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

differential flatness of two one forms in arbitrary number of variables given a differentially flat system of odes flat outputs that depend only on original variables but not on their derivatives are called zero flat outputs and systems possessing such outputs are called zero flat in this paper we present a theory of zero flatness for a system of two one forms in arbitrary number of variables t x1 xn our approach splits the task of finding zero flat outputs into two parts first part involves solving for distributions that satisfy a set of algebraic conditions the second part involves finding an integrable distribution from the solution set of the first part typically this part involves solving pdes our results are also applicable in determining if a control affine system in n states and n 2 controls has flat outputs that depend only on states we illustrate our method by examples

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

eigenfaces vs fisherfaces recognition using class specific linear projection we develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression taking a pattern classification approach we consider each pixel in an image as a coordinate in a high dimensional space we take advantage of the observation that the images of a particular face under varying illumination but fixed pose lie in a 3d linear subspace of the high dimensional image space if the face is a lambertian surface without shadowing however since faces are not truly lambertian surfaces and do indeed produce self shadowing images will deviate from this linear subspace rather than explicitly modeling this deviation we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation our projection method is based on fisher s linear discriminant and produces well separated classes in a low dimensional subspace even under severe variation in lighting and facial expressions the eigenface technique another method based on linearly projecting the image space to a low dimensional subspace has similar computational requirements yet extensive experimental results demonstrate that the proposed fisherface method has error rates that are lower than those of the eigenface technique for tests on the harvard and yale face databases

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

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

local intensity variation analysis for iris recognition as all emerging biometric for human identification iris recognition has received increasing attention in recent years this paper makes an attempt to reflect shape information of the iris by analyzing local intensity variations of an iris image in our framework a set of one dimensional 1d intensity signals is constructed to contain the most important local variations of the original 2d iris image gaussian hermite moments of such intensity signals reflect to a large extent their various spatial modes and are used as distinguishing features a resulting high dimensional feature vector is mapped into a low dimensional subspace using fisher linear discriminant and then the nearest center classifier based on cosine similarity measure is adopted for classification extensive experimental results show that the proposed method is effective and encouraging c 2004 pattern recognition society published by elsevier ltd all rights reserved

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

coarse iris classification using box counting to estimate fractal dimensions this paper proposes a novel algorithm for the automatic coarse classification of iris images using a box counting method to estimate the fractal dimensions of the iris first the iris image is segmented into sixteen blocks eight belonging to an upper group and eight to a lower group we then calculate the fractal dimension value of these image blocks and take the mean value of the fractal dimension as the upper and the lower group fractal dimensions finally all the iris images are classified into four categories in accordance with the upper and the lower group fractal dimensions this classification method has been tested and evaluated on 872 iris cases and the proportions of these categories in our database are 5 50 38 54 21 79 and 34 17 the iris images are classified with two algorithms the double threshold algorithm which classifies iris images with an accuracy of 94 61 and the backpropagation algorithm which is 93 23 accurate when we allow for the border effect the double threshold algorithm is 98 28 accurate

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

iris recognition based on bidimensional empirical mode decomposition and fractal dimension as the demand for information security increases more attention is being paid to biometrics based automated personal identification one of the most promising current biometric techniques is based on the human iris this paper attempts to detect shape information from the iris by analyzing local intensity variations of an iris image the methodology involves extraction of iris features using bidimensional empirical mode decomposition bemd and fractal dimension after the preprocessing procedure the normalized effective iris image is decomposed into 2d intrinsic mode function imf components at different spatial frequencies by bidimensional empirical mode decomposition then the texture features of each intrinsic mode function image are obtained via the differential box counting method to evaluate the efficacy of the proposed approach three different similarity measures used in recognition are adopted the experimental results using the casia and ice iris databases show that the schema presented achieves promising results for iris recognition

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

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

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

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

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

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

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

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

non regular feedback linearization of nonlinear systems via a normal form algorithm in this paper the problem of non regular static state feedback linearization of affine nonlinear systems is considered first of all a new canonical form for non regular feedback linear systems is proposed using this form a recursive algorithm is presented which yields a condition for single input linearization then the left semi tensor product of matrices is introduced and several new properties are developed using the recursive framework and new matrix product a formula is presented for normal form algorithm based on it a set of conditions for single input approximate linearizability is presented

new results on non regular linearization of non linear systems this paper presents some new results on non regular linearization of non linear systems based on a normal form and a non regular linearization technique developed recently the paper first provides a set of calculating formulas for the linearization procedure as an application the linearization of bilinear systems is investigated then it presents easily verifiable sufficient conditions for the global semi global approximate linearization finally an estimate of the region of attraction for the kth degree approximately linearized systems with state feedback control is given which illustrates one of the advantages of the approximate linearization

flatness based control by quasi static feedback illustrated on a cascade of two chemical reactors flat non linear systems are linearizable by quasi static feedback of generalized states as a consequence stable tracking of reference trajectories can be achieved with controllers which do not introduce extra dynamics into the loop if moreover the system has a series structure this may be exploited for simplifying the flatness based analysis and design the resulting method is illustrated on a series connection of two chemical reactors flatness based analysis of the stationary solution and using these results the design of reference trajectories which account for constraints are discussed in detail quasi static feedback controllers are designed and some simulations are reported

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

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

a remark on nonlinear accessibility conditions and infinite prolongations the lie rank condition for strong nonlinear accessibility is interpreted via the differential geometry of jets and prolongations of infinite order it yields to a new lie algebraic criterion and to the consideration of first integrals which apply to nonlinear systems in quite general form the latter characterization in particular is valid without distinguishing between the system variables and is independent of time scalings weak accessibility is also considered

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

a condition for dynamic feedback linearization of control affine nonlinear systems in this paper a necessary and sufficient condition for dynamic feedback linearizability by endogenous feedback of control affine nonlinear systems is presented the condition is based on a modified derived flag of a pfaffian system associated with a control system which takes into account the presence of a precompensator it is shown that the generators associated with this modified derived flag must satisfy a number of congruences the congruences ensure that the conditions of the gs algorithm are satisfied for the prolongated system and thus provide an algorithm to calculate the required feedback and state space transformations a tower structure is identified with respect to a set of indices corresponding to a set of generalized kronecker indices using these conditions a bound related to the extent of precompensation required for each input channel is obtained it is shown how linearizing outputs can be identified by studying the derived flag of the pfaffian system associated with a nonlinear system

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

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

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

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

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

differential flatness and absolute equivalence of nonlinear control systems this paper presents a formulation of differential flatness a concept originally introduced by fliess levine martin and rouchon in terms of absolute equivalence between exterior differential systems systems that are differentially flat have several useful properties that can be exploited to generate effective control strategies for nonlinear systems the original definition of flatness was given in the context of differential algebra and required that all mappings be meromorphic functions the formulation of flatness presented here does not require any algebraic structure and allows one to use tools from exterior differential systems to help characterize differentially flat systems in particular it is shown that under regularity assumptions and in the case of single input control systems i e codimension 2 pfaffian systems a system is differentially flat if and only if it is feedback linearizable via static state feedback in higher codimensions our approach does not allow one to prove that feedback linearizability about an equilibrium point and flatness are equivalent one must be careful with the role of time as well as the use of prolongations that may not be realizable as dynamic feedback in a control setting applications of differential flatness to nonlinear control systems and open questions are also discussed

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

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

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

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

brief on the linearizability of nonisothermal continuous stirred tank reactors in this paper we consider the dynamic feedback linearizability and flatness of chemical processes using an exterior calculus approach the flatness of a large class of nonisothermal continuous stirred tank chemical reactor is demonstrated it is shown that flatness is independent of reaction kinetics and heat transfer considerations for plant models with kinetics relate three chemical species or less we identify linearizing outputs that are common to all members of a given class

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

flatness based control of a nonlinear chemical reactor model the nonlinear model of a continuous stirred tank reactor is shown to be flat the flatness permits the design of suitable trajectories on the basis of the explicit stationary solution and the tracking of these trajectories asymptotically using quasi static state feedback linearization a nonlinear local observer with a time varying gain is designed allowing the realisation of the state feedback in the case of partial measurement of the state simulation results illustrate the tracking behavior of the closed loop with the observer

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

image reconstruction from continuous gaussian hermite moments implemented by discrete algorithm the problem of image reconstruction from its statistical moments is particularly interesting to researchers in the domain of image processing and pattern recognition compared to geometric moments the orthogonal moments offer the ability to recover much more easily the image due to their orthogonality which allows reducing greatly the complexity of computation in the phase of reconstruction since the 1980s various orthogonal moments such as legendre moments zernike moments and discrete tchebichef moments have been introduced early or late to image reconstruction in this paper another set of orthonormal moments the gaussian hermite moments based on hermite polynomials modulated by a gaussian envelope is proposed to be used for image reconstruction especially the paper s focus is on the determination of the optimal scale parameter and the improvement of the reconstruction result by a post processing which make gaussian hermite moments be useful and comparable with other moments for image reconstruction the algorithms for computing the values of the basis functions moment computation and image reconstruction are also given in the paper as well as a brief discussion on the computational complexity the experimental results and error analysis by comparison with other moments show a good performance of this new approach

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

flatness and defect of non linear systems introductory theory and examples we introduce flat systems which are equivalent to linear ones via a special type of feedback called endogenous their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of kalman s controllability the distance to flatness is measured by a non negative integer the defect we utilize differential algebra where flatness and defect are best defined without distinguishing between input state output and other variables many realistic classes of examples are flat we treat two popular ones the crane and the car with n trailers the motion planning of which is obtained via elementary properties of plane curves the three non flat examples the simple double and variable length pendulums are borrowed from non linear physics a high frequency control strategy is proposed such that the averaged systems become flat

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

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

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

bayesian model estimation and selection for epipolar geometry and generic manifold fitting computer vision often involves estimating models from visual input sometimes it is possible to fit several different models or hypotheses to a set of data and a decision must be made as to which is most appropriate this paper explores ways of automating the model selection process with specific emphasis on the least squares problem of fitting manifolds in particular algebraic varieties e g lines algebraic curves planes etc to data points illustrated with respect to epipolar geometry the approach is bayesian and the contribution three fold first a new bayesian description of the problem is laid out that supersedes the author s previous maximum likelihood formulations this formulation will reveal some hidden elements of the problem second an algorithm mapsac is provided to obtain the robust map estimate of an arbitrary manifold third a bayesian model selection paradigm is proposed the bayesian formulation of the manifold fitting problem uncovers an elegant solution to this problem for which a new method gric for approximating the posterior probability of each putative model is derived this approximations bears some similarity to the penalized likelihoods used by aic bic and mdl however it is far more accurate in situations involving large numbers of latent variables whose number increases with the data this will be empirically and theoretically demonstrated

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

on image analysis by moments research has been performed investigating the use of moments for pattern recognition in recent years the basic problem of the influence of discretization and noise on moment accuracy as object descriptors has been barely investigated in this paper the detailed error analysis involved in the moment method is discussed several new techniques to increase the accuracy and efficiency of moment descriptor are proposed we utilize these results for the problem of image reconstruction from the orthogonal legendre moments computed from discrete and noisy data the automatic selection of an optimal number of moments is also discussed

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

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

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

shape and motion from image streams under orthography a factorization method inferring scene geometry and camera motion from a stream of images is possible in principle but is an ill conditioned problem when the objects are distant with respect to their size we have developed a factorization method that can overcome this difficulty by recovering shape and motion under orthography without computing depth as an intermediate step an image stream can be represented by the 2fxp measurement matrix of the image coordinates of p points tracked through f frames we show that under orthographic projection this matrix is of rank 3 based on this observation the factorization method uses the singular value decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively two of the three translation components are computed in a preprocessing stage the method can also handle and obtain a full solution from a partially filled in measurement matrix that may result from occlusions or tracking failures the method gives accurate results and does not introduce smoothing in either shape or motion we demonstrate this with a series of experiments on laboratory and outdoor image streams with and without occlusions

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

a multi frame approach to visual motion perception one of the main issues in the area of motion estimation given the correspondences of some features in a sequence of images is sensitivity to error in the input the main way to attack the problem as with several other problems in science and engineering is redundancy in the data up to now all the algorithms developed either used two frames or depended on assumptions about the motion or the shape of the scene we present in this paper an algorithm based on multiple frames that employs only the rigidity assumption is simple and mathematically elegant and experimentally proves to be a major improvement over the two frame algorithms the algorithm does minimization of the squared error which we prove equivalent to an eigenvalue minimization problem one of the side effects of this mean square method is that the algorithm can have a very descriptive physical interpretation in terms of the loaded spring model

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

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

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

an algorithm for orbital feedback linearization of single input control affine systems feedback linearization is an effective design and analysis tool used in the study of nonlinear control systems however cases arise where linearizability conditions cannot be met for systems that are not linearizable by classical techniques orbital feedback linearization or feedback linearization by state dependent time scaling has been proposed to relax these conditions unfortunately approaches proposed to date have led to conditions that tend to be more difficult to check then conditions for state feedback linearization in this paper necessary and sufficient conditions for orbital feedback linearizability is presented for a class of single input nonlinear systems the conditions are simple and can be checked directly from the data of the problem using an exterior calculus approach a simple algorithm is developed to compute state dependent time scaling that yield state feedback linearizable systems it is shown that orbital feedback linearizability generalizes the concept state feedback linearizability to deal with locally weakly accessible control systems

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

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

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

gabor feature based classification using the enhanced fisher linear discriminant model for face recognition this paper introduces a novel gabor fisher 1936 classifier gfc for face recognition the gfc method which is robust to changes in illumination and facial expression applies the enhanced fisher linear discriminant model efm to an augmented gabor feature vector derived from the gabor wavelet representation of face images the novelty of this paper comes from 1 the derivation of an augmented gabor feature vector whose dimensionality is further reduced using the efm by considering both data compression and recognition generalization performance 2 the development of a gabor fisher classifier for multi class problems and 3 extensive performance evaluation studies in particular we performed comparative studies of different similarity measures applied to various classifiers we also performed comparative experimental studies of various face recognition schemes including our novel gfc method the gabor wavelet method the eigenfaces method the fisherfaces method the efm method the combination of gabor and the eigenfaces method and the combination of gabor and the fisherfaces method the feasibility of the new gfc method has been successfully tested on face recognition using 600 feret frontal face images corresponding to 200 subjects which were acquired under variable illumination and facial expressions the novel gfc method achieves 100 accuracy on face recognition using only 62 features

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