the problem of degeneracy in structure and motion recovery from uncalibrated image sequences the aim of this work is the recovery of 3d structure and camera projection matrices for each frame of an uncalibrated image sequence in order to achieve this correspondences are required throughout the sequence a significant and successful mechanism for automatically establishing these correspondences is by the use of geometric constraints arising from scene rigidity however problems arise with such geometry guided matching if general viewpoint and general structure are assumed whilst frames in the sequence and or scene structure do not conform to these assumptions such cases are termed degenerate in this paper we describe two important cases of degeneracy and their effects on geometry guided matching the cases are a motion degeneracy where the camera does not translate between frames and a structure degeneracy where the viewed scene structure is planar the effects include the loss of correspondences due to under or over fitting of geometric models estimated from image data leading to the failure of the tracking method these degeneracies are not a theoretical curiosity but commonly occur in real sequences where models are statistically estimated from image points with measurement error we investigate two strategies for tackling such degeneracies the first uses a statistical model selection test to identify when degeneracies occur the second uses multiple motion models to overcome the degeneracies the strategies are evaluated on real sequences varying in motion scene type and length from 13 to 120 frames

mean square power series solution of random linear differential equations this paper deals with the construction of random power series solutions of linear differential equations containing uncertainty through the diffusion coefficient the source term as well as the initial condition under appropriate hypotheses on the data we establish that the constructed random power series solution is mean square convergent in a certain interval whose length depends on the mean square norm of the random variable coefficient also the main statistical functions of the approximating stochastic process solution generated by truncation of the exact power series solution are given finally we apply the proposed technique to several illustrative examples

gauss and the invention of least squares the most famous priority dispute in the history of statistics is that between gauss and legendre over the discovery of the method of least squares new evidence both documentary and statistical is discussed and an attempt is made to evaluate gauss s claim it is argued though not conclusively that gauss probably possessed the method well before legendre but that he was unsuccessful in communicating it to his contemporaries data on the french meridian arc are presented that could conceivably permit a definitive verification of the claim

the equations of motion of curved pipes conveying fluid abstract the non linear differential equations of motion of a fluid conveying pipe the no flow configuration of which is in the shape of a one dimensional line arbitrarily curved and twisted in space are derived by making use of the newtonian approach the extensible dynamics of the beam is based on the timoshenko beam theory some significant differences with the equations available in the open literature are discussed the stressed by flow configuration is found to be the only equilibrium state adequate for the study of the linear stability of such pipe fluid systems

an efficient hidden variable approach to minimal case camera motion estimation in this paper we present an efficient new approach for solving two view minimal case problems in camera motion estimation most notably the so called five point relative orientation problem and the six point focal length problem our approach is based on the hidden variable technique used in solving multivariate polynomial systems the resulting algorithm is conceptually simple which involves a relaxation which replaces monomials in all but one of the variables to reduce the problem to the solution of sets of linear equations as well as solving a polynomial eigenvalue problem polyeig to efficiently find the polynomial eigenvalues we make novel use of several numeric techniques which include quotient free gaussian elimination levinson durbin iteration and also a dedicated root polishing procedure we have tested the approach on different minimal cases and extensions with satisfactory results obtained both the executables and source codes of the proposed algorithms are made freely downloadable

the equations of motion of initially stressed timoshenko tubular beams conveying fluid abstract in this paper the equations of motion of an initially stressed timoshenko tubular beam subjected to a tensile follower load and conveying fluid are derived by using the appropriate statement of hamilton s principle this latter is obtained first for open systems the instantaneous total mass of which does not necessarily remain constant in the course of deformation open denoting that there is momentum transport in and out of the system the equations of motion are derived separately for a cantilevered system and for one with both extremities of the tube clamped yet another derivation for the cantilevered tube is presented with the system considered to be quasi closed where all flow induced effects are incorporated through the virtual work as if they were external forces all three sets of equations are found to be identical these equations are then compared with those obtained more simply by the newtonian force balance approach some differences between them are found to exist the principal of which are associated with the follower or other tensile forces these are discussed at some length and the equations of motion obtained here are compared to those obtained by other researchers for timoshenko beams subjected to follower or tensile forces

practical global optimization for multiview geometry this paper presents a practical method for finding the provably globally optimal solution to numerous problems in projective geometry including multiview triangulation camera resectioning and homography estimation unlike traditional methods which may get trapped in local minima due to the non convex nature of these problems this approach provides a theoretical guarantee of global optimality the formulation relies on recent developments in fractional programming and the theory of convex underestimators and allows a unified framework for minimizing the standard l 2 norm of reprojection errors which is optimal under gaussian noise as well as the more robust l 1 norm which is less sensitive to outliers even though the worst case complexity of our algorithm is exponential the practical efficacy is empirically demonstrated by good performance on experiments for both synthetic and real data an open source matlab toolbox that implements the algorithm is also made available to facilitate further research

simultaneous camera pose and correspondence estimation with motion coherence traditionally the camera pose recovery problem has been formulated as one of estimating the optimal camera pose given a set of point correspondences this critically depends on the accuracy of the point correspondences and would have problems in dealing with ambiguous features such as edge contours and high visual clutter joint estimation of camera pose and correspondence attempts to improve performance by explicitly acknowledging the chicken and egg nature of the pose and correspondence problem however such joint approaches for the two view problem are still few and even then they face problems when scenes contain largely edge cues with few corners due to the fact that epipolar geometry only provides a soft point to line constraint viewed from the perspective of point set registration the point matching process can be regarded as the registration of points while preserving their relative positions i e preserving scene coherence by demanding that the point set should be transformed coherently across views this framework leverages on higher level perceptual information such as the shape of the contour while thus potentially allowing registration of non unique edge points the registration framework in its traditional form is subject to substantial point localization error and is thus not suitable for estimating camera pose in this paper we introduce an algorithm which jointly estimates camera pose and correspondence within a point set registration framework based on motion coherence with the camera pose helping to localize the edge registration while the ambiguous edge information helps to guide camera pose computation the algorithm can compute camera pose over large displacements and by utilizing the non unique edge points can recover camera pose from what were previously regarded as feature impoverished sfm scenes our algorithm is also sufficiently flexible to incorporate high dimensional feature descriptors and works well on traditional sfm scenes with adequate numbers of unique corners

estimating relative camera motion from the antipodal epipolar constraint this paper introduces a novel antipodal epipolar constraint on relative camera motion by using antipodal points which are available in large field of view cameras the translational and rotational motions of a camera are geometrically decoupled allowing them to be separately estimated as two problems in smaller dimensions we present a new formulation based on discrete camera motions which works over a larger range of motions compared to previous differential techniques using antipodal points the use of our constraints is demonstrated with two robust and practical algorithms one based on ransac and the other based on hough like voting as an application of the motion decoupling property we also present a new structure from motion algorithm that does not require explicitly estimating rotation it uses only the translation found with our methods finally experiments involving simulations and real image sequences will demonstrate that our algorithms perform accurately and robustly with some advantages over the state of the art

multiple view geometry under the l_ infty norm this paper presents a new framework for solving geometric structure and motion problems based on the linfin norm instead of using the common sum of squares cost function that is the l2 norm the model fitting errors are measured using the linfin norm unlike traditional methods based on l2 our framework allows for the efficient computation of global estimates we show that a variety of structure and motion problems for example triangulation camera resectioning and homography estimation can be recast as quasi convex optimization problems within this framework these problems can be efficiently solved using second order cone programming socp which is a standard technique in convex optimization the methods have been implemented in matlab and the resulting toolbox has been made publicly available the algorithms have been validated on real data in different settings on problems with small and large dimensions and with excellent performance

branch and bound methods for euclidean registration problems in this paper we propose a practical and efficient method for finding the globally optimal solution to the problem of determining the pose of an object we present a framework that allows us to use point to point point to line and point to plane correspondences for solving various types of pose and registration problems involving euclidean or similarity transformations traditional methods such as the iterative closest point algorithm or bundle adjustment methods for camera pose may get trapped in local minima due to the nonconvexity of the corresponding optimization problem our approach of solving the mathematical optimization problems guarantees global optimality the optimization scheme is based on ideas from global optimization theory in particular convex underestimators in combination with branch and bound methods we provide a provably optimal algorithm and demonstrate good performance on both synthetic and real data we also give examples of where traditional methods fail due to the local minima problem

go icp a globally optimal solution to 3d icp point set registration the iterative closest point icp algorithm is one of the most widely used methods for point set registration however being based on local iterative optimization icp is known to be susceptible to local minima its performance critically relies on the quality of the initialization and only local optimality is guaranteed this paper presents the first globally optimal algorithm named go icp for euclidean rigid registration of two 3d point sets under the l 2 error metric defined in icp the go icp method is based on a branch and bound scheme that searches the entire 3d motion space se 3 by exploiting the special structure of se 3 geometry we derive novel upper and lower bounds for the registration error function local icp is integrated into the bnb scheme which speeds up the new method while guaranteeing global optimality we also discuss extensions addressing the issue of outlier robustness the evaluation demonstrates that the proposed method is able to produce reliable registration results regardless of the initialization go icp can be applied in scenarios where an optimal solution is desirable or where a good initialization is not always available

a robust comparison of biological shapes summary localized differences in the form of two related animal skeletons are more effectively determined when resistant fitting techniques are used rather than least squares the repeated median resistant fitting algorithm is introduced the methods are tested by comparing hominid skulls with those of other primates and the male ostracode with the female in each case the resistant fit is superior to the least squares fit in that the difierences are more readily identified and agl ee more closely with the structural differences perceived on biological grounds le llltroductioll studies of allometric growth and of morphological change often run into difficulties in identifying and measuring the location and extent of relative shape deformations a reference system is needed for measuring these deformations and in the absence of an inherent fixed reference system one must be estimated the problem of estimating shape change in animal morphology provides an elegant setting for the comparison of least squares with recently developed robust and resistant statistical techniques being robust these new methods are protected against departures from the assumptions of analysis such as independent identically and normally distributed errors being resistant they are also protected against the potentially strong influences of atypical or incorrect data values two shapes can rarely be superimposed perfectly different fitting criteria will generally yield different results by allowing regions with large deformations to have a large impact on the fit least squares methods can minimize true shape differences and thereby obscure them a resistant technique however limits the influence of large deformations and the resulting fit is close in similar regions and not close in relatively deformed regions in this way resistant techniques can help to identify similarities and diflerences in form more effectively than least squares methods when sneath 1967 used least squares as a basis for some of the first quantitative estimates of relative deformation and so extended the fundamental descriptive work of thompson 1917 useful robust methods were not generally available sneath did in fact consider using the available robust methods but concluded that alternative methods that are less affected by wild values are not attractive in practice since then however the development of new theory and methods as reported by huber 1972 1981 hampel

robust regression discriminative methods e g kernel regression svm have been extensively used to solve problems such as object recognition image alignment and pose estimation from images these methods typically map image features mathbf x to continuous e g pose or discrete e g object category values a major drawback of existing discriminative methods is that samples are directly projected onto a subspace and hence fail to account for outliers common in realistic training sets due to occlusion specular reflections or noise it is important to notice that existing discriminative approaches assume the input variables mathbf x to be noise free thus discriminative methods experience significant performance degradation when gross outliers are present despite its obvious importance the problem of robust discriminative learning has been relatively unexplored in computer vision this paper develops the theory of robust regression rr and presents an effective convex approach that uses recent advances on rank minimization the framework applies to a variety of problems in computer vision including robust linear discriminant analysis regression with missing data and multi label classification several synthetic and real examples with applications to head pose estimation from images image and video classification and facial attribute classification with missing data are used to illustrate the benefits of rr

egomotion estimation using assorted features we propose a novel minimal solver for recovering camera motion across two views of a calibrated stereo rig the algorithm can handle any assorted combination of point and line features across the four images and facilitates a visual odometry pipeline that is enhanced by well localized and reliably tracked line features while retaining the well known advantages of point features the mathematical framework of our method is based on trifocal tensor geometry and a quaternion representation of rotation matrices a simple polynomial system is developed from which camera motion parameters may be extracted more robustly in the presence of severe noise as compared to the conventionally employed direct linear subspace solutions this is demonstrated with extensive experiments and comparisons against the 3 point and line sfm algorithms

trajectory based place recognition for efficient large scale localization place recognition is a core competency for any visual simultaneous localization and mapping system identifying previously visited places enables the creation of globally accurate maps robust relocalization and multi user mapping to match one place to another most state of the art approaches must decide a priori what constitutes a place often in terms of how many consecutive views should overlap or how many consecutive images should be considered together unfortunately such threshold dependencies limit their generality to different types of scenes in this paper we present a placeless place recognition algorithm using a novel match density estimation technique that avoids heuristically discretizing the space instead our approach considers place recognition as a problem of continuous matching between image streams automatically discovering regions of high match density that represent overlapping trajectory segments the algorithm uses well studied statistical tests to identify the relevant matching regions which are subsequently passed to an absolute pose algorithm to recover the geometric alignment we demonstrate the efficiency and accuracy of our methodology on three outdoor sequences including a comprehensive evaluation against ground truth from publicly available datasets that shows our approach outperforms several state of the art algorithms for place recognition furthermore we compare our overall algorithm to the currently best performing system for global localization and show how we outperform the approach on challenging indoor and outdoor datasets

self calibration under the cayley framework the cayley framework here is meant to tackle the vision problems under the infinite cayley transformation ict its main advantage lies in its numerical stability in this work the stratified self calibration under the cayley framework is investigated it is well known that the main difficulty of the stratified self calibration in multiple view geometry is to upgrade a projective reconstruction to an affine one in other words to estimate the unknown 3 vector of the plane at infinity called the normal vector to our knowledge without any prior knowledge about the scene or the camera motion the only available constraint on a moving camera with constant intrinsic parameters is the well known modulus constraint in the literature do other kinds of constraints exist if yes what they are how could they be used in this work such questions will be systematically investigated under the cayley framework our key contributions include 1 the original projective expression of the ict is simplified and a new projective expression is derived to make the upgrade easier from a projective reconstruction to a metric reconstruction 2 the constraints on the normal vector are systematically investigated for two views two constraints on the normal vector are derived one of them is the well known modulus constraint while the other is a new inequality constraint there are only these two constraints for two views for three views besides the constraints for two views two groups of new constraints are derived and each of them contains three constraints in other words there are 12 constraints in total for three views 3 based on our projective expression and these constraints a stratified cayley algorithm and a total cayley algorithm are proposed for the metric reconstruction from images it is experimentally shown that they both improve significantly the numerical stability of the classical algorithms compared with the global optimal algorithm under the infinite homography framework the cayley algorithms have comparable calibration accuracy but substantially reduce the computational load

a branch and bound approach to correspondence and grouping problems data correspondence grouping under an unknown parametric model is a fundamental topic in computer vision finding feature correspondences between two images is probably the most popular application of this research field and is the main motivation of our work it is a key ingredient for a wide range of vision tasks including three dimensional reconstruction and object recognition existing feature correspondence methods are based on either local appearance similarity or global geometric consistency or a combination of both in some heuristic manner none of these methods is fully satisfactory especially in the presence of repetitive image textures or mismatches in this paper we present a new algorithm that combines the benefits of both appearance based and geometry based methods and mathematically guarantees a global optimization our algorithm accepts the two sets of features extracted from two images as input and outputs the feature correspondences with the largest number of inliers which verify both the appearance similarity and geometric constraints specifically we formulate the problem as a mixed integer program and solve it efficiently by a series of linear programs via a branch and bound procedure we subsequently generalize our framework in the context of data correspondence grouping under an unknown parametric model and show it can be applied to certain classes of computer vision problems our algorithm has been validated successfully on synthesized data and challenging real images

a minimal solution to radial distortion autocalibration simultaneous estimation of radial distortion epipolar geometry and relative camera pose can be formulated as a minimal problem and solved from a minimal number of image points finding the solution to this problem leads to solving a system of algebraic equations in this paper we provide two different solutions to the problem of estimating radial distortion and epipolar geometry from eight point correspondences in two images unlike previous algorithms which were able to solve the problem from nine correspondences only we enforce the determinant of the fundamental matrix be zero this leads to a system of eight quadratic and one cubic equation in nine variables we first simplify this system by eliminating six of these variables and then solve the system by two alternative techniques the first one is based on the grobner basis method and the second one on the polynomial eigenvalue computation we demonstrate that our solutions are efficient robust and practical by experiments on synthetic and real data

two efficient solutions for visual odometry using directional correspondence this paper presents two new efficient solutions to the two view relative pose problem from three image point correspondences and one common reference direction this three plus one problem can be used either as a substitute for the classic five point algorithm using a vanishing point for the reference direction or to make use of an inertial measurement unit commonly available on robots and mobile devices where the gravity vector becomes the reference direction we provide a simple closed form solution and a solution based on algebraic geometry which offers numerical advantages in addition we introduce a new method for computing visual odometry with ransac and four point correspondences per hypothesis in a set of real experiments we demonstrate the power of our approach by comparing it to the five point method in a hypothesize and test visual odometry setting

application of the transfer matrix method to non conservative systems involving fluid flow in curved pipes abstract the application of the transfer matrix method to problems of fluid flow in planar curved pipes is presented also a presentation is given of how to deal with the stability of non conservative problems when using the dynamic method in the method proposed account is taken of the effect of the initial state of stress on the dynamic behaviour of the pipe three well known problems are solved to verify the convergence and applicability of the transfer matrix formulation to non conservative problems involving fluid flow

uniqueness and estimation of three dimensional motion parameters of rigid objects with curved surfaces two main results are established in this paper first we show that seven point correspondences are sufficient to uniquely determine from two perspective views the three dimensional motion parameters within a scale factor for the translations of a rigid object with curved surfaces the seven points should not be traversed by two planes with one plane containing the origin nor by a cone containing the origin second a set of essential parameters are introduced which uniquely determine the motion parameters up to a scale factor for the translations and can be estimated by solving a set of linear equations which are derived from the correspondences of eight image points the actual motion parameters can subsequently be determined by computing the singular value decomposition svd of a 3 3 matrix containing the essential parameters

global optimization through rotation space search this paper introduces a new algorithmic technique for solving certain problems in geometric computer vision the main novelty of the method is a branch and bound search over rotation space which is used in this paper to determine camera orientation by searching over all possible rotations problems can be reduced to known fixed rotation problems for which optimal solutions have been previously given in particular a method is developed for the estimation of the essential matrix giving the first guaranteed optimal algorithm for estimating the relative pose using a cost function based on reprojection errors recently convex optimization techniques have been shown to provide optimal solutions to many of the common problems in structure from motion however they do not apply to problems involving rotations the search method described in this paper allows such problems to be solved optimally apart from the essential matrix the algorithm is applied to the camera pose problem providing an optimal algorithm the approach has been implemented and tested on a number of both synthetically generated and real data sets with good performance

fast rotation search with stereographic projections for 3d registration registering two 3d point clouds involves estimating the rigid transform that brings the two point clouds into alignment recently there has been a surge of interest in using branch and bound bnb optimisation for point cloud registration while bnb guarantees globally optimal solutions it is usually too slow to be practical a fundamental source of difficulty lies in the search for the rotational parameters in this work first by assuming that the translation is known we focus on constructing a fast rotation search algorithm with respect to an inherently robust geometric matching criterion we propose a novel bounding function for bnb that is provably tighter than previously proposed bounds further we also propose a fast algorithm to evaluate our bounding function our idea is based on using stereographic projections to precompute and index all possible point matches in spatial r trees for rapid evaluations the result is a fast and globally optimal rotation search algorithm to conduct full 3d registration we co optimise the translation by embedding our rotation search kernel in a nested bnb algorithm since the inner rotation search is very efficient the overall 6dof optimisation is speeded up significantly without losing global optimality on various challenging point clouds including those taken out of lab settings our approach demonstrates superior efficiency

3d discrete rotations using hinge angles in this paper we study 3d rotations on grid points computed by using only integers for that purpose we investigate the intersection between the 3d half grid and the rotation plane from this intersection we define 3d hinge angles which determine a transit of a grid point from a voxel to its adjacent voxel during the rotation then we give a method to sort all 3d hinge angles with integer computations the study of 3d hinge angles allows us to design a 3d discrete rotation and to estimate the rotation between a pair of digital images in correspondence

sequential updating of projective and affine structure from motion a structure from motion algorithm is described which recovers structure and camera position modulo a projective ambiguity camera calibration is not required and camera parameters such as focal length can be altered freely during motion the structure is updated sequentially over an image sequence in contrast to schemes which employ a batch process a specialisation of the algorithm to recover structure and camera position modulo an affine transformation is described together with a method to periodically update the affine coordinate frame to prevent drift over time we describe the constraint used to obtain this specialisation structure is recovered from image corners detected and matched automatically and reliably in real image sequences results are shown for reference objects and indoor environments and accuracy of recovered structure is fully evaluated and compared for a number of reconstruction schemes a specific application of the work is demonstrated affine structure is used to compute free space maps enabling navigation through unstructured environments and avoidance of obstacles the path planning involves only affine constructions

fast very robust methods for the detection of multiple outliers abstract a few repeats of a simple forward search from a random starting point are shown to provide sufficiently robust parameter estimates to reveal masked multiple outliers the stability of the patterns obtained is exhibited by the stalactite plot the robust estimators used are least median of squares for regression and the minimum volume ellipsoid for multivariate outliers the forward search also has potential as an algorithm for calculation of these parameter estimates for large problems parallel computing provides appreciable reduction in computational time

balanced exploration and exploitation model search for efficient epipolar geometry estimation the estimation of the epipolar geometry is especially difficult when the putative correspondences include a low percentage of inlier correspondences and or a large subset of the inliers is consistent with a degenerate configuration of the epipolar geometry that is totally incorrect this work presents the balanced exploration and exploitation model beem search algorithm which works very well especially for these difficult scenes the algorithm handles these two problems in a unified manner it includes the following main features 1 balanced use of three search techniques global random exploration local exploration near the current best solution and local exploitation to improve the quality of the model 2 exploitation of available prior information to accelerate the search process 3 use of the best found model to guide the search process escape from degenerate models and define an efficient stopping criterion 4 presentation of a simple and efficient method to estimate the epipolar geometry from two scale invariant feature transform sift correspondences and 5 use of the locality sensitive hashing lsh approximate nearest neighbor algorithm for fast putative correspondence generation the resulting algorithm when tested on real images with or without degenerate configurations gives quality estimations and achieves significant speedups compared to the state of the art algorithms

sfm with mrfs discrete continuous optimization for large scale structure from motion recent work in structure from motion sfm has built 3d models from large collections of images downloaded from the internet many approaches to this problem use incremental algorithms that solve progressively larger bundle adjustment problems these incremental techniques scale poorly as the image collection grows and can suffer from drift or local minima we present an alternative framework for sfm based on finding a coarse initial solution using hybrid discrete continuous optimization and then improving that solution using bundle adjustment the initial optimization step uses a discrete markov random field mrf formulation coupled with a continuous levenberg marquardt refinement the formulation naturally incorporates various sources of information about both the cameras and points including noisy geotags and vanishing point vp estimates we test our method on several large scale photo collections including one with measured camera positions and show that it produces models that are similar to or better than those produced by incremental bundle adjustment but more robustly and in a fraction of the time

efficient bounded influence regression estimation abstract the least squares estimator for in the classical linear regression model is strongly efficient under certain conditions however in the presence of heavy tailed errors and or anomalous data the least squares efficiency can be markedly reduced in this article we propose an estimator that limits the influence of any small subset of the data and show that it satisfies a first order condition for strong efficiency subject to the constraint we then show that the estimator is asymptotically normal the article concludes with an outline of an algorithm for computing a bounded influence regression estimator and with an example comparing least squares robust regression as developed by huber and the estimator proposed in this article

random hermite differential equations mean square power series solutions and statistical properties abstract this paper deals with the construction of random power series solution of second order linear differential equations of hermite containing uncertainty through its coefficients and initial conditions under appropriate hypotheses on the data we establish that the constructed random power series solution is mean square convergent we provide conditions in order to obtain random polynomial solutions and as a consequence random hermite polynomial are introduced also the main statistical functions of the approximate stochastic process solution generated by truncation of the exact power series solution are given finally we apply the proposed technique to several illustrative examples comparing the numerical results with respect to those provided by other available approaches including monte carlo simulation

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

mean square numerical solution of random differential equations facts and possibilities this paper deals with the construction of numerical solutions of random initial value differential problems the random euler method is presented and the conditions for the mean square convergence are established numerical examples show that random euler method gives good results even if the sufficient convergence conditions are not satisfied

random fractional generalized airy differential equations a probabilistic analysis using mean square calculus abstract the aim of this paper is to study a generalization of fractional airy differential equations whose input data coefficient and initial conditions are random variables under appropriate hypotheses assumed upon the input data we construct a random generalized power series solution of the problem and then we prove its convergence in the mean square stochastic sense afterwards we provide reliable explicit approximations for the main statistical information of the solution process mean variance and covariance further we show a set of numerical examples where our obtained theory is illustrated more precisely we show that our results for the random fractional airy equation are in full agreement with the corresponding to classical random airy differential equation available in the extant literature finally we illustrate how to construct reliable approximations of the probability density function of the solution stochastic process to the random fractional airy differential equation by combining the knowledge of the mean and the variance and the principle of maximum entropy

the probability density function to the random linear transport equation we present a formula to calculate the probability density function of the solution of the random linear transport equation in terms of the density functions of the velocity and the initial condition we also present an expression for the joint probability density function of the solution in two different points our results have shown good agreement with monte carlo simulations

an efficient solution to the five point relative pose problem an efficient algorithmic solution to the classical five point relative pose problem is presented the problem is to find the possible solutions for relative camera pose between two calibrated views given five corresponding points the algorithm consists of computing the coefficients of a tenth degree polynomial in closed form and subsequently finding its roots it is the first algorithm well suited for numerical implementation that also corresponds to the inherent complexity of the problem we investigate the numerical precision of the algorithm we also study its performance under noise in minimal as well as overdetermined cases the performance is compared to that of the well known 8 and 7 point methods and a 6 point scheme the algorithm is used in a robust hypothesize and test framework to estimate structure and motion in real time with low delay the real time system uses solely visual input and has been demonstrated at major conferences

polynomial eigenvalue solutions to minimal problems in computer vision we present a method for solving systems of polynomial equations appearing in computer vision this method is based on polynomial eigenvalue solvers and is more straightforward and easier to implement than the state of the art grobner basis method since eigenvalue problems are well studied easy to understand and efficient and robust algorithms for solving these problems are available we provide a characterization of problems that can be efficiently solved as polynomial eigenvalue problems peps and present a resultant based method for transforming a system of polynomial equations to a polynomial eigenvalue problem we propose techniques that can be used to reduce the size of the computed polynomial eigenvalue problems to show the applicability of the proposed polynomial eigenvalue method we present the polynomial eigenvalue solutions to several important minimal relative pose problems

closed form solution of visual inertial structure from motion this paper investigates the visual inertial structure from motion problem a simple closed form solution to this problem is introduced special attention is devoted to identify the conditions under which the problem has a finite number of solutions specifically it is shown that the problem can have a unique solution two distinct solutions and infinite solutions depending on the trajectory on the number of point features and on their layout and on the number of camera images the investigation is also performed in the case when the inertial data are biased showing that in this latter case more images and more restrictive conditions on the trajectory are required for the problem resolvability

globally optimal estimates for geometric reconstruction problems we introduce a framework for computing statistically optimal estimates of geometric reconstruction problems while traditional algorithms often suffer from either local minima or non optimality or a combination of both we pursue the goal of achieving global solutions of the statistically optimal cost function our approach is based on a hierarchy of convex relaxations to solve non convex optimization problems with polynomials these convex relaxations generate a monotone sequence of lower bounds and we show how one can detect whether the global optimum is attained at a given relaxation the technique is applied to a number of classical vision problems triangulation camera pose homography estimation and last but not least epipolar geometry estimation experimental validation on both synthetic and real data is provided in practice only a few relaxations are needed for attaining the global optimum

the quadrifocal variety abstract multi view geometry is reviewed from an algebraic geometry perspective and multi focal tensors are constructed as equivariant projections of the grassmannian a connection to the principal minor assignment problem is made by considering several flatlander cameras the ideal of the quadrifocal variety is computed up to degree 8 and partially in degree 9 using the representations of gl 3 4 in the polynomial ring on the space of 3 3 3 3 tensors further representation theoretic analysis gives a lower bound for the number of minimal generators

two view motion segmentation with model selection and outlier removal by ransac enhanced dirichlet process mixture models we propose a novel motion segmentation algorithm based on mixture of dirichlet process mdp models in contrast to previous approaches we consider motion segmentation and its model selection regarding to the number of motion models as an inseparable problem our algorithm can simultaneously infer the number of motion models estimate the cluster memberships of correspondences and identify the outliers the main idea is to use mdp models to fully exploit the geometric consistencies before making premature decisions about the number of motion models to handle outliers we incorporate ransac into the inference process of mdp models in the experiments we compare the proposed algorithm with naive ransac gpca and schindler s method on both synthetic data and real image data the experimental results show that we can handle more motions and have satisfactory performance in the presence of various levels of noise and outlier

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

outlier robust corner preserving methods for reconstructing noisy images the ability to remove a large amount of noise and the ability to preserve most structure are desirable properties of an image smoother unfortunately they usually seem to be at odds with each other one can only improve one property at the cost of the other by combining m smoothing and least squares trimming the tm smoother is introduced as a means to unify corner preserving properties and outlier robustness to identify edge and corner preserving properties a new theory based on differential geometry is developed further robustness concepts are transferred to image processing in two examples the tm smoother outperforms other corner preserving smoothers a software package containing both the tm and the m smoother can be downloaded from the internet

shape ambiguities in structure from motion this paper examines the fundamental ambiguities and uncertainties inherent in recovering structure from motion by examining the eigenvectors associated with null or small eigenvalues of the hessian matrix we can quantify the exact nature of these ambiguities and predict how they affect the accuracy of the reconstructed shape our results for orthographic cameras show that the bas relief ambiguity is significant even with many images unless a large amount of rotation is present similar results for perspective cameras suggest that three or more frames and a large amount of rotation are required for metrically accurate reconstruction

motion estimation for nonoverlapping multicamera rigs linear algebraic and l geometric solutions we investigate the problem of estimating the ego motion of a multicamera rig from two positions of the rig we describe and compare two new algorithms for finding the 6 degrees of freedom 3 for rotation and 3 for translation of the motion one algorithm gives a linear solution and the other is a geometric algorithm that minimizes the maximum measurement error the optimal l solution they are described in the context of the general camera model gcm and we pay particular attention to multicamera systems in which the cameras have nonoverlapping or minimally overlapping field of view many nonlinear algorithms have been developed to solve the multicamera motion estimation problem however no linear solution or guaranteed optimal geometric solution has previously been proposed we made two contributions 1 a fast linear algebraic method using the gcm and 2 a guaranteed globally optimal algorithm based on the l geometric error using the branch and bound technique in deriving the linear method using the gcm we give a detailed analysis of degeneracy of camera configurations in finding the globally optimal solution we apply a rotation space search technique recently proposed by hartley and kahl our experiments conducted on both synthetic and real data have shown excellent results

four points in two or three calibrated views theory and practice suppose two perspective views of four world points are given and that the intrinsic parameters are known but the camera poses and the world point positions are not we prove that the epipole in each view is then constrained to lie on a curve of degree ten we derive the equation for the curve and establish many of the curve s properties for example we show that the curve has four branches through each of the image points and that it has four additional points on each conic of the pencil of conics through the four image points we show how to compute the four curve points on each conic in closed form we show that orientation constraints allow only parts of the curve and find that there are impossible configurations of four corresponding point pairs we give a novel algorithm that solves for the essential matrix given three corresponding points and one of the epipoles we then use the theory to create the most efficient solution yet to the notoriously difficult problem of solving for the pose of three views given four corresponding points the solution is a search over a one dimensional parameter domain where each point in the search can be evaluated in closed form the intended use for the solution is in a hypothesise and test architecture to solve for structure and motion

random analytic solution of coupled differential models with uncertain initial condition and source term this paper deals with the construction of random power series solution of vector initial value problems containing uncertainty in both initial condition and source term under appropriate hypothesis on the data we prove that the random series solution constructed by a random frobenius method is convergent in the mean square sense also the main statistical functions of the approximating stochastic process solution generated by truncation of the exact series solution are given finally we apply the proposed technique to several illustrative examples

pose free structure from motion using depth from motion constraints structure from motion sfm is the problem of recovering the geometry of a scene from a stream of images taken from unknown viewpoints one popular approach to estimate the geometry of a scene is to track scene features on several images and reconstruct their position in 3 d during this process the unknown camera pose must also be recovered unfortunately recovering the pose can be an ill conditioned problem which in turn can make the sfm problem difficult to solve accurately we propose an alternative formulation of the sfm problem with fixed internal camera parameters known a priori in this formulation obtained by algebraic variable elimination the external camera pose parameters do not appear as a result the problem is better conditioned in addition to involving much fewer variables variable elimination is done in three steps first we take the standard sfm equations in projective coordinates and eliminate the camera orientations from the equations we then further eliminate the camera center positions finally we also eliminate all 3 d point positions coordinates except for their depths with respect to the camera center thus obtaining a set of simple polynomial equations of degree two and three we show that when there are merely a few points and pictures these depth only equations can be solved in a global fashion using homotopy methods we also show that in general these same equations can be used to formulate a pose free cost function to refine sfm solutions in a way that is more accurate than by minimizing the total reprojection error as done when using the bundle adjustment method the generalization of our approach to the case of varying internal camera parameters is briefly discussed

motion from point matches multiple of solutions in this paper we study the multiplicity of solutions of the motion problem given n point matches between two frames how many solutions are there to the motion problem we show that the maximum number of solutions is 10 when 5 point matches are available this settles a question that has been around in the computer vision community for a while we follow two tracks we show that the two approaches are compatible and yield the same result we then describe a computer implementation of the second approach that uses maple a language for symbolic computation the program allows us to compute exactly the solutions for any configuration of 5 points some experiments are described

self calibration and metric reconstruction inspite of varying and unknown intrinsic camera parameters in this paper the theoretical and practical feasibility of self calibration in the presence of varying intrinsic camera parameters is under investigation the paper s main contribution is to propose a self calibration method which efficiently deals with all kinds of constraints on the intrinsic camera parameters within this framework a practical method is proposed which can retrieve metric reconstruction from image sequences obtained with uncalibrated zooming focusing cameras the feasibility of the approach is illustrated on real and synthetic examples besides this a theoretical proof is given which shows that the absence of skew in the image plane is sufficient to allow for self calibration a counting argument is developed which depending on the set of constraints gives the minimum sequence length for self calibration and a method to detect critical motion sequences is proposed

analytic numerical approximating processes of diffusion equation with data uncertainty this paper deals with the construction of approximating processes for solving mixed problems related to the diffusion equation where the initial condition is assumed to be a stochastic process and the diffusion coefficient is a random variable expectation and standard deviation of the approximation processes are given

least median of squares regression abstract classical least squares regression consists of minimizing the sum of the squared residuals many authors have produced more robust versions of this estimator by replacing the square by something else such as the absolute value in this article a different approach is introduced in which the sum is replaced by the median of the squared residuals the resulting estimator can resist the effect of nearly 50 of contamination in the data in the special case of simple regression it corresponds to finding the narrowest strip covering half of the observations generalizations are possible to multivariate location orthogonal regression and hypothesis testing in linear models

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

exact two image structure from motion for two image structure from motion we present a simple exact expression for a least squares image reprojection error for finite motion that depends only on the motion optimal estimates of the structure and motion can be computed by minimizing this expression just over the motion parameters also we present a solution to the triangulation problem an exact explicit expression for the optimal structure estimate given the motion we identify a new ambiguity in recovering the structure for known motion we study the exact error s properties experimentally and demonstrate that it often has several local minima for forward or backward motion estimates our experiments also show that the reflected local minimum of oliensis 2001 and soatto et al 1998 occurs for large translational motions our exact results assume that the camera is calibrated and use a least squares image reprojection error that applies most naturally to a spherical imaging surface we approximately extend our approach to the standard least squares error in the image plane and uncalibrated cameras we present an improved version of the sampson error which gives better results experimentally

the change of variance curve and optimal redescending m estimators abstract we define the change of variance curve cvc of location m estimators in order to investigate the infinitesimal stability of the asymptotic variance we also construct the so called hyperbolic tangent estimators proving their existence and performing certain numerical computations of their defining constants their introduction is motivated by a theorem that shows they are the optimally robust redescending m estimators in the sense of the cvc

homography based egomotion estimation with a common direction in this paper we explore the different minimal solutions for egomotion estimation of a camera based on homography knowing the gravity vector between calibrated images these solutions depend on the prior knowledge about the reference plane used by the homography we then demonstrate that the number of matched points can vary from two to three and that a direct closed form solution or a grobner basis based solution can be derived according to this plane many experimental results on synthetic and real sequences in indoor and outdoor environments show the efficiency and the robustness of our approach compared to standard methods

robust regression using repeated medians abstract the repeated median algorithm is a robustified u statistic in which nested medians replace the single mean unlike many generalizations of the univariate median repeated median estimates maintain the high 50 breakdown value and can resist the effects of outliers even when they comprise nearly half of the data because they are calculated directly not iteratively repeated median procedures can be used as starting values for iterative robust estimation methods for bivariate linear regression with symmetric errors repeated median estimates are unbiased and fisher consistent and their efficiency under gaussian sampling can be comparable to the efficiency of the univariate median author

quasiconvex optimization for robust geometric reconstruction geometric reconstruction problems in computer vision are often solved by minimizing a cost function that combines the reprojection errors in the 2d images in this paper we show that for various geometric reconstruction problems their reprojection error functions share a common and quasiconvex formulation based on the quasiconvexity we present a novel quasiconvex optimization framework in which the geometric reconstruction problems are formulated as a small number of small scale convex programs that are readily solvable our final reconstruction algorithm is simple and has intuitive geometric interpretation in contrast to existing local minimization approaches our algorithm is deterministic and guarantees a predefined accuracy of the minimization result the quasiconvexity also provides an intuitive method to handle directional uncertainties and outliers in measurements for a large scale problem or in a situation where computational resources are constrained we provide an efficient approximation that gives a good upper bound but not global minimum on the reconstruction error we demonstrate the effectiveness of our algorithm by experiments on both synthetic and real data

generalized weiszfeld algorithms for lq optimization in many computer vision applications a desired model of some type is computed by minimizing a cost function based on several measurements typically one may compute the model that minimizes the l 2 cost that is the sum of squares of measurement errors with respect to the model however the lq solution which minimizes the sum of the q th power of errors usually gives more robust results in the presence of outliers for some values of q for example q 1 the weiszfeld algorithm is a classic algorithm for finding the geometric l1 mean of a set of points in euclidean space it is provably optimal and requires neither differentiation nor line search the weiszfeld algorithm has also been generalized to find the l1 mean of a set of points on a riemannian manifold of non negative curvature this paper shows that the weiszfeld approach may be extended to a wide variety of problems to find an lq mean for 1 le q lt 2 while maintaining simplicity and provable convergence we apply this problem to both single rotation averaging under which the algorithm provably finds the global lq optimum and multiple rotation averaging for which no such proof exists experimental results of lq optimization for rotations show the improved reliability and robustness compared to l 2 optimization

semiparametrically efficient inference based on signed ranks in symmetric independent component models we consider semiparametric location scatter models for which the p variate observation is obtained as x lambda z mu where mu is a p vector lambda is a full rank p p matrix and the unobserved random p vector z has marginals that are centered and mutually independent but are otherwise unspecified as in blind source separation and independent component analysis ica the parameter of interest throughout the paper is lambda on the basis of n i i d copies of x we develop under a symmetry assumption on z signed rank one sample testing and estimation procedures for lambda we exploit the uniform local and asymptotic normality ulan of the model to define signed rank procedures that are semiparametrically efficient under correctly specified densities yet as usual in rank based inference the proposed procedures remain valid correct asymptotic size under the null for hypothesis testing and root n consistency for point estimation under a very broad range of densities we derive the asymptotic properties of the proposed procedures and investigate their finite sample behavior through simulations

practical structure and motion recovery from two uncalibrated images using e constrained adaptive differential evolution metric 3d reconstruction from two uncalibrated images involves estimating both the camera parameters and the 3d structure of a scene which is known to be sensitive to the quality of image correspondences in this paper the above problem is recast as a single constrained optimization problem which can be efficiently solved by a new modified e constrained adaptive differential evolution eade optimizer within which noticeable acceleration of convergence rate has been achieved by incorporating geometrically meaningful evolutionary operations the proposed approach avoids solving the inverse 3d reconstruction problem by directly searching for the globally optimal 3d structure while satisfying the epipolar geometry and the cheirality constraints given a set of outlier affected noisy image correspondences the camera calibration and scene structure can be simultaneously estimated in our global optimization framework extensive experimental validation on both synthetic data and real images were carried out the performance of our proposed method is compared with that of four well known fundamental matrix estimation methods each of which is combined with analytical focal length estimation optimal triangulation and bundle adjustment optimization statistical analysis of the results demonstrates that our method can significantly improve the accuracy of camera calibration and scene reconstruction the stable accurate numerical performance as well as fast convergence rate make our method a practical one

silhouette coherence for camera calibration under circular motion we present a new approach to camera calibration as a part of a complete and practical system to recover digital copies of sculpture from uncalibrated image sequences taken under turntable motion in this paper we introduce the concept of the silhouette coherence of a set of silhouettes generated by a 3d object we show how the maximization of the silhouette coherence can be exploited to recover the camera poses and focal length silhouette coherence can be considered as a generalization of the well known epipolar tangency constraint for calculating motion from silhouettes or outlines alone further silhouette coherence exploits all the geometric information encoded in the silhouette not just at epipolar tangency points and can be used in many practical situations where point correspondences or outer epipolar tangents are unavailable we present an algorithm for exploiting silhouette coherence to efficiently and reliably estimate camera motion we use this algorithm to reconstruct very high quality 3d models from uncalibrated circular motion sequences even when epipolar tangency points are not available or the silhouettes are truncated the algorithm has been integrated into a practical system and has been tested on more than 50 uncalibrated sequences to produce high quality photo realistic models three illustrative examples are included in this paper the algorithm is also evaluated quantitatively by comparing it to a state of the art system that exploits only epipolar tangents

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

automatic camera calibration using multiple sets of pairwise correspondences we propose a new method to add an uncalibrated node into a network of calibrated cameras using only pairwise point correspondences while previous methods perform this task using triple correspondences these are often difficult to establish when there is limited overlap between different views in such challenging cases we must rely on pairwise correspondences and our solution becomes more advantageous our method includes an 11 point minimal solution for the intrinsic and extrinsic calibration of a camera from pairwise correspondences with other two calibrated cameras and a new inlier selection framework that extends the traditional ransac family of algorithms to sampling across multiple datasets our method is validated on different application scenarios where a lack of triple correspondences might occur addition of a new node to a camera network calibration and motion estimation of a moving camera inside a camera network and addition of views with limited overlap to a structure from motion model

tracks selection for robust efficient and scalable large scale structure from motion currently global structure from motion sfm pipeline consists of four steps estimating camera rotations first then computing camera positions triangulating tracks and finally doing bundle adjustment however for large scale sfm problems the tracks are usually too noisy and redundant for the bundle adjustment thus in this work we propose a novel fast tracks selection method to improve both efficiency and robustness of the bundle adjustment firstly three selection criteria compactness accurateness and connectedness are introduced where the first two are to calculate a selection priority for each track and the third is to guarantee the completeness of scene structure then to satisfy these criteria a more informative subset of tracks is selected by covering multiple spanning trees of epipolar geometry graph since tracks selection acts only an intermediate step in the whole sfm pipeline it can be in principle embedded into any global sfm pipelines to validate the effectiveness of our tracks selection module we insert it into a state of the art global sfm system and compare it with three other selection methods extensive experiments show that by embedding our tracks selection module the new sfm system performs similarly or better than the original one in terms of reconstruction completeness and accuracy but is much more efficient and scalable for large scale scene reconstructions finally our tracks selection module is further embedded into two other global sfm systems to demonstrated its versatility c 2017 elsevier ltd all rights reserved

on the existence of epipolar matrices this paper considers the foundational question of the existence of a fundamental resp essential matrix given m point correspondences in two views we present a complete answer for the existence of fundamental matrices for any value of m we disprove the widely held beliefs that fundamental matrices always exist whenever m le 7 m 7 at the same time we prove that they exist unconditionally when m le 5 m 5 under a mild genericity condition we show that an essential matrix always exists when m le 4 m 4 we also characterize the six and seven point configurations in two views for which all matrices satisfying the epipolar constraint have rank at most one

determining shape and motion from monocular camera determining the spatial motion of a moving camera from a video is a classical problem in computer vision the difficulty of this problem is that the flow pattern directly observable in the video is generally not the complete flow pattern induced by the motion but only the partial information of it which is known as the normal flow in this paper we present a direct method which neither requires the establishment of feature correspondences nor the recovery of optical flow between two image frames but we directly utilize all observable normal flow data to recover the camera motion we propose a two stage iterative algorithm to search the solution in the motion space in a coarse to fine framework the first stage involves the use of the direction part of the normal flow each of these normal flow data can provide a constrained solution space to the direction of motion the intersection of the motion solutions from all the available normal flow data can reduce the motion ambiguity to a certain extent we then use the globality of the rotational magnitude to all image positions to constrain the motion parameters further once the camera motion is determined the depth map of the imaged scene up to an arbitrary scale can be recovered experimental results on synthetic data and real images are provided to reveal the performance of the proposed method highlightswe determine camera motion and shape directly from normal flows our method does not require optical flows or feature correspondences two constraints are developed to determine camera motion experimental results are comparable to the state of the art methods

review and analysis of solutions of the three point perspective pose estimation problem in this paper the major direct solutions to the three point perspective pose estimation problems are reviewed from a unified perspective beginning with the first solution which was published in 1841 by a german mathematician continuing through the solutions published in the german and then american photogrammetry literature and most recently in the current computer vision literature the numerical stability of these three point perspective solutions are also discussed we show that even in case where the solution is not near the geometric unstable region considerable care must be exercised in the calculation depending on the order of the substitutions utilized the relative error can change over a thousand to one this difference is due entirely to the way the calculations are performed and not due to any geometric structural instability of any problem instance we present an analysis method which produces a numerically stable calculation

a generalized kernel consensus based robust estimator in this paper we present a new adaptive scale kernel consensus askc robust estimator as a generalization of the popular and state of the art robust estimators such as random sample consensus ransac adaptive scale sample consensus assc and maximum kernel density estimator mkde the askc framework is grounded on and unifies these robust estimators using nonparametric kernel density estimation theory in particular we show that each of these methods is a special case of askc using a specific kernel like these methods askc can tolerate more than 50 percent outliers but it can also automatically estimate the scale of inliers we apply askc to two important areas in computer vision robust motion estimation and pose estimation and show comparative results on both synthetic and real data

random airy type differential equations mean square exact and numerical solutions this paper deals with the construction of power series solutions of random airy type differential equations containing uncertainty through the coefficients as well as the initial conditions under appropriate hypotheses on the data we establish that the constructed random power series solution is mean square convergent over the whole real line in addition the main statistical functions such as the mean and the variance of the approximate solution stochastic process generated by truncation of the exact power series solution are given finally we apply the proposed technique to several illustrative examples which show substantial speed up and improvement in accuracy compared to other approaches such as monte carlo simulations

the impact of outliers and leverage points for technical efficiency measurement using high breakdown procedures given that most data used for production studies have not been accumulated for such purposes it is important that the quantitative tools for messy data which can affect the accuracy of computed technical efficiency measures be found in this study high breakdown robust methods are used in conjunction with a robust distance measure defined relative to the minimum volume ellipsoid estimator the standardized robust residuals from the high breakdown estimators and the robust distance measures are used to statistically and graphically depict both multivariate outliers and leverage points once these points are found their relationship to those observations that exhibit strong technically efficient or inefficient behavior scale inefficiency and or unusual production characteristics is analyzed for three linerboard manufacturing facilities additionally the impact of the outliers and leverage points on the estimated least squares coefficients which are used by the corrected ordinary least squares methodology to compute the full frontier technical efficiency measures is explored finally a sensitivity analysis of the impact of outliers and leverage points on the computed linear programming based technical efficiency measures is presented