on cohomologically complete intersections abstract an ideal i of a local gorenstein ring r m is called cohomologically complete intersection whenever h i i r 0 for all i height i here h i i r i z denotes the local cohomology of r with respect to i for instance a set theoretic complete intersection is a cohomologically complete intersection here we study cohomologically complete intersections from various homological points of view in particular in terms of their bass numbers of h i c r c height i as a main result it is shown that the vanishing h i i r 0 for all i c is completely encoded in homological properties of h i c r in particular in its bass numbers

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

on formal local cohomology and connectedness let a denote an ideal of a local ring r m let m be a finitely generated r module there is a systematic study of the formal cohomology modules lim hmi m anm i z we analyze their r module structure the upper and lower vanishing and non vanishing in terms of intrinsic data of m and its functorial behavior these cohomology modules occur in relation to the formal completion of the punctured spectrum specr v m as a new cohomological data there is a description on the formal grade fgrade a m defined as the minimal non vanishing of the formal cohomology modules there are various exact sequences concerning the formal cohomology modules among them a mayer vietoris sequence for two ideals it applies to new connectedness results there are also relations to local cohomological dimensions

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

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

absence of diffusion in the anderson tight binding model for large disorder or low energy we prove that the green s function of the anderson tight binding hamiltonian decays exponentially fast at long distances on v with probability 1 we must assume that either the disorder is large or the energy is sufficiently low our proof is based on perturbation theory about an infinite sequence of block hamiltonians and is related to kam methods

franco american meeting on the mathematics of random and almost periodic potentials we present the abstracts of papers given at a conference held at the ecole polytechnique in june 1983 on the mathematics of random and almost periodic potentials

anderson localization for multi dimensional systems at large disorder or large energy we prove that discrete schrodinger operators on d with a random potential have almost surely only pure point spectrum and exponentially decaying eigenfunctions for large disorder or large energy this is the first proof of localization for multi dimensional anderson models

notes on local cohomology and duality abstract we provide a formula see theorem 1 5 for the matlis dual of the injective hull of r p where p is a one dimensional prime ideal in a local complete gorenstein domain r m this is related to results of enochs and xu see 4 and 5 we prove a certain dual version of the hartshorne lichtenbaum vanishing see theorem 2 2 we prove a generalization of local duality to cohomologically complete intersection ideals i in the sense that for i m we get back the classical local duality theorem we determine the exact class of modules to which a characterization of cohomologically complete intersection from 7 generalizes naturally see theorem 4 4

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

on the structure of the endomorphism ring of a certain local cohomology module let r m denote an n dimensional gorenstein ring for an ideal i r of height c we are interested in the endomorphism ring b homr hic r hic r it turns out that b is a commutative ring in the case of r m a regular local ring containing a field b is a cohen macaulay ring its properties are related to the highest lyubeznik number l dimkextrd k hic r d dimr i in particular r b if and only if l 1 moreover we show that the natural homomorphism extrd k hic r k is non zero

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

asymptotic localization of stationary states in the nonlinear schrodinger equation the mapping of the nonlinear schrodinger equation with a random potential on the fokker planck equation is used to calculate the localization length of its stationary states the asymptotic growth rates of the moments of the wave function and its derivative for the linear schrodinger equation in a random potential are computed analytically and resummation is used to obtain the corresponding growth rate for the nonlinear schrodinger equation and the localization length of the stationary states

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

anderson localization for one and quasi one dimensional systems we prove almost sure exponential localization of all the eigenfunctions and nondegeneracy of the spectrum for random discrete schrodinger operators on one and quasi one dimensional lattices this paper provides a much simpler proof of these results than previous approaches and extends to a much wider class of systems we remark in particular that the singular continuous spectrum observed in some quasiperiodic systems disappears under arbitrarily small local perturbations of the potential our results allow us to prove that e g for strong disorder the smallest positive lyapunov exponent of some products of random matrices does not vanish as the size of the matrices increases to infinity

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

on the spectrum of schrodinger operators with a random potential we investigate the spectrum of schrodinger operatorsh of the type h qi f x xi i qi and i independent identically distributed random variables i d we establish a strong connection between the spectrum ofh and the spectra of deterministic periodic schrodinger operators from this we derive a condition for the existence of forbidden zones in the spectrum ofh for random one and three dimensional kronig penney potentials the spectrum is given explicitly

on absence of diffusion near the bottom of the spectrum for a random schrodinger operator on l 2 bf r nu we consider a random schrodinger operator onl2 v of the form h omega delta v omega v omega x sigma chi c i x q i omega ci being a covering of v with unit cubes around the sites of v and qi i i d random variables with values in 0 1 we assume that theqi s are continuously distributed with bounded densityf q and that 0 p q0 1 2 1 then we show that an ergodic mean of the quantity dx x 2 exp ith x 2 t 1 vanishes provided ge h where is well localized around the origin andge is a positivec function with support in 0 e e e f our estimate ofe f is such that the set x v v x e f may contain with probability one an infinite cluster of cubes ci which are nearest neighbours the proof is based on the technique introduced by frohlich and spencer for the analysis of the anderson model

remark on the absence of absolutely continuous spectrum for d dimensional schrodinger operators with random potential for large disorder or low energy we show that there is no absolutely continuous part in the spectrum of the anderson tight binding model for large disorder or low energy the proof is based on the exponential decay of the green s function proved by frohlich and spencer the extension of this result to the continuous case is also discussed

one dimensional schrodinger operators with random or deterministic potentials new spectral types abstract we prove sufficient conditions involving only potential asymptotic near one of the infinities in order to have purely absolutely continuous components in the spectrum these deterministic results are then applied to random cases and exhibit classes of models for which with probability one one component of the spectrum is purely absolutely continuous and the rest is dense pure point with exponentially decaying eigenfunctions

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

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