camera calibration with one dimensional objects camera calibration has been studied extensively in computer vision and photogrammetry and the proposed techniques in the literature include those using 3d apparatus two or three planes orthogonal to each other or a plane undergoing a pure translation etc 2d objects planar patterns undergoing unknown motions and 0d features self calibration using unknown scene points yet the paper proposes a new calibration technique using 1d objects points aligned on a line thus filling the missing dimension in calibration in particular we show that camera calibration is not possible with free moving 1d objects but can be solved if one point is fixed a closed form solution is developed if six or more observations of such a 1d object are made for higher accuracy a nonlinear technique based on the maximum likelihood criterion is then used to refine the estimate singularities have also been studied besides the theoretical aspect the proposed technique is also important in practice especially when calibrating multiple cameras mounted apart from each other where the calibration objects are required to be visible simultaneously

self calibration of a 1d projective camera and its application to the self calibration of a 2d projective camera we introduce the concept of self calibration of a 1d projective camera from point correspondences and describe a method for uniquely determining the two internal parameters of a 1d camera based on the trifocal tensor of three 1d images the method requires the estimation of the trifocal tensor which can be achieved linearly with no approximation unlike the trifocal tensor of 2d images and solving for the roots of a cubic polynomial in one variable interestingly enough we prove that a 2d camera undergoing planar motion reduces to a 1d camera from this observation we deduce a new method for self calibrating a 2d camera using planar motions both the self calibration method for a 1d camera and its applications for 2d camera calibration are demonstrated on real image sequences

multiple motion scene reconstruction with uncalibrated cameras in this paper we describe a reconstruction method for multiple motion scenes which are scenes containing multiple moving objects from uncalibrated views assuming that the objects are moving with constant velocities the method recovers the scene structure the trajectories of the moving objects the camera motion and the camera intrinsic parameters except skews simultaneously we focus on the case where the cameras have unknown and varying focal lengths while the other intrinsic parameters are known the number of the moving objects is automatically detected without prior motion segmentation the method is based on a unified geometrical representation of the static scene and the moving objects it first performs a projective reconstruction using a bilinear factorization algorithm and then converts the projective solution to a euclidean one by enforcing metric constraints experimental results on synthetic and real images are presented

untwisting a projective reconstruction a method for upgrading a projective reconstruction to metric is presented the method compares favourably to state of the art algorithms and has been found extremely reliable for both large and small reconstructions in a large number of experiments on real data the notion of a twisted pair is generalized to the uncalibrated case the reconstruction is first transformed by considering cheirality so that it does not contain any twisted pairs it is argued that this is essential since the method then proceeds by local perturbation as is preferrable we utilize a cost function that reflects the prior likelihood of calibration matrices well it is shown that with any such cost function there is little hope of untwisting a twisted pair by local perturbation the results show that in practice it is most often sufficient to start with a reconstruction that is free from twisted pairs provided that the minimized objective function is a geometrically meaningful quantity when subjected to the common degeneracy of little or no rotation between the views the proposed method still yields a very reasonable member of the family of possible solutions furthermore the method is very fast and therefore suitable for the purpose of viewing reconstructions

cohomological dimension cofiniteness and abelian categories of cofinite modules abstract let r be a commutative noetherian ring i j be ideals of r and m be a finitely generated r module in this paper it is shown that q j m q i m cd j m i m furthermore it is shown that for any ideal i of r and any finitely generated r module m with q i m 1 the local cohomology modules h i i m are i cofinite for all integers i 0 as a consequence of this result it is shown that if q i r 1 then for any finitely generated r module m the local cohomology modules h i i m are i cofinite for all integers i 0 finally it is shown that the category of all i cofinite r modules c r i c o f is an abelian subcategory of the category of all r modules whenever r m is a complete noetherian local ring and i is an ideal of r with q i r 1 these assertions answer affirmatively two questions raised by r hartshorne in 16 in the some special cases

self calibration from one circular motion sequence and two images this paper describes a new method for self calibration of camera with constant internal parameters under circular motion using one sequence and two images captured with different camera orientations unlike the previous method in which three circular motion sequences are needed with known motion the new method computes the rotation angles and the projective reconstructions of the sequence and the images with circular constraint enforced which is called a circular projective reconstruction using a factorization based method it is then shown that the images of the circular points of each circular projective reconstruction can be readily obtained subsequently the image of the absolute conic and the calibration matrix of the camera can be determined experiments on both synthetic and real image sequence are given showing the accuracy and robustness of the new algorithm

regularized bundle adjustment to model heads from image sequences without calibration data we address the structure from motion problem in the context of head modeling from video sequences for which calibration data is not available this task is made challenging by the fact that correspondences are difficult to establish due to lack of texture and that a quasi euclidean representation is required for realism we have developed an approach based on regularized bundle adjustment it takes advantage of our rough knowledge of the head s shape in the form of a generic face model it allows us to recover relative head motion and epipolar geometry accurately and consistently enough to exploit a previously developed stereo based approach to head modeling in this way complete and realistic head models can be acquired with a cheap and entirely passive sensor such as an ordinary video camera with minimal manual intervention we chose to demonstrate and evaluate our technique mainly in the context of head modeling we do so because it is the application for which all the tools required to perform the complete reconstruction are available to us we will however argue that the approach is generic and could be applied to other tasks such as body modeling for which generic facetized models exist

cofiniteness with respect to ideals of dimension one we prove that the category of modules cofinite with respect to an ideal of dimension one in a noetherian ring is a full abelian subcategory of the category of modules the proof is based on a criterion for cofiniteness with respect to an ideal of dimension one namely for such ideals it suffices that the two first ext modules in the definition for cofiniteness are finitely generated this criterion is also used to prove very simply that all local cohomology modules of a finitely generated module with respect to an ideal of dimension one in an arbitrary noetherian ring are cofinite with respect to the ideal

understanding positioning from multiple images it is possible to recover the three dimensional structure of a scene using only correspondences between images taken with uncalibrated cameras faugeras 1992 the reconstruction obtained this way is only defined up to a projective transformation of the 3d space however this kind of structure allows some spatial reasoning such as finding a path in order to perform more specific reasoning or to perform work with a robot moving in euclidean space euclidean or affine constraints have to be added to the camera observations such constraints arise from the knowledge of the scene location of points geometrical constraints on lines etc first this paper presents a reconstruction method for the scene then it discusses how the framework of projective geometry allows symbolic or numerical information about positions to be derived and how knowledge about the scene can be used for computing symbolic or numerical relationships implementation issues and experimental results are discussed

cofiniteness of local cohomology modules for ideals of small dimension abstract let r be a commutative noetherian ring and let m be a non zero finitely generated r module let i be an ideal of r and t a non negative integer such that dim supp h i i m 1 for all i t it is shown that the r modules h i 0 m h i 1 m h i t 1 m are i cofinite and the r module hom r r i h i t m is finitely generated this immediately implies that if i has dimension one i e dim r i 1 then h i i m is i cofinite for all i 0 this is a generalization of the main results of delfino and marley d delfino t marley cofinite modules and local cohomology j pure appl algebra 121 1997 45 52 and yoshida k i yoshida cofiniteness of local cohomology modules for ideals of dimension one nagoya math j 147 1997 179 191 for an arbitrary noetherian ring r also we prove that if r is local and dim supp h i i m 2 for all i t then the r modules ext r j r i h i i m and hom r r i h i t m are weakly laskerian for all i t and all j 0 as a consequence it follows that the set of associated primes of h i i m is finite for all i 0 whenever dim r i 2

camera self calibration from bivariate polynomials derived from kruppa s equations this paper presents a new set of equations for the self calibration of a moving camera with constant intrinsic parameters unlike most existing methods that require solving equations in three or more unknowns the proposed equations are only bivariate in particular we show that the three scale factors appearing in the kruppa s equations that are due to a triplet of images are not independent but rather closely related this relationship is used to derive sextic bivariate polynomial equations and allow the recovery of the unknown scale factors using a homotopy continuation method once the scale factors are calculated an estimate of kruppa s coefficients can be linearly retrieved and then refined through a nonlinear least squares optimization procedure the results of our experiments conducted on simulated data as well as the three dimensional structure reconstruction using real images are also presented in the paper

stratified self calibration with the modulus constraint in computer vision and especially for 3d reconstruction one of the key issues is the retrieval of the calibration parameters of the camera these are needed to obtain metric information about the scene from the camera often these parameters are obtained through cumbersome calibration procedures there is a way to avoid explicit calibration of the camera self calibration is based on finding the set of calibration parameters which satisfy some constraints e g constant calibration parameters several techniques have been proposed but it often proved difficult to reach a metric calibration at once therefore in the paper a stratified approach is proposed which goes from projective through affine to metric the key concept to achieve this is the modulus constraint it allows retrieval of the affine calibration for constant intrinsic parameters it is also suited for use in conjunction with scene knowledge in addition if the affine calibration is known it can also be used to cope with a changing focal length

gauges and gauge transformations for uncertainty description of geometric structure with indeterminacy this paper presents a consistent theory for describing indeterminacy and uncertainty of three dimensional 3 d reconstruction from a sequence of images first we give a group theoretical analysis of gauges and gauge transformations we then discuss how to evaluate the reliability of the solution that has indeterminacy and extend the cramer rao lower bound to incorporate internal indeterminacy we also introduce the free gauge approach and define the normal form of a covariance matrix that is independent of particular gauges finally we show simulated and real image examples to illustrate the effect of gauge freedom on uncertainty description

self calibration with varying focal length from two images obtained by a stereo head the self calibration approach based on the absolute conic or its dual the absolute dual quadric has the merit of allowing the intrinsic camera parameters to vary in image sequence in this paper we show that certain linear equations resulting from the infinity homography can be added to a system of originally undetermined linear equations to find the absolute dual quadric for a stereo head the special stereo configurations considered here allow one camera to rotate around either one or two of the coordinate axes defined by another camera experiments with synthetic images show that satisfactory results can be obtained with only the proposed linear methods for real images obtained with non ideal stereo configurations and possibly with measurement noises results obtained from the proposed linear methods may serve as reasonable initial guesses for some non linear optimization procedure

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

generalised correlation for multi feature correspondence computing correspondences between pairs of images is fundamental to all structures from motion algorithms correlation is a popular method to estimate similarity between patches of images in the standard formulation the correlation function uses only one feature such as the gray level values of a small neighbourhood research has shown that different features such as colour edge strength corners texture measures work better under di0erent conditions we propose a framework of generalized correlation that can compute a real valued similarity measure using a feature vector whose components can be dissimilar the framework can combine the e0ects of di0erent image features such as multi spectral features edges corners texture measures etc into a single similarity measure in a 3exible manner additionally it can combine results of di0erent window sizes used for correlation with proper weighting for each relative importances of the features can be estimated from the image itself for accurate correspondence in this paper we present the framework of generalised correlation provide a few examples demonstrating its power as well as discuss the implementation issues 2002 published by elsevier science ltd on behalf of pattern recognition society

color image segmentation using fuzzy integral and mountain clustering abstract this paper presents a flexible model for the segmentation of color image data using the fuzzy integral and the mountain clustering fuzzy integral is used as a distance measure in the mountain clustering applied to find representative regions in the image the proposed approach does not require an initial estimate of cluster centers for the segmentation process segmentation results using the proposed method will depend on the griding of the image space which specifies the degree of detail in the segmentation process

globally convergent autocalibration using interval analysis we address the problem of autocalibration of a moving camera with unknown constant intrinsic parameters existing autocalibration techniques use numerical optimization algorithms whose convergence to the correct result cannot be guaranteed in general to address this problem we have developed a method where an interval branch and bound method is employed for numerical minimization thanks to the properties of interval analysis this method converges to the global solution with mathematical certainty and arbitrary accuracy and the only input information it requires from the user are a set of point correspondences and a search interval the cost function is based on the huang faugeras constraint of the essential matrix a recently proposed interval extension based on bernstein polynomial forms has been investigated to speed up the search for the solution finally experimental results are presented

self calibration of an affine camera from multiple views a key limitation of all existing algorithms for shape and motion from image sequences under orthographic weak perspective and para perspective projection is that they require the calibration parameters of the camera we present in this paper a new approach that allows the shape and motion to be computed from image sequences without having to know the calibration parameters this approach is derived with the affine camera model introduced by mundy and zisserman 1992 which is a more general class of projections including orthographic weak perspective and para perspective projection models the concept of self calibration introduced by maybank and faugeras 1992 for the perspective camera and by hartley 1994 for the rotating camera is then applied for the affine camera this paper introduces the 3 intrinsic parameters that the affine camera can have at most the intrinsic parameters of the affine camera are closely related to the usual intrinsic parameters of the pin hole perspective camera but are different in the general case based on the invariance of the intrinsic parameters methods of self calibration of the affine camera are proposed it is shown that with at least four views an affine camera may be self calibrated up to a scaling factor leading to euclidean similarity shape reconstruction up to a global scaling factor another consequence of the introduction of intrinsic and extrinsic parameters of the affine camera is that all existing algorithms using calibrated affine cameras can be assembled into the same framework and some of them can be easily extented to a batch solution experimental results are presented and compared with other methods using calibrated affine cameras

a fuzzy gould type integral in this paper we introduce and study a set valued gould type integral of a real function with respect to a fuzzy multimeasure taking values in the family of all nonempty closed subsets of a banach space x some classical properties of the integral are obtained only using the hypothesis of monotonicity for the set valued fuzzy measure

quasi perspective projection model theory and application to structure and motion factorization from uncalibrated image sequences this paper addresses the problem of factorization based 3d reconstruction from uncalibrated image sequences previous studies on structure and motion factorization are either based on simplified affine assumption or general perspective projection the affine approximation is widely adopted due to its simplicity whereas the extension to perspective model suffers from recovering projective depths to fill the gap between simplicity of affine and accuracy of perspective model we propose a quasi perspective projection model for structure and motion recovery of rigid and nonrigid objects based on factorization framework the novelty and contribution of this paper are as follows firstly under the assumption that the camera is far away from the object with small lateral rotations we prove that the imaging process can be modeled by quasi perspective projection which is more accurate than affine model from both geometrical error analysis and experimental studies secondly we apply the model to establish a framework of rigid and nonrigid factorization under quasi perspective assumption finally we propose an extended cholesky decomposition to recover the rotation part of the euclidean upgrading matrix we also prove that the last column of the upgrading matrix corresponds to a global scale and translation of the camera thus may be set freely the proposed method is validated and evaluated extensively on synthetic and real image sequences and improved results over existing schemes are observed

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

the fuzzy set valued measures generated by fuzzy random variables the fuzzy set valued measure defined by the integral of a fuzzy random variable is studied some properties of such fuzzy set valued measures are derived the decomposition theorem and extension theorem are also investigated

a note on convergence properties of interval valued capacity functionals and choquet integrals based on the classical theory of random sets feng and nguyen 2007 5 studied the convergence of capacity functionals of random sets in terms of choquet integrals in this paper we consider an interval valued capacity functional which is motivated by the goal to generalize a capacity functional and the choquet integral with respect to an interval valued capacity in particular we discuss some convergence theorems for interval valued capacity functionals and interval valued probability measures in the hausdorff metric and choquet weak sense

kruppa s equations derived from the fundamental matrix the purpose of this paper is to give a specific form for kruppa s equations in terms of the fundamental matrix kruppa s equations can be written explicitly in terms of the singular value decomposition svd of the fundamental matrix

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

affine reconstruction from perspective image pairs with a relative object camera translation in between a method is described to recover the three dimensional affine structure of a scene consisting of at least five points identified in two perspective views with a relative object camera translation in between when compared to the results for arbitrary stereo views a more detailed reconstruction is possible using less information the method presented only assumes that the two images are obtained by identical cameras but no knowledge about the intrinsic parameters of the camera s or about the performed translation is assumed by the same method affine 3d reconstruction from a single view can be achieved for parallel structures in that case four points suffice for affine reconstruction

on a category of cofinite modules which is abelian let a be a noetherian local ring and i an ideal of a of dimension one our purpose of this paper is to prove that the category mathcal m a i cof of cofinite modules is abelian consequently this assertion answers affirmatively the questions given by hartshorne invent math 9 147 1970 cf sect 2 four questions and one theorem for an ideal of dimension one over a local ring

camera calibration using symmetric objects this paper proposes a novel method for camera calibration using images of a mirror symmetric object assuming unit aspect ratio and zero skew we show that interimage homographies can be expressed as a function of only the principal point by minimizing symmetric transfer errors we thus obtain an accurate solution for the camera parameters we also extend our approach to a calibration technique using images of a 1 d object with a fixed pivoting point unlike existing methods that rely on orthogonality or pole polar relationship our approach utilizes new interimage constraints and does not require knowledge of the 3 d coordinates of feature points to demonstrate the effectiveness of the approach we present results for both synthetic and real images

characterizations of generalized differentiable fuzzy functions this article deals with generalized differentiable fuzzy functions specifically we give some characterizations of generalized hukuhara differentiable fuzzy functions through the differentiability of their endpoint functions then we introduce a differentiability concept that is more general than the generalized hukuhara differentiability and extend the above characterization to this new type of differentiability as well as to g differentiable fuzzy functions these characterizations are useful tools for the calculus of derivatives of fuzzy functions

camera calibration using one dimensional information and its applications in both controlled and uncontrolled environments camera model and its calibration are required in many applications for coordinate conversions between the two dimensional image and the real three dimensional world self calibration method is usually chosen for camera calibration in uncontrolled environments because the scene geometry could be unknown however when no reliable feature correspondences can be established or when the camera is static in relation to the majority of the scene self calibration method fails to work on the other hand object based calibration methods are more reliable than self calibration methods due to the existence of the object with known geometry however most object based calibration methods are unable to work in uncontrolled environments because they require the geometric knowledge on calibration objects though in the past few years the simplest geometry required for a calibration object has been reduced to a 1d object with at least three points it is still not easy to find such an object in an uncontrolled environment not to mention the additional metric motion requirement in the existing methods meanwhile it is very easy to find a 1d object with two end points in most scenes thus it would be very worthwhile to investigate an object based method based on such a simple object so that it would still be possible to calibrate a camera when both self calibration and existing object based calibration fail to work we propose a new camera calibration method which requires only an object with two end points the simplest geometry that can be extracted from many real life objects through observations of such a 1d object at different positions orientations on a plane which is fixed in relation to the camera both intrinsic focal length and extrinsic rotation angles and translations camera parameters can be calibrated using the proposed method the proposed method has been tested on simulated data and real data from both controlled and uncontrolled environments including situations where no explicit 1d calibration objects are available e g from a human walking sequence very accurate camera calibration results have been achieved using the proposed method

an improved algorithm for two image camera self calibration and euclidean structure recovery using absolute quadric we present an improved algorithm for two image camera self calibration and euclidean structure recovery where the effective focal lengths of both cameras are assumed to be the only unknown intrinsic parameters by using the absolute quadric it is shown that the effective focal lengths can be computed linearly from two perspective images without imposing scene or motion constraints moreover a quadratic equation derived from the absolute quadric is proposed for solving the parameters of the plane at infinity from two images which upgrades a projective reconstruction to a euclidean reconstruction

calibrating a video camera pair with a rigid bar abstract in this paper a new procedure to determine all the geometrical parameters of a stereo system is presented it is based on surveying a rigid bar carrying two markers on its extremities moved inside the working volume and it does not require grids or complex calibration structures the external parameters are estimated through the epipolar geometry up to a scale factor which is determined from the true length of the bar the focal lengths are determined using the properties of the absolute conic in the projective space the principal points are computed through a non linear minimisation carried out through an evolutionary optimisation the accuracy of the method is assessed on real data and it compares favourably with that obtained through classical approaches based on control points of known 3d coordinates

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

a robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry abstract this paper proposes a robust approach to image matching by exploiting the only available geometric constraint namely the epipolar constraint the images are uncalibrated namely the motion between them and the camera parameters are not known thus the images can be taken by different cameras or a single camera at different time instants if we make an exhaustive search for the epipolar geometry the complexity is prohibitively high the idea underlying our approach is to use classical techniques correlation and relaxation methods in our particular implementation to find an initial set of matches and then use a robust technique the least median of squares lmeds to discard false matches in this set the epipolar geometry can then be accurately estimated using a meaningful image criterion more matches are eventually found as in stereo matching by using the recovered epipolar geometry a large number of experiments have been carried out and very good results have been obtained regarding the relaxation technique we define a new measure of matching support which allows a higher tolerance to deformation with respect to rigid transformations in the image plane and a smaller contribution for distant matches than for nearby ones a new strategy for updating matches is developed which only selects those matches having both high matching support and low matching ambiguity the update strategy is different from the classical winner take all which is easily stuck at a local minimum and also from loser take nothing which is usually very slow the proposed algorithm has been widely tested and works remarkably well in a scene with many repetitive patterns

the absolute line quadric and camera autocalibration we introduce a geometrical object providing the same information as the absolute conic the absolute line quadric alq after the introduction of the necessary exterior algebra and grassmannian geometry tools we analyze the grassmannian of lines of p from both the projective and euclidean points of view the exterior algebra setting allows then to introduce the alq as a quadric arising very naturally from the dual absolute quadric we fully characterize the alq and provide clean relationships to solve the inverse problem i e recovering the euclidean structure of space from the alq finally we show how the alq turns out to be particularly suitable to address the euclidean autocalibration of a set of cameras with square pixels and otherwise varying intrinsic parameters providing new linear and non linear algorithms for this problem we also provide experimental results showing the good performance of the techniques

a gould type integral of fuzzy functions abstract in this paper a new type of integral of a fuzzy valued function relative to a non negative set function is proposed as a new useful tool in modeling uncertainties various properties of this new type of integral are established concerning the behavior with respect to the fuzzy function or to the set function several examples linking our integral with birkhoff and lebesgue integrals are provided also problems related to atomicity are addressed

differentials of fuzzy functions abstract in this paper the radstrom embedding theorem proc amer math soc 3 1952 165 is generalized and is used to define the concept of the differential of a fuzzy function

a geometric approach for the analysis and computation of the intrinsic camera parameters the authors of this paper adopted the projected characteristics of the absolute conic in terms of the pascal s theorem to propose an entirely new camera calibration method based on purely geometric thoughts the use of this theorem in the geometric algebra framework allows us to compute a projective invariant using the conics of only two images which expressed using brackets helps us to set enough equations to solve the calibration problem the method requires restricted controlled camera movements our method is less sensitive to noise as the kruppa s equation based methods experiments with simulated and real images con rm that the performance of the algorithm is reliable 2001pattern recognition society published by elsevier science ltd all rights reserved

pseudo riemann stieltjes integral an extension of the classical riemann stieltjes integral to the field of pseudo analysis is being investigated through this paper core of the construction presented here consists of generalized pseudo operations given by monotone generating function

radial multi focal tensors the 1d radial camera maps all points on a plane containing the principal axis onto the radial line which is the intersection of that plane and the image plane it is a sufficiently general model to express both central and non central cameras since the only assumption it makes is of known center of distortion in this paper we study the multi focal tensors arising out of 1d radial cameras there exist no two view constraints like the fundamental matrix for 1d radial cameras however the 3 view and 4 view cases are interesting for the 4 view case we have the radial quadrifocal tensor which has 15 d o f and 2 internal constraints for the 3 view case we have the radial trifocal tensor which has 7 d o f and no internal constraints under the assumption of a purely rotating central camera this can be used to do a non parametric estimation of the radial distortion of a 1d camera even in the case of a non rotating camera it can be used to do parametric estimation assuming a planar scene finally we examine the mixed trifocal tensor which models the case of two 1d radial cameras and one standard pin hole camera of the above radial multifocal tensors only the radial trifocal tensor is useful practically since it doesn t require any knowledge of the scene and is extremely robust we demonstrate results based on real images for this for the quadrifocal tensor too we present a way to do a metric reconstruction of the scene and to undistort the image given a sufficiently dense set of point correspondences we also show results on synthetic images however it must be noted that currently the quadrifocal and mixed trifocal tensors are useful only from a theoretical stand point

initialization method for self calibration using 2 views recently 3d structure recovery through self calibration of camera has been actively researched traditional calibration algorithm requires known 3d coordinates of the control points while self calibration only requires the corresponding points of images thus it has more flexibility in real application in general self calibration algorithm results in the nonlinear optimization problem using constraints from the intrinsic parameters of the camera thus it requires initial value for the nonlinear minimization traditional approaches get the initial values assuming they have the same intrinsic parameters while they are dealing with the situation where the intrinsic parameters of the camera may change in this paper we propose new initialization method using the minimum 2 images proposed method is based on the assumption that the least violation of the camera s intrinsic parameter gives more stable initial value synthetic and real experiment shows this result

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

euclidean reconstruction and reprojection up to subgroups the necessary and sufficient conditions for being able to estimate scene structure motion and camera calibration from a sequence of images are very rarely satisfied in practice what exactly can be estimated in sequences of practical importance when such conditions are not satisfied in this paper we give a complete answer to this question for every camera motion that fails to meet the conditions we give explicit formulas for the ambiguities in the reconstructed scene motion and calibration such a characterization is crucial both for designing robust estimation algorithms that do not try to recover parameters that cannot be recovered and for generating novel views of the scene by controlling the vantage point to this end we characterize explicitly all the vantage points that give rise to a valid euclidean reprojection regardless of the ambiguity in the reconstruction we also characterize vantage points that generate views that are altogether invariant to the ambiguity all the results are presented using simple notation that involves no tensors nor complex projective geometry and should be accessible with basic background in linear algebra

self calibration of a moving camera from pointcorrespondences and fundamental matrices we address the problem of estimating three dimensional motion and structure from motion with an uncalibrated moving camera we show that point correspondences between three images and the fundamental matrices computed from these point correspondences are sufficient to recover the internal orientation of the camera its calibration the motion parameters and to compute coherent perspective projection matrices which enable us to reconstruct 3 d structure up to a similarity in contrast with other methods no calibration object with a known 3 d shape is needed and no limitations are put upon the unknown motions to be performed or the parameters to be recovered as long as they define a projective camera the theory of the method which is based on the constraint that the observed points are part of a static scene thus allowing us to link the intrinsic parameters and the fundamental matrix via the absolute conic is first detailed several algorithms are then presented and their performances compared by means of extensive simulations and illustrated by several experiments with real images

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

camera calibration from surfaces of revolution this paper addresses the problem of calibrating a pinhole camera from images of a surface of revolution camera calibration is the process of determining the intrinsic or internal parameters i e aspect ratio focal length and principal point of a camera and it is important for both motion estimation and metric reconstruction of 3d models in this paper a novel and simple calibration technique is introduced which is based on exploiting the symmetry of images of surfaces of revolution traditional techniques for camera calibration involve taking images of some precisely machined calibration pattern such as a calibration grid the use of surfaces of revolution which are commonly found in daily life e g bowls and vases makes the process easier as a result of the reduced cost and increased accessibility of the calibration objects in this paper it is shown that two images of a surface of revolution will provide enough information for determining the aspect ratio focal length and principal point of a camera with fixed intrinsic parameters the algorithms presented in this paper have been implemented and tested with both synthetic and real data experimental results show that the camera calibration method presented is both practical and accurate

fuzzy integral in multicriteria decision making abstract this paper presents a synthesis on the use of fuzzy integral as an aggregation operator in multicriteria decision making definitions essential properties are given and compared to those of usual aggregation operators a quick survey on applications is given

using geometric constraints through parallelepipeds for calibration and 3d modeling this paper concerns the incorporation of geometric information in camera calibration and 3d modeling using geometric constraints enables more stable results and allows us to perform tasks with fewer images our approach is motivated and developed within a framework of semi automatic 3d modeling where the user defines geometric primitives and constraints between them in this paper first a duality that exists between the shape parameters of a parallelepiped and the intrinsic parameters of a camera is described then a factorization based algorithm exploiting this relation is developed using images of parallelepipeds it allows us to simultaneously calibrate cameras recover shapes of parallelepipeds and estimate the relative pose of all entities besides geometric constraints expressed via parallelepipeds our approach simultaneously takes into account the usual self calibration constraints on cameras the proposed algorithm is completed by a study of the singular cases of the calibration method a complete method for the reconstruction of scene primitives that are not modeled by parallelepipeds is also briefly described the proposed methods are validated by various experiments with real and simulated data for single view as well as multiview cases

local cohomology and serre subcategories the membership of the local cohomology modules h a n m of a module m in certain serre subcategories of the category of modules is studied from below i n generalizations of depth and regular

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

minimal projective reconstruction including missing data the minimal data necessary for projective reconstruction from image points is well known when each object point is visible in all images we formulate and propose solutions to a family of reconstruction problems for multiple images from minimal data where there are missing points in some of the images the ability to handle the minimal cases with missing data is of great theoretical and practical importance it is unavoidable to use them to bootstrap robust estimation such as ransac and lms algorithms and optimal estimation such as bundle adjustment first we develop a framework to parameterize the multiple view geometry needed to handle the missing data cases then we present a solution to the minimal case of eight points in three images where one different point is missing in each of the three images we prove that there are in general as many as 11 solutions for this minimal case furthermore all minimal cases with missing data for three and four images are catalogued finally we demonstrate the method on both simulated and real images and show that the algorithms presented in the paper can be used for practical problems

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

camera calibration with moving one dimensional objects in this paper we show that the rotating 1d calibrating object used in the literature is in essence equivalent to a familiar 2d planar calibration object in addition we also show that when the 1d object undergoes a planar motion rather than rotating around a fixed point such equivalence still holds but the traditional way fails to handle it experiments are carried out to verify the theoretical correctness and numerical robustness of our results

robust multi view feature matching from multiple unordered views this paper explores the problem of multi view feature matching from an unordered set of widely separated views a set of local invariant features is extracted independently from each view first we propose a new view ordering algorithm that organizes all the unordered views into clusters of related i e the same scene views by efficiently computing the view similarity values of all view pairs by reasonably selecting part of extracted features to match second a robust two view matching algorithm is developed to find initial matches then detect the outliers and finally incrementally find more reliable feature matches under the epipolar constraint between two views from dense to sparse based on an assumption that changes of both motion and feature characteristics of one match are consistent with those of neighbors third we establish the reliable multi view matches across related views by reconstructing missing matches in a neighboring triple of views and efficiently determining the states of matches between view pairs finally the reliable multi view matches thus obtained are used to automatically track all the views by using a self calibration method the proposed methods were tested on several sets of real images experimental results show that it is efficient and can track a large set of multi view feature matches across multiple widely separated views

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

visual modeling with a hand held camera in this paper a complete system to build visual models from camera images is presented the system can deal with uncalibrated image sequences acquired with a hand held camera based on tracked or matched features the relations between multiple views are computed from this both the structure of the scene and the motion of the camera are retrieved the ambiguity on the reconstruction is restricted from projective to metric through self calibration a flexible multi view stereo matching scheme is used to obtain a dense estimation of the surface geometry from the computed data different types of visual models are constructed besides the traditional geometry and image based approaches a combined approach with view dependent geometry and texture is presented as an application fusion of real and virtual scenes is also shown

on set valued fuzzy measures so far there have been many discussions on sugeno s fuzzy measures and fuzzy integrals but most of them are concentrated on single valued functions motivated by aumann s set valued integral j math anal appl 12 1965 1 we have introduced the fuzzy integral of set valued functions fuzzy sets syst 56 1993 237 fuzzy sets syst 76 1995 365 fuzzy sets syst 78 1996 341 ph d dissertation harbin institute of technology 1998 it is a well behaved extension of fuzzy integrals of single valued functions it is well known that arstein s set valued measure trans am math soc 165 1972 103 is an important branch in set valued analysis set valued analysis birkhauser berlin 1990 or theory of correspondences theory of correspondences wiley new york 1984 compared to it the present paper will try to establish the basic idea of set valued fuzzy measures which are monotone set valued set functions it is also a natural generalization of single valued fuzzy measures as well as an extension of set valued measures in the case of one dimension these works include the concept of set valued fuzzy measures set valued fuzzy measures defined by set valued fuzzy integrals and set valued pseudo additive measures it can be viewed as a continuation of previous work fuzzy sets syst 56 1993 237 fuzzy sets syst 76 1995 365 fuzzy sets syst 78 1996 341

efficient focus sampling through depth of field calibration due to the limited depth of field dof of conventional digital cameras only the objects within a certain distance range from the camera are in focus objects outside the dof are observed with different amounts of defocus depending on their position focus sampling consists of capturing different images of the same scene by changing the focus configuration of the camera in order to alternately bring objects at different depths into focus focus sampling is an important part of different focus related applications such as autofocus focus stacking and depth estimation this work proposes a calibration procedure for modeling the depth of field of conventional cameras in order to perform an efficient focus sampling the method is simple in terms of repeatability and can be easily implemented in different imaging devices experimental tests are presented in order to illustrate the effectiveness of the proposed approach in autofocus results demonstrate that a significant reduction in the number of frames required to capture during autofocusing can be achieved by means of the proposed methodology

restored fuzzy measures in expert decision making the paper deals with problems of fuzzy measure restoration from insufficient data on a finite set the proposed approach is constructed in the class of second order choquct capacities fuzzy sets and systems 31 1989 23 reports of the enlarged session of i vekua inst appl math 14 1999 31 ann inst fourier 5 1953 131 when the fuzzy weights of singletons are known this essentially concerns certain frequency distributions where the nature of additivity is doubtful because of the fuzzy nature of data distribution this is the indisputable condition for the introduction of a fuzzy measure but the insufficient one for its construction measures of specificity indices of uncertainty and estimators of approximations are calculated some approximation properties are proved using the approach of a kaufman s experton theory les expertons hermes paris 1987 the unique fuzzy subset fuzzy object is constructed from the associated probabilities fuzzy sets and systems 31 1989 23 of the restored fuzzy measure the application of the constructed method is illustrated by an example of the processing of certain insufficient statistical data of the georgian language as a result it becomes possible to derive estimates for the georgian language on the whole

affine approximation for direct batch recovery of euclidian structure and motion from sparse data we present a batch method for recovering euclidian camera motion from sparse image data the main purpose of the algorithm is to recover the motion parameters using as much of the available information and as few computational steps as possible the algorithm thus places itself in the gap between factorisation schemes which make use of all available information in the initial recovery step and sequential approaches which are able to handle sparseness in the image data euclidian camera matrices are approximated via the affine camera model thus making the recovery direct in the sense that no intermediate projective reconstruction is made using a little known closure constraint the fa closure we are able to formulate the camera coefficients linearly in the entries of the affine fundamental matrices the novelty of the presented work is twofold firstly the presented formulation allows for a particularly good conditioning of the estimation of the initial motion parameters but also for an unprecedented diversity in the choice of possible regularisation terms secondly the new autocalibration scheme presented here is in practice guaranteed to yield a least squares estimate of the calibration parameters as a bi product the affine camera model is rehabilitated as a useful model for most cameras and scene configurations e g wide angle lenses observing a scene at close range experiments on real and synthetic data demonstrate the ability to reconstruct scenes which are very problematic for previous structure from motion techniques due to local ambiguities and error accumulation

constrained structure and motion from multiple uncalibrated views of a piecewise planar scene this paper is about multi view modeling of a rigid scene we merge the traditional approaches of reconstructing image extractable features and of modeling via user provided geometry we use features to obtain a first guess for structure and motion fit geometric primitives correct the structure so that reconstructed features lie exactly on geometric primitives and optimize both structure and motion in a bundle adjustment manner while enforcing the underlying constraints we specialize this general scheme to the point features and the plane geometric primitives the underlying geometric relationships are described by multi coplanarity constraints we propose a minimal parameterization of the structure enforcing these constraints and use it to devise the corresponding maximum likelihood estimator the recovered primitives are then textured from the input images the result is an accurate and photorealistic model experimental results using simulated data confirm that the accuracy of the model using the constrained methods is of clearly superior quality compared to that of traditional methods and that our approach performs better than existing ones for various scene configurations in addition we observe that the method still performs better in a number of configurations when the observed surfaces are not exactly planar we also validate our method using real images

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

image based rendering using parameterized image varieties this paper addresses the problem of characterizing the set of all images of a rigid set of m points and n lines observed by a weak perspective or paraperspective camera by taking explicitly into account the euclidean constraints associated with calibrated cameras we show that the corresponding image space can be represented by a six dimensional variety embedded in cal r 2 m n and parameterized by the image positions of three reference points the coefficients defining this parameterized image variety or piv for short can be estimated from a sample of images of a scene via linear and non linear least squares the piv provides an integrated framework for using both point and line features to synthesize new images from a set of pre recorded pictures image based rendering the proposed technique does not perform any explicit three dimensional scene reconstruction but it supports hidden surface elimination texture mapping and interactive image synthesis at frame rate on ordinary pcs it has been implemented and extensively tested on real data sets

image interpolation using enhanced multiresolution critical point filters there are increasing demands for image interpolation in various fields such as virtual reality computer animation and video transmission the critical point filters cpf we have proposed previously enable completely automatic matching of two images in our previous method however it has taken a long time to compute the optimal parameter values by iterative searches this paper proposes an improved algorithm called the enhanced critical point filters ecpf where the parameters are stably computed using together the inverse mapping from the destination to the source it takes only a second to match images whose size is 64 64 the algorithm is also improved in its precision by directly handling color images while the previous algorithm has taken only the intensity value into account we apply ecpf to keyframe interpolation of video sequences we also apply ecpf to interpolating two different views of an object to generate any intermediate views in this case there are many constraints that can be used to determine the mapping between the images we propose a method to use such constraints to improve the accuracy of the mappings as the results image based pseudo 3d models are easily created from a set of views without any special devices

the evaluation of service quality using generalized choquet integral in view of the compatibility between psychology and linguistic terms this study generalizes the standard choquet integral whose measurable evidence and fuzzy measures are real numbers the proposed generalization can deal with fuzzy number types of measurable evidence and fuzzy measures in comparison with the previous research on service quality and fuzzy sets this study integrates the three column format servqual into the generalized choquet integral a numerical example evaluating the overall service quality of e stores is provided to illustrate how the generalized choquet integral evaluates service quality in the three column format servqual this integral is also compared with the possibility necessity model when measuring service quality

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

epipolar geometry and linear subspace methods a new approach to weak calibration this paper addresses the problem of estimating the epipolar geometry from point correspondences between two images taken by uncalibrated perspective cameras it is shown that jepson s and heeger s linear subspace technique for infinitesimal motion estimation can be generalized to the finite motion case by choosing an appropriate basis for projective space this yields a linear method for weak calibration the proposed algorithm has been implemented and tested on both real and synthetic images and it is compared to other linear and non linear approaches to weak calibration

a case against kruppa s equations for camera self calibration we consider the self calibration problem for perspective cameras and especially the classical kruppa equation approach it is known that for several common types of camera motion self calibration is degenerate which manifests itself through the existence of ambiguous solutions the author previously 1997 1999 studied these critical motion sequences and showed their importance for practical applications here we reveal a type of camera motion that is not critical for the generic self calibration problem but for which the kruppa equation approach fails this is the case if the optical centers of all cameras lie on a sphere and if the optical axes pass through the sphere s center a very natural situation for 3d object modeling from images results of simulated experiments demonstrate the instability of numerical self calibration algorithms in near degenerate configurations

camera autocalibration and horopter curves we describe a new algorithm for the obtainment of the affine and euclidean calibration of a camera under general motion the algorithm exploits the relationships of the horopter curves associated to each pair of cameras with the plane at infinity and the absolute conic using these properties we define cost functions whose minimization by means of general purpose techniques provides the required calibration the experiments show the good convergence properties computational efficiency and robust performance of the new techniques

camera self calibration from unknown planar structures enforcing the multiview constraints between collineations in this paper we describe an efficient method to impose the constraints existing between the collineations between images which can be computed from a sequence of views of a planar structure these constraints are usually not taken into account by multiview techniques in order not to increase the computational complexity of the algorithms however imposing the constraints is very useful since it allows a reduction of geometric errors in the reprojected features and provides a consistent set of collineations which can be used for several applications such as mosaicing reconstruction and self calibration in order to show the validity of our approach this paper focus on self calibration from unknown planar structures proposing a method exploiting the consistent set of collineations our method can deal with an arbitrary number of views and an arbitrary number of planes and varying camera internal parameters however for simplicity this papers will only discuss the case with one plane in several views the results obtained with synthetic and real data are very accurate and stable even when using only few images

a flexible new technique for camera calibration we propose a flexible technique to easily calibrate a camera it only requires the camera to observe a planar pattern shown at a few at least two different orientations either the camera or the planar pattern can be freely moved the motion need not be known radial lens distortion is modeled the proposed procedure consists of a closed form solution followed by a nonlinear refinement based on the maximum likelihood criterion both computer simulation and real data have been used to test the proposed technique and very good results have been obtained compared with classical techniques which use expensive equipment such as two or three orthogonal planes the proposed technique is easy to use and flexible it advances 3d computer vision one more step from laboratory environments to real world use

euclidean upgrading from segment lengths we address the problem of the recovery of euclidean structure of a projectively distorted n dimensional space from the knowledge of the possibly diverse lengths of a set of segments this problem is relevant in particular for euclidean reconstruction with uncalibrated cameras extending previously known results in the affine setting the key concept is the quadric of segments qos defined in a higher dimensional space by the set of segments of a fixed length from which euclidean structure can be obtained in closed form we have intended to make a thorough study of the properties of the qos including the determination of the minimum number of segments of arbitrary length that determine it and its relationship with the standard geometric objects associated to the euclidean structure of space explicit formulas are given to obtain the dual absolute quadric and the absolute quadratic complex from the qos experiments with real and synthetic images evaluate the performance of the techniques

geometric interpretations of the relation between the image of the absolute conic and sphere images a spherical object has been introduced into camera calibration for several years through utilizing the properties of an image conic which is the projection of the occluding contour of a sphere in the perspective image however in literature only an algebraic interpretation was presented for the relation between the image of the absolute conic and sphere images in this paper we propose two geometric interpretations of this relation and two novel camera calibration methods using sphere images are derived from these geometric interpretations

multiple view geometry of general algebraic curves we introduce a number of new results in the context of multi view geometry from general algebraic curves we start with the recovery of camera geometry from matching curves we first show how one can compute without any knowledge on the camera the homography induced by a single planar curve then we continue with the derivation of the extended kruppa s equations which are responsible for describing the epipolar constraint of two projections of a general algebraic curve as part of the derivation of those constraints we address the issue of dimension analysis and as a result establish the minimal number of algebraic curves required for a solution of the epipolar geometry as a function of their degree and genus we then establish new results on the reconstruction of general algebraic curves from multiple views we address three different representations of curves i the regular point representation in which we show that the reconstruction from two views of a curve of degree d admits two solutions one of degree d and the other of degree d d 1 moreover using this representation we address the problem of homography recovery for planar curves ii dual space representation tangents for which we derive a lower bound for the number of views necessary for reconstruction as a function of the curve degree and genus and iii a new representation to computer vision based on the set of lines meeting the curve which does not require any curve fitting in image space for which we also derive lower bounds for the number of views necessary for reconstruction as a function of curve degree alone