practical reliable bayesian recognition of 2d and 3d objects using implicit polynomials and algebraic invariants we treat the use of more complex higher degree polynomial curves and surfaces of degree higher than 2 which have many desirable properties for object recognition and position estimation and attack the instability problem arising in their use with partial and noisy data the scenario discussed in this paper is one where we have a set of objects that are modeled as implicit polynomial functions or a set of representations of classes of objects with each object in a class modeled as an implicit polynomial function stored in the database then given partial data from one of the objects we want to recognize the object or the object class or collect more data in order to get better parameter estimates for more reliable recognition two problems arising in this scenario are discussed 1 the problem of recognizing these polynomials by comparing them in terms of their coefficients and 2 the problem of where to collect data so as to improve the parameter estimates as quickly as possible we use an asymptotic bayesian approximation for solving the two problems the intrinsic dimensionality of polynomials and the use of the mahalanobis distance are discussed

topologically faithful fitting of simple closed curves implicit representations of curves have certain advantages over explicit representation one of them being the ability to determine with ease whether a point is inside or outside the curve inside outside functions however save for some special cases it is not known how to construct implicit representations which are guaranteed to preserve the curve s topology as a result points may be erroneously classified with respect to the curve the paper offers to overcome this problem by using a representation which is guaranteed to yield the correct topology of a simple closed curve by using homeomorphic mappings of the plane to itself if such a map carries the curve onto the unit circle then a point is inside the curve if and only if its image is inside the unit circle

the richer representation the better registration in this paper the registration problem is formulated as a point to model distance minimization unlike most of the existing works which are based on minimizing a point wise correspondence term this formulation avoids the correspondence search that is time consuming in the first stage the target set is described through an implicit function by employing a linear least squares fitting this function can be either an implicit polynomial or an implicit b spline from a coarse to fine representation in the second stage we show how the obtained implicit representation is used as an interface to convert point to point registration into point to implicit problem furthermore we show that this registration distance is smooth and can be minimized through the levengberg marquardt algorithm all the formulations presented for both stages are compact and easy to implement in addition we show that our registration method can be handled using any implicit representation though some are coarse and others provide finer representations hence a tradeoff between speed and accuracy can be set by employing the right implicit function experimental results and comparisons in 2d and 3d show the robustness and the speed of convergence of the proposed approach

a fast globally optimal algorithm for template matching using low resolution pruning template matching has many applications in signal processing image processing pattern recognition and video compression this paper proposes a fast coarse to fine template matching algorithm for finding the exact best match i e the match that may be found by a full search this is obtained by pruning the number of candidates in the full search using the results of a coarse search experimental results show that speed ups of a couple of orders of magnitude can easily be achieved using this method for typical low noise cases of two dimensional 2 d template matching

stationary waves for the discrete boltzmann equation in the half space with reflective boundaries the present paper is concerned with stationary solutions for discrete velocity models of the boltzmann equation with reflective boundary condition in the first half space we obtain a sufficient condition that guarantees the existence and the uniqueness of stationary solutions satisfying the reflective boundary condition as well as the spatially asymptotic condition given by a maxwellian state first the sufficient condition is obtained for the linearized system then this result is applied to prove the existence theorem for the nonlinear equation through the contraction mapping principle also it is shown that the stationary solution approaches the asymptotic maxwellian state exponentially as the spatial variable tends to infinity

on recovering hyperquadrics from range data this paper discusses the applications of hyperquadric models in computer vision and focuses on their recovery from range data hyperquadrics are volumetric shape models that include superquadrics as a special case a hyperquadric model can be composed of any number of terms and its geometric bound is an arbitrary convex polytope thus hyperquadrics can model more complex shapes than superquadrics hyperquadrics also possess many other advantageous properties compactness semilocal control and intuitive meaning our proposed algorithm starts with a rough fit using only six terms in 3d four in 2d and adds additional terms as necessary to improve fitting suitable constraints are used to ensure proper convergence experimental results with real 2d and 3d data are presented

implicit polynomials orthogonal distance regression and the closest point on a curve implicit polynomials i e multinomials have a number of properties that make them attractive for modeling curves and surfaces in computer vision the paper considers the problem of finding the best fitting implicit polynomial or algebraic curve to a collection of points in the plane using an orthogonal distance metric approximate methods for orthogonal distance regression have been shown by others to be prone to the problem of cusps in the solution and this is confirmed here consequently this work focuses on exact methods for orthogonal distance regression the most difficult and costly part of exact methods is computing the closest point on the algebraic curve to an arbitrary point in the plane the paper considers three methods for achieving this in detail the first is the standard newton s method the second is based on resultants which are making a resurgence in computer graphics and the third is a novel technique based on successive circular approximations to the curve it is shown that newton s method is the quickest but that it can fail sometimes even with a good initial guess the successive circular approximation algorithm is not as fast but is robust the resultant method is the slowest of the three but does not require an initial guess the driving application of this work was the fitting of implicit quartics in two variables to thinned oblique ionogram traces

existence of a stationary wave for the discrete boltzmann equation in the half space we study the existence and the uniqueness of stationary solutions for discrete velocity models of the boltzmann equation in the first half space we obtain a sufficient condition that guarantees the existence and the uniqueness of solutions connecting the given boundary data and the maxwellian state at a spatially asymptotic point first a sufficient condition is obtained for the linearized system then this result as well as the contraction mapping principle is applied to prove the existence theorem for the nonlinear equation also we show that the stationary wave approaches the maxwellian state exponentially at a spatially asymptotic point

an adaptive and stable method for fitting implicit polynomial curves and surfaces representing 2d and 3d data sets with implicit polynomials ips has been attractive because of its applicability to various computer vision issues therefore many ip fitting methods have already been proposed however the existing fitting methods can be and need to be improved with respect to computational cost for deciding on the appropriate degree of the ip representation and to fitting accuracy while still maintaining the stability of the fit we propose a stable method for accurate fitting that automatically determines the moderate degree required our method increases the degree of ip until a satisfactory fitting result is obtained the incrementability of qr decomposition with gram schmidt orthogonalization gives our method computational efficiency furthermore since the decomposition detects the instability element precisely our method can selectively apply ridge regression based constraints to that element only as a result our method achieves computational stability while maintaining fitting accuracy experimental results demonstrate the effectiveness of our method compared with prior methods

a dual bound algorithm for very fast and exact template matching recently proposed fast template matching techniques employ rejection schemes derived from lower bounds on the match measure this paper generalizes that idea and shows that in addition to lower bounds upper bounds on the match measure can be used to accelerate the search an algorithm is proposed that utilizes both lower and upper bounds to detect the k best matches in an image the performance of this dual bound algorithm is guaranteed it always detects the k best matches theoretical analysis and experimental results show that its runtime compares favorably with previously proposed real time exact template matching schemes

very fast best fit circular and elliptical boundaries by chord data many machine vision tasks require objects to be delineated during image segmentation that have shapes that are well approximated by circles or ellipses due to their computational efficiency least squares algebraic methods are a popular choice for fitting an elliptic primitive to noisy image data when real time processing is required these methods however suffer from biased estimates and sensitivity to outlier data in this paper a real time least squares method is proposed that provides an indirect geometric fit based on the quadratic polynomial form of parallel chord lengths the algorithm is shown to be more computationally efficient and more easily made robust to outlier data than algebraic methods experimental results also suggest that it provides estimates that suffer less from bias error

finding waldo or focus of attention using local color information we present a method to locate an object in a color image or more precisely to select a set of likely locations for the object the model is assumed to be of known color distribution which permits the use color space processing a new method is presented which exploits more information than the previous backprojection algorithm of swain and ballard 1990 at a competitive complexity precisely the new algorithm is based on matching local histograms with the model instead of directly replacing pixels with a confidence that they belong to the object we prove that a simple version of this algorithm degenerates into backprojection in the worst case in addition we show how to estimate the scale of the model results are shown on pictures digitized from the famous where is waldo books issues concerning the optimal choice of a color space and its quantization are carefully considered and studied in this application we also propose to use co occurrence histograms to deal with cases where important color variations can be expected

segmentation through variable order surface fitting the solution of the segmentation problem requires a mechanism for partitioning the image array into low level entities based on a model of the underlying image structure a piecewise smooth surface model for image data that possesses surface coherence properties is used to develop an algorithm that simultaneously segments a large class of images into regions of arbitrary shape and approximates image data with bivariate functions so that it is possible to compute a complete noiseless image reconstruction based on the extracted functions and regions surface curvature sign labeling provides an initial coarse image segmentation which is refined by an iterative region growing method based on variable order surface fitting experimental results show the algorithm s performance on six range images and three intensity images

on the fitting of surfaces to data with covariances we consider the problem of estimating parameters of a model described by an equation of special form specific models arise in the analysis of a wide class of computer vision problems including conic fitting and estimation of the fundamental matrix we assume that noisy data are accompanied by known covariance matrices characterizing the uncertainty of the measurements a cost function is first obtained by considering a maximum likelihood formulation and applying certain necessary approximations that render the problem tractable a newton like iterative scheme is then generated for determining a minimizer of the cost function unlike alternative approaches such as sampson s method or the renormalization technique the new scheme has as its theoretical limit the minimizer of the cost function furthermore the scheme is simply expressed efficient and unsurpassed as a general technique in our testing an important feature of the method is that it can serve as a basis for conducting theoretical comparison of various estimation approaches

use of fourier and karhunen loeve decomposition for fast pattern matching with a large set of templates we present a fast pattern matching algorithm with a large set of templates the algorithm is based on the typical template matching speeded up by the dual decomposition the fourier transform and the karhunen loeve transform the proposed algorithm is appropriate for the search of an object with unknown distortion within a short period patterns with different distortion differ slightly from each other and are highly correlated the image vector subspace required for effective representation can be defined by a small number of eigenvectors derived by the karhunen loeve transform a vector subspace spanned by the eigenvectors is generated and any image vector in the subspace is considered as a pattern to be recognized the pattern matching of objects with unknown distortion is formulated as the process to extract the portion of the input image find the pattern most similar to the extracted portion in the subspace compute normalized correlation between them at each location in the input image and find the location with the best score searching for objects with unknown distortion requires vast computation the formulation above makes it possible to decompose highly correlated reference images into eigenvectors as well as to decompose images in frequency domain and to speed up the process significantly

efficient color histogram indexing for quadratic form distance functions in image retrieval based on color the weighted distance between color histograms of two images represented as a quadratic form may be defined as a match measure however this distance measure is computationally expensive and it operates on high dimensional features o n we propose the use of low dimensional simple to compute distance measures between the color distributions and show that these are lower bounds on the histogram distance measure results on color histogram matching in large image databases show that prefiltering with the simpler distance measures leads to significantly less time complexity because the quadratic histogram distance is now computed on a smaller set of images the low dimensional distance measure can also be used for indexing into the database

localising embeddings of comodule categories with applications to tame and euler coalgebras given a k coalgebra c and an injective left c comodule e we construct a coalgebra ce and fully faithful left exact embedding e ce comod c comod of comodule categories such that the image of e is the subcategory c comode consisting of the comodules m with an injective presentation 0 m e0 e1 where e0 and e1 are direct sums of direct summands of the comodule e the functor e preserves the indecomposability the injectivity and is right adjoint to the restriction functor rese c comod ce comod applications to the study of tame coalgebras betti numbers and cosyzygy comodules of simple comodules over a left euler coalgebra c are given a localising reduction to countably dimensional euler coalgebras is presented

direct least square fitting of hyperellipsoids this paper presents two new computationally efficient direct methods for fitting n dimensional ellipsoids to noisy data they conduct the fitting by minimizing the algebraic distance in subject to suitable quadratic constraints the hyperellipsoid specific hes method is an elaboration of existing ellipse and 3d ellipsoid specific fitting methods it is shown that hes is ellipsoid specific in n dimensional space a limitation of hes is that it may provide biased fitting results with data originating from an ellipsoid with a large ratio between the longest and shortest main axis the sum of discriminants sod method does not have such a limitation the constraint used by sod rejects a subset of non ellipsoidal quadrics which enables a high tendency to produce ellipsoidal solutions moreover a regularization technique is presented to force the solutions towards ellipsoids with sod the regularization technique is compatible also with several existing 2d and 3d fitting methods the new methods are compared through extensive numerical experiments with n dimensional variants of three commonly used direct fitting approaches for quadratic surfaces the results of the experiments imply that in addition to the superior capability to create ellipsoidal solutions the estimation accuracy of the new methods is better or equal to that of the reference approaches

abelian categories almost split sequences and comodules the following are equivalent for a skeletally small abelian horn finite category over a field with enough injectives and each simple object being an epimorphic image of a projective object of finite length a each indecomposable injective has a simple subobject b the category is equivalent to the category of socle finitely copresented right comodules over a right semiperfect and right cocoherent coalgebra such that each simple right comodule is socle finitely copresented c the category has left almost split sequences

point to ellipse and point to ellipsoid distance equation analysis for the problem of distance evaluation from a point x0 to an ellipse in r2 and to an ellipsoid in r3 given by algebraic equation g x 0 we investigate the properties of the distance equation i e an algebraic equation whose zeros coincide with the critical values of the squared distance function we detail the structure of this equation and an algorithm for finding the point in the quadric nearest to x0 we also find analytical formulas for distance approximations using the expansion of the zero of distance equation into power series j 1jgj x0 exact values for the approximation error bounds are obtained via construction of an analogue of the distance equations for the curve to curve distance problem

scale affine invariant interest point detectors in this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations our scale and affine invariant detectors are based on the following recent results 1 interest points extracted with the harris detector can be adapted to affine transformations and give repeatable results geometrically stable 2 the characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives the laplacian 3 the affine shape of a point neighborhood is estimated based on the second moment matrix our scale invariant detector computes a multi scale representation for the harris interest point detector and then selects points at which a local measure the laplacian is maximal over scales this provides a set of distinctive points which are invariant to scale rotation and translation as well as robust to illumination changes and limited changes of viewpoint the characteristic scale determines a scale invariant region for each point we extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood an iterative algorithm modifies location scale and neighborhood of each point and converges to affine invariant points this method can deal with significant affine transformations including large scale changes the characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point we present a comparative evaluation of different detectors and show that our approach provides better results than existing methods the performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale affine invariant descriptors computed on the regions associated with our points

fitting curves and surfaces with constrained implicit polynomials a problem which often arises while fitting implicit polynomials to 2d and 3d data sets is the following although the data set is simple the fit exhibits undesired phenomena such as loops holes extraneous components etc previous work tackled these problems by optimizing heuristic cost functions which penalize some of these topological problems in the fit the paper suggests a different approach to design parameterized families of polynomials whose zero sets are guaranteed to satisfy certain topological properties namely we construct families of polynomials with star shaped zero sets as well as polynomials whose zero sets are guaranteed not to intersect an ellipse circumscribing the data or to be entirely contained in such an ellipse this is more rigorous than using heuristics which may fail and result in pathological zero sets the ability to parameterize these families depends heavily on the ability to parameterize positive polynomials to achieve this we use some powerful results from real algebraic geometry

the multiple window parameter transform the multiwindow transform an extension of parameter transform techniques that increase performance and scope by exploiting the long range correlated information contained in multiple portions of an image is presented multiple window transforms allow the extraction of high dimensional features with improvement in accuracy over conventional techniques while keeping linear to low order polynomial computational and space requirements with respect to image size and dimensionality of the features using correlated information provides a direct link between extracted features and supporting regions in the image this coupled with evidence integration techniques is used to suppress noisy or nonexistent feature hypotheses parameter spaces are implemented as constraint satisfaction networks where feature hypotheses with overlapping support in the image compete after an iterative relaxation phase surviving hypotheses have disjoint support forming a segmentation of the image examples show the performance and provide insight about the behavior

template matching based object recognition with unknown geometric parameters we examine the problem of locating an object in an image when size and rotation are unknown previous work has shown that with known geometric parameters an image restoration method can be useful by estimating a delta function at the object location when the geometric parameters are unknown this method becomes impractical because the likelihood surface to be minimized across size and rotation has numerous local minima and areas of zero gradient we propose a new approach where a smooth approximation of the template is used to minimize a well behaved likelihood surface a coarse to fine approximation of the original template using a diffusion like equation is used to create a library of templates using this library we can successively perform minimizations which are locally well behaved as detail is added to the template the likelihood surface gains local minima but previous estimates place us within a well behaved bowl around the global minimum leading to an accurate estimate numerical experiments are shown which verify the value of this approach for a wide range of values of the geometric parameters

bayesian clustering for unsupervised estimation of surface and texture models a method of calculating the maximum likelihood clustering for the unsupervised estimation of polynomial models for the data in images of smooth surfaces or for range data for such surfaces is presented an image or a depth map of a region of smooth 3 d surface is modeled as a polynomial plus white noise a region of physically meaningful textured image such as the image of foliage grass or road in outdoor scenes or conductor or lintburn on a thick film substrate is modeled as a colored gaussian markov random field mrf with a polynomial mean value function unsupervised model parameter estimation is accomplished by determining the segmentation and model parameter values that maximize the likelihood of the data or a more general bayesian performance functional agglomerative clustering is used for this purpose

robust image registration by increment sign correlation abstract a novel and robust statistic as a similarity measure for robust image registration is proposed the statistic is named as increment sign correlation because it is based on the average evaluation of incremental tendency of brightness in adjacent pixels it is formalized to be a binary distribution or a gaussian distribution for a large image size through statistical analysis and modeling by utilizing the proposed statistical model for example we can theoretically determine a reasonable value of threshold for verification of matching this sign correlation can also be proved to expectedly have the constant value 0 5 for any uncorrelated images to a template image and then the property of the constancy can be utilized to analyze the high robustness for occlusion the good performance for the case of saturation or highlight can also be proved through theoretical analysis and fundamental experiments a basic algorithm for image scanning search and registration over a large scene is represented with a technique for a fast version by the branch and bound approach many experimental evidences with real images are provided and discussed

a note on a discrete boltzmann equation with multiple collisions we compute a non trivial explicit solution for the one dimensional plane 6 velocity discrete boltzmann model with multiple collisions introduced in e longo r monaco on the discrete kinetic theory with multiple collisions plane six velocity and unsteady couette flow in muntz et al eds the proceedings of rarefied gas dynamics in aiaa publ vol 118 1989 pp 118 130 which asymptotically connects two particular equilibrium states we prove that such a solution exists provided that a suitable condition on the differential elastic cross sections holds

fast template matching based on normalized cross correlation with adaptive multilevel winner update in this paper we propose a fast pattern matching algorithm based on the normalized cross correlation ncc criterion by combining adaptive multilevel partition with the winner update scheme to achieve very efficient search this winner update scheme is applied in conjunction with an upper bound for the cross correlation derived from cauchy schwarz inequality to apply the winner update scheme in an efficient way we partition the summation of cross correlation into different levels with the partition order determined by the gradient energies of the partitioned regions in the template thus this winner update scheme in conjunction with the upper bound for ncc can be employed to skip unnecessary calculation experimental results show the proposed algorithm is very efficient for image matching under different lighting conditions

stable fitting of 2d curves and 3d surfaces by implicit polynomials this work deals with fitting 2d and 3d implicit polynomials ips to 2d curves and 3d surfaces respectively the zero set of the polynomial is determined by the ip coefficients and describes the data the polynomial fitting algorithms proposed in this paper aim at reducing the sensitivity of the polynomial to coefficient errors errors in coefficient values may be the result of numerical calculations when solving the fitting problem or due to coefficient quantization it is demonstrated that the effect of reducing this sensitivity also improves the fitting tightness and stability of the proposed two algorithms in fitting noisy data as compared to existing algorithms like the well known 3l and gradient one algorithms the development of the proposed algorithms is based on an analysis of the sensitivity of the zero set to small coefficient changes and on minimizing a bound on the maximal error for one algorithm and minimizing the error variance for the second simulation results show that the proposed algorithms provide a significant reduction in fitting errors particularly when fitting noisy data of complex shapes with high order polynomials as compared to the performance obtained by the above mentioned existing algorithms

using geometric distance fits for 3 d object modeling and recognition addresses the problems of automatically constructing algebraic surface models from sets of 2d and 3d images and using these models in pose computation motion and deformation estimation and object recognition we propose using a combination of constrained optimization and nonlinear least squares estimation techniques to minimize the mean squared geometric distance between a set of points or rays and a parameterized surface in modeling tasks the unknown parameters are the surface coefficients while in pose and deformation estimation tasks they represent the transformation which maps the observer s coordinate system onto the modeled surface s own coordinate system we have applied this approach to a variety of real range computerized tomography and video images

implicit polynomial representation through a fast fitting error estimation this paper presents a simple distance estimation for implicit polynomial fitting it is computed as the height of a simplex built between the point and the surface i e a triangle in 2 d or a tetrahedron in 3 d which is used as a coarse but reliable estimation of the orthogonal distance the proposed distance can be described as a function of the coefficients of the implicit polynomial moreover it is differentiable and has a smooth behavior hence it can be used in any gradient based optimization in this paper its use in a levenberg marquardt framework is shown which is particularly devoted for nonlinear least squares problems the proposed estimation is a generalization of the gradient based distance estimation which is widely used in the literature experimental results both in 2 d and 3 d data sets are provided comparisons with state of the art techniques are presented showing the advantages of the proposed approach

robust parameter estimation in computer vision estimation techniques in computer vision applications must estimate accurate model parameters despite small scale noise in the data occasional large scale measurement errors outliers and measurements from multiple populations in the same data set increasingly robust estimation techniques some borrowed from the statistics literature and others described in the computer vision literature have been used in solving these parameter estimation problems ideally these techniques should effectively ignore the outliers and measurements from other populations treating them as outliers when estimating the parameters of a single population two frequently used techniques are least median of squares lms p j rousseeuw j amer statist assoc 79 1984 pp 871 880 and m estimators robust statistics the approach based on influence functions f r hampel et al john wiley 1986 robust statistics p j huber john wiley 1981 lms handles large fractions of outliers up to the theoretical limit of 50 for estimators invariant to affine changes to the data but has low statistical efficiency m estimators have higher statistical efficiency but tolerate much lower percentages of outliers unless properly initialized while robust estimators have been used in a variety of computer vision applications three are considered here in analysis of range images images containing depth or x y z measurements at each pixel instead of intensity measurements robust estimators have been used successfully to estimate surface model parameters in small image regions in stereo and motion analysis they have been used to estimate parameters of what is called the fundamental matrix which characterizes the relative imaging geometry of two cameras imaging the same scene recently robust estimators have been applied to estimating a quadratic image to image transformation model necessary to create a composite mosaic image from a series of images of the human retina in each case a straightforward application of standard robust estimators is insufficient and carefully developed extensions are used to solve the problem

the complex representation of algebraic curves and its simple exploitation for pose estimation and invariant recognition representations are introduced for handling 2d algebraic curves implicit polynomial curves of arbitrary degree in the scope of computer vision applications these representations permit fast accurate pose independent shape recognition under euclidean transformations with a complete set of invariants and fast accurate pose estimation based on all the polynomial coefficients the latter is accomplished by a centering of a polynomial based on its coefficients followed by rotation estimation by decomposing polynomial coefficient space into a union of orthogonal subspaces for which rotations within two dimensional subspaces or identity transformations within one dimensional subspaces result from rotations in x y measured data space angles of these rotations in the two dimensional coefficient subspaces are proportional to each other and are integer multiples of the rotation angle in the x y data space by recasting this approach in terms of a complex variable i e x iy z and complex polynomial coefficients further conceptual and computational simplification results application to shape based indexing into databases is presented to illustrate the usefulness and the robustness of the complex representation of algebraic curves

three dimensional object representation and invariant recognition using continuous distance transform neural networks 3d object recognition under partial object viewing is a difficult pattern recognition task in this paper we introduce a neural network solution that is robust to partial viewing of objects and noise corruption this method directly utilizes the acquired 3d data and requires no feature extraction the object is first parametrically represented by a continuous distance transform neural network cdtnn trained by the surface points of the exemplar object the cdtnn maps any 3d coordinate into a value that corresponds to the distance between the point and the nearest surface point of the object therefore a mismatch between the exemplar object and an unknown object can be easily computed when encountered with deformed objects this mismatch information can be backpropagated through the cdtnn to iteratively determine the deformation in terms of affine transform application to 3d heart contour delineation and invariant recognition of 3d rigid body objects is presented

fast full search equivalent template matching by enhanced bounded correlation we propose a novel algorithm referred to as enhanced bounded correlation ebc that significantly reduces the number of computations required to carry out template matching based on normalized cross correlation ncc and yields exactly the same result as the full search algorithm the algorithm relies on the concept of bounding the matching function finding an efficiently computable upper bound of the ncc rapidly prunes those candidates that cannot provide a better ncc score with respect to the current best match in this framework we apply a succession of increasingly tighter upper bounding functions based on cauchy schwarz inequality moreover by including an online parameter prediction step into ebc we obtain a parameter free algorithm that in most cases affords computational advantages very similar to those attainable by optimal offline parameter tuning experimental results show that the proposed algorithm can significantly accelerate a full search equivalent template matching process and outperforms state of the art methods

least squares based fitting of paraboloids a technique for reconstructing a class of quadric surfaces from 3d data is presented the technique is driven by a linear least squares based fitting mechanism previously such fitting was restricted to recovery of central quadrics here extension of that basic mechanism to allow recovery of one commonly occurring class of non central quadric the elliptic paraboloids is described the extension uses an indirect solution approach that involves introducing a variable to the basic mechanism that is a function of a quadric surface invariant results from fitting real and synthetic data are also exhibited

invariant matching and identification of curves using b splines curve representation there have been many techniques for curve shape representation and analysis ranging from fourier descriptors to moments to implicit polynomials to differential geometry features to time series models to b splines etc the b splines stand as one of the most efficient curve surface representations and possess very attractive properties such as spatial uniqueness boundedness and continuity local shape controllability and invariance to affine transformations these properties made them very attractive for curve representation and consequently they have been extensively used in computer aided design and computer graphics very little work however has been devoted to them for recognition purposes one possible reason might be due to the fact that the b spline curve is not uniquely described by a single set of parameters control points which made the curve matching recognition process difficult when comparing the respective parameters of the curves to be matched this paper is an attempt to find matching solutions despite this limitation and as such it deals the problem of using b splines for shape recognition and identification from curves with an emphasis on the following applications affine invariant matching and classification of 2 d curves with applications in identification of aircraft types based on image silhouettes and writer identification based on handwritten text

fast template matching with polynomials template matching is widely used for many applications in image and signal processing this paper proposes a novel template matching algorithm called algebraic template matching given a template and an input image algebraic template matching efficiently calculates similarities between the template and the partial images of the input image for various widths and heights the partial image most similar to the template image is detected from the input image for any location width and height in the proposed algorithm a polynomial that approximates the template image is used to match the input image instead of the template image the proposed algorithm is effective especially when the width and height of the template image differ from the partial image to be matched an algorithm using the legendre polynomial is proposed for efficient approximation of the template image this algorithm not only reduces computational costs but also improves the quality of the approximated image it is shown theoretically and experimentally that the computational cost of the proposed algorithm is much smaller than the existing methods

robust and efficient image alignment based on relative gradient matching in this paper we present a robust image alignment algorithm based on matching of relative gradient maps this algorithm consists of two stages namely a learning based approximate pattern search and an iterative energy minimization procedure for matching relative image gradient the first stage finds some candidate poses of the pattern from the image through a fast nearest neighbor search of the best match of the relative gradient features computed from training database of feature vectors which are obtained from the synthesis of the geometrically transformed template image with the transformation parameters uniformly sampled from a given transformation parameter space subsequently the candidate poses are further verified and refined by matching the relative gradient images through an iterative energy minimization procedure this approach based on the matching of relative gradients is robust against nonuniform illumination variations experimental results on both simulated and real images are shown to demonstrate superior efficiency and robustness of the proposed algorithm over the conventional normalized correlation method

fast orthogonal haar transform patternmatching via image square sum although using image strip sum an orthogonal haar transform oht pattern matching algorithm may have good performance it requires three subtractions to calculate each haar projection value on the sliding windows by establishing a solid mathematical foundation for oht this paper based on the concept of image square sum proposes a novel fast orthogonal haar transform foht pattern matching algorithm from which a haar projection value can be obtained by only one subtraction thus higher speed ups can be achieved while producing the same results with the full search pattern matching a large number of experiments show that the speed ups of foht are very competitive with oht in most cases of matching one single pattern and generally higher than oht in all cases of matching multiple patterns exceeding other high level full search equivalent algorithms

a data driven intermediate level feature extraction algorithm an algorithm is presented that is based on the regression updating theory for fitting linearly parameterizable curves without prior classification of edge data an initial estimate of a hypothesized curve is first obtained by a statistical windowing technique a search region is determined and iteratively grown edge points in the search region are tested for their goodness of fit to the previous estimate the estimate is iteratively updated with the edge points that have favorable goodness of fit measures the edge points having poor goodness of fit measures are rejected as outliers the algorithm drives the estimate to converge to a final solution by repeatedly applying this procedure to the edge data excluded from the previous fitting all the underlying curves are reconstructed the major feature that distinguishes this approach from that of others is that classifying the edge data prior to fitting is not required advantages of this algorithm are 1 the fitting procedure achieves higher robustness and accuracy by dynamically analyzing the data consistency 2 the computational complexity increases only linearly with the number of edge data 3 the algorithm readily extends to reconstruct surfaces from range data thus the algorithm provides a powerful technique enabling a data driven intermediate level vision module to extract parametric features needed for higher level processing

bayesian recognition of local 3 d shape by approximating image intensity functions with quadric polynomials the recognition in image data of viewed patches of spheres cylinders and planes in the 3 d world is discussed as a first step to complex object recognition or complex object location and orientation estimation accordingly an image is partitioned into small square windows each of which is a view of a piece of a sphere or of a cylinder or of a plane windows are processed in parallel for recognition of content new concepts and techniques include approximations of the image within a window by 2 d quadric polynomials where each approximation is constrained by one of the hypotheses that the 3 d surface shape seen is either planar cylindrical or spherical a recognizer based upon these approximations to determine whether the object patch viewed is a piece of a sphere or a piece of a cylinder or a piece of a plane lowpass filtering of the image by the approximation the shape recognition is computationally simple and for large windows is approximately bayesian minimum probability of error recognition these classifications are useful for many purposes one such purpose is to enable a following processor to use an appropriate estimator to estimate shape and orientation and location parameters for the 3 d surface seen within a window

segmenting images corrupted by correlated noise image segmentation is fundamental to many image analysis problems it aims to partition a digital image into a set of nonoverlapping homogeneous regions the main contribution of this paper is the development of a new segmentation procedure which is designed to segment images corrupted by correlated noise this new segmentation procedure is based on rissanen s minimum description length mdl principle and consists of two components 1 an mdl based criterion in which the best segmentation is defined as its minimizer and 2 a merging algorithm which attempts to locate this minimizer the performance of this procedure is illustrated via a simulation study with promising results

coxeter transformation and inverses of cartan matrices for coalgebras abstract let c be a coalgebra and let z i c z i c z i c be the grothendieck groups of the category c o p inj and c inj of the socle finite injective right and left c comodules respectively one of the main aims of the paper is to study the coxeter transformation c z i c z i c and its dual c z i c z i c of a pointed sharp euler coalgebra c and to relate the action of c and c on a class of indecomposable finitely cogenerated c comodules n with the ends of almost split sequences starting with n or ending at n by applying chin kleiner and quinn 2002 5 we also show that if c is a pointed k coalgebra such that the every vertex of the left gabriel quiver q c of c has only finitely many neighbours then for any indecomposable non projective left c comodule n of finite k dimension there exists a unique almost split sequence 0 c n n n 0 in the category c comod f c of finitely cogenerated left c comodules with an indecomposable comodule c n we show that dim c n c dim n if c is hereditary or more generally if inj dim d n 1 and hom c c d n 0

variational problems and partial differential equations on implicit surfaces a novel framework for solving variational problems and partial differential equations for scalar and vector valued data defined on surfaces is introduced in this paper the key idea is to implicitly represent the surface as the level set of a higher dimensional function and to solve the surface equations in a fixed cartesian coordinate system using this new embedding function the equations are then both intrinsic to the surface and defined in the embedding space this approach thereby eliminates the need for performing complicated and inaccurate computations on triangulated surfaces as is commonly done in the literature we describe the framework and present examples in computer graphics and image processing applications including texture synthesis flow field visualization and image and vector field intrinsic regularization for data defined on 3d surfaces

segmented gray code kernels for fast pattern matching the gray code kernels gck family which has walsh hadamard transform on sliding windows as a member is a family of kernels that can perform image analysis efficiently using a fast algorithm such as the gck algorithm the gck has been successfully used for pattern matching in this paper we propose that the g4 gck algorithm is more efficient than the previous algorithm in computing gck the g4 gck algorithm requires four additions per pixel for three basis vectors independent of transform size and dimension based on the g4 gck algorithm we then propose the segmented gck by segmenting input data into ls parts the seggck requires only four additions per pixel for 3ls basis vectors experimental results show that the proposed algorithm can significantly accelerate the full search equivalent pattern matching process and outperforms state of the art methods

on optimally combining pieces of information with application to estimating 3 d complex object position from range data new asymptotic methods are introduced that permit computationally simple bayesian recognition and parameter estimation for many large data sets described by a combination of algebraic geometric and probabilistic models the techniques introduced permit controlled decomposition of a large problem into small problems for separate parallel processing where maximum likelihood estimation or bayesian estimation or recognition can be realized locally these results can be combined to arrive at globally optimum estimation or recognition the approach is applied to the maximum likelihood estimation of 3 d complex object position to this end the surface of an object is modeled as a collection of patches of primitive quadrics i e planar cylindrical and spherical patches possibly augmented by boundary segments the primitive surface patch models are specified by geometric parameters reflecting location orientation and dimension information the object position estimation is based on sets of range data points each set associated with an object primitive probability density functions are introduced that model the generation of range measurement points this entails the formulation of a noise mechanism in three space accounting for inaccuracies in the 3 d measurements and possibly for inaccuracies in the 3 d modeling we develop the necessary techniques for optimal local parameter estimation and primitive boundary or surface type recognition for each small patch of data and then optimal combining of these inaccurate locally derived parameter estimates in order to arrive at roughly globally optimum object position estimation

implicit b spline surface reconstruction this paper presents a fast and flexible curve and surface reconstruction technique based on implicit b spline this representation does not require any parameterization and it is locally supported this fact has been exploited in this paper to propose a reconstruction technique through solving a sparse system of equations this method is further accelerated to reduce the dimension to the active control lattice moreover the surface smoothness and user interaction are allowed for controlling the surface finally a novel weighting technique has been introduced in order to blend small patches and smooth them in the overlapping regions the whole framework is very fast and efficient and can handle large cloud of points with very low computational cost the experimental results show the flexibility and accuracy of the proposed algorithm to describe objects with complex topologies comparisons with other fitting methods highlight the superiority of the proposed approach in the presence of noise and missing data

efficient detection of symmetries of polynomially parametrized curves we present efficient algorithms for detecting central and mirror symmetry for the case of algebraic curves defined by means of polynomial parametrizations the algorithms are based on the existence of a linear relationship between two proper polynomial parametrizations of the curve which leads to a triangular polynomial system with complex unknowns that can be solved in a very fast way in particular curves parametrized by polynomials of serious degrees can be analyzed in a few seconds in our analysis we provide a good number of theoretical results on symmetries of polynomial curves algorithms for detecting rotation and mirror symmetry and closed formulas to determine the symmetry center and the symmetry axis when they exist a complexity analysis of the algorithms is also given

robust estimation for range image segmentation and reconstruction this correspondence presents a segmentation and fitting method using a new robust estimation technique we present a robust estimation method with high breakdown point which can tolerate more than 80 of outliers the method randomly samples appropriate range image points in the current processing region and solves equations determined by these points for parameters of selected primitive type from k samples we choose one set of sample points that determines a best fit equation for the largest homogeneous surface patch in the region this choice is made by measuring a residual consensus resc using a compressed histogram method which is effective at various noise levels after we get the best fit surface parameters the surface patch can be segmented from the region and the process is repeated until no pixel left the method segments the range image into planar and quadratic surfaces the resc method is a substantial improvement over the least median squares method by using histogram approach to inferring residual consensus a genetic algorithm is also incorporated to accelerate the random search

parameterized families of polynomials for bounded algebraic curve and surface fitting interest in algebraic curves and surfaces of high degree as geometric models or shape descriptors for different model based computer vision tasks has increased in recent years and although their properties make them a natural choice for object recognition and positioning applications algebraic curve and surface fitting algorithms often suffer from instability problems one of the main reasons for these problems is that while the data sets are always bounded the resulting algebraic curves or surfaces are in most cases unbounded in this paper the authors propose to constrain the polynomials to a family with bounded zero sets and use only members of this family in the fitting process for every even number d the authors introduce a new parameterized family of polynomials of degree d whose level sets are always bounded in particular its zero sets this family has the same number of degrees of freedom as a general polynomial of the same degree three methods for fitting members of this polynomial family to measured data points are introduced experimental results of fitting curves to sets of points in r sup 2 and surfaces to sets of points in r sup 3 are presented

a non trivial explicit solution for the 14 velocity cabannes kinetic model abstract we study the shock wave problem for the cabannes 14 velocity model of the boltzmann equation in one space dimension x axis and obtain a non trivial explicit solution which asymptotically connects two particular maxwellian states we prove that such a solution exists provided that a suitable condition on the differential elastic cross sections hold

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

recognition of 3d objects based on implicit polynomials closed form expressions for a new set of 3d rotation invariants that are linear quadratic and angular combinations of implicit polynomial ip coefficients are developed based on these invariants we propose a 3d object recognition method that outperforms recognition based on ip fitting after pose estimation and the mpeg 7 ssd technique

hom computable coalgebras a composition factors matrix and the euler bilinear form of an euler coalgebra abstract a composition factors matrix f c is studied for any basic hom computable k coalgebra c over an arbitrary field k in connection with a cartan matrix f c of c left euler k coalgebras c are defined they are studied by means of an euler integral bilinear form b c k 0 c k 0 c z the euler characteristic c m n of euler pairs of c comodules m and n and an euler defect c k 0 c k 0 c z of c it is shown that b c lgth m lgth n c m n c m n for all m n in c comod and c 0 if all simple c comodules are of finite injective dimension a diagrammatic characterisation of representation directed hereditary hom computable coalgebras is given

improving the stability of algebraic curves for applications an algebraic curve is defined as the zero set of a polynomial in two variables algebraic curves are practical for modeling shapes much more complicated than conics or superquadrics the main drawback in representing shapes by algebraic curves has been the lack of repeatability in fitting algebraic curves to data usually arguments against using algebraic curves involve references to mathematicians wilkinson and runge the first goal of this article is to understand the stability issue of algebraic curve fitting then a fitting method based on ridge regression and restricting the representation to well behaved subsets of polynomials is proposed and its properties are investigated the fitting algorithm is of sufficient stability for very fast position invariant shape recognition position estimation and shape tracking based on invariants and new representations among appropriate applications are shape based indexing into image databases

explicit three dimensional topology optimization via moving morphable void mmv approach abstract three dimensional 3d topology optimization problems always involve huge numbers of degrees of freedom dofs in finite element analysis fea and design variables in numerical optimization respectively this will inevitably lead to large computational efforts in the solution process in the present paper an efficient and explicit topology optimization approach which can reduce not only the number of design variables but also the number of degrees of freedom in fea is proposed based on the moving morphable voids mmvs solution framework this is achieved by introducing a set of geometry parameters e g control points of b spline surfaces to describe the boundary of a structure explicitly and removing the unnecessary dofs from the fe model at every step of numerical optimization numerical examples demonstrate that the proposed approach does can overcome the bottleneck problems associated with a 3d topology optimization problem in a straightforward way and enhance the solution efficiency significantly

subspace based discrete transform encoded local binary patterns representations for robust periocular matching on nist s face recognition grand challenge in this paper we employ several subspace representations principal component analysis unsupervised discriminant projection kernel class dependence feature analysis and kernel discriminant analysis on our proposd discrete transform encoded local binary patterns dt lbp to match periocular region on a large data set such as nist s face recognition grand challenge frgc ver2 database we strictly follow frgc experiment 4 protocol which involves 1 to 1 matching of 8014 uncontrolled probe periocular images to 16 028 controlled target periocular images 128 million pairwise face match comparisons the performance of the periocular region is compared with that of full face with different illumination preprocessing schemes the verification results on periocular region show that subspace representation on dt lbp outperforms lbp significantly and gains a giant leap from traditional subspace representation on raw pixel intensity additionally our proposed approach using only the periocular region is almost as good as full face with only 2 5 reduction in verification rate at 0 1 false accept rate yet we gain tolerance to expression occlusion and capability of matching partial faces in crowds in addition we have compared the best standalone dt lbp descriptor with eight other state of the art descriptors for facial recognition and achieved the best performance the two general frameworks are our major contribution 1 a general framework that employs various generative and discriminative subspace modeling techniques for dt lbp representation and 2 a general framework that encodes discrete transforms with local binary patterns for the creation of robust descriptors

the 3l algorithm for fitting implicit polynomial curves and surfaces to data we introduce a completely new approach to fitting implicit polynomial geometric shape models to data and to studying these polynomials the power of these models is in their ability to represent nonstar complex shapes in two 2d and three dimensional 3d data to permit fast repeatable fitting to unorganized data which may not be uniformly sampled and which may contain gaps to permit position invariant shape recognition based on new complete sets of euclidean and affine invariants and to permit fast stable single computation pose estimation the algorithm represents a significant advancement of implicit polynomial technology for four important reasons first it is orders of magnitude taster than existing fitting methods for implicit polynomial 2d curves and 3d surfaces and the algorithms for 2d and 3d are essentially the same second it has significantly better repeatability numerical stability and robustness than current methods in dealing with noisy deformed or missing data third it can easily fit polynomials of high such as 14th or 16th degree fourth additional linear constraints can be easily incorporated into the fitting process and general linear vector space concepts apply

heteroscedastic regression in computer vision problems with bilinear constraint we present an algorithm to estimate the parameters of a linear model in the presence of heteroscedastic noise i e each data point having a different covariance matrix the algorithm is motivated by the recovery of bilinear forms one of the fundamental problems in computer vision which appears whenever the epipolar constraint is imposed or a conic is fit to noisy data points we employ the errors in variables eiv model and show why already at moderate noise levels most available methods fail to provide a satisfactory solution the improved behavior of the new algorithm is due to two factors taking into account the heteroscedastic nature of the errors arising from the linearization of the bilinear form and the use of generalized singular value decomposition gsvd in the computations the performance of the algorithm is compared with several methods proposed in the literature for ellipse fitting and estimation of the fundamental matrix it is shown that the algorithm achieves the accuracy of nonlinear optimization techniques at much less computational cost

fast algorithm for walsh hadamard transform on sliding windows this paper proposes a fast algorithm for walsh hadamard transform on sliding windows which can be used to implement pattern matching most efficiently the computational requirement of the proposed algorithm is about 1 5 additions per projection vector per sample which is the lowest among existing fast algorithms for walsh hadamard transform on sliding windows

a bayesian method for fitting parametric and nonparametric models to noisy data we present a simple paradigm for fitting models parametric and nonparametric to noisy data which resolves some of the problems associated with classical mse algorithms this is done by considering each point on the model as a possible source for each data point the paradigm can be used to solve problems which are ill posed in the classical mse approach such as fitting a segment as opposed to a line it is shown to be nonbiased and to achieve excellent results for general curves even in the presence of strong discontinuities results are shown for a number of fitting problems including lines circles elliptic arcs segments rectangles and general curves contaminated by gaussian and uniform noise

a formal classification of 3d medial axis points and their local geometry this paper proposes a novel hypergraph skeletal representation for 3d shape based on a formal derivation of the generic structure of its medial axis by classifying each skeletal point by its order of contact we show that genetically the medial axis consists of five types of points which are then organized into sheets curves and points 1 sheets manifolds with boundary which are the locus of bitangent spheres with regular tangency a sub 1 sup 2 a sub k sup n notation means n distinct k fold tangencies of the sphere of contact as explained in the text two types of curves 2 the intersection curve of three sheets and the locus of centers of tritangent spheres a sub 1 sup 3 and 3 the boundary of sheets which are the locus of centers of spheres whose radius equals the larger principal curvature i e higher order contact a sub 3 points and two types of points 4 centers of quad tangent spheres a sub 1 sup 4 and 5 centers of spheres with one regular tangency and one higher order tangency a sub 1 a sub 3 the geometry of the 3d medial axis thus consists of sheets a sub 1 sup 2 bounded by one type of curve a sub 3 on their free end which corresponds to ridges on the surface and attached to two other sheets at another type of curve a sub 1 sup 3 which support a generalized cylinder description the a sub 3 curves can only end in a sub 1 a sub 3 points where they must meet an a sub 1 sup 3 curve the a sub 1 sup 3 curves meet together in fours at an a sub 1 sup 4 point this formal result leads to a compact representation for 3d shape referred to as the medial axis hypergraph representation consisting of nodes a sub 1 sup 4 and a sub 1 a sub 3 points links between pairs of nodes a sub 1 sup 3 and a sub 3 curves and hyperlinks between groups of links a sub 1 sup 2 sheets the description of the local geometry at nodes by itself is sufficient to capture qualitative aspects of shapes in analogy to 2d we derive a pointwise reconstruction formula to reconstruct a surface from this medial axis hypergraph together with the radius function thus this information completely characterizes 3d shape and lays the theoretical foundation for its use in recognition morphing design and manipulation of shapes

the enumerative geometry of projective algebraic surfaces and the complexity of aspect graphs the aspect graph is a popular viewer centered representation that enumerates all the topologically distinct views of an object building the aspect graph requires partitioning viewpoint space in view equivalent cells by a certain number of visual event surfaces if the object is piecewise smooth algebraic then all visual event surfaces are either made of lines having specified contacts with the object or made of lines supporting the points of contacts of planes having specified contacts with the object in this paper we present a general framework for studying the enumerative properties of line and plane systems the context is that of enumerative geometry and intersection theory in particular we give exact results for the degrees of all visual event surfaces coming up in the construction of aspect graphs of piecewise smooth algebraic bodies we conclude by giving a bound on the number of topologically distinet views of such objects

estimation of planar curves surfaces and nonplanar space curves defined by implicit equations with applications to edge and range image segmentation the author addresses the problem of parametric representation and estimation of complex planar curves in 2 d surfaces in 3 d and nonplanar space curves in 3 d curves and surfaces can be defined either parametrically or implicitly with the latter representation used here a planar curve is the set of zeros of a smooth function of two variables x y a surface is the set of zeros of a smooth function of three variables x y z and a space curve is the intersection of two surfaces which are the set of zeros of two linearly independent smooth functions of three variables x y z for example the surface of a complex object in 3 d can be represented as a subset of a single implicit surface with similar results for planar and space curves it is shown how this unified representation can be used for object recognition object position estimation and segmentation of objects into meaningful subobjects that is the detection of interest regions that are more complex than high curvature regions and hence more useful as features for object recognition

focused color intersection with efficient searching for object extraction we propose focused color intersection with efficient searching for identifying and extracting the objects in a complex scene based on color similarity the method matches the models against different parts of a scene called focus regions using normalized color histogram intersection the best matching focus region is determined by an efficient search strategy employing upper bound pruning this search strategy called active search concentrates its effort on parts of the scene having high similarity with the object consequently it achieves a large reduction in computational effort without sacrificing accuracy an efficient algorithm for evaluating the color histogram intersection between a model and a focus region is also given experiments conducted demonstrate that multiple known objects in complex scenes can be extracted by this process the method is stable against scale changes two dimensional rotation moderate changes in shape and partial occlusion

detection of object wings in fused range and intensity imagery abstract we present methods for detecting primitives in scenes containing objects whose surfaces are approximately piecewise quadric using a sensor that yields fused range and intensity the primitives detected in a fused image are viewpoint dependent and are called object wings which consist of adjacent fragments of object contour and surface wings are small enough so that some object parts can be sensed despite significant occlusion yet rich enough to be of use in indexing to candidate models in constraining object pose and in aggregation methods which combine primitives into larger structures or objects fitting procedures are defined for specific wing primitives experiments with both synthetic and real data show that classification within the wing types of planar spherical conical cylindrical can be achieved with over 90 accuracy contour information available in fitting fused data improves fitting relative to use of surface data alone moreover it is shown that only a small number of contour and surface samples are needed for extraction of primitives oc 1997 pattern recognition society

median spheres theory algorithms applications a generalized hypersphere is either a hyperplane or a hypersphere which consists of all points equidistant from a center geometrically a weighted median hypersphere minimizes a weighted average of the distances from it to finitely many data points as proved here for each finite data set there exists at least one weighted median generalized hypersphere moreover denote the sums of the weights of the data points inside by w outside by w and on the hypersphere by w 0 the present results show that each weighted median hypersphere is a weighted pseudo halving hypersphere in the sense that w w w 0 and passes through at least two distinct data points combinatorically a hypersphere is blocked if and only if it passes through data points in general position in the sense that no other hypersphere passes through the same data points a hypersphere is a halving hypersphere if and only if it is blocked contains exactly k data points inside confines exactly l data points outside and k l 1 in the plane the present results also show that if a median circle is not a halving circle then moving its center along a median between two data points on it until it passes through the next data point yields a halving circle relative to the center if the direction cosines of the external and internal data points have the same mean and variance then the median circle must be blocked and stays so under sufficiently small perturbations of the data moreover for every set of four points at least one unweighted median circle is blocked these results lend credence to a variant of a method used by archaeologists and explain some findings from operations research

almost split sequences for comodules abstract let be a coalgebra over a field k we introduce an operator tr that takes a right quasi finitely copresented comodule m to a left quasi finitely copresented comodule tr m if m is indecomposable not injective and tr m is finite dimensional over k we prove the existence of an almost split sequence 0 m e dtr m 0 in the category of all right comodules where d homk k if is right semiperfect and the embedding of each simple right comodule s into its injective envelope i s has the property that the socle of i s s is finite dimensional the above almost split sequence exists for each finite dimensional m and dtr m is also finite dimensional

2 d object recognition using invariant contour descriptor and projective refinement abstract this paper presents an efficient model based recognition method to recognize 2 d objects and to obtain correspondences between models and scene boundaries with a subpixel positioning error as a shape signature for a contour we propose a descriptor consisting of five point invariants which are used to index a hash table also we propose a projective refinement as a verification method to compute exact correspondences between models and scene contour points this method repeatedly computes projective transformation using a weighted pseudo inverse we present an error model for five point invariants which are used to define a similarity between two descriptors to determine a searching bound in indexing and to obtain the weights in the projective refinement in experiments using seriously distorted images of forty models this method led to the recognition of planar curved objects a transformation using the correspondence between the model and scene points on contours was also obtained

describing complicated objects by implicit polynomials this paper introduces and focuses on two problems first is the representation power of closed implicit polynomials of modest degree for curves in 2 d images and surfaces in 3 d range data super quadrics are a small subset of object boundaries that are well fitted by these polynomials the second problem is the stable computationally efficient fitting of noisy data by closed implicit polynomial curves and surfaces the attractive features of these polynomials for vision is discussed

noetherian hereditary abelian categories satisfying serre duality norwegian univ sci technol dept math sci n 7491 trondheim norway limburgs univ ctr dept wni b 3590 diepenbeek belgium reiten i norwegian univ sci technol dept math sci n 7491 trondheim norway