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

an optimum solution for scale invariant object recognition based on the multiresolution approximation this paper presents a multiresolution approximation approach to obtaining boundary representations for object recognition our technique combines a multiresolution approximation and the curvature scale space representation for obtaining representations our research consists of two main parts in the first part of our research we introduce the continuous multiresolution approximation cma in terms of the continuous wavelet transform cwt then we implement a fast algorithm to compute the cma we apply the cma to a boundary to obtain approximations of the boundary at various resolutions the cma provides a consistent interpretation of objects with scale variations moreover we can quickly compute our representations by using the fast algorithm for the cma in the second part we propose three representations for object recognition which cover most boundary based object recognition problems all three representations use the approximations obtained by the cma each representation has different features and covers different types of matching problems but all representations are constructed by using curvature zero crossings of the approximations our representations provide a general but reliable solution to most boundary based object matching problems finally we investigate the properties of our representations such as validity efficiency and reliability we verified our results experimentally to demonstrate the feasibility of using our representations for object recognition

contribution to the prediction of performances of the hough transform exact predictions of the performances of the hough detection of straight lines in two dimensional images are presented for rectangular and circular retinas in cartesian and normal parameterization in the case of noisy signals detection of circles under the same assumptions is discussed the limits of adaptive quantization to reduce intrinsic noise are presented and it is shown that a signal processing approach is especially convenient to measure the performances of a detector based on the hough transform

using polygons to recognize and locate partially occluded objects we present computer vision algorithms that recognize and locate partially occluded objects the scene may contain unknown objects that may touch or overlap giving rise to partial occlusion the algorithms revolve around a generate test paradigm the paradigm iteratively generates and tests hypotheses for compatibility with the scene until it identifies all the scene objects polygon representations of the object s boundary guide the hypothesis generation scheme choosing the polygon representation turns out to have powerful consequences in all phases of hypothesis generation and verification special vertices of the polygon called corners help detect and locate the model in the scene polygon moment calculations lead to estimates of the dissimilarity between scene and model corners and determine the model corner location in the scene an association graph represents the matches and compatibility constraints extraction of the largest set of mutually compatible matches from the association graph forms a model hypothesis using a coordinate transform that maps the model onto the scene the hypothesis gives the proposed model s location and orientation hypothesis verification requires checking for region consistency the union of two polygons and other polygon operations combine to measure the consistency of the hypothesis with the scene experimental results give examples of all phases of recognizing and locating the objects

inherent bias and noise in the hough transform considering the hough transformation as a linear imaging process recasts certain well known problems provides a useful vocab ulary and possibly indicates a source of applicable literature on the behavior of the hough transformation in various forms of noise a consideration of the analytic form of peaks in parameter space sets the stage for the idea of using complementary negative votes to cancel off peak positive votes in parameter space thus sharpening peaks and reducing bias

a new approach for aggregating edge points into line segments abstract a technique is presented for aggregating edge points into polylines which can effectively represent object contours the technique is based on a new formulation of hough transform ht for detection of line segments the space requirement of the ht is brought down by considering a different parameterization of straight lines in this method the process of edge linking and boundary approximation are combined into a single algorithm consequently the scheme is computationally more efficient than the classical boundary approximation techniques which require a separate edge linking algorithm for preparing their input the linked list of edge points experimental results presented here highlight the effectiveness of this method for approximating object boundaries of polygonal as well as curved shapes present in the images of complex multi object scenes even in the presence of noise further the parallel algorithm proposed herein for implementation of this technique makes it an ideal choice for real time applications

mathematical and numerical modeling of solute dynamics in blood flow and arterial walls the numerical modeling of solutes absorption processes by the arterial wall is of paramount interest for the understanding of the relationships between the local features of blood flow the nourishing of the inner arterial wall by the blood solutes and the pathologies that can appear when this process is for some reason perturbed in the present work two models for the solutes dynamics are investigated in the first model which is essentially based on the one introduced by rappitsch and perktold j biomech engrg 118 1996 pp 511 519 and rappitsch perktold and pernkopf internat j numer methods fluids 25 1997 pp 847 857 the navier stokes equations for an incompressible fluid describing the blood velocity and pressure fields are coupled with an advection diffusion equation for the solute concentration the wellposedness of this model is discussed the second model considers also the solutes dynamics inside the arterial wall described by a pure diffusion equation actually this is a heterogeneous model coupling different equations in different parts of the domain at hand its wellposedness is proven moreover in view of the numerical study an iterative finite element method by subdomains is proposed and its convergence properties are analyzed finally several numerical results comparing the different models in situations of physiologic interest are illustrated

multiplicity of solutions for a fourth order quasilinear nonhomogeneous equation we consider a fourth order quasilinear nonhomogeneous equation which is equivalent to a nonhomogeneous hamiltonian system the purpose of this work is to prove the existence of at least two solutions for such equation when a certain parameter is small enough furthermore under an additional hypothesis on positiveness of the nonhomogeneous part we prove that our solutions are positive

the geometry of basis sets for morphologic closing p maragos 1989 provided a framework for the decomposition of many morphologic operations into orthogonal components or basis sets using this framework a method to find the minimal basis set for the important operation of closing in two dimensions is described the closing basis sets are special because their elements are members of an ordered global set of closing shapes or primitives the selection or design of appropriate individual or multiple structuring elements for image filtering can be better understood and sometimes implemented more easily through consideration of the orthogonal closing decomposition partial closing of images using ordered fractions of a closing basis set may give a finer texture or roughness measure than that obtained from the conventional use of scaled sets of shapes such as the disc the connection between elements of the basis set for closing and the complete minimal representation of arbitrary logic functions is analyzed from a geometric viewpoint

global description of edge patterns using moments abstract shape recognition has traditionally been accomplished using well bounded segmented regions or their closed contours in this way the internal edge details of the objects are ignored there are cases such as in character recognition and in object recognition when patterns are not closed contours in this paper such patterns are defined as edge patterns and edge standard moments esm are developed which are invariant to location scale and rotation results of patterns matching with character recognition and polyhedral object recognition are presented

natural representations for straight lines and the hough transform on discrete arrays the grid of discrete sampled data points in a digital image supports a limited set of lines at angles and displacements natural to that grid the effect of this implicit line quantization on the parametrization of the hough transform is presented the function describing the discrete hough transforms line detection sensitivity is derived expressions for the orientation frequency and popularity of lines in the natural set are given the results obtained are of importance to data arrays of small size the distribution of lines in the natural set is also important as it determines the precision and reliability with which straight lines can be measured on a discrete imaging array from the natural line set concept a general a d slope offset straight line parametrization is developed for which the hough transform is compact and fast to compute and which is as easy to interpret as the class p theta parametrization

finding lines under bounded error a new algorithm for finding straight lines in images under a bounded error model is described the algorithm is based on a hierarchical and adaptive subdivision of the space of line parameters it measures errors in image space and thereby guarantees that no solution satisfying the given error bounds will be lost the algorithm can find interpretations of all the lines in the image that satisfy the constraint that each image feature supports at most one line hypothesis it can be extended to compute efficiently the maxima of the probabilistic hough transform and the generalized hough transform under a variety of statistical error models

contribution to the determination of vanishing points using hough transform we propose a method to locate three vanishing points on an image corresponding to three orthogonal directions of the scene this method is based on two cascaded hough transforms we show that even in the case of synthetic images of high quality a naive approach may fail essentially because of the errors due to the limitation of the image size we take into account these errors as well as errors due to detection inaccuracy of the image segments and provide a method efficient even in the case of real complex scenes

a coupled system of odes and quasilinear hyperbolic pdes arising in a multiscale blood flow model we study a coupled system of ordinary differential equations and quasilinear hyperbolic partial differential equations that models a blood circulatory system in the human body the mathematical system is a multiscale model in which a part of the system where the flow can be regarded as newtonian and homogeneous and the vessels are long and large is modeled by a set of hyperbolic pdes in a one spatial dimensional network and in the other part where either vessels are too thin or the flow pattern is too complicated such as in the heart the flow is modeled as a lumped element by a set of ordinary differential equations as an analog of an electric circuit the mathematical system consists of pairs of pdes one pair for each vessel coupled at each junction through a system of odes this model is a generalization of the widely studied models of arterial networks we give a proof of the well posedness of the initial boundary value problem by showing that the classical solution exists is unique and depends continuously on initial boundary and forcing functions and their derivatives

using focus of attention with the hough transform for accurate line parameter estimation abstract in this paper we describe a hough transform algorithm for finding lines in an image that can have an order of magnitude denser sampling in both parameters of the parameter space without significant increase in required memory or overhead in cpu time by increasing the sampling density we determine the line parameters for each line segment much more accurately the method circumvents the problems of requiring large amounts of memory to store the accumulator array and is not significantly slower than other hough algorithms by using a focus of attention approach we illustrate the benefits that can be obtained on a wide variety of images and quantify the improvements in line parameter estimation by performing statistical tests we also discuss the benefits that can be obtained by algorithms attempting to locate higher level features in the image and determining the 3d model of the image scene

recognition and inspection of two dimensional industrial parts using subpolygons abstract a model based scene analysis for the recognition of imperfect and possibly occluded two dimensional 2d industrial parts is described the means of recognition leads reliably to the correct association of the sides making up the unknown object to those of the model both the scene polygon and the model are divided into pairs of complementary subpolygons this is done by a cutting line drawn parallel and close to a selected side the subpolygons from the object are compared to all possible subpolygons from the model invariant moments are used in the analysis a matching process using clusters of mutually consistent features is used to hypothesize the identity of the object examples are given to illustrate the method

shape matching of two dimensional objects in this paper we present results in the areas of shape matching of nonoccluded and occluded two dimensional objects shape matching is viewed as a segment matching problem unlike the previous work the technique is based on a stochastic labeling procedure which explicitly maximizes a criterion function based on the ambiguity and inconsistency of classification to reduce the computation time the technique is hierarchical and uses results obtained at low levels to speed up and improve the accuracy of results at higher levels this basic technique has been extended to the situation where various objects partially occlude each other to form an apparent object and our interest is to find all the objects participating in the occlusion in such a case several hierarchical processes are executed in parallel for every object participating in the occlusion and are coordinated in such a way that the same segment of the apparent object is not matched to the segments of different actual objects these techniques have been applied to two dimensional simple closed curves represented by polygons and the power of the techniques is demonstrated by the examples taken from synthetic aerial industrial and biological images where the matching is done after using the actual segmentation methods

multiple positive solutions of strongly indefinite systems with critical sobolev exponents and data that change sign abstract in this paper we study the existence of multiple positive solutions to some hamiltonian elliptic systems v u u p 1 u ef x u v v q 1 v eg x in u 0 v 0 in u v 0 on where is a smooth bounded domain in r n n 3 f g c 1 p q 1 r for the subcritical and critical cases we prove that problem has at least two positive solutions for any e 0 e and has no positive solutions for any e e e in the supercritical case we find that the existence of solutions of problem for 0 is closely related to the existence of nonnegative solutions of some linear elliptic system

collinear segment detection using ht neighborhoods in this paper geometrical analysis is used to extract novel straight line segment features from the wings around the peaks of the hough transform ht based on these features a practical segment detection method is proposed which has the ability to determine complete straight line segment parameters including the location of the center length slope and the euclidean distance to the origin the proposed method does not rely on edge point verification in the image space i e the complete set of segment features are determined only using the information embodied in the ht data the proposed method can distinguish between highly collinear straight line segments segment detection is robust to disturbing edge points especially ones collinear with the object a predefined collinear segment resolution that provides a theoretical criterion to determine straight line contiguity is derived image processing and analysis experiments show consistent robust performance

discretization errors in the hough transform abstract straight line segments in a two dimensional image can be detected with the hough transform by searching peaks in a parameter space the influence on the hough transform of the quantization of the parameter space the quantization of the image and the width of the line segment is investigated in this paper the hough transform was improved by o gorman and clowes by taking into account the gradient direction the resulting scatter of the peaks can be reduced by using a weighting function in the transform examples of asbestos preparations are given

an adaptive reduction procedure for the piecewise linear approximation of digitized curves a new algorithm is presented for the piecewise linear approximation of two dimensional digitized curves against a square grid the algorithm utilizes an adaptive reduction procedure in two approximation phases to select the critical points of a digitized curve such that the deviation from the digitized curve to its final approximated curve is bounded by a uniform error tolerance the time complexity of this algorithm is o m sup 2 rather than o n sup 2 on the theoretical plane in the experiments of fixing the initial and the final processing points the performance of the algorithm has been compared to those of three prominent other algorithms regarding the required number of critical points and the total execution time of the program of the four algorithms compared the present algorithm consistently has the shortest execution time of the program and it tends most to require as few critical points as the optimum algorithm that was tested

representation and shape matching of 3 d objects a three dimensional scene analysis system for the shape matching of real world 3 d objects is presented various issues related to representation and modeling of 3 d objects are addressed a new method for the approximation of 3 d objects by a set of planar faces is discussed the major advantage of this method is that it is applicable to a complete object and not restricted to single range view which was the limitation of the previous work in 3 d scene analysis the method is a sequential region growing algorithm it is not applied to range images but rather to a set of 3 d points the 3 d model of an object is obtained by combining the object points from a sequence of range data images corresponding to various views of the object applying the necessary transformations and then approximating the surface by polygons a stochastic labeling technique is used to do the shape matching of 3 d objects the technique matches the faces of an unknown view against the faces of the model it explicitly maximizes a criterion function based on the ambiguity and inconsistency of classification it is hierarchical and uses results obtained at low levels to speed up and improve the accuracy of results at higher levels the objective here is to match the individual views of the object taken from any vantage point details of the algorithm are presented and the results are shown on several unknown views of a complicated automobile casting

spirograph theory a framework for calculations on digitized straight lines using diagrams called spirographs a general theory is developed with which one can easily perform calculations on various aspects of digitized straight lines the mathematics of the theory establishes a link between digitized straight lines and the theory of numbers farey series continued fractions to show that spirograph theory is a useful unification we derive two previously known advanced results within the framework of the theory and new results concerning the accuracy in position of a digitized straight line as a function of its slope and length

discrete representation of straight lines if a continuous straight line segment is digitized on a regular grid obviously a loss of information occurs as a result the discrete representation obtained e g a chaincode string can be coded more conveniently than the continuous line segment but measurements of properties such as line length performed on the representation have an intrinsic inaccuracy due to the digitization process in this paper two fundamental properties of the quantization of straight line segments are treated 1 it is proved that every straight chaincode string can be represented by a set of four unique integer parameters definitions of these parameters are given 2 a mathematical expression is derived for the set of all continuous line segments which could have generated a given chaincode string the relation with the chord property is briefly discussed

a fast digital radon transform an efficient means for evaluating the hough transform a fast digital radon transform based on recursively defined digital straight lines is described which has the sequential complexity of n 2 log n additions for an n x n image this transform can be used to evaluate the hough transform to detect straight lines in a digital image whilst a parallel implementation of the hough transform algorithm is difficult because of global memory access requirements the fast digital radon transform is vectorizable and therefore well suited for parallel computation the structure of the fast algorithm is shown to be quite similar to the fft algorithm for decimation in frequency it is demonstrated that even for sequential computation the fast radon transform is an attractive alternative to the classical hough transform algorithm

compressed vertex chain codes this paper introduces three new vertex chain codes firstly considering that the vertex chain code uses 2 bits to represent only three code elements a new code is introduced without increasing the average bits per code the second case introduces a variable length vertex chain code finally a new compressed chain code is proposed based on the huffman method the continuation introduces a method for quantificationally evaluating the efficiency of chain codes the efficiencies of the new vertex chain codes are then compared theoretically and practically against the most popular chain codes the result of the comparison shows that the new compressed chain code is the most efficient

unsupervised clustering in hough space for identification of partially occluded objects an automated approach for template free identification of partially occluded objects is presented the contour of each relevant object in the analyzed scene is modeled with an approximating polygon whose edges are then projected into the hough space a structurally adaptive self organizing map neural network generates clusters of collinear and or parallel edges which are used as the basis for identifying the partially occluded objects within each polygonal approximation results on a number of cases under different conditions are provided

on detecting dominant points abstract detecting dominant points is a crucial preprocessing step for shape recognition and point based motion estimation polygonal approximation has been a commonly used approach in detecting dominant points this paper presents two alternatives which detect stable dominant points in the first method we find a set of positive maximum and negative minimum curvature points along the gaussian smoothed boundary followed by a split and merge polygonal approximation algorithm the resulting break points vertices of the approximated polygon are the dominant points experimental results show that dominant points obtained by this method are less sensitive to the orientation of the boundary than other polygonal approximation algorithms in the sense that the number and the location of the dominant points along the contour remain relatively unchanged in the second method we smooth a boundary by a gaussian filter using various widths until the extreme curvature points remain relatively unchanged for a range of filter widths the resulting extreme curvature points which are stable to orientation and a reasonable range of scaling are the dominant points

on superquadratic elliptic systems in this article we study the existence of solutions for the elliptic system updelta u frac partial h partial v left u v x right text in upomega updelta v frac partial h partial v left u v x right text in upomega u 0 v 0 text on partial upomega where upomega is a bounded open subset of mathbb r n with smooth boundary partial upomega and the function h mathbb r 2 times overline upomega to mathbb r is of class c 1

recognition of occluded objects with heuristic search abstract this paper presents a new heuristic search based approach for recognition of partially obscured planar shapes based on a general scheme for representing the planar shapes in terms of their contour segments a state space formulation is obtained for the recognition problem the search in the state space is guided by an admissible heuristic function which is not dependent upon the features actually used for representing the shapes some schemes for toning up the efficiency of the method are also discussed a study of the method was carried out by experimenting with some typical objects and results of experimentation are presented

a robust boundary based object recognition in occlusion environment by hybrid hopfield neural networks this paper presents a new method of occluded object matching for machine vision applications the current methods for occluded object matching lack robustness and require high computational effort in this paper a new hybrid hopfield neural network hhn algorithm which combines the advantages of both a continuous hopfield network chn and a discrete hopfield network dhn will be described and applied for partially occluded object recognition in a multi context scenery the hhn proposed as a new approach provides great fault tolerance and robustness and requires less computation time also advantages of hhn such as reliability and speed will be discussed

an optimal o n algorithm for identifying line segments from a sequence of chain codes abstract an optimal algorithm for identifying straight lines in chain codes is described the algorithm turns the complicated problem of determining the straightness of digital arcs into a simple task by constructing a passing area around the pixels it also solves the problem of detecting all straight segments from a sequence of chain codes in o n time where n is the length of the sequence it has been found that this algorithm is not only simple and intuitive but also highly efficient

a robust solution for object recognition by mean field annealing techniques abstract object recognition in multi context scene is one of the very difficult problems to find a robust solution in many applications the annealed hopfield networks have been developed to find global solutions of a non linear system in the study it has been proven that the system temperature of mfa is equivalent to the gain of sigmoid function of hopfield network in our early work we developed the hybrid hopfield network hhn on the purpose of fast and reliable matching in the object recognition process however hhn does not guarantee global solutions and yields false matching under heavily occluded conditions because hhn is depending on initial states by its nature in this paper we present the annealed hopfield network ahn to find a robust solution for occluded object matching problems in multi context scenery in ahn the mean field theory is applied to the hybrid hopfield network in order to improve computational complexity of the annealed hopfield network and provide reliable matching under heavily occluded conditions ahn is slower than hhn however ahn provides near global solutions without initial restrictions and provides less false matching than hhn the robustness of the algorithm is proved by identifying occluded target objects with large tolerance of their features also we present a optimal boundary smoothing algorithm to extract reliable features from the boundary representation of the object heavily contaminated by noise

the use of maximum curvature points for the recognition of partially occluded objects abstract a graph theoretic optimization method is used to recognize partially occluded objects from a 2 d image through the use of maximal cliques and a weight matching algorithm the vertices of an occluded object image with high curvature values are classified by the objects which are hypothesized to be involved in the occlusion a heuristic method is also developed to further improve the computational speed a few typical examples are given to illustrate the accuracy of the optimization model as well as the simplicity of the companion heuristic method

polygonal approximation of digital curves based on the principles of perceptual organization abstract a new approach to the problem of polygonal approximation of digital shapes is presented in this paper in this approach the approximation process is divided into three stages based on the principles of perceptual organization and three algorithms are developed accordingly the linking merging algorithm is firstly proposed for low level processing the smoothing algorithm is then followed for further approximation the high level rule based algorithm is finally applied to preserve the visual feature points while reducing the number of segments in the approximated polygon as much as possible the effectiveness of the proposed algorithm is demonstrated by testing both synthetic shapes and scanned in shapes

combined effects of concave and convex nonlinearities in some elliptic problems abstract this paper deals with a class of semilinear elliptic dirichlet boundary value problems where the combined effects of a sublinear and a superlinear term allow us to establish some existence and multiplicity results

partial shape recognition by sub matrix matching for partial matching guided image labeling we propose a new partial shape recognition algorithm by sub matrix matching using a proximity based shape representation given one or more example object templates and a number of candidate object regions in an image points with local maximum curvature along contours of each are chosen as feature points to compute distance matrices for each candidate object region and example template s a sub matrix matching algorithm is then proposed to determine correspondences for evaluation of partial similarity between an example template and a candidate object region the method is translation rotation scale and reflection invariant applications of the proposed partial matching technique include recognition of partially occluded objects in images as well as significant acceleration of recognition matching of full non occluded objects for object based image labeling by learning from examples the speed up in the latter application comes from the fact that we can now search only those combinations of regions in the neighborhood of potential partial matches as soon as they are identified as opposed to all combinations of regions as was done in our prior work xu et al object formation and retrieval using a learning based hierarchical content description proceedings of the icip kobe japan 1999 experimental results are provided to demonstrate both applications

digital parallelism perpendicularity and rectangles the slope of digital line segments is defined and an algorithm to evaluate it is presented parallelism and perpendicularity of two digital line segments are also defined finally rectangular digital regions are defined and characterized and an algorithm that determines whether or not a given digital region is a digital rectangle is presented

edge replacement in the recognition of occluded objects abstract the generalized hough transform recognizes objects more successfully when all edges are visible to facilitate recognition this paper introduces a preliminary generalized hough process that restores edges which were invisible because of occlusion or because of lack of contrast between occluding and occluded areas space and time complexity of generalized hough processes are reduced by chained hashing techniques experimental results show that recognition of occluded objects via a generalized hough transform is improved if occluding objects are first recognized and subtracted out of the input picture and occluded edges are then reconstructed prior to recognition of occluded objects

on the inverse hough transform in this paper an inverse hough transform algorithm is proposed this algorithm reconstructs correctly the original image using only the data of the hough transform space and it is applicable to any binary image as a first application the inverse hough transform algorithm is used for straight line detection and filtering the lines are detected not just as continuous straight lines which is the case of the standard hough transform but as they really appear in the original image i e pixel by pixel to avoid the quantization effects in the hough transform space inversion conditions are defined which are associated only with the dimensions of the images experimental results indicate that the inverse hough transform algorithm is robust and accurate

localizing overlapping parts by searching the interpretation tree this paper discusses how local measurements of positions and surface normals may be used to identify and locate overlapping objects the objects are modeled as polyhedra or polygons having up to six degrees of positional freedom relative to the sensors the approach operates by examining all hypotheses about pairings between sensed data and object surfaces and efficiently discarding inconsistent ones by using local constraints on distances between faces angles between face normals and angles relative to the surface normals of vectors between sensed points the method described here is an extension of a method for recognition and localization of nonoverlapping parts previously described in 18 and 15

multidimensional modelling for the carotid artery blood flow abstract in this work a multidimensional 3d 1d fem model of the whole arterial tree is implemented it comprises a 3d compliant model of the carotid bifurcation coupled with a 1d model for the remaining part of the arterial tree with this approach difficulties arising from the treatment of boundary conditions for the 3d model are naturally handled the navier stokes equations are used as the governing equations for the blood flow while an elastic compliant model is implemented for the arterial wall also the a l e formulation is considered within the 3d blood regions taking into account the domain deformations produced by the moving artery wall this 3d model is complemented with a 1d model of the entire arterial tree in order to appropriately set inflow and outflow boundary conditions for the former the reduced 1d model solves the momentum and continuity equations in compliant tubes so as to reproduce the propagation of the pressure pulse in the arterial network also a volumetric flow rate is imposed at the inlet to model the systolic work of the heart the peripheral arteriole beds are simulated with the well known lumped windkessel model a standard geometry of the carotid bifurcation is discretized with p1 bubble p1 tetrahedral elements the obtained results properly reproduce the general flow patterns reported in the literature very good agreement between the outcomes of a pure 1d model and those of the combined multidimensional model was obtained it is worth noting that this kind of model may provide useful information to gain understanding in the genesis and development of arterial diseases

a hyperbolic system of equations of blood flow in an arterial network we study a coupled system of the navier stokes equation and the equation of conservation of mass in a network the system models the blood circulation in arterial networks a special feature of the system is that the equations are coupled through boundary conditions at joints of the network we use a fixed point method to prove the existence and uniqueness of the classic solution to the initial boundary value problem and discuss the continuity of dependence of the solution and its derivatives on initial boundary and forcing functions and their derivatives we develop a numerical scheme that generates discretized solutions and we also prove the convergence of the scheme

recognition of occluded objects a cluster structure algorithm clustering techniques have been used to perform image segmentation to detect lines and curves in images and to solve several other problems in pattern recognition and image analysis in this paper we apply clustering methods to a new problem domain and present a new method based on a cluster structure approach for the recognition of 2 d partially occluded objects basically the technique consists of three steps clustering of border segment transformations finding continuous sequences of segments in appropriately chosen clusters and clustering of sequence average transformation values as compared to some of the earlier methods which identify an object based on only one sequence of matched segments the new approach allows the identification of all parts of the model which match in the occluded scene we also discuss the application of the clustering techniques to 3 d scene analysis in both cases the cluster structure algorithm entails the application of clustering concepts in a hierarchical manner resulting in a decrease in the computational effort as the recognition algorithm progresses the implementation of the techniques discussed for the 2 d case has been completed and the algorithm has been evaluated with respect to a large number of examples where several objects partially occlude one another the method is able to tolerate a moderate change in scale and a significant amount of shape distortion arising as a result of segmentation and or the polygonal approximation of the boundary of the object a summary of the results is presented

an anatomically based model of transient coronary blood flow in the heart an efficient finite difference model of blood flow through the coronary vessels is developed and applied to a geometric model of the largest six generations of the coronary arterial network by constraining the form of the velocity profile across the vessel radius the three dimensional navier stokes equations are reduced to one dimensional equations governing conservation of mass and momentum these equations are coupled to a pressure radius relationship characterizing the elasticity of the vessel wall to describe the transient blood flow through a vessel segment the two step lax wendroff finite difference method is used to numerically solve these equations the flow through bifurcations where three vessel segments join is governed by the equations of conservation of mass and momentum the solution to these simultaneous equations is calculated using the multidimensional newton raphson method simulations of blood flow through a geometric model of the coronary network are presented demonstrating phy

partial shape recognition a landmark based approach a method of recognizing partially occluded objects is presented in which each object is represented by a set of landmarks given a scene consisting of partially occluded objects a model object in the scene is hypothesized by matching the landmarks of the model with those in the scene a measure of similarity between two landmarks is needed to perform this matching a local shape measure sphericity is introduced it is shown that any invariant function under a similarity transformation is a function of the sphericity to match landmarks between the model and the scene a table of compatibility is constructed a technique known as hopping dynamic programming is described to guide the landmark matching through the compatibility table the location of the model in the scene is estimated with a least squares fit among the matched landmarks a heuristic measure is then computed to decide if the model is in the scene

global solution to a hyperbolic problem arising in the modeling of blood flow in circulatory systems abstract this paper considers a system of first order hyperbolic partial differential equations in the domain of a one dimensional network the system models the blood flow in human circulatory systems as an initial boundary value problem with boundary conditions of either algebraic or differential type the differential equations are nonhomogeneous with frictional damping terms and the state variables are coupled at internal junctions the existence and uniqueness of the local classical solution have been established in our earlier work w ruan m e clark m zhao a curcio a hyperbolic system of equations of blood flow in an arterial network j appl math 64 2 2003 637 667 w ruan m e clark m zhao a curcio blood flow in a network nonlinear anal real world appl 5 2004 463 485 w ruan m e clark m zhao a curcio a quasilinear hyperbolic system that models blood flow in a network in charles v benton ed focus on mathematical physics research nova science publishers inc new york 2004 pp 203 230 this paper continues the analysis and gives sufficient conditions for the global existence of the classical solution we prove that the solution exists globally if the boundary data satisfy the dissipative condition 2 3 or 3 2 and the norms of the initial and forcing functions in a certain sobolev space are sufficiently small this is only the first step toward establishing the global existence of the solution to physiologically realistic models because in general the chosen dissipative conditions 2 3 and 3 2 do not appear to hold for the originally proposed boundary conditions 1 3 1 12

strongly indefinite systems with critical sobolev exponents we consider an elliptic system of hamiltonian type on a bounded domain in the superlinear case with critical growth rates we obtain existence and positivity results for solutions under suitable conditions on the linear terms our proof is based on an adaptation of the dual variational method as applied before to the scalar case introduction existence and non existence of solutions of semilinear elliptic srstems has been a subject of active research recently see for example ff l3 ps such systems are called variational if solutions can be viewed as critical points of an associated functional defined on a suitable function space restricting our attention to systems with two unknowns we distinguish two classes of variational elliptic systems a potential systems b hamiltonian systems potential systems are of the form a llu u v ztl2v u v where l1 and l2 are second order selfadjoint elliptic operators formally these are the euler lagrange equations of the functional f u v l1u u i l2v v th u v here is the l2 inner product for functions defined on the underlying domain and tt u v s h u x v x dx the functional f is often called the lagrangian its critical points correspond to weak soltbtions of a the appropr ate choice of the function spaces for u and v follows by requiring that the quadratic part of f be well defined this naturally leads to sobolev spaces with square irltegrable first derivatives since also a must be well defined by virtue of the embedding theorems some growth restrictions on this latter function are required an extra difficulty appears if we consider system a with a plus sign in the second equation for then the corresponding functiorl f has a strongly indefinite quadratic part for systems of superlinear type and with sllbcritical growth the mountain pass theorem ar or in the strongly indefinite case the benci rabinowitz theorem received by the editors june 5 1996 1991 mathematics subject classification primary 35j50 35j55 35j65

a shape recognition scheme based on relative distances of feature points from the centroid abstract in this paper a simple but efficient scheme to recognize shapes is proposed in our scheme all of the boundary points are used to calculate the centroid of an object then the distance between each feature point and the centroid is computed we have shown that the time complexity of our shape matching algorithm is o m where m is the number of feature points the most important advantage of our method is its independence to translation rotation and scaling of objects

curvature and tangential deflection of discrete arcs a theory based on the commutator of scatter matrix pairs and its application to vertex detection in planar shape data this paper introduces a new theory for the tangential deflection and curvature of plane discrete curves our theory applies to discrete data in either rectangular boundary coordinate or chain coded formats its rationale is drawn from the statistical and geometric properties associated with the eigenvalue eigenvector structure of sample covariance matrices specifically we prove that the nonzero entry of the commutator of a piar of scatter matrices constructed from discrete arcs is related to the angle between their eigenspaces and further we show that this entry is in certain limiting cases also proportional to the analytical curvature of the plane curve from which the discrete data are drawn these results lend a sound theoretical basis to the notions of discrete curvature and tangential deflection and moreover they provide a means for computationally efficient implementation of algorithms which use these ideas in various image processing contexts as a concrete example we develop the commutator vertex detection cvd algorithm which identifies the location of vertices in shape data based on excessive cummulative tangential deflection and we compare its performance to several well established corner detectors that utilize the alternative strategy of finding approximate curvature extrema

multiple positive solutions of nonhomogeneous elliptic systems with strongly indefinite structure and critical sobolev exponents abstract in this paper we study the existence of multiple positive solutions to some hamiltonian elliptic systems v u u p ef x u v v q g x in u v 0 in u v 0 on where is a bounded domain in r n n 3 0 f g l 1 p 1 1 q 1 n 2 n p q 1 0 using sub and supersolution method and based on an adaptation of the dual variational approach we prove the existence of at least two nontrivial positive solutions for all 0 1 and e 0 0 where 1 is the first eigenvalue of the laplace operator with zero dirichlet boundary conditions and 0 is a positive number

a scale space filtering approach for visual feature extraction this paper presents a new integrated approach for detecting visual features which include corners ends arcs and lines the effect of scale space filtering on visual features is studied in detail as it forms the theoretical basis of our work in this approach the outline of the object is first extracted and it is then smoothed by scale space filtering at different scale levels subsequently the local extreme curvature points extracted from the smoothed curve and end candidates are determined to guide the termination of the filtering process information about the curvature of each point at the largest scale level is used to detect the different kinds of visual features several algorithms are proposed to determine corners ends arcs and lines experimental results show that our approach is robust to translation rotation and scaling of the object as well as noise corruption in addition efficient visual features can also be successfully extracted with this approach

differential systems with strongly indefinite variational structure abstract the euler lagrange equations of lagrangians with a strongly indefinite quadratic part are studied by means of the direct min max method of benci and rabinowitz the simplest case is a system of two coupled semilinear poisson equations using an analytic framework of a suitable family of products of fractional sobolev spaces existence results are obtained for all nonlinearities with subcritical growth rates

on the straightness of digital arcs the straightness of a digital arc can simply be determined by the absence of unevenness in its chain code the absence of unevenness is a necessary and sufficient condition for a digital arc to have the chord property and it offers a much simpler alternative for examining whether a digital arc has the chord property or not this condition is also the most comprehensive and precise expression of the third criterion about digital straight lines given by freeman the relations among the chord property freeman s three criteria and the hierarchical structure that a digital straight line supposedly have become much more clear a procedure to detect the uneven segments and algorithms for determining the straightness of digital arcs is also included

information theoretic active polygons for unsupervised texture segmentation curve evolution models used in image segmentation and based on image region information usually utilize simple statistics such as means and variances hence can not account for higher order nature of the textural characteristics of image regions in addition the object delineation by active contour methods results in a contour representation which still requires a substantial amount of data to be stored for subsequent multimedia applications such as visual information retrieval from databases polygonal approximations of the extracted continuous curves are required to reduce the amount of data since polygons are powerful approximators of shapes for use in later recognition stages such as shape matching and coding the key contribution of this paper is the development of a new active contour model which nicely ties the desirable polygonal representation of an object directly to the image segmentation process this model can robustly capture texture boundaries by way of higher order statistics of the data and using an information theoretic measure and with its nature of the ordinary differential equations this new variational texture segmentation model is unsupervised since no prior knowledge on the textural properties of image regions is used another contribution in this sequel is a new polygon regularizer algorithm which uses electrostatics principles this is a global regularizer and is more consistent than a local polygon regularization in preserving local features such as corners

on the sensitivity of the hough transform for object recognition object recognition from sensory data involves in part determining the pose of a model with respect to a scene a common method for finding an object s pose is the generalized hough transform which accumulates evidence for possible coordinate transformations in a parameter space whose axes are the quantized transformation parameters large clusters of similar transformations in that space are taken as evidence of a correct match a theoretical analysis of the behavior of such methods is presented the authors derive bounds on the set of transformations consistent with each pairing of data and model features in the presence of noise and occlusion in the image bounds are provided on the likelihood of false peaks in the parameter space as a function of noise occlusion and tessellation effects it is argued that haphazardly applying such methods to complex recognition tasks is risky as the probability of false positives can be very high