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

dealing with segmentation errors in region based stereo matching abstract graph based matching methods have been widely used in the areas of object recognition and stereo correspondence in this paper an algorithm to deal with segmentation errors in region based matching is proposed which consists of a preprocessing stage to the classical graph based matching algorithm some regions are merged and included in the matching process in order to avoid the differences in segmentation the selection of an appropriate similarity criterion to create the initial nodes in the graph and the use of approximative algorithms to find maximal cliques are important issues in order to reduce the computational burden the experimental results show that the method is robust enough in the presence of noise

rates of approximation for general sampling type operators in the setting of filter convergence we investigate the order of approximation of a real valued function f by means of suitable families of sampling type operators which include both discrete and integral ones we give a unified approach by means of which it is possible to consider several kinds of classical operators for instance urysohn integral operators in particular mellin type convolution integrals and generalized sampling series we deal with filter convergence obtaining proper extensions of classical results

relaxation labeling in stereo image matching this paper outlines a method for solving the global stereovision matching problem using edge segments as the primitives a relaxation scheme is the technique commonly used by existing methods to solve this problem these techniques generally impose the following competing constraints similarity smoothness ordering and uniqueness and assume a bound on the disparity range the smoothness constraint is basic in the relaxation process we have verified that the smoothness and ordering constraints can be violated by objects close to the cameras and that the setting of the disparity limit is a serious problem this problem also arises when repetitive structures appear in the scene i e complex images where the existing methods produce a high number of failures we develop our approach from a relaxation labeling method 1 w j christmas j kittler m petrou structural matching in computer vision using probabilistic relaxation ieee trans pattern anal mach intell 17 8 1995 749 764 which allows us to map the above constraints the main contribution is made 1 by applying a learning strategy in the similarity constraint and 2 by introducing specific conditions to overcome the violation of the smoothness constraint and to avoid the serious problem produced by the required fixation of a disparity limit consequently we improve the stereovision matching process a better performance of the proposed method is illustrated by comparative analysis against some recent global matching methods

on the generalized navier stokes equations in this paper we present a general model of the classical navier stokes equations with the help of laplace fourier sine transforms finite fourier sine transforms and finite hankel transforms an exact solutions for three different special cases have been obtained

relaxation by hopfield network in stereo image matching abstract this paper outlines a relaxation approach using the hopfield neural network for solving the global stereovision matching problem the primitives used are edge segments the similarity smoothness and uniqueness constraints are transformed into the form of an energy function whose minimum value corresponds to the best solution of the problem we combine two methods a optimization relaxation 1 and b relaxation merit 2 with the above three constraints mapped in an energy function the main contribution is made 1 by applying a learning strategy in the similarity constraint and 2 by introducing specific conditions to overcome the violation of the smoothness constraint and to avoid the serious problem arising from the required fixation of a disparity limit so we improve the stereovision matching process a better performance of the proposed method is illustrated with a comparative analysis against a classical relaxation method

a new non standard finite difference method for analyzing the fractional navier stokes equations abstract in this paper the numerical solution of the fractional navier stokes equations fnse is derived by means of a new non standard finite difference method nsfdm the fractional differential operators are taken in sense of the riesz fractional derivative the pressure driven by the flow between two parallel plates is solved with the nsfdm and a modified trapezoidal quadrature rule of fractional order the stability and convergence of the proposed scheme are proved numerical examples illustrate the effectiveness of the proposed method

on the time fractional navier stokes equations abstract this paper is concerned with the navier stokes equations with time fractional derivative of order 0 1 this type of equations can be used to simulate anomalous diffusion in fractal media we establish the existence and uniqueness of local and global mild solutions in h q meanwhile we also give local mild solutions in j q moreover we prove the existence and regularity of classical solutions for such equations in j q

analysis of quantization error in line based stereo matching abstract quantization error generated by the quantization process of an image is inherent in computer vision because especially in stereo vision the quantization error in 2d digital images results in position errors in a reconstructed 3d scene it is necessary to analyze stochastically quantization error in stereo vision in this paper an analysis of the probability density function pdf of quantization error in line based stereo matching is presented it is shown that the theoretical pdfs of quantization errors of the reconstructed 3d point positions in line based stereo matching show general forms compared to those of the conventional error analysis in pixel based stereo matching computer simulations are observed to support the theoretical pdfs

analysis of an axis symmetric fractional diffusion wave problem this paper presents an axis symmetric fractional diffusion wave problem which is considered in polar coordinates the dynamic characteristics of the system are described with a partial fractional differential equation in terms of the riemann liouville fractional derivative this continuum problem is reduced to a countable infinite problem by using the method of separation of variables in this way the closed form solution of the problem is obtained the grunwald letnikov approach is applied to take a numerical evaluation the compatibility and effectiveness of this approach are realized by some simulation results which are obtained by a matlab program it can be seen that the analytical and numerical solutions overlap

on a family of halley like methods to find simple roots of nonlinear equations there are many methods for solving a nonlinear algebraic equation here we introduce a family of halley like methods and show that euler chebyshev and bsc are just members of the family we discuss the conjugacy maps and the effect of the extraneous roots on the basins of attraction

mild solutions to the time fractional navier stokes equations in r n abstract this paper addresses the existence and uniqueness of mild solutions to the navier stokes equations with time fractional differential operator of order 0 1 several interesting properties about the solution are also highlighted like regularity and decay rate in lebesgue spaces which will depend on the fractional exponent moreover it is shown that the l p exponent range which the solution belongs to is different from the range for the solution of the classical problem with 1

a voronovskaya type theorem for poisson cauchy type singular operators abstract in this article we continue with the study of approximation properties of smooth poisson cauchy type singular integral operators over the real line we produce voronovskaya type results and give some quantitative results regarding the rate of convergence of these singular integral operators

fuzzy cognitive maps for stereovision matching this paper outlines a method for solving the stereovision matching problem using edge segments as the primitives in stereovision matching the following constraints are commonly used epipolar similarity smoothness ordering and uniqueness we propose a new matching strategy under a fuzzy context in which such constraints are mapped the fuzzy context integrates both fuzzy clustering and fuzzy cognitive maps with such purpose a network of concepts nodes is designed each concept represents a pair of primitives to be matched each concept has associated a fuzzy value which determines the degree of the correspondence the goal is to achieve high performance in terms of correct matches the main findings of this paper are reflected in the use of the fuzzy context that allows building the network of concepts where the matching constraints are mapped initially each concept value is loaded via the fuzzy clustering and then updated by the fuzzy cognitive maps framework this updating is achieved through the influence of the remainder neighboring concepts until a good global matching solution is achieved under this fuzzy approach we gain quantitative and qualitative matching correspondences this method works as a relaxation matching approach and its performance is illustrated by comparative analysis against some existing global matching methods

global smoothness and uniform convergence of smooth poisson cauchy type singular operators in this article we introduce the smooth poisson cauchy type singular integral operators over the real line here we study their simultaneous global smoothness preservation property with respect to the l p norm 1

robust contour decomposition using a constant curvature criterion the problem of decomposing an extended boundary or contour into simple primitives is addressed with particular emphasis on laplacian of gaussian zero crossing contours a technique is introduced for partitioning such contours into constant curvature segments a nonlinear blip filter matched to the impairment signature of the curvature computation process an overlapped voting scheme and a sequential contiguous segment extraction mechanism are used this technique is insensitive to reasonable changes in algorithm parameters and robust to noise and minor viewpoint induced distortions in the contour shape such as those encountered between stereo image pairs the results vary smoothly with the data and local perturbations induce only local changes in the result robustness and insensitivity are experimentally verified

existence of global weak solutions for 3d degenerate compressible navier stokes equations in this paper we prove the existence of global weak solutions for 3d compressible navier stokes equations with degenerate viscosity the method is based on the bresch and desjardins commun math phys 238 211 223 2003 entropy conservation the main contribution of this paper is to derive the mellet and vasseur commun partial differ equ 32 431 452 2007 type inequality for weak solutions even if it is not verified by the first level of approximation this provides existence of global solutions in time for the compressible barotropic navier stokes equations the result holds for any gamma 1 in two dimensional space and for 1 gamma 3 in three dimensional space in both case with large initial data possibly vanishing on the vacuum this solves an open problem proposed by lions mathematical topics in fluid mechanics vol 2 compressible models 1998

detection of intensity changes with subpixel accuracy using laplacian gaussian masks we present a system that takes a gray level image as input locates edges with subpixel accuracy and links them into lines edges are detected by finding zero crossings in the convolution of the image with laplacian of gaussian log masks the implementation differs markedly from m i t s as we decompose our masks exactly into a sum of two separable filters instead of the usual approximation by a difference of two gaussians dog subpixel accuracy is obtained through the use of the facet model 1 we also note that the zero crossings obtained from the full resolution image using a space constant for the gaussian and those obtained from the 1 n resolution image with 1 n pixel accuracy and a space constant of n for the gaussian are very similar but the processing times are very different finally these edges are grouped into lines using the technique described in 2

on shinbrot s conjecture for the navier stokes equations marvin shinbrot conjectured that the weak solution of the navier stokes equations possess fractional derivatives in time of any order less than textstyle frac 1 2 in this paper using the hardy littlewood maximal theorem we prove that the conjecture is true in the two dimensional case and it is true conditionally in the three dimensional case

relaxation matching techniques a comparison many different relaxation schemes have been proposed for image analysis tasks we have developed a general matching procedure for comparing semantic network descriptions of images and we have implemented a variety of relaxation techniques an automatic segmentation and description system is used to produce the image representations so that the matching procedures must cope with variations in feature values missing objects and possible multiple matches this environment is used to test different relaxation matching schemes under a variety of conditions the best performance of those we compared in terms of the number of iterations and the number of errors is for the gradient based optimization approach of faugeras and price the related optimization approach of hummel and zucker performed almost as well with differences primarily in difficult matches i e where much of the evidence is against the match for instance poor segmentations the product combination rule proposed by peleg was extremely fast indeed too fast to work when global context is needed the classical rosenfeld hummel and zucker method is included for historical comparisons and performed only adequately producing fewer correct matches and taking more iterations

a stereo vision technique using curve segments and relaxation matching a multichannel feature based stereo vision technique where curve segments are used as feature primitives in the matching process is described the left image and the right image are filtered by using several laplacian of gaussian operators of different widths channels curve segments are extracted by a tracking algorithm and their centroids are obtained at each channel the generalized hough transform of each curve segment in the left and the right image is evaluated the epipolar constraint on the centroids of the curve segment and the channel size is used to limit the searching space in the right image to resolve the ambiguity of the false targets multiple matches a relaxation technique is used where the initial scores of the node assignments are updated by the compatibility measures between the centroids of the curve segments the node assignments with the highest score are chosen as the matching curve segments

analytical solution of a time fractional navier stokes equation by adomian decomposition method abstract the aim of the present analysis is to apply adomian decomposition method for the solution of a time fractional navier stokes equation in a tube by using an initial value the explicit solution of the equation has been presented in the closed form and then its numerical solution has been represented graphically the present method performs extremely well in terms of efficiency and simplicity

a new learning strategy for stereo matching derived from a fuzzy clustering method this paper presents an approach to the local stereo correspondence problem the primitives or features used are groups of collinear connected edge points called segments each segment has several associated attributes or properties we have verified that the differences of the attributes for the true matches cluster in a cloud around a center then for each current pair of primitives we compute a distance between the difference of its attributes and the cluster center the correspondence is established in the basis of the minimum distance criterion similarity constraint we have designed an image understanding system to learn the best representative cluster center for such purpose a new learning method is derived from the fuzzy c means fcm algorithm where the dispersion of the true samples in the cluster is taken into account through the mahalanobis distance this is the main contribution of this paper a better performance of the proposed local stereo matching learning method is illustrated with a comparative analysis between classical local methods without learning

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

on voronovskaja formula for linear combinations of mellin gauss weierstrass operators abstract here we give a voronovskaja formula of high order for linear combinations of the convolution operators g w r f s 0 j 1 r j k jw t f st dt t where k w is the mellin gauss weierstrass kernel this kind of operator provides a better order of pointwise approximation and leads to asymptotic formulae of type lim w w g w r f s f s a f where r n and a f is a differential operator containing the derivatives of f up to order

hybrid stereo matching with a new relaxation scheme of preserving disparity discontinuity abstract a hybrid stereo matching algorithm using a combined edge and region based method is proposed to take the advantage of each technique i e an exactly matched point and a full resolution disparity map region based matching is typically more efficient than edge based matching however a region based matcher lacks the capability of generating an accurate fine resolution disparity map the generation of such a map can be better accomplished by using edge based techniques accordingly regions and edges both play important and complimentary roles in a binocular stereo process since it is crucial that an efficient and robust stereo system utilizes the most appropriate set of primitives a nonlinear laplacian filter is modified to extract proper primitives since each pixel value of a second order differentiated image includes important information for the intensity profile information such as edge signed and zero pixels obtained by the modified nonlinear laplacian filter is used to determine the matching strategy consequently the proposed matching algorithm consists of edge signed and zero or residual pixel matching different matching strategies are adopted in each matching step adaptive windows with variable sizes and shapes are also used to consider the local information of the pixels in addition a new relaxation scheme based on the statistical distribution of matched errors and constraint functions which contain disparity smoothness uniqueness and discontinuity preservation is proposed to efficiently reduce mismatched points in unfavorable conditions unlike conventional relaxation schemes the erosion in an abrupt area of a disparity map is considerably reduced because a discontinuity preservation factor based on a survival possibility function is added to the proposed relaxation the relaxation scheme can be applied to various methods such as block feature region object based matching methods and so on by modifying the excitatory set of the smoothness constraint function experimental results show that the proposed matching algorithm is effective for various images even if the image has a high content of noise and repeated patterns the convergence rate of the relaxation and the output quality are both improved

a multi domain spectral method for time fractional differential equations this paper proposes an approach for high order time integration within a multi domain setting for time fractional differential equations since the kernel is singular or nearly singular two main difficulties arise after the domain decomposition how to properly account for the history memory part and how to perform the integration accurately to address these issues we propose a novel hybrid approach for the numerical integration based on the combination of three term recurrence relations of jacobi polynomials and high order gauss quadrature the different approximations used in the hybrid approach are justified theoretically and through numerical examples based on this we propose a new multi domain spectral method for high order accurate time integrations and study its stability properties by identifying the method as a generalized linear method numerical experiments confirm hp convergence for both time fractional differential equations and time fractional partial differential equations

the stability problem for fuzzy bidirectional associative memories abstract the fuzzy bidirectional associative memories fbams are studied in this paper it is shown that any fbam based on the s t composition is globally stable if both s and t are triangular norms or triangular conorms when t is an upper semicontinuous triangular norm some necessary and sufficient conditions are established in such a way that the fbams based on the max t composition are globally stable and the stable states and the equilibria of the fbams were studied when t is a continuous triangular norm it is proved that the sequence of reverberation states of the learning fbam is nonincreasing

finding point correspondences using simulated annealing abstract identifying corresponding points between two recordings of a point set has always been an important problem in stereo vision applications we describe this matching problem in terms of cost minimization and present an algorithm to approach the minimal cost mapping using simulated annealing the algorithm calculates the costs to match all possible point pairs and tries to minimize the sum of the costs of all matched points starting from an initial mapping it uses a random rearrangement scheme to alter the mapping towards the optimal minimal cost mapping

stochastic stereo matching over scale a stochastic optimization approach to stereo matching is presented unlike conventional correlation matching and feature matching the method provides a dense array of disparities eliminating the need for interpolation first the stereo matching problem is defined in terms of finding a disparity map that satisfies two competing constraints 1 matched points should have similar image intensity and 2 the disparity map should vary as slowly as possible these constraints are interpreted as specifying the potential energy of a system of oscillators ground states are approximated by a new variant of simulated annealing which has two important features first the microcanonical ensemble is simulated using a new algorithm that is more efficient and more easily implemented than the familiar metropolis algorithm which simulates the canonical ensemble secondly it uses a hierarchical coarse to fine control structure employing gaussian or laplacian pyramids of the stereo images in this way quickly computed results at low resolutions are used to initialize the system at higher resolutions

local in space estimates near initial time for weak solutions of the navier stokes equations and forward self similar solutions we show that the classical cauchy problem for the incompressible 3d navier stokes equations with 1 homogeneous initial data has a global scale invariant solution which is smooth for positive times our main technical tools are local in space regularity estimates near the initial time which are of independent interest

structural matching in computer vision using probabilistic relaxation in this paper we develop the theory of probabilistic relaxation for matching features extracted from 2d images derive as limiting cases the various heuristic formulae used by researchers in matching problems and state the conditions under which they apply we successfully apply our theory to the problem of matching and recognizing aerial road network images based on road network models and to the problem of edge matching in a stereo pair for this purpose each line network is represented by an attributed relational graph where each node is a straight line segment characterized by certain attributes and related with every other node via a set of binary relations

fractional variational calculus in terms of riesz fractional derivatives this paper presents extensions of traditional calculus of variations for systems containing riesz fractional derivatives rfds specifically we present generalized euler lagrange equations and the transversality conditions for fractional variational problems fvps defined in terms of rfds we consider two problems a simple fvp and an fvp of lagrange results of the first problem are extended to problems containing multiple fractional derivatives functions and parameters and to unspecified boundary conditions for the second problem we present lagrange type multiplier rules for both problems we develop the euler lagrange type necessary conditions which must be satisfied for the given functional to be extremum problems are considered to demonstrate applications of the formulations explicitly we introduce fractional momenta fractional hamiltonian fractional hamilton equations of motion fractional field theory and fractional optimal control the formulations presented and the resulting equations are similar to the formulations for fvps given in agrawal 2002 j math anal appl 272 368 2006 j phys a math gen 39 10375 and to those that appear in the field of classical calculus of variations these formulations are simple and can be extended to other problems in the field of fractional calculus of variations

analytical study on the fractional anomalous diffusion in a half plane in this study anomalous diffusion in a half plane with a constant source and a perfect sink at each half of the boundary is considered the discontinuity of the boundary condition is erased by decomposing the solution into two parts a symmetric part and an antisymmetric part the symmetric part which has been studied extensively can be solved by an integral transform method green s function method or others to obtain the solution of the antisymmetric part a separable similarity solution is assumed and the erdelyi kober type fractional derivative is used by doing so the partial differential equation reduces to an ordinary one using the mellin transform method the solution of the antisymmetric part in terms of a fox h function is obtained some figures are given to show the characters of the diffusion process and the influences of different orders of fractional derivatives

weak solutions of the time fractional navier stokes equations and optimal control abstract in this paper we deal with the navier stokes equations with the time fractional derivative of order 0 1 which can be used to simulate anomalous diffusion in fractal media we firstly give the concept of the weak solutions and establish the existence criterion of weak solutions by means of galerkin approximations in the case that the dimension n 4 moreover a complete proof of the uniqueness is given when n 2 at last we give a sufficient condition of optimal control pairs

iterative relaxational stereo matching based on adaptive support between disparities abstract an adaptive relaxation method for stereo matching using matching probability and compatibility coefficients between disparities is presented relaxation labeling is an iterative procedure which reduces local ambiguity and noise and selects the best label among several possible choices using compatibility coefficient stereo matching can be considered as labeling problem which assigns unique matches to feature points in the image the compatibility coefficient between disparity classes is determined from highly reliable matches in the initial matching result and quantitatively expressed the matching results of neighbor pixels support the center pixel through compatibility coefficients and update its matching probability as the true matching results are propagated so false matches are corrected and have high probability values the conventional matching algorithms permit a uniform support from different disparity regions and it causes the degradation phenomena on the discontinuities of object the results of experiments show that the proposed adaptive supporting method reduces the degradations and obtains fast convergence

new measurements and corner guidance for curve matching with probabilistic relaxation reliable curve matching is a difficult yet important problem in many vision based applications including image based modeling we describe in this paper two aspects of our research in this area a new algorithm for curve matching including lines within a probabilistic relaxation framework and an approach of incorporating previously matched points corners to guide curve matching we propose similarity invariant unary and binary measurements suitable for curves and introduce an additional measurement to model the uncertainty of the binary measurements the uncertainty measure is proven to be very important in computing the matching support from neighboring matches we also show how to use a set of previously matched points corners to guide the curve matching the role of the corner guidance is explicitly modeled by a set of unary measurements and a similarity function under the same relaxation framework preprocessing techniques contributing to the success of our curve matching techniques are also developed and discussed experiments with complex real scenes show that the rate of correct matching is higher than 98

prediction by samples from the past with error estimates covering discontinuous signals there are several reasons why the classical sampling theorem is rather impractical for real life signal processing first the sinc kernel is not very suitable for fast and efficient computation it decays much too slowly second in practice only a finite number n of sampled values are available so that the representation of a signal f by the finite sum would entail a truncation error which decreases rather slowly for n due to the first drawback third band limitation is a definite restriction due to the nonconformity of band and time limited signals further the samples needed extend from the entire past to the full future relative to some time t t0 this paper presents an approach to overcome these difficulties the sinc function is replaced by certain simple linear combinations of shifted b splines only a finite number of samples from the past need be available this deterministic approach can be used to process arbitrary not necessarily bandlimited nor differentiable signals and even not necessarily continuous signals best possible error estimates in terms of an lp average modulus of smoothness are presented several typical examples exhibiting the various problems involved are worked out in detail

global smoothness and uniform convergence of smooth picard singular operators in this article we continue with the study of smooth picard singular integral operators over the real line regarding their simultaneous global smoothness preservation property with respect to the l p norm 1 p by involving higher order moduli of smoothness also we study their simultaneous approximation to the unit operator with rates involving the modulus of continuity with respect to the uniform norm the produced jackson type inequalities are almost sharp containing elegant constants and they reflect the high order of differentiability of the engaged function