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

ambiguity in structure from motion sphere versus plane if 3d rigid motion can be correctly estimated from image sequences the structure of the scene can be correctly derived using the equations for image formation however an error in the estimation of 3d motion will result in the computation of a distorted version of the scene structure of computational interest are these regions in space where the distortions are such that the depths become negative because in order for the scene to be visible it has to lie in front of the image and thus the corresponding depth estimates have to be positive the stability analysis for the structure from motion problem presented in this paper investigates the optimal relationship between the errors in the estimated translational and rotational parameters of a rigid motion that results in the estimation of a minimum number of negative depth values the input used is the value of the flow along some direction which is more general than optic flow or correspondence for a planar retina it is shown that the optimal configuration is achieved when the projections of the translational and rotational errors on the image plane are perpendicular furthermore the projection of the actual and the estimated translation lie on a line through the center for a spherical retina given a rotational error the optimal translation is the correct one given a translational error the optimal rotational negative deptherror depends both in direction and value on the actual and estimated translation as well as the scene in view the proofs besides illuminating the confounding of translation and rotation in structure from motion have an important application to ecological optics the same analysis provides a computational explanation of why it is easier to estimate self motion in the case of a spherical retina and why shape can be estimated easily in the case of a planar retina thus suggesting that nature s design of compound eyes or panoramic vision for flying systems and camera type eyes for primates and other systems that perform manipulation is optimal

some aspects of the spline smoothing approach to non parametric regression curve fitting non parametric regression using cubic splines is an attractive flexible and widely applicable approach to curve estimation although the basic idea was formulated many years ago the method is not as widely known or adopted as perhaps it should be the topics and examples discussed in this paper are intended to promote the understanding and extend the practicability of the spline smoothing methodology particular subjects covered include the basic principles of the method the relation with moving average and other smoothing methods the automatic choice of the amount of smoothing and the use of residuals for diagnostic checking and model adaptation the question of providing inference regions for curves and for relevant properties of curves is approached via a finite dimensional bayesian formulation

new beams of global bifurcation points for a reaction diffusion system with inequalities or inclusions abstract we consider a reaction diffusion system of activator inhibitor or substrate depletion type which is subject to diffusion driven instability we show that an obstacle e g a unilateral membrane modeled either in terms of inequalities or of inclusions introduces whole beams of new global bifurcation points of spatially non homogeneous stationary solutions which lie in parameter domains which are excluded as bifurcation points for the problem without the obstacle

tracking while zooming using affine transfer and multifocal tensors this paper presents algorithms for tracking unknown objects in the presence of zoom since prior models are unavailable point and line matches in affine views are used to characterize the structure and to transfer a fixation point into new images in a sequence because any affine projection matrix is permitted the intrinsic camera parameters such as focal length may change freely also since the techniques do not require long feature tracks a further desirable property is insensitivity to partial occlusion caused for instance by part of the object falling off the image plane while zooming in if only point matches are available a previous method based on factorization is applied when also incorporating lines the affine trifocal and quadrifocal tensors are used for tracking in monocular and stereo systems respectively methods for computing the tensors minimizing algebraic error are developed in comparison with their projective counterparts the affine tensors offer significant advantages in terms of computation time and convenience of parameterization and the relations between the different tensors are shown to be much simpler successful tracking is demonstrated on several real image sequences

structure and motion from line segments in multiple images this paper presents a new method for recovering the three dimensional structure of a scene composed of straight line segments using the image data obtained from a moving camera the recovery algorithm is formulated in terms of an objective function which measures the total squared distance in the image plane between the observed edge segments and the projections perspective of the reconstructed lines this objective function is minimized with respect to the line parameters and the camera positions to obtain an estimate for the structure of the scene the effectiveness of this approach is demonstrated quantitatively through extensive simulations and qualitatively with actual image sequences the implementation is being made publicly available

using points at infinity for parameter decoupling in camera calibration the majority of camera calibration methods including the gold standard algorithm use point based information and simultaneously estimate all calibration parameters in contrast we propose a novel calibration method that exploits line orientation information and decouples the problem into two simpler stages we formulate the problem as minimization of the lateral displacement between single projected image lines and their vanishing points unlike previous vanishing point methods parallel line pairs are not required additionally the invariance properties of vanishing points mean that multiple images related by pure translation can be used to increase the calibration data set size without increasing the number of estimated parameters we compare this method with vanishing point methods and the gold standard algorithm and demonstrate that it has comparable performance

fitting parameterized three dimensional models to images model based recognition and motion tracking depend upon the ability to solve for projection and model parameters that will best fit a 3 d model to matching 2 d image features the author extends current methods of parameter solving to handle objects with arbitrary curved surfaces and with any number of internal parameters representing articulation variable dimensions or surface deformations numerical stabilization methods are developed that take account of inherent inaccuracies in the image measurements and allow useful solutions to be determined even when there are fewer matches than unknown parameters the levenberg marquardt method is used to always ensure convergence of the solution these techniques allow model based vision to be used for a much wider class of problems than was possible with previous methods their application is demonstrated for tracking the motion of curved parameterized objects

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

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

estimation of 3d structure and motion from image corners abstract this paper deals with motion estimation from image corner correspondences in two cases the orthogonal corner and the general corner with known space angles the contribution of the paper is in three folds first the three dimensional structure of a corner is recovered easily from its image by introducing a new coordinate system second it is shown that the one corner and two points correspondences over two views are sufficient to uniquely determine the motion i e the rotation and translation third experiments using both simulated data and real images are conducted which present good results

structure from motion using line correspondences a theory is presented for the computation of three dimensional motion and structure from dynamic imagery using only line correspondences the traditional approach of corresponding microfeatures interesting points highlights corners high curvature points etc is reviewed and its shortcomings are discussed then a theory is presented that describes a closed form solution to the motion and structure determination problem from line correspondences in three views the theory is compared with previous ones that are based on nonlinear equations and iterative methods

visually guided ranging from observations of points lines and curves via an identifier based nonlinear observer abstract in this paper we consider the problem of estimating the range information of features on an affine plane in r 3 by observing its image with the aid of a ccd camera wherein we assume that the camera is undergoing a known motion the features considered are points lines and planar curves located on planar surfaces of static objects the dynamics of the moving projections of the features on the image plane have been described as a suitable differential equation on an appropriate feature space this dynamics is used to estimate feature parameters from which the range information is readily available in this paper the proposed identification has been carried out via a newly introduced identifier based observer performance of the observer has been studied via simulation

rank conditions on the multiple view matrix geometric relationships governing multiple images of points and lines and associated algorithms have been studied to a large extent separately in multiple view geometry the previous studies led to a characterization based on multilinear constraints which have been extensively used for structure and motion recovery feature matching and image transfer in this paper we present a universal rank condition on the so called multiple view matrix m for arbitrarily combined point and line features across multiple views the condition gives rise to a complete set of constraints among multiple images all previously known multilinear constraints become simple instantiations of the new condition in particular the relationship between bilinear trilinear and quadrilinear constraints can be clearly revealed from this new approach the theory enables us to carry out global geometric analysis for multiple images as well as systematically characterize all degenerate configurations without breaking image sequence into pairwise or triple wise sets of views this global treatment allows us to utilize all incidence conditions governing all features in all images simultaneously for a consistent recovery of motion and structure from multiple views in particular a rank based multiple view factorization algorithm for motion and structure recovery is derived from the rank condition simulation results are presented to validate the multiple view matrix based approach

bifurcation for a reaction diffusion system with unilateral and neumann boundary conditions abstract we consider a reaction diffusion system of activator inhibitor or substrate depletion type which is subject to diffusion driven instability if supplemented by pure neumann boundary conditions we show by a degree theoretic approach that an obstacle e g a unilateral membrane modeled in terms of inequalities introduces new bifurcation of spatial patterns in a parameter domain where the trivial solution of the problem without the obstacle is stable moreover this parameter domain is rather different from the known case when also dirichlet conditions are assumed in particular bifurcation arises for fast diffusion of activator and slow diffusion of inhibitor which is the difference from all situations which we know

pose estimation using line based dynamic vision and inertial sensors an observer problem from a computer vision application is studied rigid body pose estimation using inertial sensors and a monocular camera is considered and it is shown how rotation estimation can be decoupled from position estimation orientation estimation is formulated as an observer problem with implicit output where the states evolve on so 3 a careful observability study reveals interesting group theoretic structures tied to the underlying system structure a locally convergent observer where the states evolve on so 3 is proposed and numerical estimates of the domain of attraction is given further it is shown that given convergent orientation estimates position estimation can be formulated as a linear implicit output problem from an applications perspective it is outlined how delayed low bandwidth visual observations and high bandwidth rate gyro measurements can provide high bandwidth estimates this is consistent with real time constraints due to the complementary characteristics of the sensors which are fused in a multirate way

bifurcation points for a reaction diffusion system with two inequalities abstract we consider a reaction diffusion system of activator inhibitor or substrate depletion type which is subject to diffusion driven instability we show that obstacles e g a unilateral membrane for both quantities modeled in terms of inequalities introduce a new bifurcation of spatially non homogeneous steady states in the domain of stability of the trivial solution of the corresponding classical problem without obstacles

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

the 3d line motion matrix and alignment of line reconstructions we study the problem of aligning two 3d line reconstructions in projective affine metric or euclidean space we introduce the 6 6 3d line motion matrix that acts on plucker coordinates we characterize its algebraic properties and its relation to the usual 4 4 point motion matrix and propose various methods for estimating 3d motion from line correspondences based on cost functions defined in images or 3d space we assess the quality of the different estimation methods using simulated data and real images

projective reconstruction and invariants from multiple images this correspondence investigates projective reconstruction of geometric configurations seen in two or more perspective views and the computation of projective invariants of these configurations from their images a basic tool in this investigation is the fundamental matrix that describes the epipolar correspondence between image pairs it is proven that once the epipolar geometry is known the configurations of many geometric structures for instance sets of points or lines are determined up to a collineation of projective 3 space spl pscrsup 3 by their projection in two independent images this theorem is the key to a method for the computation of invariants of the geometry invariants of six points in spl pscrsup 3 and of four lines in spl pscrsup 3 are defined and discussed an example with real images shows that they are effective in distinguishing different geometrical configurations since the fundamental matrix is a basic tool in the computation of these invariants new methods of computing the fundamental matrix from seven point correspondences in two images or six point correspondences in three images are given

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

motion and structure from line correspondences closed form solution uniqueness and optimization this work discusses estimating motion and structure parameters from line correspondences of a rigid scene the authors present a closed form solution to motion and structure parameters from line correspondences through three monocular perspective views the algorithm makes use of redundancy in the data to improve the accuracy of the solutions the uniqueness of the solution is established and necessary and sufficient conditions for degenerate spatial line configurations are given optimization has been employed to further improve the accuracy of the estimates in the presence of noise simulations have shown that the errors of the optimized estimates are close to the theoretical lower error bound

lines and points in three views and the trifocal tensor this paper discusses the basic role of the trifocal tensor in scene reconstruction from three views this 3 times 3 times 3 tensor plays a role in the analysis of scenes from three views analogous to the role played by the fundamental matrix in the two view case in particular the trifocal tensor may be computed by a linear algorithm from a set of 13 line correspondences in three views it is further shown in this paper that the trifocal tensor is essentially identical to a set of coefficients introduced by shashua to effect point transfer in the three view case this observation means that the 13 line algorithm may be extended to allow for the computation of the trifocal tensor given any mixture of sufficiently many line and point correspondences from the trifocal tensor the camera matrices of the images may be computed and the scene may be reconstructed for unrelated uncalibrated cameras this reconstruction will be unique up to projectivity thus projective reconstruction of a set of lines and points may be carried out linearly from three views

motion estimation via dynamic vision estimating the three dimensional motion of an object from a sequence of projections is of paramount importance in a variety of applications in control and robotics such as autonomous navigation manipulation servo tracking docking planning and surveillance although visual motion estimation is an old problem the first formulations date back to the beginning of the century only recently have tools from nonlinear systems estimation theory hinted at acceptable solutions in this paper the authors formulate the visual motion estimation problem in terms of identification of nonlinear implicit systems with parameters on a topological manifold and propose a dynamic solution either in the local coordinates or in the embedding space of the parameter manifold such a formulation has structural advantages over previous recursive schemes since the estimation of motion is decoupled from the estimation of the structure of the object being viewed and therefore it is possible to handle occlusions in a principled way

directions of motion fields are hardly ever ambiguous if instead of the full motion field we consider only the direction of the motion field due to a rigid motion what can we say about the three dimensional motion information contained in it this paper provides a geometric analysis of this question based solely on the constraint that the depth of the surfaces in view is positive the motivation behind this analysis is to provide a theoretical foundation for image constraints employing only the sign of flow in various directions and justify their utilization for addressing 3d dynamic vision problems it is shown that considering as the imaging surface the whole sphere independently of the scene in view two different rigid motions cannot give rise to the same directional motion field if we restrict the image to half of a sphere or an infinitely large image plane two different rigid motions with instantaneous translational and rotational velocities t 1 1 and t 2 2 cannot give rise to the same directional motion field unless the plane through t 1 and t 2 is perpendicular to the plane through 1 and 2 i e t 1 t 2 1 2 e 0 in addition in order to give practical significance to these uniqueness results for the case of a limited field of view we also characterize the locations on the image where the motion vectors due to the different motions must have different directions if 1 2 t 1 t 2 e 0 and certain additional constraints are met then the two rigid motions could produce motion fields with the same direction for this to happen the depth of each corresponding surface has to be within a certain range defined by a second and a third order surface similar more restrictive constraints are obtained for the case of multiple motions consequently directions of motion fields are hardly ever ambiguous a byproduct of the analysis is that full motion fields are never ambiguous with a half sphere as the imaging surface

object pose from 2 d to 3 d point and line correspondences in this paper we present a method for optimally estimating the rotation and translation between a camera and a 3 d object from point and or line correspondences first we devise an error function and second we show how to minimize this error function the quadratic nature of this function is made possible by representing rotation and translation with a dual number quaternion we provide a detailed account of the computational aspects of a trust region optimization method this method compares favourably with newton s method which has extensively been used to solve the problem at hand with faugeras toscani s linear method faugeras and toscani 1986 for calibrating a camera and with the levenberg marquardt non linear optimization method finally we present some experimental results which demonstrate the robustness of our method with respect to image noise and matching errors

on degeneracy of linear reconstruction from three views linear line complex and applications this paper investigates the linear degeneracies of projective structure estimation from line features across three views we show that the rank of the linear system of equations for recovering the trilinear tensor of three views reduces to 23 instead of 26 when the scene is a linear line complex llc a set of lines in space intersecting at a common line the llc situation is only linearly degenerate and one can obtain a unique solution when the admissibility constraints of the tensor are accounted for the line configuration described by an llc rather than being some obscure case is in fact quite typical it includes as a particular example the case of a camera moving down a hallway in an office environment or down an urban street furthermore an llc situation may occur as an artifact such as in direct estimation from spatio temporal derivatives of image brightness therefore an investigation into degeneracies and their remedy is important also in practice

smooth continuation of solutions and eigenvalues for variational inequalities based on the implicit function theorem the implicit function theorem is applied in a nonstandard way to abstract variational inequalities depending on a possibly infinite dimensional parameter in this way results on smooth continuation of solutions as well as of eigenvalues and eigenvectors are established under certain particular assumptions the abstract results are applied to a linear second order elliptic eigenvalue problem with nonlocal unilateral boundary conditions schrodinger operator with the potential as the parameter

projective reconstruction from line correspondences in multiple uncalibrated images a new approach is proposed for reconstructing 3d lines and cameras from 2d corresponding lines across multiple uncalibrated views there is no requirement that the 2d corresponding lines on different images represent the same segment of a 3d line which may not appear on all images a 3d line is reconstructed by minimizing a geometric cost function that measures the distance of the reprojected end points of the 3d segment from the measured 2d lines on different images an algorithmic procedure is provided with guaranteed convergence to a solution where the geometric cost function achieves a local minimum

linear n point camera pose determination the determination of camera position and orientation from known correspondences of 3d reference points and their images is known as pose estimation in computer vision and space resection in photogrammetry it is well known that from three corresponding points there are at most four algebraic solutions less appears to be known about the cases of four and five corresponding points we propose a family of linear methods that yield a unique solution to 4 and 5 point pose determination for generic reference points we first review the 3 point algebraic method then we present our two step 4 point and one step 5 point linear algorithms the 5 point method can also be extended to handle more than five points finally we demonstrate our methods on both simulated and real images we show that they do not degenerate for coplanar configurations and even outperform the special linear algorithm for coplanar configurations in practice

motion analysis of a homogeneously deformable object using subset correspondences abstract analysis of generalized motion parameters involves the estimation of translation rotation and the deformation parameters for a non rigid object most motion analysis methods require a preprocessing step of establishing the feature point correspondence between subsequent time frames such a preprocessing of data is computationally demanding and very often leads to erroneous results we explore the possibility of relaxing the above requirements for a homogeneously deformable object a computationally efficient method is proposed here that needs only subset correspondences between 3d feature points on the object at two different time instants instead of having explicit point correspondence the deformation parameters are obtained utilizing the changes in the euclidean distance for individual feature points belonging to different subsets under the proposed model the object may now be transformed into a rigid one utilizing the estimated deformation parameters the rotation parameters are estimated by considering the invariance properties of the principal moments simulation experiments are carried out to evaluate the performance of the proposed method the applicability of the method is also tested on a real data set

extracting straight lines this paper presents a new approach to the extraction of straight lines in intensity images pixels are grouped into line support regions of similar gradient orientation and then the structure of the associated intensity surface is used to determine the location and properties of the edge the resulting regions and extracted edge parameters form a low level representation of the intensity variations in the image that can be used for a variety of purposes the algorithm appears to be more effective than previous techniques for two key reasons 1 the gradient orientation rather than gradient magnitude is used as the initial organizing criterion prior to the extraction of straight lines and 2 the global context of the intensity variations associated with a straight line is determined prior to any local decisions about participating edge elements

affine structure from line correspondences with uncalibrated affine cameras this paper presents a linear algorithm for recovering 3d affine shape and motion from line correspondences with uncalibrated affine cameras the algorithm requires a minimum of seven line correspondences over three views the key idea is the introduction of a one dimensional projective camera this converts 3d affine reconstruction of line directions into 2d projective reconstruction of points in addition a line based factorization method is also proposed to handle redundant views experimental results both on simulated and real image sequences validate the robustness and the accuracy of the algorithm

multimodal genetic algorithms based algorithm for automatic point correspondence in this paper the problem of automatic determination of point correspondence between two images is formulated as a multimodal function optimization and the usefulness of genetic algorithms gas as a multimodal optimizer is explored initially a number of variations of gas capable of simultaneously discovering multiple extremes of an objective function are evaluated on a mathematical benchmark objective function with multiple unequal maxima the variation of the gas that performs best on the benchmark function in terms of the number of maxima discovered is selected for the determination of automatic point correspondence between two images the selected variation of the gas involves an iterative procedure for the formation of a genetic population of individuals or chromosomes each individual encodes the position of a point of interest on one of the available images as well as parameters of a local transformation that generates the position of the corresponding point on the other image the proposed algorithm aims to discover individuals that corresponds to local maxima of an objective function that measures the similarity between patches of the two images when the gas based multimodal optimization algorithm terminates pairs of corresponding points between the two images are obtained that can be used for the generation of a dense deformation field by means of the thin plate splines model the proposed algorithm is applied to 2d medical images dental and retinal images under known transformations similarity and elastic transformation and is also assessed on medical images with unknown transformations computer tomography transverse slices the proposed algorithm is compared against the iterative closest point icp algorithm and a well known non rigid registration algorithm based on free form deformations ffd using various quantitative criteria the obtained results indicate that in case of known similarity transformations the proposed multimodal gas based algorithm and the icp algorithm present equivalent performance whereas the ffd algorithm is clearly outperformed in the case of known sinousoidal deformations the proposed multimodal gas based and the ffd algorithm achieve equivalent performance and clearly outperform the icp algorithm finally in the case of unknown elastic deformations the proposed gas based algorithm appears to perform marginally better than the ffd algorithm whereas it clearly outperforms the icp algorithm

representative patterns for model based matching abstract a single intensity image of a three dimensional 3d object obtained under perspective projection can be reduced to a two dimensional 2d line drawing which contains patterns characteristic of the object and of its pose these patterns can provide clues to narrow down the search for possible objects and poses when comparing 2d view class models of 3d objects against images this paper describes a general way of representing 2d line patterns and of using the patterns to consistently label 2d models of 3d objects the representation is based on groups of three line segments that are likely to be found in most images containing man made objects but are unlikely to occur by accident experimental results using representative patterns to match 2d view class models of 3d objects against real images of the objects are included

canonical representation and multi view geometry of cylinders this paper first introduces a canonical representation for cylinders the canonical representation introduced here is closely related to the plucker line representation in this paper we show that this representation is an appropriate one for computer vision applications in particular it allows us to easily develop a series of mathematical methods for pose estimation 3d reconstruction and motion estimation one of the major novelties in this paper is the introduction of the main equations dominating the three view geometry of cylinders we show the relationship between cylinders three view geometry and that of lines spetsakis and aloimonos 1990 weng et al 1993 and points shashua 1995 defined by the trilinear tensor hartley 1997 and propose a linear method which uses the correspondences between six cylinders across three views in order to recover the motion and structure cylindrical pipes and containers are the main components in the majority of chemical water treatment and power plants oil platforms refineries and many other industrial installations we have developed a professional software called cylicon which allows efficient as built reconstruction of such installations from a series of pre calibrated images markers are used for this pre calibration process the theoretical and practical results in this paper represent the first steps towards marker less calibration and reconstruction of such industrial sites here the experimental results take advantage of the two view and three view geometry of cylinders introduced in this paper to provide initial camera calibration results

pose determination from line to plane correspondences existence condition and closed form solutions a class of pose determination problems in which the sensory data are lines and the corresponding reference data are planes is discussed the lines considered are different from edge lines in that they are not the intersection of boundary faces of the object the author describes a polynomial approach that does not require a priori knowledge about the object location closed form solutions for orthogonal parallel and coplanar feature configurations of critical importance in real applications are derived findings concerning the necessary and sufficient conditions under which the line to plane pose determination problem can be solved are described

lines in one orthographic and two perspective views we introduce a linear algorithm to recover the euclidean motion between an orthographic and two perspective cameras from straight line correspondences filling the gap in the analysis of motion estimation from line correspondences for various projection models the general relationship between lines in three views is described by the trifocal tensor euclidean structure from motion for three perspective views is a special case in which the relationship is defined by a collection of three matrices here we describe the case of two calibrated perspective views and an orthographic view similar to the other cases our linear algorithm requires 13 or more line correspondences to recover 27 coefficients of the trifocal tensor

pose estimation from line correspondences a complete analysis and a series of solutions in this paper we deal with the camera pose estimation problem from a set of 2d 3d line correspondences which is also known as pnl perspective n line problem we carry out our study by comparing pnl with the well studied pnp perspective n point problem and our contributions are three fold 1 we provide a complete 3d configuration analysis for p3l which includes the well known p3p problem as well as several existing analyses as special cases 2 by exploring the similarity between pnl and pnp we propose a new subset based pnl approach as well as a series of linear formulation based pnl approaches inspired by their pnp counterparts 3 the proposed linear formulation based methods can be easily extended to deal with the line and point features simultaneously

the geometry and matching of lines and curves over multiple views this paper describes the geometry of imaged curves in two and three views multi view relationships are developed for lines conics and non algebraic curves the new relationships focus on determining the plane of the curve in a projective reconstruction and in particular using the homography induced by this plane for transfer from one image to another it is shown that given the fundamental matrix between two views and images of the curve in each view then the plane of a conic may be determined up to a two fold ambiguity but local curvature of a curve uniquely determines the plane it is then shown that given the trifocal tensor between three views this plane defines a homography map which may be used to transfer a conic or the curvature from two views to a third simple expressions are developed for the plane and homography in each case a set of algorithms are then described for automatically matching individual line segments and curves between images the algorithms use both photometric information and the multiple view geometric relationships for image pairs the homography facilitates the computation of a neighbourhood cross correlation based matching score for putative line curve correspondences for image triplets cross correlation matching scores are used in conjunction with line curve transfer based on the trifocal geometry to disambiguate matches algorithms are developed for both short and wide baselines the algorithms are robust to deficiencies in the segment extraction and partial occlusion experimental results are given for image pairs and triplets for varying motions between views and for different scene types the methods are applicable to line curve matching in stereo and trinocular rigs and as a starting point for line curve matching through monocular image sequences

global bifurcation for quasivariational inequalities of reaction diffusion type abstract we consider a reaction diffusion system with implicit unilateral boundary conditions introduced by u mosco we show that global continua of stationary spatially nonhomogeneous solutions bifurcate in the domain of parameters where bifurcation in the case of classical boundary conditions is excluded the problem is formulated as a quasivariational inequality and the proof is based on the leray schauder degree

trinocular geometry revisited when do the visual rays associated with triplets of point correspondences converge that is intersect in a common point classical models of trinocular geometry based on the fundamental matrices and trifocal tensor associated with the corresponding cameras only provide partial answers to this fundamental question in large part because of underlying but seldom explicit general configuration assumptions this paper uses elementary tools from projective line geometry to provide necessary and sufficient geometric and analytical conditions for convergence in terms of transversals to triplets of visual rays without any such assumptions in turn this yields a novel and simple minimal parameterization of trinocular geometry for cameras with non collinear or collinear pinholes which can be used to construct a practical and efficient method for trinocular geometry parameter estimation we present numerical experiments using synthetic and real data

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

rank classification of linear line structures from images by trifocal tensor determinability the problem we address is given line correspondences over three views what is the condition of the line correspondences for the spatial relation of the three associated camera positions to be uniquely recoverable the observed set of lines in space is called critical if there are multiple projectively nonequivalent configurations of the camera positions that can picture the same image triplet of the lines we tackle the problem from the perspective of trifocal tensor a quantity that captures the relative pose of the cameras in relation to the captured views we show that the rank of a matrix that leads to the estimation of the tensor is reduced to 7 11 15 if the observed lines come from a line pencil a line bundle and a line field respectively which are line families belonging to linear line space and 12 19 23 if the lines come from a general linear ruled surface a general linear line congruence and a general linear line complex which are subclasses of linear line structures we show that the above line structures with the exception of linear line congruence and linear line complex ought to be critical line structures all of these structures are quite typical in reality and thus the findings are important to the validity and stability of practically all algorithms related to structure from motion and projective reconstruction using line correspondences

projective reconstruction of ellipses from multiple images this paper presents a new approach for reconstructing 3d ellipses including circles from a sequence of 2d images taken by uncalibrated cameras our strategy is to estimate an ellipse in 3d space by reconstructing n 5 3d points called representative points on it where the representative points are reconstructed by minimizing the distances from their projections to the measured 2d ellipses on different images i e 2d reprojection error this minimization problem is transformed into a sequence of minimization sub problems that can be readily solved by an algorithm which is guaranteed to converge to a local minimum of the 2d reprojection error our method can reconstruct multiple 3d ellipses simultaneously from multiple images and it readily handles images with missing and or partially occluded ellipses the proposed method is evaluated using both synthetic and real data

efficient estimation of the risk of a disease by quantile categories of a key predictor variable using generalized additive models suppose that one wishes to make inference to the risk of a disease by the population quartile categories of a key continuous predictor variable when one collects data on a prospective cohort the standard method is simply to categorize the key predictor variable by the empirical quartiles one may then include indicator variables for these empirical quartile categories as predictors along with other covariates in a generalized linear model glm with the observed health status of each subject as the response the standard glm method however is relatively inefficient because it treats all observations that fall in the same quartile category of the predictor variable identically regardless of whether they lie in the centre or near the boundaries of that category alternatively one may include the key predictor variable along with other covariates in a generalized additive model gam again with the observed health status of each subject as the response the alternative gam method non parametrically estimates the functional relationship between the key predictor variable and the response one may then compute statistics of interest such as proportions and odds ratios from the fitted gam equation using the empirical quartile categories simulations show that both the glm and gam methods are nearly unbiased but the latter method produces smaller variances and narrower bootstrap confidence intervals an example from nutritional epidemiology illustrates the use of these methods published in 2005 by john wiley sons ltd

feature transfer and matching in disparate stereo views through the use of plane homographies many vision tasks rely upon the identification of sets of corresponding features among different images this paper presents a method that given some corresponding features in two stereo images matches them with features extracted from a second stereo pair captured from a distant viewpoint the proposed method is based on the assumption that the viewed scene contains two planar surfaces and exploits geometric constraints that are imposed by the existence of these planes to first transfer and then match image features between the two stereo pairs the resulting scheme handles point and line features in a unified manner and is capable of successfully matching features extracted from stereo pairs that are acquired from considerably different viewpoints experimental results are presented which demonstrate that the performance of the proposed method compares favorably to that of epipolar and tensor based approaches

estimating motion and structure from correspondences of line segments between two perspective images presents an algorithm for determining 3d motion and structure from correspondences of line segments between two perspective images to the author s knowledge this paper is the first investigation of use of line segments in motion and structure from motion classical methods use their geometric abstraction namely straight lines but then three images are necessary for the motion and structure determination process in this paper the author shows that it is possible to recover motion from two views when using line segments the assumption used is that two matched line segments contain the projection of a common part of the corresponding line segment in space i e they overlap indeed this is what the author uses to match line segments between different views this assumption constrains the possible motion between two views to an open set in motion parameter space a heuristic consisting of maximizing the overlap leads to a unique solution both synthetic and real data have been used to test the proposed algorithm and excellent results have been obtained with real data containing a relatively large set of line segments

bifurcation points and eigenvalues of inequalities of reaction diffusion type on demontre certaines assertions concernant les points de bifurcation et les valeurs propres de systemes de reaction diffusion avec des conditions unilaterales

continuous stereo self calibration by camera parameter tracking this paper presents a consistent framework for continuous stereo self calibration based on a practical analysis of the sensitivity of stereo reconstruction to camera calibration uncertainties we identify important parameters for self calibration we evaluate different geometric constraints for estimation and tracking of these parameters bundle adjustment with reduced structure representation relating corresponding points in image sequences the epipolar constraint between stereo image pairs and trilinear constraints between image triplets continuous recursive calibration refinement is obtained with a robust adapted iterated extended kalman filter to achieve high accuracy physically relevant geometric optimization criteria are formulated in a gauss helmert type model the self calibration framework is tested on an active stereo system experiments with synthetic data as well as on natural indoor and outdoor imagery indicate that the different constraints are complementing each other and thus a method combining two of the above constraints is proposed while reduced order bundle adjustment gives by far the most accurate results and might suffice on its own in some environments the epipolar constraint yields instantaneous calibration that is not affected by independently moving objects in the scene hence it expedites and stabilizes the calibration process

determination of camera location from 2 d to 3 d line and point correspondences a method for the determination of camera location from two dimensional 2 d to three dimensional 3 d straight line or point correspondences is presented with this method the computations of the rotation matrix and the translation vector of the camera are separable first the rotation matrix is found by a linear algorithm using eight or more line correspondences or by a nonlinear algorithm using three or more line correspondences where the line correspondences are either given or derived from point correspondences then the translation vector is obtained by solving a set of linear equations based on three or more line correspondences or two or more point correspondences eight 2 d to 3 d line correspondences or six 2 d to 3 d point correspondences are needed for the linear approach three 2 d to 3 d line or point correspondences for the nonlinear approach good results can be obtained in the presence of noise if more than the minimum required number of correspondences are used

locally weighted regression an approach to regression analysis by local fitting abstract locally weighted regression or loess is a way of estimating a regression surface through a multivariate smoothing procedure fitting a function of the independent variables locally and in a moving fashion analogous to how a moving average is computed for a time series with local fitting we can estimate a much wider class of regression surfaces than with the usual classes of parametric functions such as polynomials the goal of this article is to show through applications how loess can be used for three purposes data exploration diagnostic checking of parametric models and providing a nonparametric regression surface along the way the following methodology is introduced a a multivariate smoothing procedure that is an extension of univariate locally weighted regression b statistical procedures that are analogous to those used in the least squares fitting of parametric functions c several graphical methods that are useful tools for understanding loess estimates and checking the a

a multi frame structure from motion algorithm under perspective projection we present a fast robust algorithm for multi frame structure from motion from point features which works for general motion and large perspective effects the algorithm is for point features but easily extends to a direct method based on image intensities experiments on synthetic and real sequences show that the algorithm gives results nearly as accurate as the maximum likelihood estimate in a couple of seconds on an iris 10000 the results are significantly better than those of an optimal two image estimate when the camera projection is close to scaled orthographic the accuracy is comparable to that of the tomasi kanade algorithm and the algorithms are comparably fast the algorithm incorporates a quantitative theoretical analysis of the bas relief ambiguity and exemplifies how such an analysis can be exploited to improve reconstruction also we demonstrate a structure from motion algorithm for partially calibrated cameras with unknown focal length varying from image to image unlike the projective approach this algorithm fully exploits the partial knowledge of the calibration it is given by a simple modification of our algorithm for calibrated sequences and is insensitive to errors in calibrating the camera center theoretically we show that unknown focal length variations strengthen the effects of the bas relief ambiguity this paper includes extensive experimental studies of two frame reconstruction and the tomasi kanade approach in comparison to our algorithm we find that two frame algorithms are surprisingly robust and accurate despite some problems with local minima we demonstrate experimentally that a nearly optimal two frame reconstruction can be computed quickly by a minimization in the motion parameters alone lastly we show that a well known problem with the tomasi kanade algorithm is often not a significant one

dual computation of projective shape and camera positions from multiple images given multiple image data from a set of points in 3d there are two fundamental questions that can be addressed what is the structure of the set of points in 3d what are the positions of the cameras relative to the points in this paper we show that for projective views and with structure and position defined projectively these problems are dual because they can be solved using constraint equations where space points and camera positions occur in a reciprocal way more specifically by using canonical projective reference frames for all points in space and images the imaging of point sets in space by multiple cameras can be captured by constraint relations involving three different kinds of parameters only coordinates of 1 space points 2 camera positions 3 image points the duality implies that the problem of computing camera positions fromp points in q views can be solved with the same algorithm as the problem of directly reconstructing q 4 points in p 4 views this unifies different approaches to projective reconstruction methods based on external calibration and direct methods exploiting constraints that exist between shape and image invariants

recovering multiple view geometry from mutual projections of multiple cameras in this paper we analyze the computation of epipolar geometry in some special cases where multiple cameras are projected each other in their images in such cases epipoles can be obtained directly from images as the projection of cameras as the result the epipolar geometry can be computed from less image correspondences with higher stability in this paper we analyze the number of corresponding points required for computing bifocal trifocal and quadrifocal tensors linearly in the case where cameras are projected mutually we next show a practical linear method for computing multifocal tensors by using the mutual projection of cameras the degenerate configurations of points and cameras is also studied and it is shown that some degenerate configurations in general cases are no longer degenerate under the mutual projection of cameras

contour matching using epipolar geometry matching features computed in images is an important process in multiview image analysis when the motion between two images is large the matching problem becomes very difficult in this paper we propose a contour matching algorithm based on geometric constraints with the assumption that the contours are obtained from images taken from a moving camera with static scenes we apply the epipolar constraint between two sets of contours and compute the corresponding points on the contours from the initial epipolar constraints obtained from corner point matching candidate contours are selected according to the epipolar geometry contour end point constraints and contour distance measures in order to reduce the possibility of false matches the number of match points on a contour is also used as a selection measure the initial epipolar constraint is refined from the matched sets of contours the algorithm can be applied to a pair or two pairs of images all of the processes are fully automatic and successfully implemented and tested with various real images

algebraic functions for recognition in the general case a trilinear relationship between three perspective views is shown to exist the trilinearity result is shown to be of much practical use in visual recognition by alignment yielding a direct reprojection method that cuts through the computations of camera transformation scene structure and epipolar geometry moreover the direct method is linear and sets a new lower theoretical bound on the minimal number of points that are required for a linear solution for the task of reprojection the proof of the central result may be of further interest as it demonstrates certain regularities across homographics of the plane and introduces new view invariants experiments on simulated and real image data were conducted including a comparative analysis with epipolar intersection and the linear combination methods with results indicating a greater degree of robustness in practice and a higher level of performance in reprojection tasks

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

degree instability and bifurcation of reaction diffusion systems with obstacles near certain hyperbolas abstract for a reaction diffusion system which is subject to turing s diffusion driven instability and which is equipped with unilateral obstacles of various types the nonexistence of bifurcation of stationary solutions near certain critical parameter values is proved the result implies assertions about a related mapping degree which in turn implies for small obstacles the existence of a new branch of bifurcation points spatial patterns induced by the obstacle

an effective search approach to camera parameter estimation using an arbitrary planar calibration object abstract in this paper we shall present a new method for camera parameter estimation using an arbitrary planar calibration object we begin with an approximate model for the perspective view and give a parameter free normalized line segment ratio relationship between the corresponding reference and sensed views this representation makes parameter decoupling possible and reduces the library dimension from six to one then the estimation problem can be viewed as a library search problem various mechanisms are provided to reduce the library search time including a library partition by clustering b sensed cluster identification by binary search and c sequential testing for view matching using sorted features in addition feature perturbation is also considered to achieve better robustness against feature noise both computer generated and real data are included in experiments illustrating how our method works

motion of points and lines in the uncalibrated case in the present paper we address the problem of computing structure and motion given a set point and or line correspondences in a monocular image sequence when the camera is not calibrated

interaction ruling animal collective behavior depends on topological rather than metric distance evidence from a field study numerical models indicate that collective animal behavior may emerge from simple local rules of interaction among the individuals however very little is known about the nature of such interaction so that models and theories mostly rely on aprioristic assumptions by reconstructing the three dimensional positions of individual birds in airborne flocks of a few thousand members we show that the interaction does not depend on the metric distance as most current models and theories assume but rather on the topological distance in fact we discovered that each bird interacts on average with a fixed number of neighbors six to seven rather than with all neighbors within a fixed metric distance we argue that a topological interaction is indispensable to maintain a flock s cohesion against the large density changes caused by external perturbations typically predation we support this hypothesis by numerical simulations showing that a topological interaction grants significantly higher cohesion of the aggregation compared with a standard metric one

using lowess to remove systematic trends over time in predictor variables prior to logistic regression with quantile categories in case control studies one may employ logistic regression to model the relationship between binary responses and continuous predictor variables that have been categorized by the empirical quartiles of the controls sometimes however systematic trends over time or drifts contaminate the laboratory measurements of predictor variables in this paper we consider the use of locally weighted robust regression lowess to estimate and remove these systematic trends when the trends for the cases and controls have a common shape one can then use the lowess adjusted data in the desired logistic regression model we illustrate these methods with a case control study that was designed to assess the risk of oesophageal cancer as a function of the quartile categories of sphinganine levels in the blood serum upon examination of the data it was discovered that the sphinganine laboratory measurements were contaminated by a systematic trend the magnitude of which depended only on the day of analysis this trend needed to be removed before performing further analyses of the data in addition we present simulations to examine the use of lowess methods to estimate and remove various shapes of trends from contaminated predictor data before constructing logistic regression models with quartile categories we found that using the trend contaminated data tends to give attenuated parameter estimates and hence lower significance and power levels than using the uncontaminated data conversely using appropriate lowess methods to adjust the data tends to give nearly unbiased parameter estimates near nominal significance levels and improved power

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

a theory of self calibration of a moving camera there is a close connection between the calibration of a single camera and the epipolar transformation obtained when the camera undergoes a displacement the epipolar transformation imposes two algebraic constraints on the camera calibration if two epipolar transformations arising from different camera displacements are available then the compatible camera calibrations are parameterized by an algebraic curve of genus four the curve can be represented either by a space curve of degree seven contained in the intersection of two cubic surfaces or by a curve of degree six in the dual of the image plane the curve in the dual plane has one singular point of order three and three singular points of order two if three epipolar transformations are available then two curves of degree six can be obtained in the dual plane such that one of the real intersections of the two yields the correct camera calibration the two curves have a common singular point of order three experimental results are given to demonstrate the feasibility of camera calibration based on the epipolar transformation the real intersections of the two dual curves are found by locating the zeros of a function defined on the interval 0 2 the intersection yielding the correct camera calibration is picked out by referring back to the three epipolar transformations

incremental model based estimation using geometric constraints we present a model based framework for incremental adaptive object shape estimation and tracking in monocular image sequences parametric structure and motion estimation methods usually assume a fixed class of shape representation splines deformable superquadrics etc that is initialized prior to tracking since the model shape coverage is fixed a priori the incremental recovery of structure is decoupled from tracking thereby limiting both processes in their scope and robustness in this work we describe a model based framework that supports the automatic detection and integration of low level geometric primitives lines incrementally such primitives are not explicitly captured in the initial model but are moving consistently with its image motion the consistency tests used to identify new structure are based on trinocular constraints between geometric primitives the method allows not only an increase in the model scope but also improves tracking accuracy by including the newly recovered features in its state estimation the formulation is a step toward automatic model building since it allows both weaker assumptions on the availability of a prior shape representation and on the number of features that would otherwise be necessary for entirely bottom up reconstruction we demonstrate the proposed approach on two separate image based tracking domains each involving complex 3d object structure and motion

estimating the heading direction using normal flow if an observer is moving rigidly with bounded rotation then normal flow measurements i e the spatiotemporal derivatives of the image intensity function give rise to a constraint on the oberver s translation this novel constraint gives rise to a robust qualitative solution to the problem of recovering the observer s heading direction by providing an area where the focus of expansion lies if the rotation of the observer is large then the solution area is large too while small rotation causes the solution area to be small thus giving rise to a robust solution in the paper the relationship between the solution area and the rotation and translation vectors is studied and experimental results using synthetic and real calibrated image sequences are presented this work demonstrates that the algorithm developed in horn and weldon 1987 for the case of pure translation if appropriately modified results in a robust algorithm that works in the case of general rigid motion with bounded rotation subsequently it has the potential to replace expensive accelerometers inertial systems and inaccurate odometers in practical navigational systems for the problem of kinetic stabilization which is a prerequisite for any other navigational ability

fourier domain representation of planar curves for recognition in multiple views recognition of planar shapes is an important problem in computer vision and pattern recognition the same planar object contour imaged from different cameras or from different viewpoints looks different and their recognition is non trivial traditional shape recognition deals with views of the shapes that differ only by simple rotations translations and scaling however shapes suffer more serious deformation between two general views and hence recognition approaches designed to handle translations rotations and or scaling would prove to be insufficient many algebraic relations between matching primitives in multiple views have been identified recently in this paper we explore how shape properties and multiview relations can be combined to recognize planar shapes across multiple views we propose novel recognition constraints that a planar shape boundary must satisfy in multiple views the constraints are on the rank of a fourier domain measurement matrix computed from the points on the shape boundary our method can additionally compute the correspondence between the curve points after a match is established we demonstrate the applications of these constraints experimentally on a number of synthetic and real images

stereo calibration from rigid motions we describe a method for calibrating a stereo pair of cameras using general or planar motions the method consists of upgrading a 3d projective representation to affine and to euclidean without any knowledge neither about the motion parameters nor about the 3d layout we investigate the algebraic properties relating projective representation to the plane at infinity and to the intrinsic camera parameters when the camera pair is considered as a moving rigid body we show that all the computations can be carried out using standard linear resolutions techniques an error analysis reveals the relative importance of the various steps of the calibration process projective to affine and affine to metric upgrades extensive experiments performed with calibrated and natural data confirm the error analysis as well as the sensitivity study performed with simulated data

structure from motion with line segments under relaxed endpoint constraints we present a novel structure from motion pipeline which estimates motion and wiry 3d structure from imaged line segments across multiple views although the position and orientation of line segments can be determined more accurately than point features the instability of their endpoints and the fact that lines are not constrained by epipolar geometry diverted most research focus away to point based methods in our approach we tackle the problem of instable endpoints by utilizing relaxed constraints on their positions both during matching and as well in the following bundle adjustment stage furthermore we gain efficiency in estimating trifocal image relations by decoupling rotation and translation to this end a novel linear solver for relative translation estimation given rotations from five line correspondences in three views is introduced extensive experiments on long image sequences show that our line based structure from motion pipeline advantageously complements point based methods giving more meaningful 3d representation for indoor scenarios

rigid motion and structure from several sets of parallel lines in a monocular image sequence abstract an image line is a very reliable feature in the feature based structure from motion sfm problem it has at least three advantages 1 it is not easily affected by occlusion 2 it can achieve subpixel accuracy 3 the correspondence problem is easier and less ambiguous although some generalized sfm algorithms using image line features have been recently developed they usually suffer from high error sensitivity and large matrix size besides in order to make their estimations more robust many line correspondences much more than the least requirement in theory are usually needed these shortages are not beneficial for practical use because many sets of parallel lines are frequently encountered in an artificial 3d environment and can be easily identified we try to utilize these identified parallel lines to simplify the generalized sfm problem and improve the performance of parameter estimation a fast and reliable algorithm is proposed in our paper both computer generated and real world images are tested and several satisfactory results have been obtained in addition its error sensitivity and data degeneracy will be discussed

analyzing bivariate continuous data grouped into categories defined by empirical quantiles of marginal distributions epidemiologists sometimes study the association between two measurements of exposure on the same subjects by grouping the original bivariate continuous data into categories that are defined by the empirical quantiles of the two marginal distributions although such grouped data are presented in a two way contingency table the cell counts in this table do not have a multinomial distribution we describe the joint distribution of counts in such a table by the term empirical bivariate quantile partitioned ebqp distribution blomqvist 1950 annals of mathematical statistics 21 539 600 gave an asymptotic ebqp theory for bivariate data partitioned by the sample medians we demonstrate that his asymptotic theory is not correct however except in special cases we present a general asymptotic theory for tables of arbitrary dimensions and apply this theory to construct confidence intervals for the kappa statistic we show by simulations that the confidence interval procedures we propose have near nominal coverage for sample sizes exceeding 60 for both 2 x 2 and 3 x 3 tables these simulations also illustrate that the asymptotic theory of blomqvist 1950 and the methods that fleiss cohen and everitt 1969 psychological bulletin 72 323 327 give for multinomial tables can yield subnominal coverage for kappa calculated from ebqp tables although in some cases the coverage for these procedures is near nominal levels

threading fundamental matrices we present a new function that operates on fundamental matrices across a sequence of views the operation we call threading connects two consecutive fundamental matrices using the trifocal tensor as the connecting thread the threading operation guarantees that consecutive camera matrices are consistent with a unique 3d model without ever recovering a 3d model applications include recovery of camera ego motion from a sequence of views image stabilization across a sequence and multi view image based rendering

motion detection using background constraints abstract we introduce a technique for detecting moving objects from a moving camera using the background constraint the camera is mounted on a platform that can both rotate and translate motion is detected by computing a mapping that corresponds pixels in successive images whenever possible assuming the background is planar provides knowledge that is used to recover projected local velocity u v background compensation can be used to eliminate the effects of rotation and translation on the mapping function to increase the robustness of this technique false motion caused by inaccuracies in sensor readings are eliminated this is achieved by using a morphological filter which consists of two successive operations erosion and dilation performed on the motion detection image experimental results with real images are presented which show the robustness of the proposed algorithm in detecting independently moving objects from a mobile platform

degree and global bifurcation for elliptic equations with multivalued unilateral conditions abstract a bifurcation problem for an elliptic multivalued boundary value problem with a real parameter is considered the existence of global bifurcation between two eigenvalues of a certain type of the laplacian is proved for a class of abstract inclusions with compact multivalued mappings in a hilbert space it is shown how the degree can be determined near the eigenvalues of a particular type of an associated linear single valued problem and the jump of the degree is proved as a consequence global bifurcation for such abstract inclusions is obtained the weak formulation of the boundary value problem mentioned is a particular case