shape description and matching using integral invariants on eccentricity transformed images matching occluded and noisy shapes is a problem frequently encountered in medical image analysis and more generally in computer vision to keep track of changes inside the breast for example it is important for a computer aided detection system to establish correspondences between regions of interest shape transformations computed both with integral invariants ii and with geodesic distance yield signatures that are invariant to isometric deformations such as bending and articulations integral invariants describe the boundaries of planar shapes however they provide no information about where a particular feature lies on the boundary with regard to the overall shape structure conversely eccentricity transforms ecc can match shapes by signatures of geodesic distance histograms based on information from inside the shape but they ignore the boundary information we describe a method that combines the boundary signature of a shape obtained from ii and structural information from the ecc to yield results that improve on them separately

globally consistent reconstruction of ripped up documents one of the most crucial steps for automatically reconstructing ripped up documents is to find a globally consistent solution from the ambiguous candidate matches however little work has been done so far to solve this problem in a general computational framework without using application specific features in this paper we propose a global approach for reconstructing ripped up documents by first finding candidate matches from document fragments using curve matching and then disambiguating these candidates through a relaxation process to reconstruct the original document the candidate disambiguation problem is formulated in a relaxation scheme in which the definition of compatibility between neighboring matches is proposed and global consistency is defined as the global criterion initially global match confidences are assigned to each of the candidate matches after that the overall local relationships among neighboring matches are evaluated by computing their global consistency then these confidences are iteratively updated using the gradient projection method to maximize the criterion this leads to a globally consistent solution and thus provides a sound document reconstruction the overall performance of our approach in several practical experiments is illustrated the results indicate that the reconstruction of ripped up documents up to 50 pieces is possibly accomplished automatically

the numerical analysis of ordinary differential equations runge kutta and general linear methods mathematical and computational introduction the euler method and its generalizations analysis of runge kutta methods general linear methods bibliography

a theoretical framework for relaxation processes in pattern recognition application to robust nonparametric contour generalization while various approaches are suggested in the literature to describe and generalize relaxation processes concerning to several objectives the wider problem addressed here is to find the best suited relaxation process for a given assignment problem or better still to construct a task dependent relaxation process for this we develop a general framework for the theoretical foundations of relaxation processes in pattern recognition the resulting structure enables 1 a description of all known relaxation processes in general terms and 2 the design of task dependent relaxation processes we show that the well known standard relaxation formulas verify our approach referring to the common problem of generating a generalized description of a contour we demonstrate the applicability of the suggested generalization in detail important characteristics of the constructed task dependent relaxation process are 1 the independency of the segmentation from any parameters 2 the invariance to geometric transformations 3 the simplicity and 4 efficiency

zero stability properties of the three ordinate variable stepsize variable formula methods consider the systemy f x y y a x a b y r n wheref is continuous and lipschitzian with respect to the second argument very often linear multistep variable stepsize variable formula methods lm vsvfm s are used to computey k y xk on the points of the grid a x 0 x1 x2 xn b the general lm vsvfm is based on formulae of the following type y k sum limits i 1 s k alpha i bar h k sk y k i sum limits i 0 s k h k i beta i bar h k s k f x k i y k i whereh k xk xk 1 bar h k h k h k 1 ldots h k s k s k k k 1 1 n the coefficients i and i depend on the lasts k 1 stepsizes and on the formula used at stepk only the zero stability properties of some special classes of lm vsvfm s as for example those based on adams formulae were investigated in the literature a class of three ordinate lm vsvfm s is defined in this paper some results concerning the zero stability properties of these methods are proved it is shown that some well known results are simple corollaries of the results found for the three ordinate lm vsvfm s it is easily seen that similar results hold for the corresponding one leg vsvfm s finally the use of the theoretical results in the practical implementations is briefly discussed

quasilinear multistep methods and variable step predictor corrector methods for neutral functional differential equations the theory of quasilinear multistep methods and predictor corrector methods for neutral functional differential equations is developed the theorem about the asymptotic behaviour of the global discretization error of quasilinear methods which forms a theoretical basis for step control strategy for predictor corrector methods for neutral equations is given some problems of implementation of these methods are also addressed and the results of numerical experiments are presented

robust detection and identification of sparse segments in ultrahigh dimensional data analysis copy number variants cnvs are alternations of dna of a genome that results in the cell having a less or more than two copies of segments of the dna cnvs correspond to relatively large regions of the genome ranging from about one kilobase to several megabases that are deleted or duplicated motivated by cnv analysis based on next generation sequencing data we consider the problem of detecting and identifying sparse short segments hidden in a long linear sequence of data with an unspecified noise distribution we propose a computationally efficient method that provides a robust and near optimal solution for segment identification over a wide range of noise distributions we theoretically quantify the conditions for detecting the segment signals and show that the method near optimally estimates the signal segments whenever it is possible to detect their existence simulation studies are carried out to demonstrate the efficiency of the method under different noise distributions we present results from a cnv analysis of a hapmap yoruban sample to further illustrate the theory and the methods

invariant geometric evolutions of surfaces and volumetric smoothing the study of geometric flows for smoothing multiscale representation and analysis of two and three dimensional objects has received much attention in the past few years in this paper we first survey the geometric smoothing of curves and surfaces via geometric heat type flows which are invariant under the groups of euclidean and affine motions second using the general theory of differential invariants we determine the general formula for a geometric hypersurface evolution which is invariant under a prescribed symmetry group as an application we present the simplest affine invariant flow for convex surfaces in three dimensional space which like the affine invariant curve shortening flow will be of fundamental importance in the processing of three dimensional images

stability restrictions on time stepsize for numerical integration of first order partial differential equations mathematical models described by partial differential equations appear often when different phenomena related to atmospheric transport for example advection and diffusion processes are studied truncated fourier series can be used in the discretization of the space derivatives resulting in a pseudospectral method in this way the partial differential equation is transformed into a system of ordinary differential equations this system is normally solved by so called step by step integration methods the stability properties of these methods are studied some bounds for the time stepsize are derived several formulae and predictor corrector schemes with large stability intervals on the imaginary axis are constructed numerical experiments with eight time integration algorithms are carried out some recommendations concerning the choice of the time integration algorithms in three different situations are given it is emphasized that in a package for the solution of partial differential equations describing transport processes in the atmospheric environment one should have several time integration algorithms each of which can be chosen optionally finally the possibility of using variable stepsize variable formula time integration algorithms is briefly discussed

implementation of a variable stepsize variable formula method in the time integration part of a code for treatment of long range transport of air pollutants abstract a mathematical model consisting of two partial differential equations is used to study the long range transport of sulphur di oxide and sulphate over europe the discretization of the first order space derivatives the advection terms is carried out by a pseudospectral fourier algorithm a special technique is applied in the discretization of the second order space derivatives the diffusion terms two large systems of ordinary differential equations are solved at each time step it is shown that these systems can efficiently be treated by a variable stepsize variable formula method vsvfm based on the use of predictor corrector schemes the stepsize selection strategy and the formula selection strategy are discussed in detail an attempt to carry out both an accuracy control and a stability control is made at each time step the great efficiency of the vsvfm implemented in our software as well as the reliability of the results are illustrated by numerical experiments in which real meteorological data for 1979 at the grid points of a space domain covering the whole of europe were used the main ideas implemented in the time integration part might be applied in many other situations where the systems of ordinary differential equations arising after the space discretization are only moderately stiff so that the stability requirements are dominant over the accuracy requirements on a large part of the time interval but the use of implicit time integration algorithms that require solving systems of algebraic equations at each time step is not justified as an illustration only it should be mentioned that such an application has been carried out in connection with models describing long range transport of nitrogen pollutants over europe

similarity invariant signatures for partially occluded planar shapes a methodology is described for associating local invariant signature functions to smooth planar curves in order to enable their translation rotation and scale invariant recognition from arbitrarily clipped portions the suggested framework incorporates previous approaches based on locating inflections curvature extrema breakpoints and other singular points on planar object boundaries and provides a systematic way of deriving novel invariant signature functions based on curvature or cumulative turn angle of curves these new signatures allow the specification of arbitrarily dense feature points on smooth curves whose locations are invariant under similarity transformations the results are useful for detecting and recognizing partially occluded planar objects a key task in low level robot vision

geometric computation of curvature driven plane curve evolutions we present a new numerical scheme for planar curve evolution with a normal velocity equal to f kappa where kappa is the curvature and f is a nondecreasing function such that f 0 0 and either x mapsto f x 3 is lipschitz with lipschitz constant less than or equal to 1 or f x x gamma for gamma geq 1 3 the scheme is completely geometrical and avoids some drawbacks of finite difference schemes in particular no special parameterization is needed and the scheme is monotone that is if a curve initially surrounds another one then this remains true during their evolution which guarantees numerical stability we prove consistency and convergence of this scheme in a weak sense finally we display some numerical experiments on synthetic and real data

foundations of semi differential invariants this paper elaborates the theoretical foundations of a semi differential framework for invariance semi differential invariants combine coordinates and their derivatives with respect to some contour parameter at several points of the image contour thus allowing for an optimal trade off between identification of points and the calculation of derivatives a systematic way of generating complete and independent sets of such invariants is presented it is also shown that invariance under reparametrisation can be cast in the same framework the theory is illustrated by a complete analysis of 2d affine transformations in a companion paper pauwels et al 1995 these affine semi differential invariants are implemented in the computer program form flat object recognition method for the recognition of planar contours under pseudo perspective projection

affine geometry curve flows and invariant numerical approximations abstract a new geometric approach to the affine geometry of curves in the plane and to affine invariant curve shortening is presented we describe methods of approximating the affine curvature with discrete finite difference approximations based on a general theory of approximating differential invariants of lie group actions by joint invariants applications to computer vision are indicated

analyzing skewed symmetries symmetry is pervasive in both man made objects and nature since symmetries project to skew symmetries finding axes of skew symmetry is an important vision task this paper presents a linear time algorithm for finding the axes of skew symmetry where the degree of symmetry is known first we present a review and critique of current methods for finding the axes of skew symmetry next we decompose the problem of finding skew symmetry into the subproblems of solving for the rotational parameter of a shear symmetry and recovering the shear parameter of a reflexive symmetry using this approach the authors derive a direct non heuristic moment based technique for finding the axes of skew symmetry for skew symmetric figures with degree of symmetry less than five we obtain a closed form solution the method does not rely on continuous contours but assumes there is no occlusion and requires knowing the contour s degree of symmetry it is the first algorithm to find the axes of skew symmetry ino n time where n is the number of contour points the method is especially suited to industrial applications where the degree of symmetry is often knowna priori examples of the method are presented for both real and synthetic images and an error analysis of the method is given

nonparametric segmentation of curves into various representations this paper describes and demonstrates the operation and performance of an algorithm for segmenting connected points into a combination of representations such as lines circular elliptical and superelliptical arcs and polynomials the algorithm has a number of interesting properties including being scale invariant nonparametric general purpose and efficient

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

on the selection of 2d krawtchouk moments for face recognition sparse representation of images using orthogonal two dimensional krawtchouk moments 2d kcms for face recognition is motivated by their ability to capture region based higher order hidden nonlinear structures from discrete coordinates of finitely supported images and the invariance of affine transformations of these moments to common geometric distortions this paper presents the effectiveness of selecting the discriminatory set of kcms as the global and local face features as opposed to traditional features obtained from heuristic choice of fixed order moments or projection of the moments for recognizing an identity the selection of significantly sparse 2d kcm based features according to the proposed approach results in highly efficient face recognition method as compared to the other methods that use orthogonal moments such as the 2d zernike 2d tchebichef or 2d gaussian hermite experiments on challenging databases viz frgc and ck auc and comparisons with the well established projection texture and moment based methods indicate superior recognition performance in terms of mean accuracy and robustness of the proposed holistic or hybrid type discriminative kcm based method especially when sample sizes are small and the intraclass faces have significant variations due to expressions highlightshybrid type face recognition using discriminative selection of krawtchouk moments a comparative study of different moment based discriminative face features experiments on two challenging databases show superiority of the proposed selection fisher scoring is preferable to lda projection for moment based face recognition effective facial parts are identified for recognition of expression variant faces

on affine plane curve evolution abstract an affine invariant curve evolution process is presented in this work the evolution studied is the affine analogue of the euclidean curve shortening flow evolution equations for both affine and euclidean invariants are developed an affine version of the classical euclidean isoperimetric inequality is proved this inequality is used to show that in the case of affine evolution of convex plane curves the affine isoperimetric ratio is a non decreasing function of time convergence of this affine isoperimetric ratio to the ellipse s value 8 2 as well as convergence in the hausdorff metric of the evolving curve to an ellipse is also proved

noise resistant invariants of curves projective invariants are shape descriptors that are independent of the point of view from which the shape is seen and therefore are of major importance in object recognition they make it possible to match an image of an object to one stored in a database without the need for searching for the correct viewpoint an invariant representation of a general curve is obtained the calculation is local and does not suffer from the occlusion problem of global descriptors to make the method robust differentiation techniques that give much more reliable results than previous ones are developed these differentiation methods are useful in many other applications as well

optimal detection of heterogeneous and heteroscedastic mixtures the problem of detecting heterogeneous and heteroscedastic gaussian mixtures is considered the focus is on how the parameters of heterogeneity heteroscedasticity and proportion of non null component influence the difficulty of the problem we establish an explicit detection boundary which separates the detectable region where the likelihood ratio test is shown to reliably detect the presence of non null effect from the undetectable region where no method can do so in particular the results show that the detection boundary changes dramatically when the proportion of nonnull component shifts from the sparse regime to the dense regime furthermore it is shown that the higher criticism test which does not require the specific information of model parameters is optimally adaptive to the unknown degrees of heterogeneity and heteroscedasticity in both the sparse and dense cases

the patch transform the patch transform represents an image as a bag of overlapping patches sampled on a regular grid this representation allows users to manipulate images in the patch domain which then seeds the inverse patch transform to synthesize modified images possible modifications include the spatial locations of patches the size of the output image or the pool of patches from which an image is reconstructed when no modifications are made the inverse patch transform reduces to solving a jigsaw puzzle the inverse patch transform is posed as a patch assignment problem on a markov random field mrf where each patch should be used only once and neighboring patches should fit to form a plausible image we find an approximate solution to the mrf using loopy belief propagation introducing an approximation that encourages the solution to use each patch only once the image reconstruction algorithm scales well with the total number of patches through label pruning in addition structural misalignment artifacts are suppressed through a patch jittering scheme that spatially jitters the assigned patches we demonstrate the patch transform and its effectiveness on natural images

stochastic level set method for shape optimisation we present a new method for stochastic shape optimisation of engineering structures the method generalises an existing deterministic scheme in which the structure is represented and evolved by a level set method coupled with mathematical programming the stochastic element of the algorithm is built on the methods of statistical mechanics and is designed so that the system explores a boltzmann gibbs distribution of structures in non convex optimisation problems the deterministic algorithm can get trapped in local optima the stochastic generalisation enables sampling of multiple local optima which aids the search for the globally optimal structure the method is demonstrated for several simple geometrical problems and a proof of principle calculation is shown for a simple engineering structure

stability of multistep methods on variable grids this paper is concerned with the stability of multistep methods for ordinary initial value problems on grids with variable mesh sizes a necessary and sufficient condition for stability is given from which generalizations of recent results by gear et al and by zlatev can be obtained as special cases as an application the stability of the variable bdf formulas is treated

differential and numerically invariant signature curves applied to object recognition we introduce a new paradigm the differential invariant signature curve or manifold for the invariant recognition of visual objects a general theorem of e cartan implies that two curves are related by a group transformation if and only if their signature curves are identical the important examples of the euclidean and equi affine groups are discussed in detail secondly we show how a new approach to the numerical approximation of differential invariants based on suitable combination of joint invariants of the underlying group action allows one to numerically compute differential invariant signatures in a fully group invariant manner applications to a variety of fundamental issues in vision including detection of symmetries visual tracking and reconstruction of occlusions are discussed

an efficiently computable metric for comparing polygonal shapes a method for comparing polygons that is a metric invariant under translation rotation and change of scale reasonably easy to compute and intuitive is presented the method is based on the l sub 2 distance between the turning functions of the two polygons it works for both convex and nonconvex polygons and runs in time o mn log mn where m is the number of vertices in one polygon and n is the number of vertices in the other some examples showing that the method produces answers that are intuitively reasonable are presented

similarity and affine invariant distances between 2d point sets we develop expressions for measuring the distance between 2d point sets which are invariant to either 2d affine transformations or 2d similarity transformations of the sets and assuming a known correspondence between the point sets we discuss the image normalization to be applied to the images before their comparison so that the computed distance is symmetric with respect to the two images we then give a general metric definition of the distance between images which leads to the same expressions for the similarity and affine cases this definition avoids ad hoc decisions about normalization moreover it makes it possible to compute the distance between images under different conditions including cases where the images are treated asymmetrically we demonstrate these results with real and simulated images

mathematical model for studying the sulphur pollution over europe the long range transport of sulphur pollutants in the atmosphere is an important environmental problem a mathematical model consisting of a system of partial differential equations has been developed at the danish agency of environmental protection for studying this phenomenon the model is handled numerically a pseudospectral fourier algorithm is used in the space discretization phase a variable stepsize variable formula method vsvfm based on predictor corrector schemes may be specified during the time discretization part the time integration formulae are especially constructed so that a the predictor corrector schemes have good absolute stability properties on the imaginary axis and b the fundamental properties consistency zero stability and convergence of the global vsvfm are not affected by the changes of the stepsize and or the predictor corrector scheme both the accuracy requirements and the stability requirements are taken into account in the stepsize selection strategy as well as in the formula selection strategy this double check leads to a great efficiency in the numerical treatment of problems arising in atmospheric environments this is demonstrated by many numerical results the question of the reliability of the results obtained in runs of real physical problems is discussed some results obtained in the comparison of calculated results with measurements are reported an illustration where the model is applied in studying the air pollution in the area around denmark due to danish sources is presented

a robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry abstract this paper proposes a robust approach to image matching by exploiting the only available geometric constraint namely the epipolar constraint the images are uncalibrated namely the motion between them and the camera parameters are not known thus the images can be taken by different cameras or a single camera at different time instants if we make an exhaustive search for the epipolar geometry the complexity is prohibitively high the idea underlying our approach is to use classical techniques correlation and relaxation methods in our particular implementation to find an initial set of matches and then use a robust technique the least median of squares lmeds to discard false matches in this set the epipolar geometry can then be accurately estimated using a meaningful image criterion more matches are eventually found as in stereo matching by using the recovered epipolar geometry a large number of experiments have been carried out and very good results have been obtained regarding the relaxation technique we define a new measure of matching support which allows a higher tolerance to deformation with respect to rigid transformations in the image plane and a smaller contribution for distant matches than for nearby ones a new strategy for updating matches is developed which only selects those matches having both high matching support and low matching ambiguity the update strategy is different from the classical winner take all which is easily stuck at a local minimum and also from loser take nothing which is usually very slow the proposed algorithm has been widely tested and works remarkably well in a scene with many repetitive patterns

numerical solution of ordinary differential equations is there anything left to do two decades ago many people thought that there was very little left to occupy the researcher in the numerical initial value problem for ordinary differential equations but there has since been an enormous increase in the effort devoted to this problem and related software is everything finally done so we can turn to more difficult areas this paper examines the development of numerical solution techniques from the identification of a problem to the never final preparation of automatic codes for the solution of classes of similar problems it discusses a number of ode problems that are only a part of the way along this path of development these problems include ones with highly oscillatory solutions ones with frequent discontinuities and ones in which very little accuracy is needed and which should be integrated at low cost there is a spectrum of problems from ones that can now be solved using very robust software to ones that we still do not know how to solve effectively the paper then surveys s

planar object recognition using projective shape representation we describe a model based recognition system called lewis for the identification of planar objects based on a projectively invariant representation of shape the advantages of this shape description include simple model acquisition direct from images no need for camera calibration or object pose computation and the use of index functions we describe the feature construction and recognition algorithms in detail and provide an analysis of the combinatorial advantages of using index functions index functions are used to select models from a model base and are constructed from projective invariants based on algebraic curves and a canonical projective coordinate frame examples are given of object recognition from images of real scenes with extensive object libraries successful recognition is demonstrated despite partial occlusion by unmodelled objects and realistic lighting conditions

geometric invariants and object recognition we discuss the role of the general invariance concept in object recognition and review the classical and recent literature on projective invariance invariants help solve major problems of object recognition for instance different images of the same object often differ from each other because of the different viewpoint from which they were obtained to match the two images common methods thus need to find the correct viewpoint a difficult problem that can involve search in a high dimensional space of all possible points of view and or finding point correspondences geometric invariants are shape descriptors computed from the geometry of the shape that remain unchanged under geometric transformations such as changing the viewpoint thus they can be matched without search deformations of objects are another important class of geometric changes for which invariance is useful

shape matching using multiscale integral invariants we present a shape descriptor based on integral kernels shape is represented in an implicit form and it is characterized by a series of isotropic kernels that provide desirable invariance properties the shape features are characterized at multiple scales which form a signature that is a compact description of shape over a range of scales the shape signature is designed to be invariant with respect to group transformations which include translation rotation scaling and reflection in addition the integral kernels that characterize local shape geometry enable the shape signature to be robust with respect to undesirable perturbations while retaining discriminative power use of our shape signature is demonstrated for shape matching based on a number of synthetic and real examples

efficient solution to the 3d problem of automatic wall paintings reassembly this paper introduces a new approach for the automated reconstruction reassembly of fragmented objects having one surface near to plane on the basis of the 3d representation of their constituent fragments the whole process starts by 3d scanning of the available fragments the obtained representations are properly processed so that they can be tested for possible matches next four novel criteria are introduced that lead to the determination of pairs of matching fragments these criteria have been chosen so as the whole process imitates the instinctive reassembling method dedicated scholars apply the first criterion exploits the volume of the gap between two properly placed fragments the second one considers the fragments overlapping in each possible matching position criteria 3 4 employ principles from calculus of variations to obtain bounds for the area and the mean curvature of the contact surfaces and the length of contact curves which must hold if the two fragments match the method has been applied with great success both in the reconstruction of objects artificially broken by the authors and most importantly in the virtual reassembling of parts of wall paintings belonging to the mycenaic civilization c 1300 bc excavated in a highly fragmented condition in tyrins greece

detecting similarity of rational plane curves a novel and deterministic algorithm is presented to detect whether two given rational plane curves are related by means of a similarity which is a central question in pattern recognition as a by product it finds all such similarities and the particular case of equal curves yields all symmetries a complete theoretical description of the method is provided and the method has been implemented and tested in the sage system for curves of moderate degrees

integral invariants for space motion trajectory matching and recognition motion trajectories provide a key and informative clue in motion characterization of humans robots and moving objects in this paper we propose some new integral invariants for space motion trajectories which benefit effective motion trajectory matching and recognition integral invariants are defined as the line integrals of a class of kernel functions along a motion trajectory a robust estimation of the integral invariants is formulated based on the blurred segment of noisy discrete curve then a non linear distance of the integral invariants is defined to measure the similarity for trajectory matching and recognition such integral invariants in addition to being invariant to transformation groups have some desirable properties such as noise insensitivity computational locality and uniqueness of representation experimental results on trajectory matching and sign recognition show the effectiveness and robustness of the proposed integral invariants in motion trajectory matching and recognition a meaningful definition of integral invariants for space trajectories is proposed we derive a novel estimation method of integral invariants for discrete trajectories a non linear distance is defined to measure the similarity between trajectories integral invariants show robustness to noise occlusions and transformations experiments are carried out to examine their effectiveness and robustness in applications

the convergence of variable stepsize variable formula multistep methods in this paper variable stepsize variable formula multistep methods for the numerical solution of ordinary differential equations are considered some more general results on stability than are given in the papers of gear tu siam j numer anal 11 1974 pp 1025 1043 and gear watanabe siam j numer anal 11 1974 pp 1044 1058 are obtained further the asymptotic behavior of the error in the variable stepsize fixed formula case is studied finally the above study is extended to predictor corrector methods

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

handwritten chinese text line segmentation by clustering with distance metric learning separating text lines in unconstrained handwritten documents remains a challenge because the handwritten text lines are often un uniformly skewed and curved and the space between lines is not obvious in this paper we propose a novel text line segmentation algorithm based on minimal spanning tree mst clustering with distance metric learning given a distance metric the connected components ccs of document image are grouped into a tree structure from which text lines are extracted by dynamically cutting the edges using a new hypervolume reduction criterion and a straightness measure by learning the distance metric in supervised learning on a dataset of pairs of ccs the proposed algorithm is made robust to handle various documents with multi skewed and curved text lines in experiments on a database with 803 unconstrained handwritten chinese document images containing a total of 8 169 lines the proposed algorithm achieved a correct rate 98 02 of line detection and compared favorably to other competitive algorithms

the local projective shape of smooth surfaces and their outlines this article examines projectively invariant local geometric properties of smooth curves and surfaces oriented projective differential geometry is proposed as a general framework for establishing such invariants and characterizing the local projective shape of surfaces and their outlines it is applied to two problems 1 the projective generalization of koenderink s famous characterization of convexities concavities and inflections of the apparent contours of solids bounded by smooth surfaces and 2 the image based construction of rim meshes which provide a combinatorial description of the arrangement induced on the surface of an object by the contour generators associated with multiple cameras observing it

recognition of planar shapes under affine distortion methods for the recognition ofplanar shapes from arbitrary viewpoints are described the adopted model of projection is orthographic the invariant descriptions derived for this group are one dimensional shape signatures comparable to the well known curvature as a function of arc length description of euclidean geometry since the use of such differential invariants in the affine case would lead to unacceptably high orders of derivatives affine invariant descriptions based onsemi differential invariants are proposed as an alternative a systematic discussion of different types of these invariants is given the usefulness and viability of this methodology is demonstrated on a database containing more than 40 objects

the stability of variable stepsize nordsieck methods conditions are given for the stability of multistep methods that vary the stepsize using the interpolation technique of nordsieck if the stepsize selection function is variation bounded then these methods are stable alternatively there exist constants a b c depending on the method and satisfying a leqq b 1 c such that if the stepsize ratio h n 1 h n satisfies either 0 h n 1 h n leqq a or b h n 1 h n leqq c then the method is stable as the frequency of stepsize changing decreases the methods become more stable in the sense that the intervals defined by a b and c are larger tables and graphs are given for the adams and backward differentiation methods indicating how stability changes with frequency of changing stepsize in particular it is shown that k 1 value adams formulas k leqq 6 are stable for 0 h n 1 h n leqq c that is it is shown that stability is maintained whenever the stepsize is decreased by an arb

a unified curvature definition for regular polygonal and digital planar curves in this paper we propose a new definition of curvature called visual curvature it is based on statistics of the extreme points of the height functions computed over all directions by gradually ignoring relatively small heights a multi scale curvature is obtained the theoretical properties and the experiments presented demonstrate that multi scale visual curvature is stable even in the presence of significant noise to our best knowledge the proposed definition of visual curvature is the first ever that applies to regular curves as defined in differential geometry as well as to turn angles of polygonal curves moreover it yields stable curvature estimates of curves in digital images even under sever distortions we also show a relation between multi scale visual curvature and convexity of simple closed curves

the heat equation shrinks embedded plane curves to round points soit c 0 s 1 r 2 une courbe lisse plongee dans le plan alors c s 1 0 t r 2 existe en satisfaisant c t k n ou k est la courbure de c et n est son vecteur unite normal entrant c t est lisse pour tout t il converge vers un point quand t t et sa forme limite quand t t est un cercle rond avec convergence dans norme c

integral invariants for shape matching for shapes represented as closed planar contours we introduce a class of functionals which are invariant with respect to the euclidean group and which are obtained by performing integral operations while such integral invariants enjoy some of the desirable properties of their differential counterparts such as locality of computation which allows matching under occlusions and uniqueness of representation asymptotically they do not exhibit the noise sensitivity associated with differential quantities and therefore do not require presmoothing of the input shape our formulation allows the analysis of shapes at multiple scales based on integral invariants we define a notion of distance between shapes the proposed distance measure can be computed efficiently and allows warping the shape boundaries onto each other its computation results in optimal point correspondence as an intermediate step numerical results on shape matching demonstrate that this framework can match shapes despite the deformation of subparts missing parts and noise as a quantitative analysis we report matching scores for shape retrieval from a database

recognizing solid objects by alignment with an image in this paper we consider the problem of recognizing solid objects from a single two dimensional image of a three dimensional scene we develop a new method for computing a transformation from a three dimensional model coordinate frame to the two dimensional image coordinate frame using three pairs of model and image points we show that this transformation always exists for three noncollinear points and is unique up to a reflective ambiguity the solution method is closed form and only involves second order equations we have implemented a recognition system that uses this transformation method to determine possible alignments of a model with an image each of these hypothesized matches is verified by comparing the entire edge contours of the aligned object with the image edges using the entire edge contours for verification rather than a few local feature points reduces the chance of finding false matches the system has been tested on partly occluded objects in highly cluttered scenes

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

the heat equation shrinking convex plane curves soient m et m des varietes de riemann et f m m une application reguliere si m est une courbe convexe plongee dans le plan r 2 l equation de la chaleur contracte m a un point

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

numerically invariant signature curves corrected versions of the numerically invariant expressions for the affine and euclidean signature of a planar curve introduced by calabi et al in int j comput vision 26 107 135 1998 are presented the new formulas are valid for fine but otherwise arbitrary partitions of the curve we also give numerically invariant expressions for the four differential invariants parameterizing the three dimensional version of the euclidean signature curve namely the curvature the torsion and their derivatives with respect to arc length

shapes shocks and deformations i the components of two dimensional shape and the reaction diffusion space we undertake to develop a general theory of two dimensional shape by elucidating several principles which any such theory should meet the principles are organized around two basic intuitions first if a boundary were changed only slightly then in general its shape would change only slightly this leads us to propose an operational theory of shape based on incremental contour deformations the second intuition is that not all contours are shapes but rather only those that can enclose physical material a theory of contour deformation is derived from these principles based on abstract conservation principles and hamilton jacobi theory these principles are based on the work of sethian 1985a c the osher sethian 1988 level set formulation the classical shock theory of lax 1971 1973 as well as curve evolution theory for a curve evolving as a function of the curvature and the relation to geometric smoothing of gage hamilton grayson 1986 1989 the result is a characterization of the computational elements of shape deformations parts bends and seeds which show where to place the components of a shape the theory unifies many of the diverse aspects of shapes and leads to a space of shapes the reaction diffusion space which places shapes within a neighborhood of similar ones such similarity relationships underlie descriptions suitable for recognition

invariant submanifold flows given a lie group acting on a manifold our aim is to analyze the evolution of differential invariants under invariant submanifold flows the constructions are based on the equivariant method of moving frames and the induced invariant variational bicomplex applications to integrable soliton dynamics and to the evolution of differential invariant signatures used in equivalence problems and object recognition and symmetry detection in images are discussed

asymptotic equivalence and adaptive estimation for robust nonparametric regression asymptotic equivalence theory developed in the literature so far are only for bounded loss functions this limits the potential applications of the theory because many commonly used loss functions in statistical inference are unbounded in this paper we develop asymptotic equivalence results for robust nonparametric regression with unbounded loss functions the results imply that all the gaussian nonparametric regression procedures can be robustified in a unified way a key step in our equivalence argument is to bin the data and then take the median of each bin the asymptotic equivalence results have significant practical implications to illustrate the general principles of the equivalence argument we consider two important nonparametric inference problems robust estimation of the regression function and the estimation of a quadratic functional in both cases easily implementable procedures are constructed and are shown to enjoy simultaneously a high degree of robustness and adaptivity other problems such as construction of confidence sets and nonparametric hypothesis testing can be handled in a similar fashion

optimal and fast detection of spatial clusters with scan statistics we consider the detection of multivariate spatial clusters in the bernoulli model with n locations where the design distribution has weakly dependent marginals the locations are scanned with a rectangular window with sides parallel to the axes and with varying sizes and aspect ratios multivariate scan statistics pose a statistical problem due to the multiple testing over many scan windows as well as a computational problem because statistics have to be evaluated on many windows this paper introduces methodology that leads to both statistically optimal inference and computationally efficient algorithms the main difference to the traditional calibration of scan statistics is the concept of grouping scan windows according to their sizes and then applying different critical values to different groups it is shown that this calibration of the scan statistic results in optimal inference for spatial clusters on both small scales and on large scales as well as in the case where the cluster lives on one of the marginals methodology is introduced that allows for an efficient approximation of the set of all rectangles while still guaranteeing the statistical optimality results described above it is shown that the resulting scan statistic has a computational complexity that is almost linear in n

psqp puzzle solving by quadratic programming in this article we present the first effective method based on global optimization for the reconstruction of image puzzles comprising rectangle pieces puzzle solving by quadratic programming psqp the proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function which is solved via a gradient ascent approach the proposed method is deterministic and can deal with arbitrary identical rectangular pieces we provide experimental results showing its effectiveness when compared to state of the art approaches although the method was developed to solve image puzzles we also show how to apply it to the reconstruction of simulated strip shredded documents broadening its applicability

robust nonparametric estimation via wavelet median regression in this paper we develop a nonparametric regression method that is simultaneously adaptive over a wide range of function classes for the regression function and robust over a large collection of error distributions including those that are heavy tailed and may not even possess variances or means our approach is to first use local medians to turn the problem of nonparametric regression with unknown noise distribution into a standard gaussian regression problem and then apply a wavelet block thresholding procedure to construct an estimator of the regression function it is shown that the estimator simultaneously attains the optimal rate of convergence over a wide range of the besov classes without prior knowledge of the smoothness of the underlying functions or prior knowledge of the error distribution the estimator also automatically adapts to the local smoothness of the underlying function and attains the local adaptive minimax rate for estimating functions at a point a key technical result in our development is a quantile coupling theorem which gives a tight bound for the quantile coupling between the sample medians and a normal variable this median coupling inequality may be of independent interest

advance in the theory of variable stepsize variable formula methods for ordinary differential equations the theory of the constant stepsize constant formula methods cscfm s for solving initial value problems for ordinary differential equations ode s is well developed however the integration methods are often used as variable stepsize variable formula methods vsvfm s in the codes for automatic solution of ode s this fact explains why it is necessary to develop a rigorous theory for the vsvfm s also results obtained until now in the efforts to develop a theory for the vsvfm s are presented in a systematic way and compared with the well known results for cscfm s the comparison is used to outline the directions in which further efforts in the attempt to improve the theoretical results and to obtain new results are most needed the integration methods can be separated into two large groups implicit methods and explicit methods including here the predictor corrector schemes it is discussed what kind of results are needed for each of these two groups assume that a set f of cscfm s is given from a practical point of view it is highly desirable that the cscfm s belonging to set f have the following property if every cscfm from set f is consistent zero stable and convergent then any vsvfm induced by the cscfm s of set f is also consistent zero stable and convergent for a sufficiently large class of grids a theorem concerning a class of cscfm s with this property is presented the application of this theorem in the selection of methods for solving large systems of ode s arising after the space discretization of air pollution models is discussed it is explained why the vsvfm s based on this class provide a very efficient computational process in the treatment of air pollution models