numerical generation of periodic traveling wave solutions of some nonlinear dispersive wave systems in this paper a numerical procedure to generate approximations to periodic traveling wave profiles of some nonlinear dispersive wave systems is introduced the method is based on a suitable modification of a fixed point algorithm of petviashvili type and solves several drawbacks of some previous algorithms presented in the literature by way of illustration the method is applied to generate numerically periodic traveling waves of two problems of interest the fractional kdv type equations and the extended boussinesq system we propose a method to compute periodic traveling waves the method can be applied to some nonlinear dispersive systems it is checked in fractional kdv equations and boussinesq systems

a survey of the theory of source coding with a fidelity criterion the purpose of this paper is threefold 1 to acquaint the reader with the types of problems that have been considered in the area of source coding with a fidelity criterion 2 to survey results that have been obtained on these problems and 3 to outline future research trends in the area

clique descriptor of affine invariant regions for robust wide baseline image matching assuming that the image distortion between corresponding regions of a stereo pair of images with wide baseline can be approximated as an affine transformation if the regions are reasonably small recent image matching algorithms have focused on affine invariant region ir detection and its description to increase the robustness in matching however the distinctiveness of an intensity based region descriptor tends to deteriorate when an image includes homogeneous texture or repetitive pattern to address this problem we investigated the geometry of a local ir cluster also called a clique and propose a new clique based image matching method in the proposed method the clique of an ir is estimated by delaunay triangulation in a local affine frame and the hausdorff distance is adopted for matching an inexact number of multiple descriptor vectors we also introduce two adaptively weighted clique distances where the neighbour distance in a clique is appropriately weighted according to characteristics of the local feature distribution experimental results show the clique based matching method produces more tentative correspondences than variants of the sift based method

newton conjugate gradient methods for solitary wave computations in this paper the newton conjugate gradient methods are developed for solitary wave computations these methods are based on newton iterations coupled with conjugate gradient iterations to solve the resulting linear newton correction equation when the linearization operator is self adjoint the preconditioned conjugate gradient method is proposed to solve this linear equation if the linearization operator is non self adjoint the preconditioned biconjugate gradient method is proposed to solve the linear equation the resulting methods are applied to compute both the ground states and excited states in a large number of physical systems such as the two dimensional nls equations with and without periodic potentials the fifth order kdv equation and the fifth order kp equation numerical results show that these proposed methods are faster than the other leading numerical methods often by orders of magnitude in addition these methods are very robust and always converge in all the examples being tested furthermore they are very easy to implement it is also shown that the nonlinear conjugate gradient methods are not robust and inferior to the proposed methods

symmetry maps of free form curve segments via wave propagation this paper presents an approach for computing the symmetries skeletons of an edge map consisting of a collection of curve segments this approach is a combination of analytic computations in the style of computational geometry and discrete propagations on a grid in the style of the numerical solutions of pde s specifically waves from each of the initial curve segments are initialized and propagated as a discrete wavefront along discrete directions in addition to avoid error built up due to the discrete nature of propagation shockwaves are detected and explicitly propagated along a secondary dynamic grid the propagation of shockwaves integrated with the propagation of the wavefront along discrete directions leads to an exact simulation of propagation by the eikonal equation the resulting symmetries are simply the collection of shockwaves formed in this process which can be manipulated locally exactly and efficiently under local changes in an edge map gap completion removal of spurious elements etc the ability to express grouping operations in the language of symmetry maps makes it an appropriate intermediate representation between low level edge maps and high level object hypotheses

texture segmentation using voronoi polygons textures are defined in terms of primitives called tokens a texture segmentation algorithm based on the voronoi tessellation is discussed the algorithm first builds the voronoi tessellation of the tokens that make up the textured image it then computes a feature vector for each voronoi polygon these feature vectors are used in a probabilistic relaxation labeling on the tokens to identify the interior and the border regions of the textures some experimental results are shown

a review of the fractal image coding literature fractal image compression is a technique based on the representation of an image by a contractive transform on the space of images for which the fixed point is close to the original image this broad principle encompasses a very wide variety of coding schemes many of which have been explored in the rapidly growing body of published research while certain theoretical aspects of this representation are well established relatively little attention has been given to the construction of a coherent underlying image model that would justify its use most purely fractal based schemes are not competitive with the current state of the art but hybrid schemes incorporating fractal compression and alternative techniques have achieved considerably greater success this review represents a survey of the most significant advances both practical and theoretical since the publication of jacquin s 1990 original fractal coding scheme

medial axis transformation of a planar shape the medial axis transformation is a means first proposed by blum to describe a shape in this paper we present a 0 n log n algorithm for computing the medial axis of a planar shape represented by an n edge simple polygon the algorithm is an improvement over most previously known results interms of both efficiency and exactness and has been implemented in fortran some computer plotted output of the program are also shown in the paper

adaptive image segmentation by combining photometric invariant region and edge information an adaptive image segmentation scheme is proposed employing the delaunay triangulation for image splitting the tessellation grid of the delaunay triangulation is adapted to the semantics of the image data by combining region and edge information to achieve robustness against imaging conditions e g shading shadows illumination and highlights photometric invariant similarity measures and edge computation are proposed experimental results on synthetic and real images show that the segmentation method is robust to edge orientation partially weak object boundaries and noisy but homogeneous regions furthermore the method is robust to a large degree to varying imaging conditions

a tuned mesh generation strategy for image representation based on data dependent triangulation a mesh generation framework for image representation based on data dependent triangulation is proposed the proposed framework is a modified version of the frameworks of rippa and garland and heckbert that facilitates the development of more effective mesh generation methods as the proposed framework has several free parameters the effects of different choices of these parameters on mesh quality are studied leading to the recommendation of a particular set of choices for these parameters a mesh generation method is then introduced that employs the proposed framework with these best parameter choices this method is demonstrated to produce meshes of higher quality both in terms of squared error and subjectively than those generated by several competing approaches at a relatively modest computational and memory cost

energy dissipating flows for solving nonlinear eigenpair problems abstract this work is concerned with computing nonlinear eigenpairs which model solitary waves and various other physical phenomena we aim at solving nonlinear eigenvalue problems of the general form t u q u in our setting t is a variational derivative of a convex functional such as the laplacian operator with respect to the dirichlet energy q is an arbitrary bounded nonlinear operator and is an unknown real eigenvalue we introduce a flow that numerically generates an eigenpair solution by its steady state analysis for the general case is performed showing a monotone decrease in the convex functional throughout the flow when t is the laplacian operator a complete discretized version is presented and anlalyzed we implement our algorithm on korteweg and de vries kdv and nonlinear schrodinger nls equations in one and two dimensions the proposed approach is very general and can be applied to a large variety of models moreover it is highly robust to noise and to perturbations in the initial conditions compared to classical petiashvili based methods

iteration free fractal image coding based on efficient domain pool design the domain pool design is one of the dominant issues which affect the coding performance of fractal image compression in this paper we employ the lbg algorithm and propose a block averaging method to design the efficient domain pools based on a proposed iteration free fractal image codec the redundancies between the generated domain blocks are reduced by the proposed methods therefore we can obtain the domain pools that are more efficient than those in the conventional fractal coding schemes and thus the coding performance is improved on the other hand the iteration process in the conventional fractal coding scheme not only requires a large size of memory and a high computation complexity but also prolongs the decoding process the proposed iteration free fractal codec can overcome the problems above in computer simulation both the lbg based and block averaging methods for the domain pool design in the proposed iteration free scheme achieve excellent performances for example based on the proposed block averaging method the decoded lena image has at least a 0 5 db higher psnr under the same bit rate and an eight time faster decoding speed than the conventional fractal coding schemes that require iterations

pyramidal lattice vector quantization for multiscale image coding introduces a new image coding scheme using lattice vector quantization the proposed method involves two steps biorthogonal wavelet transform of the image and lattice vector quantization of wavelet coefficients in order to obtain a compromise between minimum distortion and bit rate we must truncate and scale the lattice suitably to meet this goal we need to know how many lattice points lie within the truncated area we investigate the case of laplacian sources where surfaces of equal probability are spheres for the l sup 1 metric pyramids for arbitrary lattices we give explicit generating functions for the codebook sizes for the most useful lattices like z sup n d sub n e sub s spl and sub 16

entropy and distance of random graphs with application to structural pattern recognition the notion of a random graph is formally defined it deals with both the probabilistic and the structural aspects of relational data by interpreting an ensemble of attributed graphs as the outcomes of a random graph we can use its lower order distribution to characterize the ensemble to reflect the variability of a random graph shannon s entropy measure is used to synthesize an ensemble of attributed graphs into the distribution of a random graph or a set of distributions we propose a distance measure between random graphs based on the minimum change of entropy before and after their merging when the ensemble contains more than one class of pattern graphs the synthesis process yields distributions corresponding to various classes this process corresponds to unsupervised learning in pattern classification using the maximum likelihood rule and the probability computed for the pattern graph based on its matching with the random graph distributions of different classes we can classify the pattern graph to a class

modification of hough transform for circles and ellipses detection using a 2 dimensional array abstract the hough transform is a robust technique which is useful in detecting straight lines in an edge enhanced picture however the extension of the conventional hough transform to recover circles and ellipses has been limited by slow speed and excessive memory this paper presents techniques aimed at improving the efficiency and reducing the memory size of the accumulator array based on these techniques only a 2 dimensional array is needed for the detection of circles and ellipses the approach centres on the use of parallel edge points and a method on reducing the dimension of the accumulator array

conjugate gradient method for finding fundamental solitary waves abstract the conjugate gradient method cgm is known to be the fastest generic iterative method for solving linear systems with symmetric sign definite matrices in this paper we modify this method so that it can find fundamental solitary waves of nonlinear hamiltonian equations the main obstacle that such a modified cgm overcomes is that the operator of the equation linearized about a solitary wave is not sign definite instead it has a finite number of eigenvalues on the opposite side of zero than the rest of its spectrum we present versions of the modified cgm that can find solitary waves with prescribed values of either the propagation constant or power we also extend these methods to handle multi component nonlinear wave equations convergence conditions of the proposed methods are given and their practical implications are discussed we demonstrate that our modified cgms converge much faster than say petviashvili s or similar methods especially when the latter converge slowly

a fast ellipse circle detector using geometric symmetry through the use of a global geometric symmetry a fast ellipse circle detector is proposed in this paper based on the geometric symmetry the proposed method first locates candidates of ellipse and circle centers in the meantime according to these candidate centers all feature points in an input image are grouped into several subimages then for each subimage by using geometric symmetry again all ellipses and circles are obtained the method significantly reduces the time required to evaluate all possible parameters without using edge direction information experimental results are given to show the correctness and effectiveness of the proposed method

simplicial complex with approximate rotational symmetry a general class of simplicial complexes abstract we study the transformation of the vertices of a certain simple simplicial complex in n dimensional euclidian space and prove that the resulting set of simplices is a simplicial complex with an approximate rotational symmetry such simplicial complexes have applications in computing lyapunov function for nonlinear dynamical systems using linear optimization and are also of interest for other applications

a fast approach for accurate content adaptive mesh generation mesh modeling is an important problem with many applications in image processing a key issue in mesh modeling is how to generate a mesh structure that well represents an image by adapting to its content we propose a new approach to mesh generation which is based on a theoretical result derived on the error bound of a mesh representation in the proposed method the classical floyd steinberg error diffusion algorithm is employed to place mesh nodes in the image domain so that their spatial density varies according to the local image content delaunay triangulation is next applied to connect the mesh nodes the result of this approach is that fine mesh elements are placed automatically in regions of the image containing high frequency features while coarse mesh elements are used to represent smooth areas the proposed algorithm is noniterative fast and easy to implement numerical results demonstrate that at very low computational cost the proposed approach can produce mesh representations that are more accurate than those produced by several existing methods moreover it is demonstrated that the proposed algorithm performs well with images of various kinds even in the presence of noise

tomographic image reconstruction based on a content adaptive mesh model in this paper we explore the use of a content adaptive mesh model camm for tomographic image reconstruction in the proposed framework the image to be reconstructed is first represented by a mesh model an efficient image description based on nonuniform sampling in the camm image samples represented as mesh nodes are placed most densely in image regions having fine detail tomographic image reconstruction in the mesh domain is performed by maximum likelihood ml or maximum a posteriori map estimation of the nodal values from the measured data a camm greatly reduces the number of unknown parameters to be determined leading to improved image quality and reduced computation time we demonstrated the method in our experiments using simulated gated single photon emission computed tomography spect cardiac perfusion images a channelized hotelling observer cho was used to evaluate the detectability of perfusion defects in the reconstructed images a task based measure of image quality a minimum description length mdl criterion was also used to evaluate the effect of the representation size in our application both mdl and cho suggested that the optimal number of mesh nodes is roughly five to seven times smaller than the number of projection bins when compared to several commonly used methods for image reconstruction the proposed approach achieved the best performance in terms of defect detection and computation time the research described in this paper establishes a foundation for future development of a four dimensional space time reconstruction framework for image sequences in which a built in deformable mesh model is used to track the image motion

structural matching by discrete relaxation this paper describes a bayesian framework for performing relational graph matching by discrete relaxation our basic aim is to draw on this framework to provide a comparative evaluation of a number of contrasting approaches to relational matching broadly speaking there are two main aspects to this study firstly we focus on the issue of how relational inexactness may be quantified we illustrate that several popular relational distance measures can be recovered as specific limiting cases of the bayesian consistency measure the second aspect of our comparison concerns the way in which structural inexactness is controlled we investigate three different realizations of the matching process which draw on contrasting control models the main conclusion of our study is that the active process of graph editing outperforms the alternatives in terms of its ability to effectively control a large population of contaminating clutter

edcircles a real time circle detector with a false detection control we propose a real time parameter free circle detection algorithm that has high detection rates produces accurate results and controls the number of false circle detections the algorithm makes use of the contiguous connected set of edge segments produced by our parameter free edge segment detector the edge drawing parameter free edpf algorithm hence the name edcircles the proposed algorithm first computes the edge segments in a given image using edpf which are then converted into line segments the detected line segments are converted into circular arcs which are joined together using two heuristic algorithms to detect candidate circles and near circular ellipses the candidates are finally validated by an a contrario validation step due to the helmholtz principle which eliminates false detections leaving only valid circles and near circular ellipses we show through experimentation that edcircles works real time 10 20ms for 640x480 images has high detection rates produces accurate results and is very suitable for the next generation real time vision applications including automatic inspection of manufactured products eye pupil detection circular traffic sign detection etc

numerical methods for computing nonlinear eigenpairs part i iso homogeneous cases with a rayleigh quotient formulation a local minimax method is developed to solve a class of iso homogeneous nonlinear eigenpair problems for multiple solutions in banach spaces following their instability order the algorithm is implemented to compute weighted eigenpairs of the p laplacian numerical eigenfunctions are illustrated by their graphics several interesting phenomena have been observed and are open for further investigation mathematical analysis related to convergence and instability order of computed eigenfunctions etc is also presented

convergence of petviashvili s iteration method for numerical approximation of stationary solutions of nonlinear wave equations we analyze a heuristic numerical method suggested by v i petviashvili in 1976 for approximation of stationary solutions of nonlinear wave equations the method is used to construct numerically the solitary wave solutions such as solitons lumps and vortices in a space of one and higher dimensions assuming that the stationary solution exists we find conditions when the iteration method converges to the stationary solution and when the rate of convergence is the fastest the theory is illustrated with examples of physical interest such as generalized korteweg de vries benjamin ono zakharov kuznetsov kadomtsev petviashvili and klein gordon equations

image coding using wavelet transform a scheme for image compression that takes into account psychovisual features both in the space and frequency domains is proposed this method involves two steps first a wavelet transform used in order to obtain a set of biorthogonal subclasses of images the original image is decomposed at different scales using a pyramidal algorithm architecture the decomposition is along the vertical and horizontal directions and maintains constant the number of pixels required to describe the image second according to shannon s rate distortion theory the wavelet coefficients are vector quantized using a multiresolution codebook to encode the wavelet coefficients a noise shaping bit allocation procedure which assumes that details at high resolution are less visible to the human eye is proposed in order to allow the receiver to recognize a picture as quickly as possible at minimum cost a progressive transmission scheme is presented it is shown that the wavelet transform is particularly well adapted to progressive transmission

a minimisation approach for computing the ground state of gross pitaevskii systems in this paper we present a minimisation method for computing the ground state of systems of coupled gross pitaevskii equations our approach relies on a spectral decomposition of the solution into hermite basis functions inserting the spectral representation into the energy functional yields a constrained nonlinear minimisation problem for the coefficients for its numerical solution we employ a newton like method with an approximate line search strategy we analyse this method and prove global convergence appropriate starting values for the minimisation process are determined by a standard continuation strategy numerical examples with two and three component two dimensional condensates are included these experiments demonstrate the reliability of our method and nicely illustrate the effect of phase segregation

fractal image compression based on delaunay triangulation and vector quantization presents a new scheme for fractal image compression based on adaptive delaunay triangulation such a partition is computed on an initial set of points obtained with a split and merge algorithm in a grey level dependent way the triangulation is thus fully flexible and returns a limited number of blocks allowing good compression ratios moreover a second original approach is the integration of a classification step based on a modified version of the lloyd algorithm vector quantization in order to reduce the encoding complexity the vector quantization algorithm is implemented on pixel histograms directly generated from the triangulation the aim is to reduce the number of comparisons between the two sets of blocks involved in fractal image compression by keeping only the best representative triangles in the domain blocks set quality coding results are achieved at rates between 0 25 0 5 b pixel depending on the nature of the original image and on the number of triangles retained

image compression with variable block size segmentation high quality variable rate image compression is achieved by segmenting an image into regions of different sizes classifying each region into one of several perceptually distinct categories and using a distinct coding procedure for each category segmentation is performed with a quadtree data structure by isolating the perceptually more important areas of the image into small regions and separately identifying larger random texture blocks since the important regions have been isolated the remaining parts of the image can be coded at a lower rate than would be otherwise possible high quality coding results are achieved at rates between 0 35 and 0 7 b p depending on the nature of the original image and satisfactory results have been obtained at 0 25 b p

petviashvili type methods for traveling wave computations i analysis of convergence in this paper a family of fixed point algorithms for the numerical resolution of some systems of nonlinear equations is designed and analyzed the family introduced here generalizes the petviashvili method and can be applied to the numerical generation of traveling waves in some nonlinear dispersive systems conditions for the local convergence are derived and numerical comparisons between different elements of the family are carried out

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

matching delaunay graphs this paper describes a bayesian framework for matching delaunay triangulations relational structures of this sort are ubiquitous in intermediate level computer vision being used to represent both voronoi tessellations of the image plane and volumetric surface data our matching process is realised in terms of probabilistic relaxation the novelty of our method stems from its use of a support function specified in terms of face units of the graphs under match in this way we draw on more expressive constraints than is possible at the level of edge units alone in order to apply this new relaxation process to the matching of realistic imagery requires a model of the compatibility between faces of the data and model graphs we present a particularly simple compatibility model that is entirely devoid of free parameters it requires only knowledge of the numbers of nodes edges and faces in the model graph the resulting matching scheme is evaluated on radar images and compared with its edge based counterpart we establish the operational limits and noise sensitivity on the matching of random dot patterns

randomized circle detection with isophotes curvature analysis circle detection is a critical issue in image analysis and object detection although hough transform based solvers are largely used randomized approaches based on the iterative sampling of the edge pixels are object of research in order to provide solutions less computationally expensive this work presents a randomized iterative work flow which exploits geometrical properties of isophotes in the image to select the most meaningful edge pixels and to classify them in subsets of equal isophote curvature the analysis of candidate circles is then performed with a kernel density estimation based voting strategy followed by a refinement algorithm based on linear error compensation the method has been applied to a set of real images on which it has also been compared with two leading state of the art approaches and hough transform based solutions the achieved results show how discarding up to 57 of unnecessary edge pixels it is able to accurately detect circles within a limited number of iterations maintaining a sub pixel accuracy even in the presence of high level of noise highlightsan iterative randomized circle detection algorithm is proposed curvature of isophotes is used to reduce the number of necessary iterations edges on circumference s are selected by a kernel density estimation strategy sub pixel accuracy was maintained on real images even in presence of high noise levels isophotes analysis reduces the influence of the used edge map on the results

optimizing schrodinger functionals using sobolev gradients applications to quantum mechanics and nonlinear optics in this paper we study the application of the sobolev gradients technique to the problem of minimizing several schrodinger functionals related to timely and difficult nonlinear problems in quantum mechanics and nonlinear optics we show that these gradients act as preconditioners over traditional choices of descent directions in minimization methods and show a computationally inexpensive way to obtain them using a discrete fourier basis and a fast fourier transform we show that the sobolev preconditioning provides a great convergence improvement over traditional techniques for finding solutions with minimal energy as well as stationary states and suggest a generalization of the method using arbitrary linear operators

matching invariant to translations rotations and scale changes abstract an optimization approach to invariant matching is proposed in this approach an object or a pattern is invariantly represented by an object centred description called an attributed relational structure ars embedding invariant properties and relations between the primitives of the pattern such as line segments and points noise effect is taken into account such that a scene can consist of noisy sub parts of a model the matching is then to find the optimal mapping between the arss of the scene and the model a gain functional is formulated to measure the goodness of fit and is to be maximized by using the relaxation labelling method experiments are shown to illustrate the matching algorithm and to demonstrate that the approach is truly invariant to arbitrary translations rotations and scale changes under noise

stereo correspondence through feature grouping and maximal cliques the authors propose a method for solving the stereo correspondence problem the method consists of extracting local image structures and matching similar such structures between two images linear edge segments are extracted from both the left and right images each segment is characterized by its position and orientation in the image as well as its relationships with the nearby segments a relational graph is thus built from each image for each segment in one image as set of potential assignments is represented as a set of nodes in a correspondence graph arcs in the graph represent compatible assignments established on the basis of segment relationships stereo matching becomes equivalent to searching for sets of mutually compatible nodes in this graph sets are found by looking for maximal cliques the maximal clique best suited to represent a stereo correspondence is selected using a benefit function numerous results obtained with this method are shown

an entropy satisfying boundary layer surface mesh generation a method is presented to generate surface boundary layers the novelty of the method consists in a uniform treatment of the concave and convex regions based on offsetting the initial front in particular concave situations are enforced to respect the entropy satisfying solution local solutions of the offset of edges in the planes and triangles in the three dimensional space are also given showing the relationship between normal computation distance extrusion and the generalized voronoi diagram the boundary layer mesh generation is cast as a weak solution of the eikonal equation computed locally layer by layer to mimic the hyperbolic character of the eikonal equation augmented by a possibly nonbijective mapping between layers this provides a theoretical framework to rely on for practical answers such as configurations where the adjacent topologies to a boundary layer may be curved or at least not aligned with the offset direction or if the boundary layer mesh must be generated as a mapping betw

a fast and robust circle detection method using isosceles triangles sampling circle detection using randomized sampling has been developed in recent years to reduce computational intensity however randomized sampling is sensitive to noise that can lead to reduced accuracy and false positive candidates to improve on the robustness of randomized circle detection under noisy conditions this paper presents a new methodology for circle detection based upon randomized isosceles triangles sampling it is shown that the geometrical property of isosceles triangles provides a robust criterion to find relevant edge pixels which in turn offers an efficient means to estimate the centers and radii of circles for best efficiency the estimated results given by the sampling from individual connected components of the edge map were analyzed using a simple clustering approach to further improve on the accuracy we applied a two step refinement process using chords and linear error compensation with gradient information of the edge pixels extensive experiments using both synthetic and real images have been performed the results are compared to leading state of the art algorithms and it is shown that the proposed methodology has a number of advantages it is efficient in finding circles with a low number of iterations it has high rejection rate of false positive circle candidates and it has high robustness against noise all this makes it adaptive and useful in many vision applications a new circle detection algorithm based on randomized sampling of isosceles triangles its is presented sampling of isosceles triangles provides distinctive probability distribution for circular shapes a low amount of iterations are needed by using a simple clustering approch the proposed algorithm has short execution time high accuracy and high robustness against noise

on the foundations of relaxation labeling processes a large class of problems can be formulated in terms of the assignment of labels to objects frequently processes are needed which reduce ambiguity and noise and select the best label among several possible choices relaxation labeling processes are just such a class of algorithms they are based on the parallel use of local constraints between labels this paper develops a theory to characterize the goal of relaxation labeling the theory is founded on a definition of con sistency in labelings extending the notion of constraint satisfaction in certain restricted circumstances an explicit functional exists that can be maximized to guide the search for consistent labelings this functional is used to derive a new relaxation labeling operator when the restrictions are not satisfied the theory relies on variational cal culus it is shown that the problem of finding consistent labelings is equivalent to solving a variational inequality a procedure nearly identical to the relaxation operator derived under restricted circum stances serves in the more general setting further a local convergence result is established for this operator the standard relaxation labeling formulas are shown to approximate our new operator which leads us to conjecture that successful applications of the standard methods are explainable by the theory developed here observations about con vergence and generalizations to higher order compatibility relations are described

markov random field texture models we consider a texture to be a stochastic possibly periodic two dimensional image field a texture model is a mathematical procedure capable of producing and describing a textured image we explore the use of markov random fields as texture models the binomial model where each point in the texture has a binomial distribution with parameter controlled by its neighbors and number of tries equal to the number of gray levels was taken to be the basic model for the analysis a method of generating samples from the binomial model is given followed by a theoretical and practical analysis of the method s convergence examples show how the parameters of the markov random field control the strength and direction of the clustering in the image the power of the binomial model to produce blurry sharp line like and blob like textures is demonstrated natural texture samples were digitized and their parameters were estimated under the markov random field model a hypothesis test was used for an objective assessment of goodness of fit under the markov random field model overall microtextures fit the model well the estimated parameters of the natural textures were used as input to the generation procedure the synthetic microtextures closely resembled their real counterparts while the regular and inhomogeneous textures did not

voronoi diagram and medial axis algorithm for planar domains with curved boundaries i theoretical foundations in this first installment of a two part paper the underlying theory for an algorithm that computes the voronoi diagram and medial axis of a planar domain bounded by free form polynomial or rational curve segments is presented an incremental approach to computing the voronoi diagram is used wherein a single boundary segment is added to an existing boundary segment set at each step the introduction of each new segment entails modifying the voronoi regions of the existing boundary segments and constructing the voronoi region of the new segment we accomplish this by i computing the bisector of the new segment with each of the current boundary segments ii updating the voronoi regions of the current boundary segments by partitioning them with these bisectors and iii constructing the voronoi region of the new segment as a union of regions obtained from the partitioning in ii when all boundary segments are included and their voronoi regions have been constructed the voronoi diagram of the boundary is obtained as the union of the voronoi polygons for each boundary segment to construct the medial axis of a planar domain we first compute the voronoi diagram of its boundary the medial axis is then obtained from the voronoi diagram by i removing certain edges of the voronoi diagram that do not belong to the medial axis and ii adding certain edges that do belong to the medial axis but are absent from the voronoi diagram unambiguous characterizations for edges in both these categories are given details of algorithms based on this theory are deferred to the second installment of this two part paper

jacobi s last geometric statement extends to a wider class of liouville surfaces numerical evidence is presented which strongly suggests that jacobi s last geometric statement that the conjugate locus from a point has exactly four cusps and the corresponding cut locus consists of only one topological segment holds for compact real analytic liouville surfaces diffeomorphic to s 2 if the gaussian curvature is everywhere positive and has exactly six critical points these being two saddles two global minima and two global maxima as is the case for an ellipsoid our experiments suggest that this is a sufficient rather than a necessary condition furthermore for compact real analytic liouville surfaces diffeomorphic to s 2 upon which the gaussian curvature can be negative but has exactly six critical points these being two saddles two global minima and two global maxima it appears that the cut locus is always a subarc of a line given by x 1 const or x 2 const where x 1 x 2 are canonical coordinates with respect to which the metric has the form f 1 x 1 f 2 x 2 dx 2 1 dx 2 2 in the case of an ellipsoid these curves are lines of curvature

computing the ground state solution of bose einstein condensates by a normalized gradient flow in this paper we present a continuous normalized gradient flow cngf and prove its energy diminishing property which provides a mathematical justification of the imaginary time method used in the physics literature to compute the ground state solution of bose einstein condensates bec we also investigate the energy diminishing property for the discretization of the cngf two numerical methods are proposed for such discretizations one is the backward euler centered finite difference befd method the other is an explicit time splitting sine spectral tssp method energy diminishing for befd and tssp for the linear case and monotonicity for befd for both linear and nonlinear cases are proven comparison between the two methods and existing methods e g crank nicolson finite difference cnfd or forward euler finite difference fefd shows that befd and tssp are much better in terms of preserving the energy diminishing property of the cngf numerical results in one two and three dimensions with magnetic trap confinement potential as well as a potential of a stirrer corresponding to a far blue detuned gaussian laser beam are reported to demonstrate the effectiveness of befd and tssp methods furthermore we observe that the cngf and its befd discretization can also be applied directly to compute the first excited state solution in bec when the initial data is chosen as an odd function

relative sensitivity of a family of closet point graphs in computer vision applications abstract various graph theoretic definitions of neighborhood have been used in the past in computer vision and clustering applications in this paper we study the properties of a set of four related closest point graphs using monte carlo methods i the delaunay triangulation dt and its dual voronoi tessellation ii the gabriel graph gg iii the relative neighborhood graph rng and iv the minimum spanning tree mst we examine the suitability of these graphs in the detection of structure in noisy images using the hough transform we also explore each graph s structural stability under random positional noise delaunay triangulation is shown to be the least sensitive to such noisy conditions

symbol recognition by error tolerant subgraph matching between region adjacency graphs we propose an error tolerant subgraph isomorphism algorithm formulated in terms of region adjacency graphs rag a set of edit operations to transform one rag into another one are defined as regions are represented by polylines and string matching techniques are used to measure their similarity the algorithm follows a branch and bound approach driven by the rag edit operations this formulation allows matching computing under distorted inputs and also reaching a solution in a near polynomial time the algorithm has been used for recognizing symbols in hand drawn diagrams

labeled point pattern matching by delaunay triangulation and maximal cliques abstract in many problems of pattern recognition objects in an image may be efficiently represented by a set of labeled points this paper describes a method for matching labeled point patterns with one of the prototypes the delaunay triangulation is used to partition a point pattern into a set of triangles and the largest maximal clique of the consistency graph for each triangle is used to obtain the largest set of mutually consistent point pairs the proposed method is invariant under affine transformation of point patterns and allows for additions and deletions of points and some random perturbations in their relative locations the method is applied to the matching of constellations

representing stereo data with the delaunay triangulation abstract this article proposes a coherent way of interpolating three dimensional data obtained by stereo for example with a simplicial polyhedral surface the proposed method is based on the use of the constrained delaunay triangulation the polyhedral surface is obtained by using a simple visibility property to mark tetrahedra likely to be empty the method is intrinsically discontinuity preserving works for multiple viewpoints and yields both a surface representation of objects and a volume representation of free space which may be useful in robotics algorithms to implement the method are described and their complexity analyzed in the worst case and average case situations where tools of probabilistic geometry are used

computational geometry an introduction from the reviews this book offers a coherent treatment at the graduate textbook level of the field that has come to be known in the last decade or so as computational geometry the book is well organized and lucidly written a timely contribution by two founders of the field it clearly demonstrates that computational geometry in the plane is now a fairly well understood branch of computer science and mathematics it also points the way to the solution of the more challenging problems in dimensions higher than two

a flexible content adaptive mesh generation strategy for image representation based on the greedy point removal gpr scheme of demaret and iske a simple yet highly effective framework for constructing triangle mesh representations of images called gprfs is proposed by using this framework and ideas from the error diffusion ed scheme for mesh generation of yang a highly effective mesh generation method called gprfs ed is derived and presented since the ed scheme plays a crucial role in our work factors affecting the performance of this scheme are also studied in detail through experimental results our gprfs ed method is shown to be capable of generating meshes of quality comparable to and in many cases better than the state of the art gpr scheme while requiring substantially less computation and memory furthermore with our gprfs ed method one can easily trade off between mesh quality and computational memory complexity a reduced complexity version of the gprfs ed method called gprfs med is also introduced to further demonstrate the computational memory complexity scalability of our gprfs ed method

inexact graph matching for model based recognition evaluation and comparison of optimization algorithms a method for segmentation and recognition of image structures based on graph homomorphisms is presented in this paper it is a model based recognition method where the input image is over segmented and the obtained regions are represented by an attributed relational graph arg this graph is then matched against a model graph thus accomplishing the model based recognition task this type of problem calls for inexact graph matching through a homomorphism between the graphs since no bijective correspondence can be expected because of the over segmentation of the image with respect to the model the search for the best homomorphism is carried out by optimizing an objective function based on similarities between object and relational attributes defined on the graphs the following optimization procedures are compared and discussed deterministic tree search for which new algorithms are detailed genetic algorithms and estimation of distribution algorithms in order to assess the performance of these algorithms using real data experimental results on supervised classification of facial features using face images from public databases are presented

efficient sampling strategy and refinement strategy for randomized circle detection circle detection is fundamental in pattern recognition and computer vision the randomized approach has received much attention for its computational benefit when compared with the hough transform in this paper a multiple evidence based sampling strategy is proposed to speed up the randomized approach next an efficient refinement strategy is proposed to improve the accuracy based on different kinds of ten test images experimental results demonstrate the computation saving and accuracy effects when plugging the proposed strategies into three existing circle detection methods

gradient match and side match fractal vector quantizers for images in this paper we propose gradient match fractal vector quantizers gmfvqs and side match fractal vector quantizers smfvqs which are two classes of finite state fractal vector quantizers fsfvqs for the image coding framework in our previous work we proposed the noniterative fractal block coding fbc technique to improve the decoding speed and the coding performance for conventional fbc techniques to reduce the number of bits for denoting the fractal code of the range block the concepts of the gradient match vector quantizers gmvqs and the side match vector quantizers smvqs are employed to the noniterative fbc technique unlike ordinary vector quantizers the super codebooks in the proposed gmfvqs and smfvqs are generated from the affine transformed domain blocks in the noniterative fbc technique the codewords in the state codebook are dynamically extracted from the super codebook with the side match and gradient match criteria the redundancy in the affine transformed domain blocks is greatly reduced and the compression ratio can be significantly increased our simulation results show that 15 20 of the bit rates in the noniterative fbc technique are saved by using the proposed gmfvqs

a metric for comparing relational descriptions relational models are frequently used in high level computer vision finding a correspondence between a relational model and an image description is an important operation in the analysis of scenes in this paper the process of finding the correspondence is formalized by defining a general relational distance measure that computes a numeric distance between any two relational descriptions a model and an image description two models or two image descriptions the distance measure is proved to be a metric and is illustrated with examples of distance between object models a variant measure used in our past studies is shown not to be a metric

text region extraction in a document image based on the delaunay tessellation in this paper delaunay triangulation is applied for the extraction of text areas in a document image by representing the location of connected components in a document image with their centroids the page structure is described as a set of points in two dimensional space when imposing delaunay triangulation on these points the text regions in the delaunay triangulation will have distinguishing triangular features from image and drawing regions for analysis the delaunay triangles are divided into four classes the study reveals that specific triangles in text areas can be clustered together and identified as text body using this method text regions in a document image containing fragments can also be recognized accurately experiments show the method is also very efficient

voronoi diagram and medial axis algorithm for planar domains with curved boundaries ii detailed algorithm description abstract details of algorithms to construct the voronoi diagrams and medial axes of planars domain bounded by free form polynomial or rational curve segments are presented based on theoretical foundations given in the first installment ramamurthy and farouki j comput appl math 1999 102 119 141 of this two part paper in particular we focus on key topological and computational issues that arise in these constructions the topological issues include i the data structures needed to represent various geometrical entities bisectors voronoi regions etc and ii the boolean operations i e union intersection and difference on planar sets required by the algorithm specifically representations for the voronoi polygons of boundary segments and for individual voronoi diagram or medial axis edges are proposed since these edges may be segments of a nonrational algebraic curves curve curve bisectors b rational curves point curve bisectors or c straight lines point point bisectors data structures tailored to each of these geometrical entities are introduced the computational issues addressed include the curve intersection algorithms required in the boolean operations and iterative schemes used to precisely locate bifurcation or n prong points n 3 of the voronoi diagram and medial axis a selection of computed voronoi diagram and medial axis examples is included to illustrate the capabilities of the algorithm

content adaptive mesh representation of images using binary space partitions the interest in content adaptive mesh generation of images has been arising lately due to its wide area of applications in image processing the major issue is to represent an image with a low number of pixels while preserving its content these pixels or the nonuniform samples are then used to generate a mesh that approximates the corresponding image this work presents a novel method based on binary space partitions in combination with three clustering schemes to approximate an image with a mesh the algorithm has the ability to simultaneously reduce the number of pixels and generate the mesh approximation the idea is to assume each triangle of the mesh as a plane consequently it will be possible to reconstruct the inlying pixels with planar equations defined from the three nodes of each triangle if a triangle s equation does not have the ability to reconstruct the pixels lying within up to a predefined error it is split into two new triangles tested on several real images the proposed method leads to reduced size meshes in a fast manner while retaining the visual quality of the reconstructed images in addition it is parallelizable due to the property of binary space partitions which facilitates its application in real time scenarios

parallel and deterministic algorithms from mrfs surface reconstruction deterministic approximations to markov random field mrf models are derived one of the models is shown to give in a natural way the graduated nonconvexity gnc algorithm proposed by a blake and a zisserman 1987 this model can be applied to smooth a field preserving its discontinuities a class of more complex models is then proposed in order to deal with a variety of vision problems all the theoretical results are obtained in the framework of statistical mechanics and mean field techniques a parallel iterative algorithm to solve the deterministic equations of the two models is presented together with some experiments on synthetic and real images

inexact graph matching using genetic search this paper describes a framework for performing relational graph matching using genetic search there are three novel ingredients to the work firstly we cast the optimisation process into a bayesian framework by exploiting the recently reported global consistency measure of wilson and hancock as a fitness measure the second novel idea is to realise the crossover process at the level of subgraphs rather than employing string based or random crossover finally we accelerate convergence by employing a deterministic hill climbing process prior to selection since we adopt the bayesian consistency measure as a fitness function the basic measure of relational distance underpinning the technique is hamming distance our standpoint is that genetic search provides a more attractive means of performing stochastic discrete optimisation on the global consistency measure than alternatives such as simulated annealing moreover the action of the optimisation process is easily understood in terms of its action in the hamming distance domain we demonstrate empirically not only that the method possesses polynomial convergence time but also that the convergence rate is more rapid than simulated annealing we provide some experimental evaluation of the method in the matching of aerial stereograms and evaluate its sensitivity on synthetically generated graphs

texture classification using spectral histograms based on a local spatial frequency representation we employ a spectral histogram as a feature statistic for texture classification the spectral histogram consists of marginal distributions of responses of a bank of filters and encodes implicitly the local structure of images through the filtering stage and the global appearance through the histogram stage the distance between two spectral histograms is measured using spl chi sup 2 statistic the spectral histogram with the associated distance measure exhibits several properties that are necessary for texture classification a filter selection algorithm is proposed to maximize classification performance of a given dataset our classification experiments using natural texture images reveal that the spectral histogram representation provides a robust feature statistic for textures and generalizes well comparisons show that our method produces a marked improvement in classification performance finally we point out the relationships between existing texture features and the spectral histogram suggesting that the latter may provide a unified texture feature

estimation and choice of neighbors in spatial interaction models of images some aspects of statistical inference for a class of spatial interaction models for finite images are presented primarily the simultaneous autoregressive sar models and conditional markov cm models each of these models is characterized by a set of neighbors a set of coefficients and a noise sequence of specified characteristics we are concerned with two problems the estimation of the unknown parameters in both sar and cm models and the choice of an appropriate model from a class of such competing models assuming gaussian distributed variables we discuss maximum likelihood ml estimation methods in general the ml scheme leads to nonlinear optimization problems to avoid excessive computation an iterative scheme is given for sar models which gives approximate ml estimates in the gaussian case and reasonably good estimates in some non gaussian situations as well likewise for cm models an easily computable consistent estimate is given the asymptotic mean squared error mse of this estimate for a four neighbor cm model is shown tn be substantially less than the mse of the popular coding estimate asymptotically consistent decision rules are given for choosing an appropriate sar or cm model the usefulness of the estimation scheme and the decision rule for the choice of neighbors is illustrated by using synthetic patterns synthetic patterns obeying known sar and cm models are generated and the models corresponding to true and several competing neighbor sets are fitted the estimation scheme yields estimates close to the parameters of the true models and the decision rule for the choice of neighbors picks up the true model from the class of competing models

a transform for multiscale image segmentation by integrated edge and region detection describes a transform to extract image regions at all geometric and photometric scales it is argued that linear approaches have the shortcoming that they require a priori models of region shape the proposed transform avoids this by letting the structure emerge bottom up from interactions among pixels the transform involves global computations on pairs of pixels followed by vector integration of the results an attraction force field is computed over the image in which pixels belonging to the same region are mutually attracted and the region is characterized by a convergent flow it is shown that the transform possesses properties that allow multiscale segmentation or extraction of original unblurred structure at all different geometric and photometric scales present this is in contrast with much previous work wherein multiscale structure is viewed as the smoothed structure in a multiscale signal decimation scale is an integral parameter of the force computation and the number and values of scale parameters associated with the image can be estimated automatically regions are detected at all a priori unknown scales resulting in automatic construction of a segmentation tree in which each pixel is annotated with descriptions of all the regions it belongs to transform properties are presented for piecewise constant images but hold for more general ones thus the proposed method is intended as a solution to the problem of multiscale integrated edge and region detection or low level image segmentation experimental results are given

an energy function and continuous edit process for graph matching the contributions of this article are twofold first we develop a new nonquadratic energy function for graph matching the starting point is a recently reported mixture model that gauges relational consistency using a series of exponential functions of the hamming distances between graph neighborhoods we compute the effective neighborhood potentials associated with the mixture model by identifying the single probability function of zero kullback divergence this new energy function is simply a weighted sum of graph hamming distances the second contribution is to locate matches by graduated assignment rather than solving the meanfield saddle point equations which are intractable for our nonquadratic energy function we apply the soft assign ansatz to the derivatives of our energy function here we introduce a novel departure from the standard graduated assignment formulation of graph matching by allowing the connection strengths of the data graph to update themselves the aim is to provide a means by

fuzzy morphisms between graphs a generic definition of fuzzy morphism between graphs gfm is introduced that includes classical graph related problem definitions as sub cases such as graph and subgraph isomorphism the gfm uses a pair of fuzzy relations one on the vertices and one on the edges each relation is a mapping between the elements of two graphs these two fuzzy relations are linked with constraints derived from the graph structure and the notion of association graph the theory extends the properties of fuzzy relation to the problem of generic graph correspondence we introduce two complementary interpretations of gfm from which we derive several interesting properties the first interpretation is the generalization of the notion of association compatibility the second is the new notion of edge morphism one immediate application is the introduction of several composition laws each property has a theoretical and a practical interpretation in the problem of graph correspondence that is explained throughout the paper special attention is paid to the formulation of a non algorithmical theory in order to propose a first step towards a unified theoretic framework for graph morphisms

evaluating the boundary and covering degree of planar minkowski sums and other geometrical convolutions algorithms are developed based on topological principles to evaluate the boundary and internal structure of the minkowski sum of two planar curves a graph isotopic to the envelope curve is constructed by computing its characteristic points the edges of this graph are in one to one correspondence with a set of monotone envelope segments a simple formula allows a degree to be assigned to each face defined by the graph indicating the number of times its points are covered by the minkowski sum the boundary can then be identified with the set of edges that separate faces of zero and non zero degree and the boundary segments corresponding to these edges can be approximated to any desired geometrical accuracy for applications that require only the minkowski sum boundary the algorithm minimizes geometrical computations on the internal envelope edges that do not contribute to the final boundary in other applications this internal structure is of interest and the algorithm provides comprehensive information on the covering degree for different regions within the minkowski sum extensions of the algorithm to the computation of minkowski sums in r 3 and other forms of geometrical convolution are briefly discussed

a generalized petviashvili iteration method for scalar and vector hamiltonian equations with arbitrary form of nonlinearity the petviashvili s iteration method has been known as a rapidly converging numerical algorithm for obtaining fundamental solitary wave solutions of stationary scalar nonlinear wave equations with power law nonlinearity mu up 0 where m is a positive definite self adjoint operator and p const in this paper we propose a systematic generalization of this method to both scalar and vector hamiltonian equations with arbitrary form of nonlinearity and potential functions for scalar equations our generalized method requires only slightly more computational effort than the original petviashvili method