identification of physical parameters in structures systems abstract linear time invariant systems with a limited number of unknowns corresponding to physical component values often exhibit certain structural conditions on the way in which these values appear in the transfer functions in this paper the problem of identifying these unknowns is considered the structure translates to an associated identification problem which is multilinear in the unknowns this is exploited in the design of two algorithms which use measurements of input and output and knowledge of the polynomial coefficients of the multilinear combinations of the system parameters conditions are established for the uniform asymptotic stability of these algorithms

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

image sequence analysis using relational structures abstract time varying images are usually analyzed to obtain a description of the observed objects and of their actions an abstraction process is necessary which converts the input images into symbolic descriptions the attributes of image symbols and the relationship between symbols are computed from the sampled intensity or colour measurements relational structures are a formal tool to describe not only the symbolic image representation but furthermore stored models as prototypes of objects and objects as instantiations of such prototypes following this paradigm an essential task of image sequence analysis is the generation of mappings between images to establish the correspondence relationship and between images and prototypes to identify objects different types of morphisms between relational structures rs morphisms are proposed together with an approach for computing them by searching for cliques in a compatibility graph of hypothetical assignments of elements from both structures the common formalism presented here aims at a unification of methods for those steps necessary to instantiate objects and follow them through the sequence one practical reason for this attempt is to make relational database systems available to store and retrieve the large amount of data whidch might be generated during the exploration of a real world image sequence

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

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

optimal statistical decisions about some alternative financial models abstract we study neyman pearson testing and bayesian decision making based on observations of the price dynamics x t t 0 t of a financial asset when the hypothesis is the classical geometric brownian motion with a given constant growth rate and the alternative is a different random diffusion process with a given possibly price dependent growth rate examples of asset price observations are introduced and used throughout the paper to demonstrate the applicability of the theory by a rigorous mathematical approach we obtain exact formulae and bounds for the most common statistical characteristics of testing and decision making such as the power of test type ii error probability the bayes factor and its moments power divergences and the bayes risk or bayes error these bounds can be much more easily evaluated than the exact formulae themselves and consequently they are useful for practical applications an important theoretical conclusion of this paper is that for the class of alternatives considered neither the risk nor the errors converge to zero faster than exponentially in the observation time t we illustrate in concrete decision situations that the actual rate of convergence is well approximated by the bounds given 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

empirical likelihood and general estimating equations for some time so called empirical likelihoods have been used heuristically for purposes of nonparametric estimation owen showed that empirical likelihood ratio statistics for various parameters theta f of an unknown distribution f have limiting chi square distributions and may be used to obtain tests or confidence intervals in a way that is completely analogous to that used with parametric likelihoods our objective in this paper is twofold first to link estimating functions or equations and empirical likelihood second to develop methods of combining information about parameters we do this by assuming that information about f and theta is available in the form of unbiased estimating functions empirical likelihoods for parameters are developed and shown to have properties similar to those for parametric likelihood efficiency results for estimates of both theta and f are obtained the methods are illustrated on several problems and areas for future investigation are noted

full volumetric descriptions from three intensity images we address the problem of recovering high level volumetric and segmented or part based descriptions of objects from intensity images as input we use three closely spaced images of an object and recover descriptions based on generalized cylinders gcs we start by extracting a hierarchy of groups from contour images in the three views grouping is based on proximity parallelism and symmetry the groups in the three views are matched and their contours are labeled as true edges we then infer the gc axis its cross section and the scaling function the cross section is recovered if seen in the images else it is inferred using the visible surfaces and gc properties we consider groups with true edges limb edges or a combination of both the coarse volumetric descriptions obtained are refined to include surface details as seen in the intensity images we demonstrate results on real images of moderately complex objects with texture and shadows

empirical likelihood ratio confidence intervals for a single functional summary the empirical distribution function based on a sample is well known to be the maximum likelihood estimate of the distribution from which the sample was taken in this paper the likelihood function for distributions is used to define a likelihood ratio function for distributions it is shown that this empirical likelihood ratio function can be used to construct confidence intervals for the sample mean for a class of m estimates that includes quantiles and for differentiable statistical functionals the results are nonparametric extensions of wilks s 1938 theorem for parametric likelihood ratios the intervals are illustrated on some real data and compared in a simulation to some bootstrap confidence intervals and to intervals based on student s t statistic a hybrid method that uses the bootstrap to determine critical values of the likelihood ratio is introduced

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

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

confidence intervals in generalized method of moments models we consider the construction of confidence intervals for parameters characterized by moment restrictions in the standard approach to generalized method of moments gmm estimation confidence intervals are based on the normal approximation to the sampling distribution of the parameters there is often considerable disagreement between the nominal and actual coverage rates of these intervals especially in cases with a large degree of overidentification we consider alternative confidence intervals based on empirical likelihood methods which exploit the normal approximation to the lagrange multipliers calculated as a byproduct in empirical likelihood estimation in large samples such confidence intervals are identical to the standard gmm ones but in finite samples their properties can be substantially different in some of the examples we consider the proposed confidence intervals have coverage rates much closer to the nominal coverage rates than the corresponding gmm intervals

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

improving dynamic programming to solve image registration a new method of dynamic programming dp is presented a picture is paired with a reference map in order to arrive at picture registration an ordered sequence of primitive patterns is formed from the map an attempt is made to locate a similar sequence from the picture using classical picture processing methods this yields a distorted and unordered sequence marked by noise dp is then used to search for a common match to the two sequences both the initial and final registration states are however unknown moreover the continuity of the path is frequently interrupted due to shortcomings in detection or perhaps occlusions thus classical dp algorithms appear to give only poor results under practical conditions when well adapted to treat signals issued from a first order markovian process they can be used as this method shows to treat kth order processes the concept of the virtual state kept in memory suspends broken paths until they can be reconnected thus bridging the existing gaps between the different parts of the path the proposed algorithm has been applied to satellite images with their contours sectioned by clouds the result leads to the guarantee of very good registration in spite of image contours badly hampered by noise and or clouds

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

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

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

independent motion detection in 3d scenes this paper presents an algorithmic approach to the problem of detecting independently moving objects in 3d scenes that are viewed under camera motion there are two fundamental constraints that can be exploited for the problem 1 two multiview camera motion constraint for instance the epipolar trilinear constraint and 2 shape constancy constraint previous approaches to the problem either use only partial constraints or rely on dense correspondences or flow we employ both the fundamental constraints in an algorithm that does not demand a priori availability of correspondences or flow our approach uses the plane plus parallax decomposition to enforce the two constraints it is also demonstrated that for a class of scenes called sparse 3d scenes in which genuine parallax and independent motions may be confounded how the plane plus parallax decomposition allows progressive introduction and verification of the fundamental constraints results of the algorithm on some difficult sparse 3d scenes are promising

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

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

bootstrap critical values for tests based on generalized method of moments estimators monte carlo experiments have shown that tests based on generalized method ofmoments estimators often have true levels that differ greatly from their nominal levels when asymptotic critical values are used this paper gives conditions under which the bootstrap provides asymptotic refinements to the critical values of t tests and the test of overidentifying restrictions particular attention is given to the case of dependent data it is shown that with such data the bootstrap must sample blocks of data and that the formulae for the bootstrap versions of test statistics differ from the formulae that apply with the original data the results of monte carlo experiments on the numerical performance of the bootstrap show that it usually reduces the errors in level that occur when critical values based on first order asymptotic theory are used the bootstrap also provides an indication of the accuracy of critical values obtained from first order asymptotic theory

a computational approach for corner and vertex detection corners and vertexes are strong and useful features in computer vision for scene analysis stereo matching and motion analysis here we deal with the development of a computational approach to these important features we consider first a corner model and study analytically its behavior once it has been smoothed using the well known gaussian filter this allows us to clarify the behavior of some well knowncornerness measure based approaches used to detect these points of interest most of these classical approaches appear to detect points that do not correspond to the exact position of the corner a new scale space based approach that combines useful properties from the laplacian and beaudet s measure beaudet 1978 is then proposed in order to correct and detect exactly the corner position an extension of this approach is then developed to solve the problem of trihedral vertex characterization and detection in particular it is shown that a trihedral vertex has two elliptic maxima on extremal contrast surfaces if the contrast is sufficient and this allows us to classify trihedral vertexes in 2 classes vertex and vertex as corner the corner detection approach developed is applied to accurately detect trihedral vertexes using an additional test in order to make a distinction between trihedral vertexes and corners many experiments have been carried out using noisy synthetic data and real images containing corners and vertexes most of the promising results obtained are used to illustrate the experimental section of this paper

stable adaptive observers for nonlinear time varying systems an adaptive observer identifier for single input single output observable nonlinear systems that can be transformed to a certain observable canonical form is described sufficient conditions for stability of this observer are provided these conditions are in terms of the structure of the system and canonical form the boundedness of the parameter variations and the sufficient richness of some signals the scope of the canonical form and the use of the observer identifier is motivated by the presentation of applications to time invariant bilinear systems nonlinear systems in phase variable form a biotechnological process and a robot manipulator in each case the specific stability conditions are presented

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

a maximum entropy approach to recovering information from multinomial response data abstract the classical maximum entropy me approach to estimating the unknown parameters of a multinomial discrete choice problem which is equivalent to the maximum likelihood multinomial logit ml estimator is generalized the generalized maximum entropy gme model includes noise terms in the multinomial information constraints each noise term is modeled as the mean of a finite set of a priori known points in the interval 1 1 with unknown probabilities where no parametric assumptions about the error distribution are made a gme model for the multinomial probabilities and for the distributions associated with the noise terms is derived by maximizing the joint entropy of multinomial and noise distributions under the assumption of independence the gme formulation reduces to the me in the limit as the sample grows large or when no noise is included in the entropy maximization further even though the gme and the logit estimators are conceptually different the dual gme model is related to a gener

impsac synthesis of importance sampling and random sample consensus this paper proposes a new method for recovery of epipolar geometry and feature correspondence between images which have undergone a significant deformation either due to large rotation or wide baseline of the cameras the method also encodes the uncertainty by providing an arbitrarily close approximation to the posterior distribution of the two view relation the method operates on a pyramid from coarse to fine resolution thus raising the problem of how to propagate information from one level to another in a statistically consistent way the distribution of the parameters at each resolution is encoded nonparametrically as a set of particles at the coarsest level a random sample consensus monte carlo markov chain ransac mcmc estimator is used to initialize this set of particles the posterior can then be approximated as a mixture of gaussians fitted to these particles the distribution at a coarser level influences the distribution at a finer level using the technique of sampling importance resampling sir and mcmc which allows for asymptotically correct approximations of the posterior distribution the estimate of the posterior distribution at the level above is being used as the importance sampling function to generate a new set of particles which can be further improved by mcmc it is shown that the method is superior to previous single resolution ransac style feature matchers

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 highly robust estimator through partially likelihood function modeling and its application in computer vision the authors present a highly robust estimator known as the model fitting mf estimator for general regression they explain that high robustness becomes possible through partially but completely modeling the unknown log likelihood function the partial modeling takes place by taking the bayesian statistical decision rule and a number of important heuristics into consideration while maximizing the log likelihood function applications include the automatic selection of multiple thresholds single rigid motion estimation or multiple rigid motion segmentation and estimation from two perspective views it is believed that the proposed mf estimator will aid in solving many robust estimation problems that demand an estimator that is either highly robust or capable of handling contaminated gaussian mixture models

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

stereo correspondence through feature grouping and maximal cliques the authors propose a method for solving the stereo correspondence problem the method consists of extracting local image structures and matching similar such structures between two images linear edge segments are extracted from both the left and right images each segment is characterized by its position and orientation in the image as well as its relationships with the nearby segments a relational graph is thus built from each image for each segment in one image as set of potential assignments is represented as a set of nodes in a correspondence graph arcs in the graph represent compatible assignments established on the basis of segment relationships stereo matching becomes equivalent to searching for sets of mutually compatible nodes in this graph sets are found by looking for maximal cliques the maximal clique best suited to represent a stereo correspondence is selected using a benefit function numerous results obtained with this method are shown

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

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

high gain observer based estimation of parameter variations with delay alignment this technical note analyzes the estimation delay in a high gain observer where the state estimates may lag behind the actual states due to the observer s non zero phase response the technical note proves that for a slowly time varying system subject to bounded noises the estimation delay depends on the observer gain but is independent of the variations of system parameters rather than estimating the delay a novel method is proposed to calculate the delay from the observer s phase response in terms of system identification the delay is compensated by aligning other measurements with the lagged estimate so that they have the same lag the simulation results of an aero engine model show significant improvements in estimation on one hand the proposed approach improves the estimation accuracy and on the other hand it removes the assumption of zero delay and gives a new insight into the high gain observer design

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

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

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

euclidean shape and motion from multiple perspective views by affine iterations we describe a method for solving the euclidean reconstruction problem with a perspective camera model by incrementally performing euclidean reconstruction with either a weak or a paraperspective camera model with respect to other methods that compute shape and motion from a sequence of images with a calibrated camera this method converges in a few iterations is computationally efficient and solves for the sign reversal ambiguity we give a detailed account of the method analyze its convergence and test it with both synthetic and real data

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

some properties of the e matrix in two view motion estimation in the eight point linear algorithm for determining 3d motion structure from two perspective views using point correspondences the e matrix plays a central role the e matrix is defined as a skew symmetrical matrix containing the translation components postmultiplied by a rotation matrix the authors show that a necessary and sufficient condition for a 3 3 matrix to be so decomposable is that one of its singular values is zero and the other two are equal several other forms of this property are presented some applications are briefly described

indirect techniques for adaptive input output linearization of non linear systems abstract a technique of indirect adaptive control based on certainty equivalence for input output linearization of non linear systems is proven convergent it does not surfer from the overparameterization drawbacks of the direct adaptive control techniques on the same plant this paper also contains a semi indirect adaptive controller which has several attractive features of both the direct and indirect schemes

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

a new easy camera calibration technique based on circular points inspired by zhang s work a new easy technique for calibrating a camera based on circular points is proposed the proposed technique only requires the camera to observe a newly designed planar calibration pattern referred to as the model plane hereinafter which includes a circle and a pencil of lines passing through the circle s center at a few at least three different unknown orientations then all the five intrinsic parameters can be determined linearly the main point of our new technique is that it needs to know neither metric measurement on the model plane nor the correspondences between points on the model plane and image ones hence it can be done fully automatically the proposed technique is particularly useful for those people who are not familiar with computer vision experiments with simulated data as well as with real images show that our new technique is robust and accurate

an information theoretic alternative to generalized method of moments estimation while optimally weighted gmm estimation has desirable large sample properties its small sample performance is poor in some applications we propose a computationally simple alternative for weakly dependent data generating mechanisms based on minimization of the kullback leibler information criterion conditions are derived under which the large sample properties of this estimator are similar to gmm i e the estimator will be consistent and asymptotically normal with the same asymptotic covariance matrix as gmm in addition we propose overidentifying and parametric restrictions tests as alternatives to analogous gmm procedures

state observer for a class of nonlinear systems and its application to machine vision in this note we consider the state observer problem for a class of nonlinear systems which are usually encountered in the machine vision study the formulation of the state observer is motivated by the sliding mode methods and adaptive control techniques the proposed observer is applied to the identification problems of the motion parameters and space position of a moving object by using the perspective observation of a single point it is clarified that the rotation parameters can be observed by using the observation of one camera and the position and translation parameters cannot be observed by using one camera and must appeal to stereo vision simulation results show that the proposed algorithm is effective

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

image registration by matching relational structures abstract we present a method of image registration where we use relational structures as representations of images and we register two images by finding a match between the two relational structures it is better than traditional cross correlation like techniques in several aspects it is insensitive to scaling rotation gray level modification and small relative motion between the two images the matching process makes use of star structures which have several advantages over conventional node structures

moment preserving pattern matching abstract an accurate template matching algorithm of low computational complexity that facilitates low cost hardware design and vlsi implementation is highly desired by many image processing applications this paper describes a template matching method called moment preserving pattern matching mppm which reduces the computational complexity of template matching significantly and provides several advantages in hardware implementation the methodology is based on the concepts of pairing function and moment preserving quantization the experimental results show that it is computationally fast and accurate in locating the template if noise corruption is not too severe for obtaining a template matching algorithm of high accuracy and robustness against noise and low computational cost mppm is applied to a two stage matching scheme a statistical model for estimating the correlation threshold is also given

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

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

motion recovery by using stereo perspective observation the motion recovery for a class of movements in the space is considered in this note by using the stereo perspective observation of at least three points the motion equation that is considered can cover a wide class of practical movements in the space the asymptotic estimation of the motion parameters which are all time dependent variables is developed based on the second method of lyapunov furthermore the proposed algorithm can be modified to deal with occlusion phenomenon to illustrate the performance of the proposed algorithm it is compared with the extended kalman filter ekf by computer simulations

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

the curvature primal sketch in this paper we introduce a novel representation of the significant changes in curvature along the bounding contour of planar shape we call the representation the curvature primal sketch because of the close analogy to the primal sketch representation advocated by marr for describing significant intensity changes we define a set of primitive parameterized curvature discontinuities and derive expressions for their convolutions with the first and second derivatives of a gaussian we describe an implemented algorithm that computes the curvature primal sketch by matching the multiscale convolutions of a shape and illustrate its performance on a set of tool shapes several applications of the representation are sketched

robust adaptive regulation with minimal prior knowledge a robust adaptive regulator is designed under minimal prior knowledge namely the order of a nominal plant model in a well defined sense the involved robustness means that the closed loop stability is guaranteed in the presence of some class of time varying parameters and unmodeled dynamics the main design feature of the proposed adaptive regulator consists in its self excitation capability together with an appropriate identification stabilization time splitting unlike in the available literature concerning robust adaptive control the involved self excitation is established independently of the parameter estimator properties the use of the robustness oriented modifications as deadzone and parameter projection or contraction which are aimed at achieving the parameter estimates boundedness is no longer required beforehand thereby reducing the underlying prior knowledge

information theoretic approaches to inference in moment condition models one step efficient gmm estimation has been developed in the recent papers of back and brown 1990 imbens 1993 and qin and lawless 1994 these papers emphasized methods that correspond to using owen s 1988 method of empirical likelihood to reweight the data so that the reweighted sample obeys all the moment restrictions at the parameter estimates in this paper we consider an alternative klic motivated weighting and show how it and similar discrete reweightings define a class of unconstrained optimization problems which includes gmm as a special case such klic motivated reweightings introduce m auxiliary tilting parameters where m is the number of moments parameter and overidentification hypotheses can be recast in terms of these tilting parameters such tests when appropriately conditioned on the estimates of the original parameters are often startlingly more effective than their conventional counterparts this is apparently due to the local ancillarity of the original parameters for the tilting parameters

observer based parameter identifiers for nonlinear systems with parameter dependencies a class of nonlinear dynamical systems whose dynamics depend linearly on the unknown parameter vector is considered after reviewing a standard observer based identifier for estimating the unknown parameters we propose a family of new identifiers which exploit the a priori known parameter dependencies we then establish under mild assumptions on the dynamical system that 1 the proposed identifiers are stable and 2 the weighted norm of state parameter errors using the proposed identifiers are less than the corresponding errors using the standard identifier for a length of time after t 0 the main contribution of this paper is that it introduces a family of observer based identifiers which exhibit better transient performance than the standard identifier

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

heteroscedastic regression in computer vision problems with bilinear constraint we present an algorithm to estimate the parameters of a linear model in the presence of heteroscedastic noise i e each data point having a different covariance matrix the algorithm is motivated by the recovery of bilinear forms one of the fundamental problems in computer vision which appears whenever the epipolar constraint is imposed or a conic is fit to noisy data points we employ the errors in variables eiv model and show why already at moderate noise levels most available methods fail to provide a satisfactory solution the improved behavior of the new algorithm is due to two factors taking into account the heteroscedastic nature of the errors arising from the linearization of the bilinear form and the use of generalized singular value decomposition gsvd in the computations the performance of the algorithm is compared with several methods proposed in the literature for ellipse fitting and estimation of the fundamental matrix it is shown that the algorithm achieves the accuracy of nonlinear optimization techniques at much less computational cost

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

optimization on lie manifolds and pattern recognition several pattern recognition problems can be reduced in a natural way to the problem of optimizing a nonlinear function over a lie manifold however optimization on lie manifolds involves in general a large number of nonlinear equality constraints and is hence one of the hardest optimization problems we show that exploiting the special structure of lie manifolds allows one to devise a method for optimizing on lie manifolds in a computationally efficient manner the new method relies on the differential geometry of lie manifolds and the underlying connections between lie groups and their associated lie algebras we describe an application of the new lie group method to the problem of diagnosing malignancy in the cytological extracts of breast tumors the diagnosis method that we present has a mean sensitivity of 98 086 and a predictive index of 0 0602 making it the most accurate and reliable diagnostic method reported thus far

new measurements and corner guidance for curve matching with probabilistic relaxation reliable curve matching is a difficult yet important problem in many vision based applications including image based modeling we describe in this paper two aspects of our research in this area a new algorithm for curve matching including lines within a probabilistic relaxation framework and an approach of incorporating previously matched points corners to guide curve matching we propose similarity invariant unary and binary measurements suitable for curves and introduce an additional measurement to model the uncertainty of the binary measurements the uncertainty measure is proven to be very important in computing the matching support from neighboring matches we also show how to use a set of previously matched points corners to guide the curve matching the role of the corner guidance is explicitly modeled by a set of unary measurements and a similarity function under the same relaxation framework preprocessing techniques contributing to the success of our curve matching techniques are also developed and discussed experiments with complex real scenes show that the rate of correct matching is higher than 98

a two stage cross correlation approach to template matching two stage template matching with sum of absolute differences as the similarity measure has been developed by vanderburg and rosenfeld 1 2 this correspondence shows the development of two stage template matching with cross correlation as the similarity measure the threshold value of the first stage is derived analytically and its validity is verified experimentally considerable speed up over the one stage process can be obtained by introducing only a small false dismissal probability

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

detecting moving objects using the rigidity constraint a method for visually detecting moving objects from a moving camera using point correspondences in two orthographic views is described the method applies a simple structure from motion analysis and then identifies those points inconsistent with the interpretation of the scene as a single rigid object it is effective even when the actual motion parameters cannot be recovered demonstrations are presented using point correspondences automatically determined from real image sequences

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

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

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

reduced multilinear constraints theory and experiments this paper deals with the problem of reconstructing the locations of n points in space from m different images without camera calibration we will show how these reconstruction problems for different n and m can be put into a similar theoretical framework this will be done using a special choice of coordinates both in the object and in the images called reduced affine coordinates this choice of coordinates simplifies the analysis of the multilinear geometry and gives simpler forms of the multilinear tensors in particular we will investigate the cases which can be solved by linear methods i e 8 points in 2 images 7 points in 3 images and 6 points in 4 images a new concept the reduced fundamental matrix is introduced which gives bilinear expressions in the image coordinates it has six nonzero elements which depend on just four parameters and can be used to make reconstruction from 2 images we also introduce the concept of the reduced trifocal tensor which gives trilinear expressions in the image coordinates in 3 images it has 15 nonzero elements and depends on nine parameters and can be used to make reconstruction from 3 images finally the reduced quadfocal tensor is introduced which describes the relations between points in 4 images and gives quadlinear expressions in the image coordinates this tensor has 36 nonzero elements which depend on 14 independent parameters and can be used to make reconstruction from 4 images these tensors give the possibility to calculate linear solutions from 8 points in 2 images 7 points in 3 images and also from 6 points in 4 images furthermore a canonical form of the camera matrices in a sequence is presented and it is shown that the quadlinear constraints can be calculated from the trilinear ones and that in general the trilinear constraints can be calculated from the bilinear ones