generalizing the hough transform to detect arbitrary shapes abstract the hough transform is a method for detecting curves by exploiting the duality between points on a curve and parameters of that curve the initial work showed how to detect both analytic curves 1 2 and non analytic curves 3 but these methods were restricted to binary edge images this work was generalized to the detection of some analytic curves in grey level images specifically lines 4 circles 5 and parabolas 6 the line detection case is the best known of these and has been ingeniously exploited in several applications 7 8 9 we show how the boundaries of an arbitrary non analytic shape can be used to construct a mapping between image space and hough transform space such a mapping can be exploited to detect instances of that particular shape in an image furthermore variations in the shape such as rotations scale changes or figure ground reversals correspond to straightforward transformations of this mapping however the most remarkable property is that such mappings can be composed to build mappings for complex shapes from the mappings of simpler component shapes this makes the generalized hough transform a kind of universal transform which can be used to find arbitrarily complex shapes

a general decomposition theory for random cascades this announcement describes a probabilistic approach to cascades which in addition to providing an entirely probabilistic proof of the kahane peyriere theorem for independent cascades readily applies to general dependent cascades moreover this unifies various seemingly disparate cascade decompositions including kahane s t martingale decomposition and dimension disintegration 1 brief history of the problem a theory of positive t martingales was introduced in k3 as the general framework for independent multiplicative cascades and random coverings this includes spatial distributions of interest in both probability theory and in the physical sciences e g ccd ck de dg df dm f gw ms mw tls pw s for basic definitions let t be a locally compact metric space with borel sigmafield b and let f p be a probability space together with an increasing sequence fn n 1 2 of sub sigmafields of f a positive t martingale is a sequence qn of non negative functions on t such that i for each t t qn t n 1 2 is a martingale adapted to fn n 1 2 ii for p a s qn n 1 2 is a sequence of borel measurable nonnegative real valued functions on t let m t denote the space of positive borel measures on t and suppose that qn t is a positive t martingale for m t let qn denote the random measure defined by qn and dqn d t qn t t t denote the space of bounded continuous functions on t by cb t then essentially by the martingale convergence theorem one obtains a random borel measure q such that with probability one k3

exact hausdorff measure on the boundary of a galton watson tree a necessary and sufficient condition for the almost sure existence of an absolutely continuous with respect to the branching measure exact hausdorff measure on the boundary of a galton watson tree is obtained in the case where the absolutely continuous exact hausdorff measure does not exist almost surely a criterion which classifies gauge functions 0 according to whether 0 hausdorff measure of the boundary minus a certain exceptional set is zero or infinity is given important examples are discussed in four additional theorems in particular hawkes s conjecture in 1981 is solved problems of determining the exact local dimension of the branching measure at a typical point of the boundary are also solved

determination of robot location using generalized cylindrical object shapes abstract in this paper a new approach to the determination of robot location using the generalized cylindrical object such as circular cylinders elliptic cylinders triangular cylinders etc are proposed from a monocular image of the object image processing and numerical analysis techniques are applied to extract the projection characteristics of the generalized cylindrical portion of the object from which the position and the rotation parameters of a camera mounted robot can be determined owing to the full linearity of the derivation this approach can achieve high speed requirement in addition no prerequisite restriction is imposed on the image grabbing process experimental results show that the location determination time is about 1 2 sec in a 33 mhz ibm compatible pc at computer system and the location error is less than 5 in average

projections of planar mandelbrot random measures abstract let be a planar mandelbrot measure and its orthogonal projection on one of the principal axes we study the thermodynamic and geometric properties of we first show that is exact dimensional with dim min dim dim where is the bernoulli product measure obtained as the expectation of we also prove that is absolutely continuous with respect to if and only if dim dim our results provides a new proof of dekking grimmett falconer formula for the hausdorff and box dimension of the topological support of as well as a new variational interpretation we obtain the free energy function of on a wide subinterval 0 q c of r for q 0 1 it is given by a variational formula which sometimes yields phase transitions of order larger than 1 for q 1 it is given by min which can exhibit first order phase transitions this is in contrast with the analyticity of over 0 q c also we prove the validity of the multifractal formalism for at each q c 0

reconstructing the 3 d medial axes of coronary arteries in single view cineangiograms describes a technique for reconstructing the skeletal structure of coronary arteries from a succession of frames of a single view cineangiogram the authors use local features in each frame to determine correspondences of arterial segments in successive frames they define a similarity measure in 2d image space as the change in angular coordinates of corresponding pairs they use a form of gradient descent to find those depth coordinates that minimize the average deviation of the 3d angular coordinates of all points on the skeleton from the coordinates produced by a 3d scaling transformation in experiments with software models the reconstruction error was approximately two pixels when the initial guessed reconstruction was as large as 30 pixels

multifractal analysis of bernoulli convolutions associated with salem numbers abstract we consider the multifractal structure of the bernoulli convolution where 1 is a salem number in 1 2 let q denote the l q spectrum of we show that if 0 then the level set e x r lim r 0 log x r x r log r is non empty and dim h e where denotes the legendre transform of this result extends to all self conformal measures satisfying the asymptotically weak separation condition we point out that the interval 0 is not a singleton when 1 is the largest real root of the polynomial x n x n 1 x 1 n 4 an example is constructed to show that absolutely continuous self similar measures may also have rich multifractal structures

stability results for polyhedral complementarity problems in this work we study the multivalued complementarity problem for polyhedral multifunctions under homogeneity assumptions we employ an approach that consists in approximating the equivalent variational inequality formulation of the problem and studying the asymptotic behavior of sequences of solutions to these approximation problems to do this we employ results and the language of variational analysis the novelty of this approach lies in the fact that it allows us to obtain not only existence results but also stability ones we consider that our results can be used for developing numerical algorithms for solving multivalued complementarity problems

retinal vessel segmentation using multiwavelet kernels and multiscale hierarchical decomposition we propose a comprehensive method for segmenting the retinal vasculature in fundus camera images our method does not require preprocessing and training and can therefore be used directly on different images sets we enhance the vessels using matched filtering with multiwavelet kernels mfmk separating vessels from clutter and bright localized features noise removal and vessel localization are achieved by a multiscale hierarchical decomposition of the normalized enhanced image we show a necessary condition to achieve the optimal decomposition and derive the associated value of the scale parameter controlling the amount of details captured finally we obtain a binary map of the vasculature by locally adaptive thresholding generating a threshold surface based on the vessel edge information extracted by the previous processes we report experimental results on two public retinal data sets drive and stare demonstrating an excellent performance in comparison with retinal vessel segmentation methods reported recently

a high accuracy method for solving odes with discontinuous right hand side ordinary differential equations with discontinuities in the state variables require a differential inclusion formulation to guarantee existence 8 from this formulation a high accuracy method for solving such initial value problems is developed which can give any order of accuracy and tracks the discontinuities the method uses an active set approach and determines appropriate active sets from solutions to linear complementarity problems convergence results are established under some non degeneracy assumptions the method has been implemented and results compare favourably with previously published methods 7 21

retinal vessel centerline extraction using multiscale matched filters confidence and edge measures motivated by the goals of improving detection of low contrast and narrow vessels and eliminating false detections at nonvascular structures a new technique is presented for extracting vessels in retinal images the core of the technique is a new likelihood ratio test that combines matched filter responses confidence measures and vessel boundary measures matched filter responses are derived in scale space to extract vessels of widely varying widths a vessel confidence measure is defined as a projection of a vector formed from a normalized pixel neighborhood onto a normalized ideal vessel profile vessel boundary measures and associated confidences are computed at potential vessel boundaries combined these responses form a six dimensional measurement vector at each pixel a training technique is used to develop a mapping of this vector to a likelihood ratio that measures the vesselness at each pixel results comparing this vesselness measure to matched filters alone and to measures based on the hessian of intensities show substantial improvements both qualitatively and quantitatively the hessian can be used in place of the matched filter to obtain similar but less substantial improvements or to steer the matched filter by preselecting kernel orientations finally the new vesselness likelihood ratio is embedded into a vessel tracing framework resulting in an efficient and effective vessel centerline extraction algorithm

x ray fluoroscopy spatio temporal filtering with object detection one potential way to reduce patient and staff x ray fluoroscopy dose is to reduce the quantum exposure to the detector and compensate the additional noise with digital filtering a new filtering method spatio temporal filtering with object detection is described that reduces noise while minimizing motion and spatial blur as compared to some conventional motion detection filtering schemes this object detection method incorporates additional a priori knowledge of image content i e much of the motion occurs in isolated long thin objects catheters guide wires etc we create object likelihood images and use these to control spatial and recursive temporal filtering such as to reduce blurring the objects of interest we use automatically computed receiver operating characteristic roc curves to optimize the object likelihood enhancement method and determine that oriented matched filter kernels with 4 orientations are appropriate the matched filter kernels are simple projected cylinders we demonstrate the method on several representative x ray fluoroscopy sequences to which noise is added to simulate very low dose acquisitions with processing we find that noise variance is significantly reduced with slightly less noise reduction near moving objects we estimate an effective exposure reduction greater than 80

directed polymers on trees a martingale approach the authors use martingale methods and simple convexity arguments to compute rigorously the limiting free energy in the problem of directed polymers on a tree the limit is a degenerate random variable and convergence holds almost surely the only assumption on the common distribution of the random potentials attached to the bonds of the tree is that its laplace transform exists everywhere in 0 infinity

a partial characterization of a class of matrices defined by solutions to the linear complementarity problem in this paper we analyze the class of matrices q0 characterized as all n n matrices m for which the linear complementarity problem w mz q w z 0 w z 0 has a solution whenever q is feasible the method is to analyze the faces of the linear cone cone i m where i is the n n identity essentially a labelling requirement for the faces is shown necessary for m to be in q0 with proper restrictions and nondegenerate assumptions sufficiency is also shown these results arc related to the signs of the minors of m and some conjectures in this area are also discussed

application of degree theory in stability of the complementarity problem in this paper we study the behavior of a solution of the complementarity problem when the problem is perturbed the basic result is that if the degree of a certain function is nonzero then the problem is stable we show that several well known conditions for the existence of a solution to the problem also imply stability of the problem we also show that in the nondegenerate case there are simple conditions that ensure stability

on the structure of mandelbrot s percolation process and other random cantor sets we consider generalizations of mandelbrot s percolation process for the process which we call the random sierpinski carpet we show that it passes through several different phases as its parameter increases from zero to one the final section treats the percolation phase

dimension spectrum of axiom a diffeomorphisms i the bowen margulis measure we compute the dimension spectrum f ct of the singularity sets of the bowenmargulis measure defined on a two dimensional compact manifold and invariant with respect to a c 2 axiom a diffeomorphism it is proved that f is the legendre fenchel transform of a free energy function which is real analytic linear in the degenerate case the function f is also real analytic on its definition domain defined in one point in the degenerate case and is related to the hausdorff dimensions of gibbs measures singular with respect to each other and whose supports are the singularity sets and we decompose these sets

hausdorff and packing spectra large deviations and free energy for branching random walks in mathbb r d consider an mathbb r d valued branching random walk brw on a supercritical galton watson tree without any assumption on the distribution of this brw we compute almost surely and simultaneously the hausdorff and packing dimensions of the level sets e k of infinite branches in the boundary of the tree endowed with its standard metric along which the averages of the brw have a given closed connected set of limit points k this goes beyond multifractal analysis which only considers those level sets when k ranges in the set of singletons alpha alpha in mathbb r d we also give a 0 law for the hausdorff and packing measures of the level sets e and compute the free energy of the associated logarithmically correlated random energy model in full generality moreover our results complete the previous works on multifractal analysis by including the levels which do not belong to the range of the gradient of the free energy this covers in particular a situation that was until now badly understood namely the case where a first order phase transition occurs as a consequence of our study we can also describe the whole singularity spectrum of mandelbrot measures as well as the associated free energy function or lq spectrum when a first order phase transition occurs

the dimension of projections of fractal percolations fractal percolation or mandelbrot percolation is one of the most well studied families of random fractals in this paper we study some of the geometric measure theoretical properties dimension of projections and structure of slices of these random sets although random the geometry of those sets is quite regular our results imply that denoting by e subset mathbb r 2 a typical realization of the fractal percolation on the plane if dim rm h e 1 then for all lines l the orthogonal projection el of e to l has the same hausdorff dimension as e if dim rm h e 1 then for any smooth real valued function f which is strictly increasing in both coordinates the image f e contains an interval the second statement is quite interesting considering the fact that e is almost surely a cantor set a random dust for a large part of the parameter domain see chayes et al probab theory relat fields 77 3 307 324 1988 finally we solve a related problem about the existence of an interval in the algebraic sum of d 2 one dimensional fractal percolations

chaotic cascades with kolmogorov 1941 scaling we define a chaotic deterministic variant of random multiplicative cascade models of turbulence it preserves the hierarchical tree structure thanks to the addition of infinitesimal noise the zero noise limit can be handled by perron frobenius theory just like the zero diffusivity limit for the fast dynamo problem random multiplicative models do not possess kolmogorov 1941 k41 scaling because of a large deviations effect our numerical studies indicate thatdeterministic multiplicative models can be chaotic and still have exact k41 scaling a mechanism is suggested for avoiding large deviations which is present in maps with a neutrally unstable fixed point

a multifractal formalism let x be a metric space and a borel probability measure on x for q t r and e x write formula then hq t and pq t are borel measures hq t is a multifractal generalization of the centered hausdorff measure and pq t is a multifractal generalization of the packing measure the measures hq t and pq t define for a fixed q in the usual way a generalized hausdorff dimension dimq e and a generalized packing dimension dimq e of subsets e of x we study the functions b q dimq supp b q dimq supp and their relation to the so called multifractal spectra functions of formula we prove among other things that f f is bounded from above by the legendre transform of b b and that equality holds for graph directed self similar measures and cookie cutter measures finally we discuss the connection with generalized renyi dimensions

a comparative analysis of several transformations for enhancement and segmentation of magnetic resonance image scene sequences the performance of the eigenimage filter is compared with those of several other filters as applied to magnetic resonance image mri scene sequences for image enhancement and segmentation comparisons are made with principal component analysis matched modified matched maximum contrast target point ratio log ratio and angle image filters signal to noise ratio snr contrast to noise ratio cnr segmentation of a desired feature sdf and correction for partial volume averaging effects cpv are used as performance measures for comparison analytical expressions for snrs and cnrs of filtered images are derived and cpv by a linear filter is studied properties of filters are illustrated through their applications to simulated and acquired mri sequences of a phantom study and a clinical case advantages and weaknesses are discussed the conclusion is that the eigenimage filter is the optimal linear filter that achieves sdf and cpv simultaneously

junction detection for linear structures based on hessian correlation and shape information junctions have been demonstrated to be important features in many visual tasks such as image registration matching and segmentation as they can provide reliable local information this paper presents a method for detecting junctions in 2d images with linear structures as well as providing the number of branches and branch orientations the candidate junction points are selected through a new measurement which combines hessian information and correlation matrix then the locations of the junction centers are refined and the branches of the junctions are found using the intensity information of a stick shaped window at a number of orientations and the correlation value between the intensity of a local region and a gaussian shaped multi scale stick template the multi scale template is used here to detect the structures with various widths we present the results of our algorithm on images of different types and compare our algorithm with three other methods the results have shown that the proposed approach can detect junctions more accurately

on edge detection edge detection is the process that attempts to characterize the intensity changes in the image in terms of the physical processes that have originated them a critical intermediate goal of edge detection is the detection and characterization of significant intensity changes this paper discusses this part of the edge detection problem to characterize the types of intensity changes derivatives of different types and possibly different scales are needed thus we consider this part of edge detection as a problem in numerical differentiation we show that numerical differentiation of images is an ill posed problem in the sense of hadamard differentiation needs to be regularized by a regularizing filtering operation before differentiation this shows that this part of edge detection consists of two steps a filtering step and a differentiation step following this perspective the paper discusses in detail the following theoretical aspects of edge detection 1 the properties of different types of filters with minimal uncertainty with a bandpass spectrum and with limited support are derived minimal uncertainty filters optimize a tradeoff between computational efficiency and regularizing properties 2 relationships among several 2 d differential operators are established in particular we characterize the relation between the laplacian and the second directional derivative along the gradient zero crossings of the laplacian are not the only features computed in early vision 3 geometrical and topological properties of the zero crossings of differential operators are studied in terms of transversality and morse theory

3 d image reconstruction of brain blood vessels from angiograms abstract this paper presents a reconstruction process to build the three dimensional structure of cerebral vessels from a pair of dsa digital subtraction angiogram images to segment the blood vessels from the background not only the local thresholding but also global thresholding was used to bilevel the input image thinning process and the b spline curve are applied to extract and smooth the skeleton of the vessels the skeleton is then tracked to find the branch points which will be used as the feature points for matching for each feature point in the first image we use the epipolar constraint and the property of feature points to find its correspondence on the other image from the dsa machine structure and the correspondence information the real 3 d position of the skeleton is calculated by least squares estimation and the reconstructed 3 d shading images for various viewing angles and light source directions are obtained using the gouraud shading method experimental results show that the proposed algorithm work well on our data and can be applied on similar data without intervention most of the time

connectivity properties of mandelbrot s percolation process in 1974 mandelbrot introduced a process in 0 1 2 which he called canonical curdling and later used in this book s on fractals to generate self similar random sets with hausdorff dimension d 0 2 in this paper we will study the connectivity or percolation properties of these sets proving all of the claims he made in sect 23 of the fractal geometry of nature and a new one that he did not anticipate there is a probability pc 0 1 so that if p pc then the set is duslike i e the largest connected component is a point whereas if p pc notice the opposing sides are connected with positive probability and furthermore if we tile the plane with independent copies of the system then there is with probability one a unique unbounded connected component which intersects a positive fraction of the tiles more succinctly put the system has a first order phase transition

analyticity of the partition function of the random energy model we consider the random energy model with complex temperature for beta lying in a suitable set the function zn beta ezn beta is at the thermodynamic limit an analytic function of beta analytic properties of the high temperature free energy follow directly

a fast geometrical approach to camera extrinsic parameters abstract a fast geometrical approach is proposed to determine the camera extrinsic parameters using a trihedral normal angle tna no intrinsic camera parameters are known in advance so alignment error can be avoided the formula derived by this approach can be computed analytically the line and point features required in deriving the extrinsic parameters can be extracted by simple well developed image processing techniques thus the method is more accurate and faster than other methods in which complicated procedures are essential in finding curve or surface features from the experimental results the time for calculating the camera parameters is 0 8 sec and the measurement error is less than 3 on average

scaling exponents and multifractal dimensions for independent random cascades this paper is concerned with mandelbrot s stochastic cascade measures the problems of i scaling exponents of structure functions of the measure q and ii multifractal dimensions are considered for cascades with a generator vector w1 wc of the general type these problems were previously studied for independent strongly bounded variableswi 0 a wi c consequently a broad class of models used in applications including kolmogorov s long normal model in turbulence long stable universal cascades in atmospheric dynamics has not been covered roughly speaking problems i ii are here solved under the condition that the scaling exists the function is calculated for all arguments previously this was done for positiveq and a new effect emerges the function can generally involve discontinuities in the first derivative as well as in the second

complex derivative filters steerable filters are a valuable tool for various low level vision tasks in this paper we argue for the use of complex analysis in the context of 2 d steerable filters in particular we recommend the use of complex partial derivatives as a computational basis complex derivatives have a major advantage in comparison to real derivatives they show a canonical rotation behavior namely a rotation affects the derivative just by a multiplication with a complex unit number so the complex derivatives can be steered in a more elegant way and above that they are less expensive to compute we present several analytical formulas for common and new filter kernels in terms of complex derivatives further we relate the complex derivatives of a gaussian with the gauss laguerre transform and show that the gauss laguerre functions provide an optimal signal representation for local and smooth images we discuss various finite difference schemes for the realization of the derivatives and use them in practice in a first experiment we use a newly introduced filter kernel for anisotropic blurring the complex formalism offers an elegant way to locally adapt the shape and orientation of the kernel second we use the proposed filters as matched filters to detect vessels in retinal images

convergence of splitting and newton methods for complementarity problems an application of some sensitivity results this paper is concerned with two well known families of iterative methods for solving the linear and nonlinear complementarity problems for the linear complementarity problem we consider the class of matrix splitting methods and establish under a finiteness assumption on the number of solutions a necessary and sufficient condition for the convergence of the sequence of iterates produced a rate of convergence result for this class of methods is also derived under a stability assumption on the limit solution for the nonlinear complementarity problem we establish the convergence of the newton method under the assumption of a pseudo regular solution which generalizes robinson s concept of a strongly regular solution in both instances the convergence proofs rely on a common sensitivity result of the linear complementarity problem under perturbation

generalized potlatch and smoothing processes we consider simple generalizations of the potlatch and smoothing processes which were introduced in 8 and studied in 5 these generalizations provide relatively simple examples of infinite interacting systems which exhibit phase transition the original potlatch and smoothing processes do not exhibit phase transition our results show that for the generalized processes phase transition does not usually occur in one or two dimensions but usually does occur in higher dimensions upper and lower bounds for the relevant critical values are obtained as one application of our results we obtain the limiting behavior of the critical values for the linear contact process in d dimensions as d thus answering a question we raised in 3 this is done by comparing the contact process with an appropriate generalized smoothing process

three dimensional digital subtraction angiography a dye edge tracking algorithm was used to determine the corresponding points in the two images anterior posterior and lateral of the digital subtraction biplane angiography this correspondence was used to reconstruct three dimensional images of cerebral arteries in a dog experiment and a clinical observation the method was tested by comparing the measured image of oblique view to the computed reconstructed image for the present study we have developed three new algorithms the first algorithm is to determine the corresponding dye edge points using the fact that the density of contrast media at the moving edge shows the same changing pattern in the two projection views this moving pattern of dye edge density is computed using a matching method of cross correlation for the two sequential frames dye density the second algorithm is for simplified perspective transformation and the third is to identify the corresponding points using a complementary method for locating the approximate points on the small vessels the present method can be applied to compute the velocity of blood flow using the dye edge displacement and the three dimensional distance data

large deviations for multiplicative chaos the local singularities for a class of random measures obtained by random iterated multiplications are investigated using the thermodynamic formalism this analysis can be interpreted as a rigorous study of the phase transition of a system with random interactions

multifractal formalism for almost all self affine measures we conduct the multifractal analysis of self affine measures for almost all family of affine maps besides partially extending falconer s formula of lq spectrum outside the range 1 q 2 the multifractal formalism is also partially verified

some perturbation results for the linear complementarity problem it has been shown previously that the linear complementarity problem is stable when the defining matrix is positive semidefinite and when locally the set of solutions is nonempty and bounded we enlarge the class of matrices for which this is true and also demonstrate how the boundedness condition leads to other stability type questions

detection of blood vessels in retinal images using two dimensional matched filters blood vessels usually have poor local contrast and the application of existing edge detection algorithms yield results which are not satisfactory an operator for feature extraction based on the optical and spatial properties of objects to be recognized is introduced the gray level profile of the cross section of a blood vessel is approximated by a gaussian shaped curve the concept of matched filter detection of signals is used to detect piecewise linear segments of blood vessels in these images twelve different templates that are used to search for vessel segments along all possible directions are constructed various issues related to the implementation of these matched filters are discussed the results are compared to those obtained with other methods

a new method for linear feature and junction enhancement in 2d images based on morphological operation oriented anisotropic gaussian function and hessian information abstract feature enhancement is an important preprocessing step in many image processing tasks it is the process of adjusting image intensities so that the enhanced results are more suitable for analysis good enhancement results for linear structures such as vessels or neurites can be used as inputs for segmentation and other operations in this paper a novel linear feature enhancement filter an adaptive multi scale morpho gaussian filter which can enhance and smooth linear features is proposed based on morphological operation anisotropic gaussian function and hessian information this filter can enhance and smooth along the local orientation of the linear structures and the hessian measurement is used to further enhance the linear features we utilize the hessian matrix to calculate the orientation information for our directional morphological operation and the oriented anisotropic gaussian smoothing we also propose a novel method for junction enhancement which can solve the problem of junction suppression we decompose the junctions and enhance along each linear structure within a junction region we present the test results of our algorithm on images of different types and compare our method with three existing methods the experimental results show that the proposed approach can achieve better results

applications of degree theory to linear complementarity problems in this paper we consider two applications of degree theory to linear complementarity problems in the first application we study the stability of an lcp at a solution point specifically we prove the stability of an lcp corresponding to a p0 matrix at an isolated solution using a recent degree formula due to stewart 1991 we strengthen a stability result of gowda and pang 1992 in the second application we use the same degree formula of stewart to describe the number of solutions of lcpm q when m is a negative almost n matrix this analysis leads to a lipschitzian characterization of the solution map i q solm q corresponding to a nondegenerate negative matrix

anomalies in multifractal formalism for local time of brownian motion the renyi function for the logical time measure of brownian motion is found it is shown that this function the legendre transform of the multifractal spectrum of and the function derived by the reciprocal measure formalism are not identical more examples of having similar anomalies are discussed

multifractal measures and a weak separation condition abstract we define a new separation property on the family of contractive similitudes that allows certain overlappings this property is weaker than the open set condition of hutchinson it includes the well known class of infinite bernoulli convolutions associated with the p v numbers and the solutions of the two scale dilation equations our main purpose in this paper is to prove the multifractal formalism under such condition

existence principles for nonresonant operator and integral equations abstract features of resonant operator equations are discussed and existence results presented for nonlinear resonant integral equations

on solution stability of the linear complementarity problem in the paper 5 c d ha introduced the notion of stability of a linear complementarity problem at a solution point and established several sufficient conditions for stability to hold in the present paper we derive some new stability results which significantly improve ha s results included in these new results are i a complete characterization of the stability condition under a nonsingularity assumption and ii further characterizations of solution stability in the case of a linear complementarity problem with a fully semimonotone matrix

superbranching processes and projections of random cantor sets we study sequences x 0 x 1 of random variables taking values in the positive integers which grow faster than branching processes in the sense that x m n geqq sum limits i 1 x m x n m i for m n 0 where the x n m i are distributed as x n and have certain properties of independence we prove that under appropriate conditions x 1 almost surely and in l 1 where sup e x n 1 n our principal application of this result is to study the lebesgue measure and hausdorff dimension of certain projections of sets in a class of random cantor sets being those obtained by repeated random subdivisions of the m adic subcubes of 0 1 d we establish a necessary and sufficient condition for the lebesgue measure of a projection of such a random set to be non zero and determine the box dimension of this projection

solving camera parameters from the perspective projection of a parameterized curve abstract given the two dimensional perspective projection of a known conic or polygon of unknown size and position in three dimensional space we show how to determine the camera look angles relative to the plane where the curve lies separate cases are discussed for conic and polygons we then show that this technique can be used to solve for any planar or nonplanar curves as long as they can be represented in parametric forms

combining multifractal additive and multiplicative chaos the purpose of this article is the study of the new class of multifrac tal measures which combines additive and multiplicative chaos defined by x j 1 b j j 2 x

the dimension spectrum of some dynamical systems we analyze the dimension spectrum previously introduced and measured experimentally by jensen kadanoff and libchaber using large deviation theory we prove for some invariant measures of expanding markov maps that the hausdorff dimensionf of the set on which the measure has a singularity is a well defined concave and regular function in particular we show that this is the case for the accumulation of period doubling and critical mappings of the circle with golden rotation number we also show in these particular cases that the functionf is universal

retinal vessel segmentation using a probabilistic tracking method vessel structures such as retinal vasculature are important features for computer aided diagnosis in this paper a probabilistic tracking method is proposed to detect blood vessels in retinal images during the tracking process vessel edge points are detected iteratively using local grey level statistics and vessel s continuity properties at a given step a statistic sampling scheme is adopted to select a number of vessel edge points candidates in a local studying area local vessel s sectional intensity profiles are estimated by a gaussian shaped curve a bayesian method with the maximum a posteriori map probability criterion is then used to identify local vessel s structure and find out the edge points from these candidates evaluation is performed on both simulated vascular and real retinal images different geometric shapes and noise levels are used for computer simulated images whereas real retinal images from the review database are tested evaluation performance is done using the segmentation matching factor smf as a quality parameter our approach performed better when comparing it with sun s and chaudhuri s methods roc curves are also plotted showing effective detection of retinal blood vessels true positive rate with less false detection false positive rate than sun s method

structural and stability properties of p 0 nonlinear complementarity problems we consider p0 nonlinear complementarity problems and study the connectedness and stability of the solutions by applying degree theory and the mountain pass theorem to a smooth reformulation of the complementarity problem we show that the solution set is connected and bounded if a bounded isolated component of the solution set exists and that a solution is locally unique if and only if it is globally unique furthermore we prove that a solution is stable in ha s sense if and only if it is globally unique while the complementarity problem is stable if and only if the solution set is bounded

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

matching by monotonic tone mapping in this paper a novel dissimilarity measure called matching by monotonic tone mapping mmtm is proposed the mmtm technique allows matching under non linear monotonic tone mappings and can be computed efficiently when the tone mappings are approximated by piecewise constant or piecewise linear functions the proposed method is evaluated in various template matching scenarios involving simulated and real images and compared to other measures developed to be invariant to monotonic intensity transformations the results show that the mmtm technique is a highly competitive alternative of conventional measures in problems where possible tone mappings are close to monotonic

segmentation of vessel like patterns using mathematical morphology and curvature evaluation this paper presents an algorithm based on mathematical morphology and curvature evaluation for the detection of vessel like patterns in a noisy environment such patterns are very common in medical images vessel detection is interesting for the computation of parameters related to blood flow its tree like geometry makes it a usable feature for registration between images that can be of a different nature in order to define vessel like patterns segmentation is performed with respect to a precise model we define a vessel as a bright pattern piece wise connected and locally linear mathematical morphology is very well adapted to this description however other patterns fit such a morphological description in order to differentiate vessels from analogous background patterns a cross curvature evaluation is performed they are separated out as they have a specific gaussian like profile whose curvature varies smoothly along the vessel the detection algorithm that derives directly from this modeling is based on four steps 1 noise reduction 2 linear pattern with gaussian like profile improvement 3 cross curvature evaluation 4 linear filtering we present its theoretical background and illustrate it on real images of various natures then evaluate its robustness and its accuracy with respect to noise

on degeneracy in linear complementarity problems abstract let m be an n n matrix and q an n th order vector then the linear complementarity problem lcp q m is defined as follows determine x 0 such that w mx q 0 and x t w 0 a vector x which satisfies these conditions is called a solution of the problem and a solution for which x i w i 0 for at least one value of i is termed degenerate if the solutions of lcp q m are nondegenerate and their number is odd even we say that the solution set has odd even parity and murty has shown that this parity is determined uniquely by m in this paper the idea of parity is extended to degenerate solutions and through these to solution sets containing both degenerate and nondegenerate solutions these results are then used to give a generalization of lemke s method and to analyse the stability of certain degenerate solutions of linear complementarity problems

stability of the linear complementarity problem at a solution point in this paper we study the behavior of a solution of the linear complementarity problem when data are perturbed we give characterizations of strong stability of the linear complementarity problem at a solution in the case of stability we give sufficient and necessary conditions

nonresonant nonlinear singular problems in the limit circle case existence results are presented for the resonant singular boundary value problem tfrac 1 p py prime prime lambda m qy f t y a e on 0 1 with limt 0 py y 1 0 here we donot assume int 0 1 tfrac ds p s infty but only that int 0 1 tfrac 1 p s left int 0 s p x q x dx right tfrac 1 2 ds infty

robustness and nondegenerateness for linear complementarity problems in this paper the main focus is on a stability concept for solutions of a linear complementarity problem a solution of such a problem is robust if it is stable against slight perturbations of the data of the problem relations are investigated between the robustness the nondegenerateness and the isolatedness of solutions it turns out that an isolated nondegenerate solution is robust and also that a robust nondegenerate solution is isolated since the class of linear complementarity problems with only robust solutions or only nondegenerate solutions is not an open set attention is paid to garcia s classgn of linear complementarity problems the nondegenerate problems ingn form an open set

stability analysis of variational inequalities and nonlinear complementarity problems via the mixed linear complementarity problem and degree theory this paper is concerned with the mixed linear complementarity problem and the role it and its variants play in the stability analysis of the nonlinear complementarity problem and the karush kuhn tucker system of a variational inequality problem under a nonsingular assumption the mixed linear complementarity problem can be converted to the standard problem in this case the rich theory of the latter can be directly applied to the former in this work we employ degree theory to derive some sufficient conditions for the existence of a solution to the mixed linear complementarity problem in the absence of the nonsingularity property next we extend this existence theory to the mixed nonlinear complementarity problem and establish a main stability result under a certain degree theoretic assumption concerning the linearized problem we then specialize this stability result and its consequences to the parametric variational inequality problem under the assumption of a unique set of multipliers finally we

different averages of a fuzzy set with an application to vessel segmentation image segmentation is a major problem in image processing particularly in medical image analysis a great number of segmentation procedures produce intermediate gray scale images that can be understood as fuzzy sets additionally some segmentation procedures tend to leave free tuning parameters very influential in the final binary image for the user these different binary images can be easily aggregated into a fuzzy set by making use of fuzzy set theory in any case a single binary image is required so our interest is to associate a crisp set to a given fuzzy set in an intelligent and unsupervised manner the main idea of this paper is to define the averages of a given fuzzy set by using different definitions of the mean of a random compact set in particular the average distance of baddeley molchanov and the mean of vorob ev have been used a theoretical study of some new definitions of fuzzy set averages has been performed in particular these averages have been obtained for l r fuzzy numbers finally we present a medical image application that of retinal vessel detection some recent segmentation procedures have been revisited and modified using these new averages the experimental results are very promising

general retinal vessel segmentation using regularization based multiconcavity modeling detecting blood vessels in retinal images with the presence of bright and dark lesions is a challenging unsolved problem in this paper a novel multiconcavity modeling approach is proposed to handle both healthy and unhealthy retinas simultaneously the differentiable concavity measure is proposed to handle bright lesions in a perceptive space the line shape concavity measure is proposed to remove dark lesions which have an intensity structure different from the line shaped vessels in a retina the locally normalized concavity measure is designed to deal with unevenly distributed noise due to the spherical intensity variation in a retinal image these concavity measures are combined together according to their statistical distributions to detect vessels in general retinal images very encouraging experimental results demonstrate that the proposed method consistently yields the best performance over existing state of the art methods on the abnormal retinas and its accuracy outperforms the human observer which has not been achieved by any of the state of the art benchmark methods most importantly unlike existing methods the proposed method shows very attractive performances not only on healthy retinas but also on a mixture of healthy and pathological retinas

multifractal analysis of complex random cascades we achieve the multifractal analysis of a class of complex valued statistically self similar continuous functions for we use multifractal formalisms associated with pointwise oscillation exponents of all orders our study exhibits new phenomena in multifractal analysis of continuous functions in particular we find examples of statistically self similar such functions obeying the multifractal formalism and for which the support of the singularity spectrum is the whole interval 0

a cascade decomposition theory with applications to markov and exchangeable cascades a multiplicative random cascade refers to a positive t martingale in the sense of kahane on the ultrametric space t 0 1 b 1 a new approach to the study of multiplicative cascades is introduced the methods apply broadly to the problems of i non degeneracy criterion ii dimension spectra of carrying sets and iii divergence of moments criterion specific applications are given to cascades generated by markov and exchangeable processes as well as to homogeneous independent cascades 1 positive t martingales positive t martingales were introduced by jean pierre kahane as the general framework for independent multiplicative cascades and random coverings although originating in statistical theories of turbulence the general framework also includes certain spin glass and random polymer models as well as various other spatial distributions of interest in both probability theory and the physical sciences for basic definitions let t be a compact metric space with borel sigmafield b and let f p be a probability space together with an increasing sequence fn n 1 2 of sub sigmafields of f a positive t martingale is a sequence qn of b f measurable non negative functions on t such that i for each t t qn t n 0 1 is a martingale adapted to fn n 0 1 ii for p a s qn n 0 1 is a sequence of borel measurable non negative real valued functions on t let m t denote the space of positive borel measures on t and suppose that qn t is a positive t martingale for m t such that q t eqn t l let n qn denote the random measure defined by qn and dqn d t qn t t t then essentially by the martingale convergence theorem one obtains a random borel measure q such that for f c t 1 1 lim n t f t qn t dt t f t q dt a s received by the editors august 18 1994 1991 mathematics subject classification primary 60g57 60g30 60g42 secondary 60k35 60d05 60j10 60g09

dimension spectrum of axiom a diffeomorphisms ii gibbs measures we compute the dimension spectrum f t of the singularity sets of a gibbs measure defined on a two dimensional compact manifold and invariant with respect to a c 2 axiom a diffeomorphism this case is the generalization of the case where the measure studied is the bowen margulis measure the one that realizes the topological entropy we obtain similar results for example the function f is the legendre fenchel transform of a free energy function which is real analytic linear in the degenerate case the function fis also real analytic on its definition domain defined in one point in the degenerate case and is related to the hausdorff dimensions of gibbs measures singular with respect to each other and whose supports are the singularity sets and we finally decompose these sets

retina verification system based on biometric graph matching this paper presents an automatic retina verification framework based on the biometric graph matching bgm algorithm the retinal vasculature is extracted using a family of matched filters in the frequency domain and morphological operators then retinal templates are defined as formal spatial graphs derived from the retinal vasculature the bgm algorithm a noisy graph matching algorithm robust to translation non linear distortion and small rotations is used to compare retinal templates the bgm algorithm uses graph topology to define three distance measures between a pair of graphs two of which are new a support vector machine svm classifier is used to distinguish between genuine and imposter comparisons using single as well as multiple graph measures the classifier achieves complete separation on a training set of images from the varia database 60 of the data equaling the state of the art for retina verification because the available data set is small kernel density estimation kde of the genuine and imposter score distributions of the training set are used to measure performance of the bgm algorithm in the one dimensional case the kde model is validated with the testing set a 0 eer on testing shows that the kde model is a good fit for the empirical distribution for the multiple graph measures a novel combination of the svm boundary and the kde model is used to obtain a fair comparison with the kde model for the single measure a clear benefit in using multiple graph measures over a single measure to distinguish genuine and imposter comparisons is demonstrated by a drop in theoretical error of between 60 and more than two orders of magnitude

fast localization of the optic disc using projection of image features optic disc od localization is an important pre processing step that significantly simplifies subsequent segmentation of the od and other retinal structures current od localization techniques suffer from impractically high computation times few minutes per image in this work we present a fast technique that requires less than a second to localize the od the technique is based upon obtaining two projections of certain image features that encode the x and y coordinates of the od the resulting 1 d projections are then searched to determine the location of the od this avoids searching the 2 d image space and thus enhances the speed of the od localization process image features such as retinal vessels orientation and the od brightness are used in the current method four publicly available databases including stare and drive are used to evaluate the proposed technique the od was successfully located in 330 images out of 340 images 97 with an average computation time of 0 65 s

a space time property of a class of measure valued branching diffusions si d on montre que la diffusion ramifiee d dimensionnelle d indice etudiee par dawson et d autres distribue sa masse sur un support aleatoire de facon uniforme relativement a la mesure de hausdorff

a novel vessel segmentation algorithm for pathological retina images based on the divergence of vector fields in this paper a method is proposed for detecting blood vessels in pathological retina images in the proposed method blood vessel like objects are extracted using the laplacian operator and noisy objects are pruned according to the centerlines which are detected using the normalized gradient vector field the method has been tested with all the pathological retina images in the publicly available stare database experiment results show that the method can avoid detecting false vessels in pathological regions and can produce reliable results for healthy regions