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

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

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

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

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

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

the generalized cattaneo partial slip plane contact problem i theory the cattaneo problem is considered for a general plane contact between elastically similar materials i e a monotonically increasing tangential load starting from zero with normal loading held fixed instead of the classical argument on the displacement field in the stick zone of cattaneo solution we attack the problem implicitly from the governing integral equations in the stick zones after discussing and solving the full stick case we move to the more realistic for finite friction case of partial slip we show that upon isolating the effect of full sliding the equalities and inequalities governing the corrective solution for the corrective shearing tractions in the stick zone are exactly the same as those governing the solution of the normal contact problem with a lower load but the same rotation as the actual one this analogy permits us to deduce several general properties and gives a general procedures for solving partial slip cattaneo problems as frictionless normal indentation ones therefore the general solutions for single multiple and periodic contacts is given a comprehensive set of explicit results is given in the part ii of the paper

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

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

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

an application of flows to time shift and time reversal in stochastic processes a simple proposition theorem 1 on flows allows the investigation of random time shift and time reversal in markov processes without assuming any regularity of paths theorem 5 is a generalization of nagasawa s time reversal theorem and theorem 4 generalizes a recent result of getoor and glover 1 flows 1 1 we consider a flow in a measurable space 2 y that is a family of transformations at t e r such that oat 0s t for all s t e r and t c oto e a e r x 4 for all a e f r is the borel a algebra in r we put oty x y otw for every function y and pot a p 0t71a a e y p pot dt for every measure p we denote by the collection of all sets a e y such that t1a a for all t e r a function y is measurable with respect to the a algebra wif and only if it is measurable and invariant under all transformations ot obviously p a 0 or oo for all a e sl nevertheless we prove theorem 1 if p is a finite over y it determines uniquely the values p a for all a e 1 2 as a tool we use stationary times a stationary time t is a measurable mapping from 2 to the extended real line oo oo such that ott t t for all t e r suppose that y coincides with its completion with respect to the class of all probability measures then the first hitting time of a set a e y ta inf t ot e a and the last exit time from a ta sup t ot co a are stationary times2 the measurability follows from 5 chapter 3 1 received by the editors march 13 1984 1980 mathematics subject classification primary 60g 601 1 supported in part by national science foundation grant mcs 8202286 2we put inf oo sup oo c1985 american mathematical society 0002 9947 85 1 00 25 per page

new analytical and numerical results for two dimensional contact profiles recently a generalized coulomb law for elastic bodies in contact has been developed by the author which assumes that the tangential traction is the difference of the slip stress of the contact and the stick area whereby each stick area corresponds to a smaller contact area it holds for multiple contact regions also several applications for elastic half planes half spaces thin and thick layers and impact problems have been published for plane contact of equal bodies with friction it provides exact solutions and the interior stress field can be expressed with analytical results in closed form in this article a singular superposition of flat punch solutions is outlined in which the punches are aligned with an edge of the contact area it is shown that this superposition satisfies coulomb s inequalities directly and new results for the muskhelishvili potentials of several profiles are presented it is illustrated how problems of singularity and multi valuedness of complex functions can be solved in closed form and the chebyshev approximation used by earlier authors can be avoided for comparison some previous solutions for symmetric profiles are appended some results for the interior stress field the pressure the frictional traction and the surface displacements are compared with fem solutions of an equivalent problem the small differences between both methods show characteristic features of the fem model and the theoretical assumptions and are shortly explained further this example can be used as benchmark test for fem and bem programs

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

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

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

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

the generalized cattaneo partial slip plane contact problem ii examples this second part of the paper uses the method devised in the part i to give explicit solution to several cases of cattaneo s plane contact problem where a monotonically increasing tangential load starting from zero is applied to the bodies in contact with normal loading held fixed the method consists in reducing the partial slip problem to a superposition of frictionless normal contact problems for which several results are available including some recent cases studied by the author therefore a comprehensive set of results is given for single multiple and periodical contacts

an accurate elasto plastic frictional tangential force displacement model for granular flow simulations displacement driven formulation we present in this paper the displacement driven version of a tangential force displacement tfd model that accounts for both elastic and plastic deformations together with interfacial friction occurring in collisions of spherical particles this elasto plastic frictional tfd model with its force driven version presented in l vu quoc l lesburg x zhang an accurate tangential force displacement model for granular flow simulations contacting spheres with plastic deformation force driven formulation journal of computational physics 196 1 2004 298 326 is consistent with the elasto plastic frictional normal force displacement nfd model presented in l vu quoc x zhang an elasto plastic contact force displacement model in the normal direction displacement driven version proceedings of the royal society of london series a 455 1991 4013 4044 both the nfd model and the present tfd model are based on the concept of additive decomposition of the radius of contact area into an elastic part and a plastic part the effect of permanent indentation after impact is represented by a correction to the radius of curvature the effect of material softening due to plastic flow is represented by a correction to the elastic moduli the proposed tfd model is accurate and is validated against nonlinear finite element analyses involving plastic flows in both the loading and unloading conditions the proposed consistent displacement driven elasto plastic nfd and tfd models are designed for implementation in computer codes using the discrete element method dem for granular flow simulations the model is shown to be accurate and is validated against nonlinear elasto plastic finite element analysis

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