generalizing the hough transform to detect arbitrary shapes abstract the hough transform is a method for detecting curves by exploiting the duality between points on a curve and parameters of that curve the initial work showed how to detect both analytic curves 1 2 and non analytic curves 3 but these methods were restricted to binary edge images this work was generalized to the detection of some analytic curves in grey level images specifically lines 4 circles 5 and parabolas 6 the line detection case is the best known of these and has been ingeniously exploited in several applications 7 8 9 we show how the boundaries of an arbitrary non analytic shape can be used to construct a mapping between image space and hough transform space such a mapping can be exploited to detect instances of that particular shape in an image furthermore variations in the shape such as rotations scale changes or figure ground reversals correspond to straightforward transformations of this mapping however the most remarkable property is that such mappings can be composed to build mappings for complex shapes from the mappings of simpler component shapes this makes the generalized hough transform a kind of universal transform which can be used to find arbitrarily complex shapes

a front remeshing technique for a lagrangian description of moving interfaces in two fluid flows the numerical analysis of two fluid flows involves the treatment of a discontinuity that appears at the separating interface classical lagrangian schemes applied to update the front position between two immiscible incompressible fluids have been long recognized to provide a sharp representation of the interface however the main drawback of these approaches is the progressive distortion in the distribution of the markers used to identify the material front to avoid this problem an interface remeshing algorithm based on the diffuse approximation of the interface curvature is proposed in this work in addition the remeshed front is enforced to preserve the global volume these new aspects are incorporated in an existing fluid dynamics formulation for the analysis of two fluid flows problems the resulting formulation is called in this work as the moving lagrangian interface remeshing technique mlirt copyright 2005 john wiley sons ltd

the hough transform versus the upwrite this paper compares the hough transform and the upwrite for the detection of lines circles and ellipses both ideal and noisy images are tested the upwrite is found to be more robust for images containing perturbation noise for ideal images and images with speckle noise the results are found to depend on the complexity of the object being detected with more complex objects favoring the upwrite

consistent least squares fitting of ellipsoids a parameter estimation problem for ellipsoid fitting in the presence of measurement errors is considered the ordinary least squares estimator is inconsistent and due to the nonlinearity of the model the orthogonal regression estimator is inconsistent as well i e these estimators do not converge to the true value of the parameters as the sample size tends to infinity a consistent estimator is proposed based on a proper correction of the ordinary least squares estimator the correction is explicitly given in terms of the true value of the noise variance

active contours without edges we propose a new model for active contours to detect objects in a given image based on techniques of curve evolution mumford shah 1989 functional for segmentation and level sets our model can detect objects whose boundaries are not necessarily defined by the gradient we minimize an energy which can be seen as a particular case of the minimal partition problem in the level set formulation the problem becomes a mean curvature flow like evolving the active contour which will stop on the desired boundary however the stopping term does not depend on the gradient of the image as in the classical active contour models but is instead related to a particular segmentation of the image we give a numerical algorithm using finite differences finally we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable also the initial curve can be anywhere in the image and interior contours are automatically detected

threshold dynamics for the piecewise constant mumford shah functional we propose an efficient algorithm for minimizing the piecewise constant mumford shah functional of image segmentation it is based on the threshold dynamics of merriman bence and osher for evolving an interface by its mean curvature we show that a very fast minimization can be achieved by alternating the solution of a linear parabolic partial differential equation and simple thresholding

spline based deforming ellipsoids for interactive 3d bioimage segmentation we present a new fast active contour model a k a snake for image segmentation in 3d microscopy we introduce a parametric design that relies on exponential b spline bases and allows us to build snakes that are able to reproduce ellipsoids we design our bases to have the shortest possible support subject to some constraints thus computational efficiency is maximized the proposed 3d snake can approximate blob like objects with good accuracy and can perfectly reproduce spheres and ellipsoids irrespective of their position and orientation the optimization process is remarkably fast due to the use of gauss theorem within our energy computation scheme our technique yields successful segmentation results even for challenging data where object contours are not well defined this is due to our parametric approach that allows one to favor prior shapes in addition this paper provides a software that gives full control over the snakes via an intuitive manipulation of few control points

new approach for numerical solution of hammerstein integral equations in this paper we use a numerical procedure for solving a class of nonlinear integral equations of the hammerstein type using the globally defined sinc basis functions properties of the sinc procedure are utilized to reduce the computation of the hammerstein equations to some algebraic equations we used some numerical examples to illustrate the accuracy and the implementation of the method

multivariate adaptive regression splines a new method is presented for flexible regression modeling of high dimensional data the model takes the form of an expansion in product spline basis functions where the number of basis functions as well as the parameters associated with each one product degree and knot locations are automatically determined by the data this procedure is motivated by the recursive partitioning approach to regression and shares its attractive properties unlike recursive partitioning however this method produces continuous models with continuous derivatives it has more power and flexibility to model relationships that are nearly additive or involve interactions in at most a few variables in addition the model can be represented in a form that separately identifies the additive contributions and those associated with the different multivariable interactions

bootstrap resampling for image registration uncertainty estimation without ground truth we address the problem of estimating the uncertainty of pixel based image registration algorithms given just the two images to be registered for cases when no ground truth data is available our novel method uses bootstrap resampling it is very general applicable to almost any registration method based on minimizing a pixel based similarity criterion we demonstrate it using the ssd sad correlation and mutual information criteria we show experimentally that the bootstrap method provides better estimates of the registration accuracy than the state of the art cramer rao bound method additionally we evaluate also a fast registration accuracy estimation frae method which is based on quadratic sensitivity analysis ideas and has a negligible computational overhead frae mostly works better than the cramer rao bound method but is outperformed by the bootstrap method

classification of invariant image representations using a neural network a neural network nn based approach for classification of images represented by translation scale and rotation invariant features is presented the utilized network is a multilayer perceptron mlp classifier with one hidden layer back propagation learning is used for its training two types of features are used moment invariants derived from geometrical moments of the image and features based on zernlike moments which are the mapping of the image onto a set of complex orthogonal polynomials the performance of the mlp is compared to the bayes nearest neighbor and minimum mean distance statistical classifiers through extensive experimentation with noiseless as well as noisy binary images of all english characters 26 classes the following conclusions are reached 1 the mlp outperforms the other three classifiers especially when noise is present 2 the nearest neighbor classifier performs about the same as the nn for the noiseless case 3 the nn can do well even with a very small number of training samples 4 the nn has a good degree of fault tolerance and 5 the zernlike moment based features possess strong class separability power and are more powerful than moment invariants

a cell based particle method for modeling dynamic interfaces abstract we propose several modifications to the grid based particle method gbpm 21 for moving interface modeling there are several nice features of the proposed algorithm the new method can significantly improve the distribution of sampling particles on the evolving interface unlike the original gbpm where footpoints sampling points tend to cluster to each other the sampling points in the new method tend to be better separated on the interface moreover by replacing the grid based discretization using the cell based discretization we naturally decompose the interface into segments so that we can easily approximate surface integrals as a possible alternative to the local polynomial least square approximation we also study a geometric basis for local reconstruction in the resampling step we will show that such modification can simplify the overall implementations numerical examples in two and three dimensions will show that the algorithm is computationally efficient and accurate

multiresolution subdivision snakes we present a new family of snakes that satisfy the property of multiresolution by exploiting subdivision schemes we show in a generic way how to construct such snakes based on an admissible subdivision mask we derive the necessary energy formulations and provide the formulas for their efficient computation depending on the choice of the mask such models have the ability to reproduce trigonometric or polynomial curves they can also be designed to be interpolating a property that is useful in user interactive applications we provide explicit examples of subdivision snakes and illustrate their use for the segmentation of bioimages we show that they are robust in the presence of noise and provide a multiresolution algorithm to enlarge their basin of attraction which decreases their dependence on initialization compared to singleresolution snakes we show the advantages of the proposed model in terms of computation and segmentation of structures with different sizes

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

unbiased estimation of ellipses by bootstrapping a general method for eliminating the bias of nonlinear estimators using bootstrap is presented instead of the traditional mean bias we consider the definition of bias based on the median the method is applied to the problem of fitting ellipse segments to noisy data no assumption beyond being independent identically distributed is made about the error distribution and experiments with both synthetic and real data prove the effectiveness of the technique

parameter uniform optimal order numerical approximation of a class of singularly perturbed system of reaction diffusion problems involving a small perturbation parameter abstract in this work we consider an optimal accurate numerical approximation for the boundary layer adaptive solution of a system of reaction diffusion problems involving a small perturbation parameter to generate the layer adaptive mesh we use the equidistribution of a positive monitor function this technique enables the mesh movement to follow the rapidly changing behavior of the solution it is observed that the discrete solution is second order convergent on the layer adaptive equidistributed nonuniform mesh irrespective of the value of the perturbation parameter this convergence rate is optimal with respect to the discretization of the continuous problem we illustrate the performance of the present method based on a moving mesh algorithm by numerical experiments

three dimensional elastic matching of volumes registering volumes that have been deformed with respect to each other involves recovery of the deformation a 3 d elastic matching algorithm has been developed to use surface information for registering volumes surface extraction is performed in two steps extraction of contours in 2 d image planes using active contours and forming triangular patch surface models from the stack of 2 d contours one volume is modeled as being deformed with respect to another goal volume correspondences between surfaces in the two image volumes are used to warp the deformed volume towards its goal this process of contour extraction surface formation and matching and warping is repeated a number of times with decreasing image volume stiffness as the iterations continue the stretched volume is refined towards its goal volume registration examples of deformed volumes are presented

edge curvature and convexity based ellipse detection method in this paper we propose a novel ellipse detection method for real images the proposed method uses the information of edge curvature and their convexity in relation to other edge contours as clues for identifying edge contours that can be grouped together a search region is computed for every edge contour that contains other edge contours eligible for grouping with the current edge contour a two dimensional hough transform is performed in an intermediate step in which we use a new relationship score for ranking the edge contours in a group instead of the conventional histogram count the score is found to be more selective and thus more efficient in addition we use three novel saliency criteria that are non heuristic and consider various aspects for quantifying the goodness of the detected elliptic hypotheses and finally selecting good elliptic hypotheses the thresholds for selection of elliptic hypotheses are determined by the detected hypotheses themselves such that the selection is free from human intervention the method requires a few seconds in most cases so it is suitable for practical applications the performance of the proposed ellipse detection method has been tested on a dataset containing 1200 synthetic images and the caltech 256 dataset containing real images in both cases the results show that the proposed ellipse detection method performs far better than existing methods and is close to the ideal results with precision recall and f measure all very close to 1 further the method is robust to the increase in the complexity of the images such as overlapping ellipses occluded ellipses while the performance of the contemporary methods deteriorates significantly

signal matching through scale space given a collection of similar signals that have been deformed with respect to each other the general signal matching problem is to recover the deformation we formulate the problem as the minimization of an energy measure that combines a smoothness term and a similarity term the minimization reduces to a dynamic system governed by a set of coupled first order differential equations the dynamic system finds an optimal solution at a coarse scale and then tracks it continuously to a fine scale among the major themes in recent work on visual signal matching have been the notions of matching as constrained optimization of variational surface reconstruction and of coarse to fine matching our solution captures these in a precise succinct and unified form results are presented for one dimensional signals a motion sequence and a stereo pair

delineating elliptical objects with an application to cardiac scintigrams to delineate the myocardium in planar thallium 201 scintigrams of the left ventricle a method based on the hough transformation is presented the method maps feature points x y y where y reflects the direction of the tangent in edge point x y into the two dimensional space of the axis lengths of the ellipse within this space a probability density function pdf can be estimated when the center of the ellipse or its orientation are unknown the 2 d pdf of the lengths of the axes is extended to a 5 d pdf of all parameters of the ellipse lengths of the axes coordinates of the center and the orientation it is shown that the variance of the edge point based estimates of the axis lengths increases when the location error of the center of the supposed ellipse or its orientation error increases the likelihood of the estimates is expected to decrease with increasing variance therefore local search algorithms can be applied to find the maximum likelihood estimate of the parameters of the ellipse curves describing the convergency of the algorithm are presented as well as an example of the application of the algorithm to real scintigrams the method is able to detect contours even if they are only partly visualized as in thallium scintigrams of the myocardium of patients with ischemic heart disease as long as the number of parameters describing the contour is relatively low such an algorithm is also suitable for application to differently curved contours

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

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

regularization of inverse visual problems involving discontinuities inverse problems such as the reconstruction problems that arise in early vision tend to be mathematically ill posed through regularization they may be reformulated as well posed variational principles whose solutions are computable standard regularization theory employs quadratic stabilizing functionals that impose global smoothness constraints on possible solutions discontinuities present serious difficulties to standard regularization however since their reconstruction requires a precise spatial control over the smoothing properties of stabilizers this paper proposes a general class of controlled continuity stabilizers which provide the necessary control over smoothness these nonquadratic stabilizing functionals comprise multiple generalized spline kernels combined with noncontinuous continuity control functions in the context of computational vision they may be thought of as controlled continuity constraints these generic constraints are applicable to visual reconstruction problems that involve both continuous regions and discontinuities for which global smoothness constraints fail

statistical bias of conic fitting and renormalization introducing a statistical model of noise in terms of the covariance matrix of the n vector we point out that the least squares conic fitting is statistically biased we present a new fitting scheme called renormalization for computing an unbiased estimate by automatically adjusting to noise relationships to existing methods are discussed and our method is tested using real and synthetic data

a binary level set model and some applications to mumford shah image segmentation in this paper we propose a pde based level set method traditionally interfaces are represented by the zero level set of continuous level set functions instead we let the interfaces be represented by discontinuities of piecewise constant level set functions each level set function can at convergence only take two values i e it can only be 1 or 1 thus our method is related to phase field methods some of the properties of standard level set methods are preserved in the proposed method while others are not using this new method for interface problems we need to minimize a smooth convex functional under a quadratic constraint the level set functions are discontinuous at convergence but the minimization functional is smooth we show numerical results using the method for segmentation of digital images

stabilization of parametric active contours using a tangential redistribution term depending on implementation active contours have been classified as geometric or parametric active contours parametric contours irrespective of representation are known to suffer from the problem of irregular bunching and spacing out of curve points during the curve evolution in a spline based implementation of active contours this leads to occasional formation of loops locally and subsequently the curve blows up due to instabilities in this paper we analyze the reason for this problem and propose a solution to alleviate the same we propose an ordinary differential equation ode for controlling the curve parametrization during evolution by including a tangential force we show that the solution of the proposed ode is bounded we demonstrate the effectiveness of the proposed method for segmentation and tracking tasks on closed as well as open contours

use of high accuracy schemes to handle free surfaces in computing unsteady two phase flows abstract this paper shows that it is possible to use high accuracy convective interpolation schemes to compute multidimensional two phase flows successfully including accurate simulations of free surface flows a code pool3d has been developed which solves the equations of two phase two fluid flows using high accuracy convective interpolation schemes a combination of bounded quickest for the momentum equations and bounded sou for the mass equations special attention is paid to the interpolations needed to compute the void fraction in staggered grids which is a crucial issue for the accuracy of the free surface simulations numerical results are presented first of a standard incompressible flow benchmark steady lid driven cavity and then of a free surface benchmark collapse of a water column

symmetry seeking models and 3d object reconstruction we propose models of 3d shape which may be viewed as deformable bodies composed of simulated elastic material in contrast to traditional purely geometric models of shape deformable models are active their shapes change in response to externally applied forces we develop a deformable model for 3d shape which has a preference for axial symmetry symmetry is represented even though the model does not belong to a parametric shape family such as generalized cylinders rather a symmetry seeking property is designed into internal forces that constrain the deformations of the model we develop a framework for 3d object reconstruction based on symmetry seeking models instances of these models are formed from monocular image data through the action of external forces derived from the data the forces proposed in this paper deform the model in space so that the shape of its projection into the image plane is consistent with the 2d silhouette of an object of interest the effectiveness of our approach is demonstrated using natural images

boundary vector field for parametric active contours snakes are widely used in the fields of computer vision and image processing there are a number of shortcomings of the traditional snakes including the capture range problem and the concave object extraction problem gradient vector flow snake enhances the concave object extraction capability however it suffers from high computational requirement in this paper we present a new external force which is generated by a novel interpolation scheme which reduces the computational requirement significantly and at the same time improves the capture range and concave object extraction capability

global regularizing flows with topology preservation for active contours and polygons active contour and active polygon models have been used widely for image segmentation in some applications the topology of the object s to be detected from an image is known a priori despite a complex unknown geometry and it is important that the active contour or polygon maintain the desired topology in this work we construct a novel geometric flow that can be added to image based evolutions of active contours and polygons in order to preserve the topology of the initial contour or polygon we emphasize that unlike other methods for topology preservation the proposed geometric flow continually adjusts the geometry of the original evolution in a gradual and graceful manner so as to prevent a topology change long before the curve or polygon becomes close to topology change the flow also serves as a global regularity term for the evolving contour and has smoothness properties similar to curvature flow these properties of gradually adjusting the original flow and global regularization prevent geometrical inaccuracies common with simple discrete topology preservation schemes the proposed topology preserving geometric flow is the gradient flow arising from an energy that is based on electrostatic principles the evolution of a single point on the contour depends on all other points of the contour which is different from traditional curve evolutions in the computer vision literature

the fundamental matrix theory algorithms and stability analysis in this paper we analyze in some detail the geometry of a pair of cameras i e a stereo rig contrarily to what has been done in the past and is still done currently for example in stereo or motion analysis we do not assume that the intrinsic parameters of the cameras are known coordinates of the principal points pixels aspect ratio and focal lengths this is important for two reasons first it is more realistic in applications where these parameters may vary according to the task active vision second the general case considered here captures all the relevant information that is necessary for establishing correspondences between two pairs of images this information is fundamentally projective and is hidden in a confusing manner in the commonlyused formalism of the essential matrix introduced by longuet higgins 1981 this paper clarifies the projective nature of the correspondence problem in stereo and shows that the epipolar geometry can be summarized in one 3 x 3 matrix of rank 2 which we propose to call the fundamental matrix after this theoretical analysis we embark on the task of estimating the fundamental matrix from point corre spondences a task which is of practical importance we analyze theoretically and compare experimentally using synthetic and real data several methods of estimation the problem of the stability of the estimation is studied from two complementary viewpoints first we show that there is an interesting relationship between the fundamental matrix and three dimensional planes which induce homographies between the images and create unstabilities in the estimation procedures second we point to a deep relation between the unstability of the estimation procedure and the presence in the scene of so called critical surfaces which have been studied in the context of motion analysis finally we conclude by stressing the fact that we believe that the fundamental matrix will play a crucial role in future applications of three dimensional computer vision by greatly increasing its versatility robustness and hence applicability to real difficult problems

overlapping cell nuclei segmentation using a spatially adaptive active physical model a method for the segmentation of overlapping nuclei is presented which combines local characteristics of the nuclei boundary and a priori knowledge about the expected shape of the nuclei a deformable model whose behavior is driven by physical principles is trained on images containing a single nuclei and attributes of the shapes of the nuclei are expressed in terms of modal analysis based on the estimated modal distribution and driven by the image characteristics we develop a framework to detect and describe the unknown nuclei boundaries in images containing two overlapping nuclei the problem of the estimation of an accurate nucleus boundary in the overlapping areas is successfully addressed with the use of appropriate weight parameters that control the contribution of the image force in the total energy of the deformable model the proposed method was evaluated using 152 images of conventional pap smears each containing two overlapping nuclei comparisons with other segmentation methods indicate that our method produces more accurate nuclei boundaries which are closer to the ground truth

b spline snakes a flexible tool for parametric contour detection we present a novel formulation for b spline snakes that can be used as a tool for fast and intuitive contour outlining we start with a theoretical argument in favor of splines in the traditional formulation by showing that the optimal curvature constrained snake is a cubic spline irrespective of the form of the external energy field unfortunately such regularized snakes suffer from slow convergence speed because of a large number of control points as well as from difficulties in determining the weight factors associated to the internal energies of the curve we therefore propose an alternative formulation in which the intrinsic scale of the spline model is adjusted a priori this leads to a reduction of the number of parameters to be optimized and eliminates the need for internal energies i e the regularization term in other words we are now controlling the elasticity of the spline implicitly and rather intuitively by varying the spacing between the spline knots the theory is embedded into a multiresolution formulation demonstrating improved stability in noisy image environments validation results are presented comparing the traditional snake using internal energies and the proposed approach without internal energies showing the similar performance of the latter several biomedical examples of applications are included to illustrate the versatility of the method

model based deformable surface finding for medical images describes a new global shape parameterization for smoothly deformable three dimensional 3 d objects such as those found in biomedical images whose diversity and irregularity make them difficult to represent in terms of fixed features or parts this representation is used for geometric surface matching to 3 d medical image data such as from magnetic resonance imaging mri the parameterization decomposes the surface into sinusoidal basis functions four types of surfaces are modeled tori open surfaces closed surfaces and tubes this parameterization allows a wide variety of smooth surfaces to be described with a small number of parameters extrinsic model based information is incorporated by introducing prior probabilities on the parameters surface finding is formulated as an optimization problem results of the method applied to synthetic images and 3 d medical images of the heart and brain are presented

efficient shape priors for spline based snakes parametric active contours are an attractive approach for image segmentation thanks to their computational efficiency they are driven by application dependent energies that reflect the prior knowledge on the object to be segmented we propose an energy involving shape priors acting in a regularization like manner thereby the shape of the snake is orthogonally projected onto the space that spans the affine transformations of a given shape prior the formulation of the curves is continuous which provides computational benefits when compared with landmark based discrete methods we show that this approach improves the robustness and quality of spline based segmentation algorithms while its computational overhead is negligible an interactive and ready to use implementation of the proposed algorithm is available and was successfully tested on real data in order to segment drosophila flies and yeast cells in microscopic images

snakes with an ellipse reproducing property we present a new class of continuously defined parametric snakes using a special kind of exponential splines as basis functions we have enforced our bases to have the shortest possible support subject to some design constraints to maximize efficiency while the resulting snakes are versatile enough to provide a good approximation of any closed curve in the plane their most important feature is the fact that they admit ellipses within their span thus they can perfectly generate circular and elliptical shapes these features are appropriate to delineate cross sections of cylindrical like conduits and to outline bloblike objects we address the implementation details and illustrate the capabilities of our snake with synthetic and real data

geometrically induced force interaction for three dimensional deformable models in this paper we propose a novel 3 d deformable model that is based upon a geometrically induced external force field which can be conveniently generalized to arbitrary dimensions this external force field is based upon hypothesized interactions between the relative geometries of the deformable model and the object boundary characterized by image gradient the evolution of the deformable model is solved using the level set method so that topological changes are handled automatically the relative geometrical configurations between the deformable model and the object boundaries contribute to a dynamic vector force field that changes accordingly as the deformable model evolves the geometrically induced dynamic interaction force has been shown to greatly improve the deformable model performance in acquiring complex geometries and highly concave boundaries and it gives the deformable model a high invariancy in initialization configurations the voxel interactions across the whole image domain provide a global view of the object boundary representation giving the external force a long attraction range the bidirectionality of the external force field allows the new deformable model to deal with arbitrary cross boundary initializations and facilitates the handling of weak edges and broken boundaries in addition we show that by enhancing the geometrical interaction field with a nonlocal edge preserving algorithm the new deformable model can effectively overcome image noise we provide a comparative study on the segmentation of various geometries with different topologies from both synthetic and real images and show that the proposed method achieves significant improvements against existing image gradient techniques

robust ellipse detection with gaussian mixture models the euclidian distance between gaussian mixtures has been shown to be robust to perform point set registration jian and vemuri 2011 we propose to extend this idea for robustly matching a family of shapes ellipses optimisation is performed with an annealing strategy and the search for occurrences is repeated several times to detect multiple instances of the shape of interest we compare experimentally our approach to other state of the art techniques on a benchmark database for ellipses and demonstrate the good performance of our approach highlightswe extend the framework based on l2 to estimate a parametric family of curves we propose a non isotropic and multidimensional modeling for the density functions we propose a method for detecting multiple instances of an ellipse

a hybrid method for ellipse detection in industrial images a hybrid method with high reliability to detect ellipses in low snr industrial images is proposed using candidate elliptic arcs with high fitting precision as seed arcs to group with other arcs a novel method to extract regions which may contain one ellipse is proposed new selection scores for evaluating hypothetical ellipse are used experimental results show high reliability of proposed method many ellipse detection methods have been proposed for detecting ellipses in images however they are unsuitable for industrial images due to low signal to noise ratios snr this paper presents an ellipse detection method combining the advantages of hough transform ht based methods and the advantages of edge following methods which is capable of detecting fragmented ellipses and is both computational and memory efficient our method works in two steps in the first step an edge following method is proposed to quickly and accurately extract the majority of ellipses for ellipses missed in the first step candidate regions where each may contain one missed ellipse are extracted in the second step using cluster analysis and then a ht based method is performed on these regions to extract the missed ellipses this can not only guarantee the accuracy of the ht based method but also save the memory and computation time we test the performance of our method using both synthetic images and low snr industrial images experimental results demonstrate that the proposed method performs far better than existing methods in terms of recall precision f measure and reliability especially in term of reliability our method has achieved a very high value close to 1 while the reliabilities of state of the art methods are almost less than 0 5

a new one parametric fitting method for planar objects this paper is an extension of the already published paper by voss and suesse 1997 we developed a new region based fitting method using the method of normalization there we demonstrated the zero parametric fitting of lines triangles parallelograms circles and ellipses we discuss this normalization idea for fitting of closed regions using circular segments elliptical segments and super ellipses as features we use the area based low order moments we show that we have to solve only one dimensional optimization problems in these cases

deb definite error bounded tangent estimator for digital curves we propose a simple and fast method for tangent estimation of digital curves this geometric based method uses a small local region for tangent estimation and has a definite upper bound error for continuous as well as digital conics i e circles ellipses parabolas and hyperbolas explicit expressions of the upper bounds for continuous and digitized curves are derived which can also be applied to nonconic curves our approach is benchmarked against 72 contemporary tangent estimation methods and demonstrates good performance for conic nonconic and noisy curves in addition we demonstrate a good multigrid and isotropic performance and low computational complexity of o 1 and better performance than most methods in terms of maximum and average errors in tangent computation for a large variety of digital curves

facial age estimation based on label sensitive learning and age oriented regression this paper provides a new age estimation approach which distinguishes itself with the following three contributions first we combine distance metric learning and dimensionality reduction to better explore the connections between facial features and age labels second to exploit the intrinsic ordinal relationship among human ages and overcome the potential data imbalance problem a label sensitive concept and several imbalance treatments are introduced in the system training phase finally an age oriented local regression is presented to capture the complicated facial aging process for age determination the simulation results show that our approach achieves the lowest estimation error against existing methods

least squares orthogonal distances fitting of circle sphere ellipse hyperbola and parabola the least squares fitting minimizes the squares sum of error of fit in predefined measures by the geometric fitting the error distances are defined with the orthogonal or shortest distances from the given points to the geometric feature to be fitted for the geometric fitting of circle sphere ellipse hyperbola parabola simple and robust nonparametric algorithms are proposed these are based on the coordinate description of the corresponding point on the geometric feature for the given point where the connecting line of the two points is the shortest path from the given point to the geometric feature to be fitted

comparison of a priori and a posteriori meshes for singularly perturbed nonlinear parameterized problems this paper deals with the adaptive mesh generation for singularly perturbed nonlinear parameterized problems with a comparative research study on them we propose an a posteriori error estimate for singularly perturbed parameterized problems by moving mesh methods with fixed number of mesh points the well known a priori meshes are compared with the proposed one the comparison results show that the proposed numerical method is highly effective for the generation of layer adapted a posteriori meshes a numerical experiment of the error behavior on different meshes is carried out to highlight the comparison of the approximated solutions

a reliable treatment to solve nonlinear fredholm integral equations with non separable kernel abstract this work is devoted to solve integral equations formulated in terms of the kernel functions and nemytskii operators this type of equations appear in different applied problems such as electrostatics and radiative heat transfer problems we deal with both cases separable and non separable kernels by setting the theoretical semilocal convergence results for an adequate iterative scheme that can be useful for approximating the solution of the infinite dimensional problem we pay special attention to non separable kernels avoiding the solution given in previous works where the original nonlinear integral equation has been approximated by means of an equation with separable kernel however in this case we introduce an approximation of the derivative operator that it is needed for applying the iterative scheme considered moreover we study the localization and separation of possible solutions of nonlinear integral equation by means of a result of semilocal convergence for the iterative scheme considered the theoretical results obtained have been tested with some applied problems showing competitive results

the ovuscule we propose an active contour a k a snake that takes the shape of an ellipse its evolution is driven by surface terms made of two contributions the integral of the data over an inner ellipse counterbalanced by the integral of the data over an outer elliptical shell we iteratively adapt the active contour to maximize the contrast between the two domains which results in a snake that seeks elliptical bright blobs we provide analytic expressions for the gradient of the snake with respect to its defining parameters which allows for the use of efficient optimizers an important contribution here is the parameterization of the ellipse which we define in such a way that all parameters have equal importance this creates a favorable landscape for the proceedings of the optimizer we validate our construct with synthetic data and illustrate its use on real data as well

enlarging the convergence domain in local convergence studies for iterative methods in banach spaces in this work we introduce a new form of setting the general assumptions for the local convergence studies of iterative methods in banach spaces that allows us to improve the convergence domains specifically a local convergence result for a family of higher order iterative methods for solving nonlinear equations in banach spaces is established under the assumption that the frechet derivative satisfies the lipschitz continuity condition for some values of the parameter these iterative methods are of fifth order the importance of our work is that it avoids the usual practice of boundedness conditions of higher order derivatives which is a drawback for solving some practical problems the existence and uniqueness theorem that establishes the convergence balls of these methods is obtained we have considered a number of numerical examples including a nonlinear hammerstein equation and computed the radii of the convergence balls it is found that the radius of convergence ball obtained by our approach is much larger when compared with some other existing methods the global convergence properties of the family are explored by analyzing the dynamics of the corresponding operator on complex quadratic polynomials

ellipse fitting using the finite rate of innovation sampling principle standard approaches for ellipse fitting are based on the minimization of algebraic or geometric distance between the given data and a template ellipse when the data are noisy and come from a partial ellipse the state of the art methods tend to produce biased ellipses we rely on the sampling structure of the underlying signal and show that the x and y coordinate functions of an ellipse are finite rate of innovation fri signals and that their parameters are estimable from partial data we consider both uniform and nonuniform sampling scenarios in the presence of noise and show that the data can be modeled as a sum of random amplitude modulated complex exponentials a low pass filter is used to suppress noise and approximate the data as a sum of weighted complex exponentials the annihilating filter used in fri approaches is applied to estimate the sampling interval in the closed form we perform experiments on simulated and real data and assess both objective and subjective performances in comparison with the state of the art ellipse fitting methods the proposed method produces ellipses with lesser bias furthermore the mean squared error is lesser by about 2 to 10 db we show the applications of ellipse fitting in iris images starting from partial edge contours and to free hand ellipses drawn on a touch screen tablet

a probabilistic hough transform abstract the hough transform for straight line detection is considered it is shown that if just a small subset of the edge points in the image selected at random is used as input for the hough transform the performance is often only slightly impaired thus the execution time can be considerably shortened the performance of the resulting probabilistic hough transform is analysed the analysis is supported by experimental evidence

ellipse fitting for imaged cross sections of a surface of revolution this paper addresses the problem of accurately fitting the elliptical projections of the cross sections of a surface of revolution sor with the given intrinsic matrix of a camera by the new approach proposed in this paper the image points of the sor cross sections are fitted under the two geometric constraints which are derived from the configuration characteristics of sor it is demonstrated by comparison with other previous methods that our method can fit the elliptical projections of sor cross sections more accurately and robustly in this paper we also describe the applications of the algorithm in euclidean reconstruction of sor and pose estimation for sor shaped object such as spacecraft we accurately fit the imaged cross sections of a surface of revolution the ellipses can be fitted under the circular point and orthogonality constraints an effective optimization is elaborately designed the method can serve for reconstruction and localization of a surface of revolution

a method to detect and characterize ellipses using the hough transform we describe a new technique for detecting and characterizing ellipsoidal shapes automatically from any type of image this technique is a single pass algorithm which can extract any group of ellipse parameters or characteristics which can be computed from those parameters without having to detect all five parameters for each ellipsoidal shape moreover the method can explicitly incorporate any a priori knowledge the user may have concerning ellipse parameters the method is based on techniques from projective geometry and on the hough transform this technique can significantly reduce interpretation and computation time by automatically extracting only those features or geometric parameters of interest from images and making exact use of a priori information

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

fitting a second degree curve in the presence of error this correspondence presents a statistically sound simple and fast method to estimate the parameters of a second degree curve from a set of noisy points that originated from the curve

global minimum for active contour models a minimal path approach a new boundary detection approach for shape modeling is presented it detects the global minimum of an active contour model s energy between two end points initialization is made easier and the curve is not trapped at a local minimum by spurious edges we modify the snake energy by including the internal regularization term in the external potential term our method is based on finding a path of minimal length in a riemannian metric we then make use of a new efficient numerical method to find this shortest path it is shown that the proposed energy though based only on a potential integrated along the curve imposes a regularization effect like snakes we explore the relation between the maximum curvature along the resulting contour and the potential generated from the image the method is capable to close contours given only one point on the objects boundary by using a topology based saddle search routine we show examples of our method applied to real aerial and medical images

elastic model based segmentation of 3 d neuroradiological data sets this paper presents a new technique for the automatic model based segmentation of three dimensional 3 d objects from volumetric image data the development closely follows the seminal work of taylor and cootes on active shape models but is based on a hierarchical parametric object description rather than a point distribution model the segmentation system includes both the building of statistical models and the automatic segmentation of new image data sets via a restricted elastic deformation of shape models geometric models are derived from a sample set of image data which have been segmented by experts the surfaces of these binary objects are converted into parametric surface representations which are normalized to get an invariant object centered coordinate system surface representations are expanded into series of spherical harmonics which provide parametric descriptions of object shapes it is shown that invariant object surface parametrization provides a good approximation to automatically determine object homology in terms of sets of corresponding sets of surface points gray level information near object boundaries is represented by 1 d intensity profiles normal to the surface considering automatic segmentation of brain structures as their driving application the authors choice of coordinates for object alignment was the well accepted stereotactic coordinate system major variation of object shapes around the mean shape also referred to as shape eigenmodes are calculated in shape parameter space rather than the feature space of point coordinates segmentation makes use of the object shape statistics by restricting possible elastic deformations into the range of the training shapes the mean shapes are initialized in a new data set by specifying the landmarks of the stereotactic coordinate system the model elastically deforms driven by the displacement forces across the object s surface which are generated by matching local intensity profiles elastical deformations are limited by setting bounds for the maximum variations in eigenmode space the technique has been applied to automatically segment left and right hippocampus thalamus putamen and globus pallidus from volumetric magnetic resonance scans taken from schizophrenia studies the results have been validated by comparison of automatic segmentation with the results obtained by interactive expert segmentation

learning to track the visual motion of contours abstract a development of a method for tracking visual contours is described given an untrained tracker a training motion of an object can be observed over some extended time and stored as an image sequence the image sequence is used to learn parameters in a stochastic differential equation model these are used in turn to build a tracker whose predictor imitates the motion in the training set tests show that the resulting trackers can be markedly tuned to desired curve shapes and classes of motions

detection and segmentation of generic shapes based on affine modeling of energy in eigenspace this paper presents a novel approach for detection and segmentation of man made generic shapes in cluttered images the set of shapes to be detected are members of affine transformed versions of basic geometric shapes such as rectangles circles etc the shape set is represented by its vectorial edge map transformed over a wide range of affine parameters we use vectorial boundary instead of regular boundary to improve the robustness to noise background clutter and partial occlusion our approach consists of a detection stage and a verification stage in the detection stage we first derive the energy from the principal eigenvectors of the set next an a posteriori probability map of energy distribution is computed from the projection of the edge map representation in a vectorial eigen space local peaks of the posterior probability map are located and indicate candidate detections we use energy probability based detection since we find that the underlying distribution is not gaussian and resembles a hypertoroid in the verification stage each candidate is verified using a fast search algorithm based on a novel representation in angle space and the corresponding pose information of the detected shape is obtained the angular representation used in the verification stage yields better results than a euclidean distance representation experiments are performed in various interfering distortions and robust detection and segmentation are achieved

a variational approach for the segmentation of the left ventricle in cardiac image analysis in this paper we propose a level set method to segment mr cardiac images our approach is based on a coupled propagation of two cardiac contours and integrates visual information with anatomical constraints the visual information is expressed through a gradient vector flow based boundary component and a region term that aims at best separating the cardiac contours regions according to their global intensity properties in order to deal with misleading visual support an anatomical constraint is considered that couples the propagation of the cardiac contours according to their relative distance the resulting motion equations are implemented using a level set approach and a fast and stable numerical approximation scheme the additive operator splitting encouraging experimental results are provided using real data

information theoretic active polygons for unsupervised texture segmentation curve evolution models used in image segmentation and based on image region information usually utilize simple statistics such as means and variances hence can not account for higher order nature of the textural characteristics of image regions in addition the object delineation by active contour methods results in a contour representation which still requires a substantial amount of data to be stored for subsequent multimedia applications such as visual information retrieval from databases polygonal approximations of the extracted continuous curves are required to reduce the amount of data since polygons are powerful approximators of shapes for use in later recognition stages such as shape matching and coding the key contribution of this paper is the development of a new active contour model which nicely ties the desirable polygonal representation of an object directly to the image segmentation process this model can robustly capture texture boundaries by way of higher order statistics of the data and using an information theoretic measure and with its nature of the ordinary differential equations this new variational texture segmentation model is unsupervised since no prior knowledge on the textural properties of image regions is used another contribution in this sequel is a new polygon regularizer algorithm which uses electrostatics principles this is a global regularizer and is more consistent than a local polygon regularization in preserving local features such as corners

large sample confidence regions based on subsamples under minimal assumptions in this article the construction of confidence regions by approximating the sampling distribution of some statistic is studied the true sampling distribution is estimated by an appropriate normalization of the values of the statistic computed over subsamples of the data in the i i d context the method has been studied by wu in regular situations where the statistic is asymptotically normal the goal of the present work is to prove the method yields asymptotically valid confidence regions under minimal conditions essentially all that is required is that the statistic suitably normalized possesses a limit distribution under the true model unlike the bootstrap the convergence to the limit distribution need not be uniform in any sense the method is readily adapted to parameters of stationary time series or more generally homogeneous random fields for example an immediate application is the construction of a confidence interval for the spectral density function of a homogeneous random field