoconvex domains does not preserve smoothness as measured by sobolev norms let q be a smooth bounded pseudoconvex domain in c and let p t denote the orthogonal projection from l2 f onto the bergman subspace b ff l2 f3 r with respect to the weighted norm i fll j olf z l 2 e t lzll2dv l 2 let wk t denote the sobolev space consisting of functions whose derivatives of order to k g2 on the other hand there is a large collection of results implying that for certain types of domains the unweighted bergman projection p pr preserves w k for all k 0 see fk for the strictly pseudoconvex case for results on weakly pseudoconvex domains the reader may consult ko2 ca si and the recent bstl ch as well as the references cited therein most of these results are focused on the a neumann operator rather than p see bst2 for the connection also except for kol positive results in this area are typically valid for any choice of smooth positive weight function on 0 the question of whether or not p is similarly well behaved for all weakly pseudoconvex domains has remained open for many years in this paper we show that this is not the case in fact when q is the so called worm domain of diederich and forna ss then p does not map w to w k when k zr total amount of winding this latter quantity is explained in section 4 below where the construction of the worm is reviewed and the main result is proved the proof depends on computations for a piecewise levi flat model domain depending in turn on certain one dimensional computations these are treated in sections 3 and 2 respectively section 5 contains additional remarks and questions

segmentation of overlapping elliptical objects in silhouette images segmentation of partially overlapping objects with a known shape is needed in an increasing amount of various machine vision applications this paper presents a method for segmentation of clustered partially overlapping objects with a shape that can be approximated using an ellipse the method utilizes silhouette images which means that it requires only that the foreground objects and background can be distinguished from each other the method starts with seedpoint extraction using bounded erosion and fast radial symmetry transform extracted seedpoints are then utilized to associate edge points to objects in order to create contour evidence finally contours of the objects are estimated by fitting ellipses to the contour evidence the experiments on one synthetic and two different real data sets showed that the proposed method outperforms two current state of art approaches in overlapping objects segmentation

enclosure transform for interest point detection from speckle imagery we present a fast enclosure transform et to localize complex objects of interest from speckle imagery this approach explores the spatial confinement on regional features from a sparse image feature representation unrelated broken ridge features surrounding an object are organized collaboratively giving rise to the enclosureness of the object three enclosure likelihood measures are constructed consisting of the enclosure force potential energy and encloser count in the transform domain the local maxima manifest the locations of objects of interest for which only the intrinsic dimension is known a priori the discrete et algorithm is computationally efficient being on the order of o mn using n measuring distances across an image of m ridge pixels it involves easy and few parameter settings we demonstrate and assess the performance of et on the automatic detection of the prostate locations from supra pubic ultrasound images et yields superior results in terms of positive detection rate accuracy and coverage

inference in smoothing spline analysis of variance summary smoothing spline analysis of variance decomposes a multivariate function into additive components this decomposition not only provides an efficient way to model a multivariate function but also leads to meaningful inference by testing whether a certain component equals 0 no formal procedure is yet available to test such a hypothesis we propose an asymptotic method based on the likelihood ratio to test whether a functional component is 0 this test allows us to choose an optimal model and to compare groups of curves we first develop the general theory by exploiting the connection between mixed effects models and smoothing splines we then apply this to compare two groups of curves and to select an optimal model in a two dimensional problem a small simulation is used to assess the finite sample performance of the likelihood ratio test