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

inequality systems and minimax theorems abstract this paper is a comprehensive study of the results about the consistency of inequality systems the minimax theorems are the main tools used in proceeding to this survey most of the known results are quoted and some of them are weakened or generalized to infinite dimensional spaces applications to programming are given

domain decomposition algorithms for mixed methods for second order elliptic problems domain decomposition algorithms for mixed finite element methods for linear second order elliptic problems in r 2 and r 3 are developed a convergence theory for two level and multilevel schwarz methods applied to the algorithms under consideration is given it is shown that the condition number of these iterative methods is bounded uniformly from above in the same manner as in the theory of domain decomposition methods for conforming and nonconforming finite element methods for the same differential problems numerical experiments are presented to illustrate the present techniques

multigrid method and multilevel additive preconditioner for mixed element method for non self adjoint and indefinite problems in this paper a v cycle multigrid method is proposed for mixed element method for non self adjoint and indefinite second order elliptic problems and the uniform convergence of the v cycle multigrid method is proven under minimal regularity assumption meanwhile a multilevel additive preconditioner is given for these problems and an optimal convergence rate for preconditioned gmres method is obtained under minimal regularity assumption

on the stability of the parallel sum of maximal monotone operators identifying operators with their graphs we study the continuity of the parallel sum of two monotone operators with respect to set convergence and we examine its stability from a quantitative point of view

on the implementation of mixed methods as nonconforming methods for second order elliptic problems in this paper we show that mixed finite element methods for a fairly general second order elliptic problem with variable coefficients can be given a nonmixed formulation lower order terms are treated so our results apply also to parabolic equations we define an approximation method by incorporating some projection operators within a standard galerkin method which we call a projection finite element method it is shown that for a given mixed method if the projection method s finite element space m h satisfies three conditions then the two approximation methods are equivalent these three conditions can be simplified for a single element in the case of mixed spaces possessing the usual vector projection operator we then construct appropriate nonconforming spaces m h for the known triangular and rectangular elements the lowest order raviart thomas mixed solution on rectangular finite elements in r 2 and r 3 on simplices or on prisms is then implemented as a nonconforming method modified in a simple and computationally trivial manner this new nonconforming solution is actually equivalent to a postprocessed version of the mixed solution a rearrangement of the computation of the mixed method solution through this equivalence allows us to design simple and optimal order multigrid methods for the solution of the linear system

robust partial shape classification using invariant breakpoints and dynamic alignment abstract a system for classifying partially occluded noisy shapes in varying positions orientations and dimensions is described an iterative algorithm derived from the colinearity principle is developed to locate invariant breakpoints on a shape contour the set of invariant breakpoints partitions the contour into a sequence of contour segments each contour segment is described by an ordered sequence that represents the euclidean distance between the pixels in the contour segment and the centroid of the region formed by connecting the end points of the contour segment by a straight line two stages of dynamic alignment with the appropriate constraints are formulated to determine shape similarity the first stage gives a distance measure of contour segment similarity and in the second stage the intersegment distances are used to optimally align contour segments so that a final measure of shape similarity is obtained the performance of the system is demonstrated by considering the classification of aircraft shapes belonging to four classes and classification results are presented as functions of noise and occlusion levels the results indicate that reasonable classification is obtained for noisy shapes with 0 to 30 occlusion

non linear alignment of neural net outputs for partial shape classification abstract a neural network approach to the partial shape classification problem is derived although neural networks are generally robust static pattern classifiers they are not effective in classifying patterns with inherent temporal variations in order to compensate for temporal variations resulting from random partial occlusion a multi neural network system which includes a dynamic alignment procedure at the neural net outputs is proposed in formulating the dynamic alignment stage a similarity measure between an input and the neural net outputs is defined combining the robustness of neural networks with the non linear alignment capability of dynamic alignment results in a classifier which can tolerate high degrees of random noise and random occlusion in shapes

parameter estimation for optimal object recognition theory andapplication object recognition systems involve parameters such as thresholds bounds and weights these parameters have to be tuned before the system can perform successfully a common practice is to choose such parameters manually on an it add hoc basis which is a disadvantage this paper presents a novel theory of parameter estimation for optimization based object recognition where the optimal solution is defined as the global minimum of an energy function the theory is based on supervised learning from examples it correctness and it instability are established as criteria for evaluating the estimated parameters a correct estimate enables the labeling implied in each exemplary configuration to be encoded in a unique global energy minimum the instability is the ease with which the minimum is replaced by a non exemplary configuration after a perturbation the optimal estimate minimizes the instability algorithms are presented for computing correct and minimal instability estimates the theory is applied to the parameter estimation for mrf based recognition and promising results are obtained

a new shape representation scheme and its application to shape discrimination using a neural network abstract a new method of shape representation and feature extraction is suggested a shape is approximated by a constant point polygon in which between any two adjacent vertices of the polygon the number of points on the contour of the shape is constant this representation is applicable for both concave and convex shapes and there is no chance of missing any spikes on the boundary the sequence of the angle of variation between two consecutive line segments is taken as the primary feature representation of the shape this sequence is then modelled by an autoregressive ar process and the least square error estimate of the ar coefficient vector is used as input to a multilayer perceptron mlp network for learning and classification robustness of the shape representation scheme and the mlp classifier is also investigated empirically adaptive ar modelling is used for estimating the numerically stable and robust coefficient vector

two dimensional object recognition using a two dimensional polar transform abstract a two dimensional 2d transform is proposed for the classification of planar objects with a centroid referenced polar representation it samples the multiple intersections of n radii with the object using the mass center translation invariance is achieved and with an appropriate amplitude normalization the transform is also made invariant to scaling the modules of its 2d fast fourier transform coefficients which are rotation invariant are used as the feature vector simultaneously translation scaling and rotation parameters are estimated the high performance of this algorithm is shown with computer simulations and its advantages and disadvantages are analysed in comparison with existing methods

robust hausdorff distance matching algorithms using pyramidal structures abstract this paper proposes two hausdorff distance hd matching algorithms in which robust hd measures are implemented in pyramidal structures by computer simulations the matching performance of the conventional hd measures and the proposed robust hd matching algorithms using pyramidal structures is compared with real images which are degraded by noise and occlusions

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

perturbation of nonlinear operators and their parallel sum on donne une version de la formule de kubo a b s lime 0 a ei b ei pour a et b des operateurs non lineaires

symmetric phase only matched filtering of fourier mellin transforms for image registration and recognition presents a new method to match a 2d image to a translated rotated and scaled reference image the approach consists of two steps the calculation of a fourier mellin invariant fmi descriptor for each image to be matched and the matching of the fmi descriptors the fmi descriptor is translation invariant and represents rotation and scaling as translations in parameter space the matching of the fmi descriptors is achieved using symmetric phase only matched filtering spomf the performance of the fmi spomf algorithm is the same or similar to that of phase only matched filtering when dealing with image translations the significant advantage of the new technique is its capability to match rotated and scaled images accurately and efficiently the innovation is the application of spomf to the fmi descriptors which guarantees high discriminating power and excellent robustness in the presence of noise this paper describes the principle of the new method and its discrete implementation for either image detection problems or image registration problems practical results are presented for various applications in medical imaging remote sensing fingerprint recognition and multiobject identification

two dimensional object alignment based on the robust oriented hausdorff similarity measure this paper proposes an oriented hausdorff similarity ohs measure for robust object alignment the ohs measure is introduced by replacing the distance concept of conventional hausdoff distance hd algorithms by the similarity concept of the hough transform ht the proposed algorithm can be considered as the modified directed ht using the distance transform dt the orientation information at each pixel is also used to remove incorrect correspondences

a transformation invariant matching algorithm for handwritten chinese character recognition abstract all the chinese characters are composed of some fundamental characters called radicals the algorithms we present here are used to match the radicals stored in the data base with the input chinese character from the radicals in the input chinese character we can know what this input chinese character really is the matching process is equivalent to checking the validity of the relation that the radical is a sub character of the input chinese character the least square error estimation and some properties of the chinese characters are also used here to check whether the relation mentioned above is satisfied and if this relation is satisfied the sub character matched with the radical is extracted this matching algorithm has some superior merits which are 1 transformation scaling rotation and translation invariant and furthermore 2 invulnerable to the inherent defects of the thinning algorithms it overcomes these defects at the expense of more computation time but it can be run in parallel so large computation time is no longer a very serious problem experiments with 114 characters and 62 radicals have been conducted and we find that the success rate of our matching algorithms is above 99 thus we conclude that our algorithms are very reliable

preconditioning of indefinite and almost singular finite element elliptic equations this paper deals with two ways of solving discretized finite element elliptic equations with indefinite and almost singular matrices such problems typically arise when applying the shifted inverse power iteration sipi method to the generalized eigenvalue problem a bf u lambda b bf u where a is defined from some discretized equation by a finite element self adjoint coercive second order elliptic operator and b is a mass matrix operator both methods explore two by two block partitioning of the given matrices one of the main matrix blocks corresponds to a coarse space or equivalently to coarse grid degrees of freedom and contains the main singularity of the original problem the other major block possibly indefinite is not as close to singular as the original matrix and is inverted by a preconditioned minimal residual minres method in the first method the second method which we use for comparison exploits preconditioned minres iterations for the reduced problem obtained by eliminating the block unknowns that correspond to the coarse discretization space here each iteration involves solving a coarse grid problem numerical examples are presented that demonstrate the various aspects of both approaches for solving generalized eigenvalue problems applied to second order finite element elliptic equations

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

representative patterns for model based matching abstract a single intensity image of a three dimensional 3d object obtained under perspective projection can be reduced to a two dimensional 2d line drawing which contains patterns characteristic of the object and of its pose these patterns can provide clues to narrow down the search for possible objects and poses when comparing 2d view class models of 3d objects against images this paper describes a general way of representing 2d line patterns and of using the patterns to consistently label 2d models of 3d objects the representation is based on groups of three line segments that are likely to be found in most images containing man made objects but are unlikely to occur by accident experimental results using representative patterns to match 2d view class models of 3d objects against real images of the objects are included

convergence analysis of multigrid algorithms for nonselfadjoint and indefinite elliptic problems a convergence estimate is established for nonsymmetric multigrid algorithms for finite element methods for nonselfadjoint and indefinite elliptic problems it is shown without further regularity assumption beyond h 1 necessary to define the weak form that the v cycle algorithm converges with rate bounded by 1 cj 1 for sufficiently small coarse mesh size h 1 where j is the number of levels in the multigrid algorithm

an integrated approach to 2d object recognition a multilevel markov random field mrf energy environment has been developed that simultaneously performs delineation representation and classification of two dimensional objects by using a global optimization technique this environment supports a multipolar shape representation which establishes a dynamic mrf structure this structure is initialized as a single center polar representation and uses minimum description length tests to determine whether to establish new polar centers the polar representations at these centers are compared with a database of such representations in order to identify pieces of objects and the results of these comparisons are used to compile evidence for global object identifications this method is potentially more robust than conventional multistaged approaches to object recognition because it incorporates all the information about the objects into a single adaptive decision process and its use of a multipolar representation allows it to handle partially occluded objects

global estimates for mixed methods for second order elliptic equations global error estimates in l2 92 l 9 and h s q 2 in r2 or a re derived for a mixed finite element method for the dirichlet problem for the elliptic operator lp div a grad p bp cp based on the raviart thomas nedelec space vh x wh c h div 92 x l2 g2 optimal order estimates are obtained for the approximation of p and the associated velocity field u a grad p bp in l2 g2 and h s 92 0 6 s k 1 and if q c r2 forp in lv2

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

matching of 3d polygonal arcs we define a distance measure between 3d polygonal arcs of equal length and show that the minimum value of this distance measure is the smallest eigenvalue of a certain matrix using this we develop a mismatch measure and a matching algorithm for 3d polygonal arcs of unequal lengths

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

uniform convergence and schwarz method for the mortar projection nonconforming and mixed element methods for nonselfadjoint and indefinite problems abstract in this paper two mortar versions of the so called projection nonconforming and the mixed element methods are proposed respectively for nonselfadjoint and indefinite second order elliptic problems it is proven that the mortar mixed element method is equivalent to the mortar projection nonconforming element method based on this equivalence the existence uniqueness and uniform convergence of the solution for mortar mixed element method are shown only under minimal regularity assumption meanwhile the optimal error estimate is obtained under certain regularity assumption furthermore an additive schwarz preconditioning method is proposed for solving the discrete problem and the nearly optimal convergence rate for the preconditioned gmres method is proven under minimal regularity assumption finally the practical implementation of the method is adderssed and numerical experiments are presented

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

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

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

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

deformable shape detection and description via model based region grouping a method for deformable shape detection and recognition is described deformable shape templates are used to partition the image into a globally consistent interpretation determined in part by the minimum description length principle statistical shape models enforce the prior probabilities on global parametric deformations for each object class once trained the system autonomously segments deformed shapes from the background while not merging them with adjacent objects or shadows the formulation can be used to group image regions obtained via any region segmentation algorithm e g texture color or motion the recovered shape models can be used directly in object recognition experiments with color imagery are reported

some new error estimates for ritz galerkin methods with minimal regularity assumptions new uniform error estimates are established for finite element approximations u h of solutions u of second order elliptic equations lu f using only the regularity assumption u 1 c f 1 using an aubin nitsche type duality argument we show for example that for arbitrary fixed e sufficiently small there exists an h 0 such that for 0 h h 0 u u h 0 e u u h 1 here s denotes the norm on the sobolev space h s other related results are established

planar shape matching based on binary tree shape representation abstract in this paper we suggest a new way of representing planar two dimensional shapes and a shape matching method which utilizes the new representation through merging of the neighboring boundary runs a shape can be partitioned into a set of triangles these triangles are inherently connected according to a binary tree structure here we use the binary tree with the triangles as its nodes to represent the shape this representation is found to be insensitive to shape translation rotation scaling and skewing changes due to viewer s location changes or the object s pose changes furthermore the representation is of multiresolution in shape matching we compare the two trees representing two given shapes node by node according to the breadth first tree traversing sequence the comparison is done from top of the tree and moving downward which means that we first compare the lower resolution approximations of the two shapes if the two approximations are different the comparison stops otherwise it goes on and compares the finer details of the two shapes only when the two shapes are very similar will the two corresponding trees be compared entirely thus the matching algorithm utilizes the multiresolution characteristic of the tree representation and appears to be very efficient

convergence and quasi optimality of adaptive nonconforming finite element methods for some nonsymmetric and indefinite problems recently an adaptive nonconforming finite element method anfem has been developed by carstensen and hoppe in numer math 103 251 266 2006 in this paper we extend the result to some nonsymmetric and indefinite problems the main tools in our analysis are a posteriori error estimators and a quasi orthogonality property in this case we need to overcome two main difficulties one stems from the nonconformity of the finite element space the other is how to handle the effect of a nonsymmetric and indefinite bilinear form an appropriate adaptive nonconforming finite element method featuring a marking strategy based on the comparison of the a posteriori error estimator and a volume term is proposed for the lowest order crouzeix raviart element it is shown that the anfem is a contraction for the sum of the energy error and a scaled volume term between two consecutive adaptive loops moreover quasi optimality in the sense of quasi optimal algorithmic complexity can be shown for the anfem the results of numerical experiments confirm the theoretical findings

classification of partial 2 d shapes using fourier descriptors we present a method for the classification of 2 d partial shapes using fourier descriptors we formulate the problem as one of estimating the fourier descriptors of the unknown complete shape from the observations derived from an arbitrarily rotated and scaled shape with missing segments the method used for obtaining the estimates of the fourier descriptors minimizes a sum of two terms the first term of which is a least square fit to the given data subject to the condition that the number of missing boundary points is not known and the second term is the perimeter2 area of the unknown shape experiments with synthetic and real boundaries show that estimates closer to the true values of fourier descriptors of complete boundaries are obtained also classification experiments performed using real boundaries indicate that reasonable classification accuracies are obtained even when 20 30 percent of the data is missing

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

preconditioning nonconforming finite element methods this paper is concerned with the h sup 1 condition number and singular value distribution of preconditioned nonself adjoint discrete elliptic operators in particular a wide class of nonconforming finite element methods are investigated the main results give a precise interval on which the singular values cluster results of this kind have an important bearing on the convergence behavior of the conjugate gradient method applied to the normal equations

uniform convergence and preconditioning methods for projection nonconforming and mixed methods for nonselfadjoint and indefinite problems abstract the purpose of this paper is to prove the existence uniqueness and uniform convergence of the solutions of so called projection nonconforming and mixed element methods and the equivalence between projection nonconforming element method and mixed element method with nonquasi uniform partition for nonselfadjoint and indefinite second order elliptic problems under minimal regularity assumption meanwhile the optimal error estimate of the solution of mixed element method is obtained under h 2 smoothness hypothesis for nonselfadjoint and indefinite elliptic problems without h 2 regularity finally the discrete compactness result for nonconforming element space with nonquasi uniform partition is proven and some preconditioning methods for projection nonconforming and mixed element methods with nonquasi uniform partition are given it is proven that the h 1 condition number of preconditioned operator is uniformly bounded and its singular values cluster in a relatively small finite interval

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

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

preconditioning projection nonconforming element method for the lowest order raviart thomas mixed triangular element method this paper is concerned with the h 1 condition number and the b h singular value distribution of preconditioned operators b h 1a h 0 h 1 where a h is the projection nonconforming element discretization of the nonself adjoint and possibly indefinite second order elliptic operator a b h is the nonconforming element discretization of the self adjoint and positive definite second order elliptic operator b the projection nonconforming element method is equivalent to the lowest order raviart thomas mixed triangular element method for second order elliptic problems it is proved that the h 1 condition number of operators b h 1a h 0 h 1 are uniformly bounded and the b h singular values cluster in a positive finite interval finally a simple v cycle multigrid implementation of b h 1 is given

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

a comparison of approaches to high level image interpretation abstract a critical comparison of methods of high level interpretation of segmented images is presented and illustrated by examples drawn from two dimensional image analysis the methods discussed include boundary correlation generalized hough transformation relational distance measures graph matching heuristic search and relaxation labelling each technique is considered in terms of its reliability in interpreting noisy and cluttered scenes and in terms of the dynamic complexity of the algorithm as a function of the input data although 2 d analysis of linearly segmented scenes is used as a mechanism for comparison many of the arguments are applicable to three dimensional image interpretation based on surface modelling for example

improving consistency and reducing ambiguity in stochastic labeling an optimization approach we approach the problem of labeling a set of objects from a quantitative standpoint we define a world model in terms of transition probabilities and propose a definition of a class of global criteria that combine both ambiguity and consistency a projected gradient algorithm is developed to minimize the criterion we show that the minimization procedure can be implemented in a highly parallel manner results are shown on several examples and comparisons are made with relaxation labeling techniques

uniform convergence of finite volume element method with crouzeix raviart element for non self adjoint and indefinite elliptic problems in this paper we consider the finite volume element method based on the crouzeix raviart element and prove the existence uniqueness and uniform convergence of the finite volume element approximations for the non self adjoint and indefinite elliptic problems under minimal elliptic regularity assumption

flexible syntactic matching of curves and its application to automatic hierarchical classification of silhouettes curve matching is one instance of the fundamental correspondence problem our flexible algorithm is designed to match curves under substantial deformations and arbitrary large scaling and rigid transformations a syntactic representation is constructed for both curves and an edit transformation which maps one curve to the other is found using dynamic programming we present extensive experiments where we apply the algorithm to silhouette matching in these experiments we examine partial occlusion viewpoint variation articulation and class matching where silhouettes of similar objects are matched based on the qualitative syntactic matching we define a dissimilarity measure and we compute it for every pair of images in a database of 121 images we use this experiment to objectively evaluate our algorithm first we compare our results to those reported by others second we use the dissimilarity values in order to organize the image database into shape categories the veridical hierarchical organization stands as evidence to the quality of our matching and similarity estimation

on the accuracy of the mortar finite volume element method with lagrange multipliers abstract in this paper the mortar finite volume element mfve method with lagrange multipliers is considered for second order elliptic boundary value problems we prove l 2 error estimates which are affected by regularities in both the exact solution and the source term meanwhile the uniform convergence of the solution is obtained for the mfve method under minimal regularity assumption

segmentation of images having unimodal distributions a gradient relaxation method based on maximizing a criterion function is studied and compared to the nonlinear probabilistic relaxation method for the purpose of segmentation of images having unimodal distributions although both methods provide comparable segmentation results the gradient method has the additional advantage of providing control over the relaxation process by choosing three parameters which can be tuned to obtain the desired segmentation results at a faster rate examples are given on two different types of scenes

object matching algorithms using robust hausdorff distance measures a hausdorff distance hd is one of commonly used measures for object matching this work analyzes the conventional hd measures and proposes two robust hd measures based on m estimation and least trimmed square lts which are more efficient than the conventional hd measures by computer simulation the matching performance of the conventional and proposed hd measures is compared with synthetic and real images

numerical analysis of diffraction by periodic structures tm polarization the diffraction of a time harmonic wave in tm polarization by some periodic inhomogeneous material is studied in this paper the diffraction problem is modeled by a generalized helmholtz equation with transparent boundary conditions existence and uniqueness are proved for the model problem uniform error estimates for the finite element approximation of the solution are established error estimates are also obtained when the truncation of the nonlocal boundary operators takes place

local multilevel methods for adaptive finite element methods for nonsymmetric and indefinite elliptic boundary value problems in this paper we propose some local multilevel algorithms for solving linear systems arising from adaptive finite element approximations of nonsymmetric and indefinite elliptic boundary value problems two types of local smoothers are constructed one is based on the original nonsymmetric problems and the other is defined in terms of the associated symmetric problems it is shown that the local multilevel methods for the nonsymmetric and indefinite elliptic boundary value problems are optimal which means that the convergence rates of the local multilevel methods are independent of mesh sizes and mesh levels provided that the coarsest grid is sufficiently fine numerical experiments are reported to confirm our theory

the parallel sum of nonlinear monotone operators on definit la somme parallele d operateurs non lineaires dans un espace de hilbert a l aide de leurs graphes

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

convergence analysis of the schwarz algorithm and multilevel decomposition iterative methods ii nonselfadjoint and indefinite elliptic problems convergence estimate for the schwarz alternating algorithm applied to nonselfadjoint and indefinite elliptic problems is established for a certain overlapping domain decomposition multilevel iterative algorithms are proposed and analyzed for the finite element method for the same problem with locally refined grids the author shows that the algorithm based on the hierarchical basis decomposition converges with rate bounded by 1 cj 2 where j is the number of levels the author also analyzes the algorithm based on the full multigrid decomposition and shows that the algorithm converges with rate 1 cj 1 for problems of any dimension all the results are established without regularity assumption for the differential equation

iterative schemes for nonsymmetric and indefinite elliptic boundary value problems the purpose of this paper is twofold the first is to describe some simple and robust iterative schemes for nonsymmetric and indefinite elliptic boundary value problems the schemes are based in the sobolev space h omega and require minimal hypotheses the second is to develop algorithms utilizing a coarse grid approximation this leads to iteration matrices whose eigenvalues lie in the right half of the complex plane in fact for symmetric indefinite problems the iteration is reduced to a well conditioned symmetric positive definite system which can be solved by conjugate gradient interation applications of the general theory as well as numerical examples are given 20 refs 8 tabs

convergence and domain decomposition algorithm for nonconforming and mixed methods for nonselfadjoint and indefinite problems in this paper the existence uniqueness and convergence of the solutions of nonconforming and mixed methods with non quasi uniform partition are proven for nonselfadjoint and indefinite second order elliptic problems under minimal regularity assumption moreover uniform convergence of the solution of nonconforming method is obtained meanwhile the domain decomposition algorithm which suits non quasi uniform partition is proposed for nonconforming and mixed methods

non conventional algorithm for representing and recognizing complicated two dimensional objects abstract a non conventional method for representing and recognizing shape descriptions is described for any shape s a modified cobweb form representation which is referred to as a shell descriptor sd is established for the most significant vertex v the shell descriptor is then used as a registered description for the shape s at vertex v this method is computationally efficient as compared to most of the conventional techniques in shape recognition the new algorithm provides an effective and reliable tool for shape representation and classification especially for complicated objects such as logos