nonlinear joint inversion of tomographic data using swarm intelligence geophysical techniques offer the potential to tomographically image physical parameter variations in the ground in two or three dimensions due to the limited number and accuracy of the recorded data geophysical model generation by inversion suffers ambiguity linking the model generation process of disparate data by jointly inverting two or more data sets allows for improved model reconstruction fully nonlinear inversion using optimization techniques searching the solution space of the inverse problem globally enables quantitative assessment of the ambiguity inherent to the model reconstruction we used two different multiobjective particle swarm optimization approaches to jointly invert synthetic crosshole tomographic data sets comprising radar and p wave traveltimes respectively beginning with a nonlinear joint inversion founded on the principle of pareto optimality and game theoretic concepts we obtained a set of pareto optimal solutions comprising commonly structured radar and p wave velocity models for low computational costs however the efficiency of the approach goes along with some risk of achieving a final model ensemble not adequately illustrating the ambiguity inherent to the model reconstruction process taking advantage of the results of the first approach we inverted the database using a different nonlinear joint inversion approach reducing the multiobjective optimization problem to a single objective one computational costs were significantly higher but the final models were obtained mutually independently allowing for objective appraisal of model parameter determination despite the high computational effort the approach was found to be an efficient nonlinear joint inversion formulation compared to what could be extracted from individual nonlinear inversions of both data sets

construction of idempotent 2 cocycles abstract let f g g l be a weak 2 cocycle where l k is a finite galois field extension with galois group g and a f l k f be the associated weak crossed product k algebra we associate a partition of g to a f and construct idempotent 2 cocycles of a f

dense mirroring surface recovery from 1d homographies and sparse correspondences in this work we recover the 3d shape of mirrors sunglasses and stainless steel implements a computer monitor displays several images of parallel stripes each image at a different angle reflections of these stripes in a mirroring surface are captured by the camera for every image point the direction of the displayed stripes and their reflections in the image are related by a 1d homography matrix computed with a robust version of the statistically accurate heteroscedastic approach by focusing on a sparse set of image points for which monitor image correspondence is computed the depth and the local shape may be estimated from these homographies the depth estimation relies on statistically correct minimization and provides accurate reliable results even for the image points where the depth estimation process is inherently unstable we are able to characterize this instability and develop an algorithm to detect and correct it after correcting the instability dense surface recovery of mirroring objects is performed using constrained interpolation which does not simply interpolate the surface depth values but also uses the locally computed 1d homographies to solve for the depth the correspondence and the local surface shape the method was implemented and the shape of several objects was densely recovered at submillimeter accuracy

statistical optimization for geometric fitting theoretical accuracy bound and high order error analysis a rigorous accuracy analysis is given to various techniques for estimating parameters of geometric models from noisy data first it is pointed out that parameter estimation for vision applications is very different in nature from traditional statistical analysis and hence a different mathematical framework is necessary after a general framework is formulated typical numerical techniques are selected and their accuracy is evaluated up to high order terms as a byproduct our analysis leads to a hyperaccurate method that outperforms existing methods

stabilizing the focal length computation for 3 d reconstruction from two uncalibrated views in order to reconstruct 3 d shape from two uncalibrated views one needs to resolve two problems i the computed focal lengths can be imaginary ii the computation fails for fixated images we present a practical remedy for these by subsampling feature points and fixing the focal length we first summarize theoretical backgrounds and then do simulations which reveal a rather surprising fact that when the focal length is actually fixed not using that knowledge yields better results for non fixated images we give an explanation to this seeming paradox and derive a hybrid method switching the computation by judging whether or not the images are fixated doing simulations and real image experiments we demonstrate the effectiveness of our method

an analysis of linear subspace approaches for computer vision and pattern recognition linear subspace analysis lsa has become rather ubiquitous in a wide range of problems arising in pattern recognition and computer vision the essence of these approaches is that certain structures are intrinsically or approximately low dimensional for example the factorization approach to the problem of structure from motion sfm and principal component analysis pca based approach to face recognition in lsa the singular value decomposition svd is usually the basic mathematical tool however analysis of the performance in the presence of noise has been lacking we present such an analysis here first the denoising capacity of the svd is analysed specifically given a rank r matrix corrupted by noise how much noise remains in the rank r projected version of that corrupted matrix second we study the learning capacity of the lsa based recognition system in a noise corrupted environment specifically lsa systems that attempt to capture a data class as belonging to a rank r column space will be affected by noise in both the training samples measurement noise will mean the learning samples will not produce the true subspace and the test sample which will also have measurement noise on top of the ideal clean sample belonging to the true subspace these results should help one to predict aspects of performance and to design more optimal systems in computer vision particularly in tasks such as sfm and face recognition our analysis agrees with certain observed phenomenon and these observations together with our simulations verify the correctness of our theory

motion recovery by integrating over the joint image manifold recovery of epipolar geometry is a fundamental problem in computer vision the introduction of the joint image manifold jim allows to treat the recovery of camera motion and epipolar geometry as the problem of fitting a manifold to the data measured in a stereo pair the manifold has a singularity and boundary therefore special care must be taken when fitting it four fitting methods are discussed direct algebraic geometric and the integrated maximum likelihood iml based method the first three methods are the exact analogues of three common methods for recovering epipolar geometry the more recently introduced iml method seeks the manifold which has the highest support in the sense that the largest measure of its points are close to the data while computationally more intensive than the other methods its results are better in some scenarios both simulations and experiments suggest that the advantages of iml manifold fitting carry over to the task of recovering epipolar geometry especially when the extent of the data and or the motion are small

epipolar geometry estimation based on evolutionary agents this paper presents a novel approach based on the use of evolutionary agents for epipolar geometry estimation in contrast to conventional nonlinear optimization methods the proposed technique employs each agent to denote a minimal subset to compute the fundamental matrix and considers the data set of correspondences as a 1d cellular environment in which the agents inhabit and evolve the agents execute some evolutionary behavior and evolve autonomously in a vast solution space to reach the optimal or near optima result then three different techniques are proposed in order to improve the searching ability and computational efficiency of the original agents subset template enables agents to collaborate more efficiently with each other and inherit accurate information from the whole agent set competitive evolutionary agent cea and finite multiple evolutionary agent fmea apply a better evolutionary strategy or decision rule and focus on different aspects of the evolutionary process experimental results with both synthetic data and real images show that the proposed agent based approaches perform better than other typical methods in terms of accuracy and speed and are more robust to noise and outliers

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

factorization with uncertainty factorization using singular value decomposition svd is often used for recovering 3d shape and motion from feature correspondences across multiple views svd is powerful at finding the global solution to the associated least square error minimization problem however this is the correct error to minimize only when the x and y positional errors in the features are uncorrelated and identically distributed but this is rarely the case in real data uncertainty in feature position depends on the underlying spatial intensity structure in the image which has strong directionality to it hence the proper measure to minimize is covariance weighted squared error or the mahalanobis distance in this paper we describe a new approach to covariance weighted factorization which can factor noisy feature correspondences with high degree of directional uncertainty into structure and motion our approach is based on transforming the raw data into a covariance weighted data space where the components of noise in the different directions are uncorrelated and identically distributed applying svd to the transformed data now minimizes a meaningful objective function in this new data space this is followed by a linear but suboptimal second step to recover the shape and motion in the original data space we empirically show that our algorithm gives very good results for varying degrees of directional uncertainty in particular we show that unlike other svd based factorization algorithms our method does not degrade with increase in directionality of uncertainty even in the extreme when only normal flow data is available it thus provides a unified approach for treating corner like points together with points along linear structures in the image

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

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

when are simple ls estimators enough an empirical study of ls tls and gtls a variety of least squares estimators of significantly different complexity and generality are available to solve over constrained linear systems the most theoretically general may not necessarily be the best choice in practice problem conditions may be such that simpler and faster algorithms if theoretically inferior would yield acceptable errors we investigate when this may happen using homography estimation as the reference problem we study the errors of ls tls equilibrated tls and gtls algorithms with different noise types and varying intensity and correlation levels to allow direct comparisons with algorithms from the applied mathematics and computer vision communities we consider both inhomogeneous and homogeneous systems we add noise to image co ordinates and system matrix entries in separate experiments to take into account the effect on noise properties heteroscedasticity of pre processing data transformations we find that the theoretically most general algorithms may not always be worth their higher complexity comparable results are obtained with moderate levels of noise intensity and correlation we identify such levels quantitatively for the reference problem thus suggesting when simpler algorithms can be applied with limited errors in spite of their restrictive assumptions

three dimensional gravity inversion using graph theory to delineate the skeleton of homogeneous sources abstractwe developed a new strategy based on graph theory concepts to invert gravity data using an ensemble of simple point masses our method consisted of a genetic algorithm with elitism to generate a set of possible solutions each estimate was associated to a graph to solve the minimum spanning tree mst problem to produce unique and stable estimates we restricted the position of the point masses by minimizing the statistical variance of the distances of an mst jointly with the data misfit function during the iterations of the genetic algorithm hence the 3d spatial distribution of the point masses identified the skeleton of homogeneous gravity sources in addition our method also gave an estimation of the anomalous mass of the source so together with the anomalous mass the skeleton could aid other 3d methods with promising geometric a priori parameters several tests with different values of regularizing parameter were made to bespeak this new regularizing strategy the inversion results ap

a closed form expression of the positional uncertainty for 3d point clouds we present a novel closed form expression of positional uncertainty measured by a near monostatic and time of flight laser range finder with consideration of its measurement uncertainties an explicit form of the angular variance of the estimated surface normal vector is also derived this expression is useful for the precise estimation of the surface normal vector and the outlier detection for finding correspondence in order to register multiple three dimensional point clouds two practical algorithms using these expressions are presented a method for finding optimal local neighbourhood size which minimizes the variance of the estimated normal vector and a resampling method of point clouds

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

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

on weak crossed products frobenius algebras and the weak bruhat ordering abstract the weak crossed product algebra was studied first by haile larson and sweedler amer j math 105 1983 689 they gave interesting properties for such an algebra one of which is that if a f is a weak crossed product induced by a weak 2 cocycle f defined on a galois group g gal k f and h is the inertial subgroup of g then a f has a wedderburn splitting that is a f b j where j is the radical of a f and b is a k h central simple algebra the purpose of this paper is to give the necessary and sufficient condition for a weak crossed product to be frobenius and to describe an algorithm for constructing lower subtractive graphs from a finite group g and a generating set s a special case of this construction is the so called weak bruhat ordering on a coxeter group g s we show that the nilcoxeter algebra associated to g s is a special case of the restricted algebra associated to a lower subtractive graph

a new test for the parametric form of the variance function in non parametric regression in the common non parametric regression model the problem of testing for the parametric form of the conditional variance is considered a stochastic process based on the difference between the empirical processes that are obtained from the standardized non parametric residuals under the null hypothesis of a specific parametric form of the variance function and the alternative is introduced and its weak convergence established this result is used for the construction of a kolmogorov smimov and a cramer von mises type of statistic for testing the parametric form of the conditional variance the consistency of a bootstrap approximation is established and the finite sample properties of this approximation are investigated by means of a simulation study in particular the new procedure is compared with some of the currently available methods for this problem

traveltime inversion for 2 d anomaly structures this work presents a traveltime inversion method that uses parametric functions to represent 2 d anomaly structures these functions are described by a small set of unknown parameters which in turn are obtained after solving a highly nonlinear optimization problem via simulated annealing sa the procedure favors neither smooth nor high contrasting anomalies and keeps the number of unknowns very small so as to make the problem tractable using sa yet the strategy allows one to accommodate a large class of velocity models results indicate that this new approach typically yields better images than a standard linearized inversion based on a cell parameterization scheme

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

an information fusion framework for robust shape tracking existing methods for incorporating subspace model constraints in shape tracking use only partial information from the measurements and model distribution we propose a unified framework for robust shape tracking optimally fusing heteroscedastic uncertainties or noise from measurement system dynamics and a subspace model the resulting nonorthogonal subspace projection and fusion are natural extensions of the traditional model constraint using orthogonal projection we present two motion measurement algorithms and introduce alternative solutions for measurement uncertainty estimation we build shape models offline from training data and exploit information from the ground truth initialization online through a strong model adaptation our framework is applied for tracking in echocardiograms where the motion estimation errors are heteroscedastic in nature each heart has a distinct shape and the relative motions of epicardial and endocardial borders reveal crucial diagnostic features the proposed method significantly outperforms the existing shape space constrained tracking algorithm due to the complete treatment of heteroscedastic uncertainties the strong model adaptation and the coupled tracking of double contours robust performance is observed even on the most challenging cases

techniques for generating analytic covariance expressions for eigenvalues and eigenvectors one of the key problems in data fusion is the estimation of a parameter vector from a set of noisy measurements in many cases the optimal estimate of such a parameter vector can be solved through the least squares problem there are however a number of important problems whose solution instead takes the form of an eigenvalue eigenvector problem furthermore knowledge of the uncertainty of the optimal estimate is as important as the estimate itself for many practical applications and this uncertainty is typically captured in the form of a covariance matrix while the covariance matrix for a least squares estimate has been well studied there has been substantially less research on the covariance of an optimal estimate originating from an eigenvalue eigenvector problem in this paper we develop general expressions that determine the uncertainty in a vector estimate obtained from an eigenvalue eigenvector problem given the uncertainty of the matrix this includes developing expressions for the analytic derivatives of the eigenvalues and eigenvectors with respect to the matrix from which they come finally the techniques developed are numerically validated with forward finite differencing and a monte carlo analysis and then used to determine covariance expressions for an ellipse fitting technique and the estimation of attitude quaternions

scaled total least squares fundamentals the standard approaches to solving overdetermined linear systems bx approx c construct minimal corrections to the vector c and or the matrix b such that the corrected system is compatible in ordinary least squares ls the correction is restricted to c while in data least squares dls it is restricted to b in scaled total least squares stls 22 corrections to both c and b are allowed and their relative sizes depend on a real positive parameter gamma stls unifies several formulations since it becomes total least squares tls when gamma 1 and in the limit corresponds to ls when gamma rightarrow 0 and dls when gamma rightarrow infty this paper analyzes a particularly useful formulation of the stls problem the analysis is based on a new assumption that guarantees existence and uniqueness of meaningful stls solutions for all parameters gamma 0 it makes the whole stls theory consistent our theory reveals the necessary and sufficient condition for preserving the smallest singular value of a matrix while appending or deleting a column this condition represents a basic matrix theory result for updating the singular value decomposition as well as the rank one modification of the hermitian eigenproblem the paper allows complex data and the equivalences in the limit of stls with dls and ls are proven for such data it is shown how any linear system bx approx c can be reduced to a minimally dimensioned core system satisfying our assumption consequently our theory and algorithms can be applied to fully general systems the basics of practical algorithms for both the stls and dls problems are indicated for either dense or large sparse systems our assumption and its consequences are compared with earlier approaches

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

unbiased estimation and statistical analysis of 3 d rigid motion from two views the problem of estimating 3d rigid motion from point correspondences over two views is formulated as nonlinear least squares ls optimization and the statistical behaviors of the errors in the solution are analyzed by introducing a realistic model of noise described in terms of the covariance matrices of n vectors it is shown that the ls solution based on the epipolar constraint is statistically biased the geometry of this bias is described in both quantitative and qualitative terms finally an unbiased estimation scheme is presented and random number simulations are conducted to observe its effectiveness

unscented transformation based estimation of parameters of nonlinear models using heteroscedastic data this paper addresses the issue of estimating the parameters of nonlinear models using heteroscedastic data a weighted least squares problem formulation where the sum of the mahalanobis distance for all measurements is minimized forms the framework of this paper determining the mahalanobis distance requires the gradient of the cost function with respect to the noisy measurements which can be computationally expensive and infeasible for model which are discontinuous a derivative free approach to determine the mahalanobis distance as an error metric is proposed using the unscented transformation the advantages of using the proposed approach include a black box approach to evaluate the gradient weighted objective function precluding the need for analytical gradients and an improved estimation of the covariance numerical results for various applications such as triangulation using radar measurements ellipse and super ellipse fitting demonstrate the benefits of the proposed approach heteroscedastic data resulting from real x ray images are also used to illustrate the potential of the proposed approach highlightsderivative free approach of solving gradient weighted least squares problems improved approximation of the geometric distance for curve fitting improved performance of proposed technique demonstrated on three benchmarks monte carlo used to benchmark the reduction in bias in estimated parameters relevant to model fitting problems with heteroscedastic data

in defense of the eight point algorithm the fundamental matrix is a basic tool in the analysis of scenes taken with two uncalibrated cameras and the eight point algorithm is a frequently cited method for computing the fundamental matrix from a set of eight or more point matches it has the advantage of simplicity of implementation the prevailing view is however that it is extremely susceptible to noise and hence virtually useless for most purposes this paper challenges that view by showing that by preceding the algorithm with a very simple normalization translation and scaling of the coordinates of the matched points results are obtained comparable with the best iterative algorithms this improved performance is justified by theory and verified by extensive experiments on real images

tomographic traveltime inversion using natural pixels traditionally in the problem of tomographic traveltime inversion the model is divided into a number of rectangular cells of constant slowness inversion consists of finding these constant values using the measured traveltimes the inversion process can demand a large computational effort if a high resolution result is desired we show how to use a different kind of parameterization of the model based on beam propagation paths this parameterization is obtained within the framework of reconstruction in hilbert spaces by minimizing the error between the true model and the estimated model the traveltimes are interpreted as the projections of the slowness along the beampaths although the actual beampaths are described by complicated spatial functions we simplify the computations by approximating these functions with functions of constant width and height i e fat rays which collectively form a basis set of natural pixels with a simple numerical example we demonstrate that the main advantage of this

point matching under large image deformations and illumination changes to solve the general point correspondence problem in which the underlying transformation between image patches is represented by a homography a solution based on extensive use of first order differential techniques is proposed we integrate in a single robust m estimation framework the traditional optical flow method and matching of local color distributions these distributions are computed with spatially oriented kernels in the 5d joint spatial color space the estimation process is initiated at the third level of a gaussian pyramid uses only local information and the illumination changes between the two images are also taken into account subpixel matching accuracy is achieved under large projective distortions significantly exceeding the performance of any of the two components alone as an application the correspondence algorithm is employed in oriented tracking of objects

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

consistency of robust estimators in multi structural visual data segmentation a theoretical framework is presented to study the consistency of robust estimators used in vision problems involving extraction of fine details a strong correlation between asymptotic performance of a robust estimator and the asymptotic bias of its scale estimate is mathematically demonstrated where the structures are assumed to be linear corrupted by gaussian noise a new measure for the inconsistency of scale estimators is defined and formulated by deriving the functional forms of four recent high breakdown robust estimators for each estimator the inconsistency measures are numerically evaluated for a range of mutual distances between structures and inlier ratios and the minimum mutual distance between the structures for which each estimator returns a non bridging fit is calculated

an adaptive contour closure algorithm and its experimental evaluation the potential of edge based complete image segmentation into regions has not gained the due attention in the literature thus far the present paper attempts to explore this potential by proposing an adaptive grouping algorithm to solve the contour closure problem that is the key to a successful edge based complete image segmentation the effectiveness of the proposed algorithm is extensively tested in the range image domain and compared to several region based segmentation methods within a rigorous comparison framework on three range image databases of varying quality acquired by different range scanners it is shown that the proposed approach is able to achieve very appealing performance with respect to both segmentation quality and computation time

from fns to heiv a link between two vision parameter estimation methods problems requiring accurate determination of parameters from image based quantities arise often in computer vision two recent independently developed frameworks for estimating such parameters are the fns and heiv schemes here it is shown that fns and a core version of heiv are essentially equivalent solving a common underlying equation via different means the analysis is driven by the search for a nondegenerate form of a certain generalized eigenvalue problem and effectively leads to a new derivation of the relevant case of the heiv algorithm this work may be seen as an extension of previous efforts to rationalize and interrelate a spectrum of estimators including the renormalization method of kanatani and the normalized eight point method of hartley

the development and comparison of robust methodsfor estimating the fundamental matrix this paper has two goals the first is to develop a variety of robust methods for the computation of the fundamental matrix the calibration free representation of camera motion the methods are drawn from the principal categories of robust estimators viz case deletion diagnostics m estimators and random sampling and the paper develops the theory required to apply them to non linear orthogonal regression problems although a considerable amount of interest has focussed on the application of robust estimation in computer vision the relative merits of the many individual methods are unknown leaving the potential practitioner to guess at their value the second goal is therefore to compare and judge the methods comparative tests are carried out using correspondences generated both synthetically in a statistically controlled fashion and from feature matching in real imagery in contrast with previously reported methods the goodness of fit to the synthetic observations is judged not in terms of the fit to the observations per se but in terms of fit to the ground truth a variety of error measures are examined the experiments allow a statistically satisfying and quasi optimal method to be synthesized which is shown to be stable with up to 50 percent outlier contamination and may still be used if there are more than 50 percent outliers performance bounds are established for the method and a variety of robust methods to estimate the standard deviation of the error and covariance matrix of the parameters are examined the results of the comparison have broad applicability to vision algorithms where the input data are corrupted not only by noise but also by gross outliers

nonlinear inversion of resistivity sounding data the resistivity interpretation problem involves the estimation of resistivity as a function of depth from the apparent resistivity values measured in the field as a function of electrode separation this is commonly done either by curve matching using master curves or by more formal linearized inversion methods the problems with linearized inversion schemes are fairly well known they require that the starting model be close to the true solution in this paper we report the results from the application of a nonlinear global optimization method known as simulated annealing sa in the direct interpretation of resistivity sounding data this method does not require a good starting model but is computationally more expensive we used the heat bath algorithm of simulated annealing in which the mean square error difference between observed and synthetic data is used as the energy function that we attempt to minimize samples are drawn from the gibbs probability distribution while the control parameter the

rank constraints for homographies over two views revisiting the rank four constraint it is well known that one can collect the coefficients of five or more homographies between two views into a large rank deficient matrix in principle this implies that one can refine the accuracy of the estimates of the homography coefficients by exploiting the rank constraint however the standard rank projection approach is impractical for two different reasons it requires many homographies to even score a modest gain and secondly correlations between the errors in the coefficients will lead to poor estimates in this paper we study these problems and provide solutions to each firstly we show that the matrices of the homography coefficients can be recast into two parts each consistent with ranks of only one this immediately establishes the prospect of realistically that is with as few as only three or four homographies exploiting the redundancies of the homographies over two views we also tackle the remaining issue correlated coefficients we compare our approach with the gold standard that is non linear bundle adjustment initialized from the ground truth estimate the ideal initialization the results confirm our theory and show one can implement rank constrained projection and come close to the gold standard in effectiveness indeed our algorithm by itself or our algorithm further refined by a bundle adjustment stage may be a practical algorithm providing generally better results than the standard dlt direct linear transformation algorithm and even better than the bundle adjustment result with the dlt result as the starting point our unoptimized version has roughly the same cost as bundle adjustment and yet can generally produce close to the gold standard estimate as illustrated by comparison with bundle adjustment initialized from the ground truth independent of the merits or otherwise of our algorithm we have illuminated why the naive approach of direct rank projection is relatively doomed to failure moreover in revealing that there are further rank constraints not previously known we have added to the understanding of these issues and this may pave the way for further improvements

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 new invariant for c over r almost invertible cohomology theory and the classification of idempotent cohomology classes and algebras by partially ordered sets with a galois group action

determining the epipolar geometry and its uncertainty a review two images of a single scene object are related by the epipolar geometry which can be described by a 3 3 singular matrix called the essential matrix if images internal parameters are known or the fundamental matrix otherwise it captures all geometric information contained in two images and its determination is very important in many applications such as scene modeling and vehicle navigation this paper gives an introduction to the epipolar geometry and provides a complete review of the current techniques for estimating the fundamental matrix and its uncertainty a well founded measure is proposed to compare these techniques projective reconstruction is also reviewed the software which we have developed for this review is available on the internet

estimation of nonlinear errors in variables models for computer vision applications in an errors in variables eiv model all the measurements are corrupted by noise the class of eiv models with constraints separable into the product of two nonlinear functions one solely in the variables and one solely in the parameters is general enough to represent most computer vision problems we show that the estimation of such nonlinear eiv models can be reduced to iteratively estimating a linear model having point dependent i e heteroscedastic noise process particular cases of the proposed heteroscedastic errors in variables heiv estimator are related to other techniques described in the vision literature the sampson method renormalization and the fundamental numerical scheme in a wide variety of tasks the heiv estimator exhibits the same or superior performance as these techniques and has a weaker dependence on the quality of the initial solution than the levenberg marquardt method the standard approach toward estimating nonlinear models

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

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

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

multiple ellipses detection in noisy environments a hierarchical approach detection of multiple ellipses in noisy environments is a basic yet challenging task in many vision related problems the key area of difficulty is on distinguishing the pixels pertaining to each target in the presence of noise to tackle with the issue we propose a hierarchical approach which is motivated by the fact that any segment of an ellipse can identify itself in ellipse reconstruction first we find all the neat edges without any branches followed by an ellipse fitting on each of them second some target candidates are estimated based on the neat edges by a proposed grouping strategy finally the targets are detected based on the candidates by a proposed selective competitive algorithm to distinguish the true pixels of each target a real application of the proposed method is illustrated in addition to some other demonstrative experiments

on the optimization criteria used in two view motion analysis the three best known criteria in two view motion analysis are based respectively on the distances between points and their corresponding epipolar lines on the gradient weighted epipolar errors and on the distances between points and the re projections of their reconstructed points the last one has a better statistical interpretation but is significantly slower than the first two the author shows that given a reasonable initial guess of the epipolar geometry the last two criteria are equivalent when the epipoles are at infinity and differ from each other only a little even when the epipoles are in the image as shown experimentally the first two criteria are equivalent only when the epipoles are at infinity and when the observed object scene has the same scale in the two images this suggests that the second criterion is sufficient in practice because of its computational efficiency experiments with several thousand computer simulations and four sets of real data confirm the analysis

robust regression methods for computer vision a review regression analysis fitting a model to noisy data is a basic technique in computer vision robust regression methods that remain reliable in the presence of various types of noise are therefore of considerable importance we review several robust estimation techniques and describe in detail the least median of squares lmeds method the method yields the correct result even when half of the data is severely corrupted its efficiency in the presence of gaussian noise can be improved by complementing it with a weighted least squares based procedure the high time complexity of the lmeds algorithm can be reduced by a monte carlo type speed up technique we discuss the relationship of lmeds with the ransac paradigm and its limitations in the presence of noise corrupting all the data and we compare its performance with the class of robust m estimators references to published applications of robust techniques in computer vision are also given

the generic bilinear calibration estimation problem we identify a very general recurring pattern in a number of well known problems in biological and machine vision many problems are of a peculiar double sided nature one attempts to estimate certain properties of the environment using a certain type of equipment and simultaneously one attempts to calibrate the same equipment on the structure of the environment at first sight this appears the kind of the chicken and the egg problem that might well prove to be insoluble however due to basic constraints that universally apply e g the world is only three dimensional a solution up to a certain class of ambiguity transformations often exists the more complicated the problem is the less important the remaining ambiguity will be at least in a relative sense many well known problems are special in that they can be cast in bilinear form sometimes after transformation or the introduction of dummy variables instances include photometric stereo photometric estimations e g of lightness local differential image operators a variety of photogrammetric problems etc it turns out that many of these problems and together these make up a large fraction of the generic problems in machine vision today can be cast in a simple universal framework this framework enables one to handle arbitrarily large that is not minimal consistent configurations noisy thus inconsistent date sets automatically the level at which prior information either of a deterministic or a statistical nature is used assumptions such as constant albedo rigidity uniform distributions etc is clearly separated as an additional typically nonlinear stage

implementing a multi model estimation method we revisit the problem of parameter estimation in computer vision reconsidering and implementing what may be called the kanatani s estimation method presented here as a simple optimisation problem so a without any direct reference to a probabilistic framework but b considering i non linear implicit measurement equations and parameter constraints plus ii robust estimation in the presence of outliers and iii multi model comparisons here a a projection algorithm based on generalisations of square root decompositions allows an efficient and numerically stable local resolution of a set of non linear equations on the other hand b a robust estimation module of a hierarchy of non linear models has been designed and validated a step ahead c the software architecture of the estimation module is discussed with the goal of being integrated in reactive software environments or within applications with time constraints while an experimentation considering the parameterisation of retinal displacements between two views is proposed as an illustration of the estimation module