discriminative least squares regression for multiclass classification and feature selection this paper presents a framework of discriminative least squares regression lsr for multiclass classification and feature selection the core idea is to enlarge the distance between different classes under the conceptual framework of lsr first a technique called e dragging is introduced to force the regression targets of different classes moving along opposite directions such that the distances between classes can be enlarged then the e draggings are integrated into the lsr model for multiclass classification our learning framework referred to as discriminative lsr has a compact model form where there is no need to train two class machines that are independent of each other with its compact form this model can be naturally extended for feature selection this goal is achieved in terms of l2 1 norm of matrix generating a sparse learning model for feature selection the model for multiclass classification and its extension for feature selection are finally solved elegantly and efficiently experimental evaluation over a range of benchmark datasets indicates the validity of our method

estimating three dimensional motion parameters of a rigid planar patch ii singular value decomposition we show that the three dimensional 3 d motion parameters of a rigid planar patch can be determined by computing the singular value decomposition svd of a 3 3 matrix containing the eight so called pure parameters furthermore aside from a scale factor for the translation parameters the number of solutions is either one or two depending on the multiplicity of the singular values of the matrix

a comment on analysis of video image sequences using point and line correspondences abstract in this paper we would like to contest the results of y f wang n karandikar and j k aggarwal pattern recognition 24 1065 1085 1991 raising two fundamental claims a line does not contribute anything to recognition of motion parameters from two images four traceable points are not sufficient to recover motion parameters from two perspective projections to be constructive however we show that four traceable points are sufficient to recover motion parameters from two frames under orthogonal projection and that five points are sufficient to simplify the solution of the two frame problem under orthogonal projection to solving a linear equation system

motion and structure from point correspondences with error estimation planar surfaces the determination of motion and structure of a planar scene from monocular image sequences is studied a new and simpler linear algorithm that gives closed form solutions for motion and structure parameters using point correspondences between two images assuming that the coplanar points undergo a rigid motion in 3 d space is presented a series of analytical results is established from two perspective views of a planar scene which is undergoing a rigid motion there are generally two normalized interpretations for motion parameters and the positions of the object plane these two interpretations one vertical and the other illusive are both valid in the sense that they render the same pair of images the authors identify all the special cases in which the number of interpretations is not two and derive necessary and sufficient geometrical conditions for those special cases to occur the approach to error estimation is based on the first order perturbation the estimated errors provide quantitative assessment for the accuracy of the solutions they also indicate degenerate or nearly degenerate configurations in the presence of noise

determining motion parameters using intensity guided range sensing abstract this paper describes a method for the direct computation of rotation and translation parameters of an object using multisensory data gathered from intensity and range sensors intensity images which can be gathered rapidly are used as the basis for guiding the extraction of a small set of correspondent points whose three dimensional coordinates can be determined by a range sensing device library model centered motion transformations are computed using a least squares approach object centered motion parameters are derived by computing the transformation between successive positions of the object results are presented for range and intensity images of synthetic and laboratory scenes

estimation of object motion parameters from noisy images an approach is presented for the estimation of object motion parameters based on a sequence of noisy images the problem considered is that of a rigid body undergoing unknown rotational and translational motion the measurement data consists of a sequence of noisy image coordinates of two or more object correspondence points by modeling the object dynamics as a function of time estimates of the model parameters including motion parameters can be extracted from the data using recursive and or batch techniques this permits a desired degree of smoothing to be achieved through the use of an arbitrarily large number of images some assumptions regarding object structure are presently made results are presented for a recursive estimation procedure the case considered here is that of a sequence of one dimensional images of a two dimensional object thus the object moves in one transverse dimension and in depth preserving the fundamental ambiguity of the central projection image model loss of depth information an iterated extended kalman filter is used for the recursive solution noise levels of 5 10 percent of the object image size are used approximate cramer rao lower bounds are derived for the model parameter estimates as a function of object trajectory and noise level this approach may be of use in situations where it is difficult to resolve large numbers of object match points but relatively long sequences of images 10 to 20 or more are available

estimating three dimensional motion parameters of a rigid planar patch iii finite point correspondences and the three view problem two results are presented in this paper first it is shown that in estimating three dimensional motion of a rigid planar patch the eight pure parameters used in 1 and 2 are uniquely determined from the image correspondences of four points no three collinear and can be estimated by solving a set of linear equations the second result concerns the three view problem it is proved that given four image point correspondences in three perspective views of a planar patch undergoing general three dimensional rigid body motion the number of solutions for the motion parameters is one as opposed to two 2 when only two perspective views are given

optimal visual motion estimation a note the problem of estimating 3d motion in an optimal manner using correspondences of features in two views is analyzed the importance of having an optimal estimator is twofold first for the estimation itself and second for the bound it offers on how much sensitivity one can expect from a two frame point based motion algorithm the optimal estimator turns out to be nonlinear and for that reason techniques that provide very good initial guesses for the iterative computation of the optimal estimator are developed

motion parameter estimation from global flow field data presented are two methods for the determination of the parameters of motion of a sensor given the vector flow field induced by an imaging system governed by a perspective transformation of a rigid scene both algorithms integrate global data to determine motion parameters the first the flow circulation algorithm determines the rotational parameters the second the foe search algorithm determines the translational parameters of the motion independently of the first algorithm several methods for determining when the function has the appropriate form are suggested one method involves filtering the function by a collection of circular surround zero mean receptive fields the other methods project the function onto a linear space of quadratic polynomials and measures the distance between the two functions the error function for the first two methods is a quadratic polynomial of the candidate position yielding a very rapid search strategy

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

minimax risk bounds in extreme value theory asymptotic minimax risk bounds for estimators of a positive extreme value index under zero one loss are investigated in the classical i i d setup to this end we prove the weak convergence of suitable local experiments with pareto distributions as center of localization to a white noise model which was previously studied in the context of nonparametric local density estimation and regression from this result we derive upper and lower bounds on the asymptotic minimax risk in the local and in certain global models as well finally the implications for fixed length confidence intervals are discussed in particular asymptotic confidence intervals with almost minimal length are constructed while the popular hill estimator is shown to yield a little longer confidence intervals

motion estimation with more than two frames the development of a general motion estimation system based on using three or more frames is reported the relevant portion of the sequence is treated as a whole thus simplifying the process of estimating the motion parameters and making possible the computation of the motion parameters in terms of the natural center of motion a general description of this motion estimation method is presented with the derivation of motion equations for three cases three points in three frames two points in four frames and one point in five frames results are given for real and synthetic images for the case of one point in five and six frames on the average the program converged quickly to the right answer for noiseless data for noisy data the answers were reasonable and their accuracy was directly a function of the amount of noise in the disparity vector

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

three dimensional modeling from two dimensional video this paper presents the surface based factorization method to recover three dimensional 3 d structure i e the 3 d shape and 3 d motion of a rigid object from a two dimensional 2 d video sequence the main ingredients of our approach are as follows 1 we describe the unknown shape of the 3 d rigid object by polynomial patches 2 projections of these patches in the image plane move according to parametric 2 d motion models 3 we recover the parameters describing the 3 d shape and 3 d motion from the 2 d motion parameters by factorizing a matrix that is rank 1 in a noiseless situation our method is simultaneously an extension and a simplification of the original factorization method of tomasi and kanade 1992 we track regions where the 2 d motion in the image plane is described by a single set of parameters avoiding the need to track a large number of pointwise features in general a difficult task then our method estimates the parameters describing the 3 d structure by factoring a rank 1 matrix not rank 3 as in tomasi and kanade this allows the use of fast iterative algorithms to compute the 3 d structure that best fits the data experimental results with real life video sequences illustrate the good performance of our approach

a general aperture problem for direct estimation of 3 d motion parameters the necessary and sufficient conditions that an object should satisfy so that motion can be uniquely determined by a direct method are discussed this direct method based on the temporal spatial gradient scheme can estimate the three dimensional 3 motion parameters of a rigid moving object from an image sequence by utilizing depth information of the object it is shown that the 3 d motion cannot be uniquely determined for only eight kinds of objects with special geometric structure and surface pattern

the feasibility of motion and structure from noisy time varying image velocity information this research addresses the problem of noise sensitivity inherent in motion and structure algorithms the motion and structure paradigm is a two step process first we measure image velocities and perhaps their spatial and temporal derivatives are obtained from time varying image intensity data and second we use these data to compute the motion of a moving monocular observer in a stationary environment under perspective projection relative to a single 3 d planar surface the first contribution of this article is an algorithm that uses time varying image velocity information to compute the observer s translation and rotation and the normalized surface gradient of the 3 d planar surface the use of time varying image velocity information is an important tool in obtaining a more robust motion and structure calculation the second contribution of this article is an extensive error analysis of the motion and structure problem any motion and structure algorithm that uses image velocity information as its input should exhibit error sensitivity behavior compatible with the results reported here we perform an average and worst case error analysis for four types of image velocity information full and normal image velocities and full and normal sets of image velocity and its derivatives these derivatives are simply the coefficients of a truncated taylor series expansion about some point in space and time the main issues we address here are just how sensitive is a motion and structure computation in the presence of noisy input or alternately how accurate must our image velocity information be how much and what type of input data is needed and under what circumstances is motion and structure feasible that is when can we be sure that a motion and structure computation will produce usable results we base our answers on a numerical error analysis we conduct for a large number of motions

experiments on estimating egomotion and structure parameters using long monocular image sequences this paper presents a simple but robust model based approach to estimating the kinematics of a moving camera and the structure of the objects in a stationary environment using long noisy monocular image sequences both batch and recursive algorithms are presented and the problem due to occlusion is addressed the approach is based on representing the constant translational velocity and constant angular velocity of the camera motion using nine rectilinear motion parameters which are 3 d vectors of the position of the rotation center linear and angular velocities the structure parameters are 3 d coordinates of the salient feature points in the inertial coordinate system due to redundancies in parameterization the total number of independent parameters to be estimated is 3m 7 wherem is the number of feature points the image plane coordinates of these feature points in each frame are first detected and matched over the frames these noisy image coordinates serve as the input to our algorithms due to the nonlinear nature of perspective projection a nonlinear least squares method is formulated for the batch algorithm and a conjugate gradient method is then applied to find the solution a recursive method using an iterated extended kalman filter iekf for incremental estimation of motion and structure is also presented since the plant model is simple in our formulation closed form solutions for the state and covariance transition equations are easily derived experimental results for simulated imagery as well as several real image sequences are included

recursive estimation of time varying motion and structure parameters we present a computational framework for recovering both first order motion parameters observer direction of translation and observer rotation second order motion parameters observer rotational acceleration and relative depth maps from time varying optical flow we recover translation speed and acceleration in units which are scaled relative to the distance to the object our assumption is that the observer rotational motion is no more than second order in other words observer motion is either constant or has at most constant acceleration we examine the effect of noise on the solution of the motion and structure parameters this ensemble of unknowns comprises a solution to the classical structure and motion from optic flow problem our complete framework utilizes a method for interpreting the bilinear image velocity equation by solving simple systems of linear equations since our noise analysis yields uncertainty measures for each parameter a kalman filter is employed to incrementally integrate new measurements as they become available as each additional frame in the sequence is processed we conclude by analysing this reduction of uncertainty over time as the system converges to a stable solution for both synthetic and real image sequences

adaptive model based motion estimation a general discrete time adaptive multidimensional framework is introduced for estimating the motion of one or several object features from their successive nonlinear projections on an image plane the motion model consists of a set of linear difference equations with parameters estimated recursively from a nonlinear observation equation the model dimensionality corresponds to that of the original nonprojected motion space thus allowing to compensate for variable projection characteristics such as paning and zooming of the camera extended recursive least squares and linear quadratic tracking algorithms are used to adaptively adjust the model parameters and minimize the errors of either smoothing filtering or prediction of the object trajectories in the projection plane both algorithms are derived using a second order approximation of the projection nonlinearities all the results presented here use a generalized vectorial notation suitable for motion estimation of any finite number of object features and various approximations of the nonlinear projection the application of the model based motion estimator for temporal decimation interpolation in digital video sequence compression systems is presented

convexity classification and risk bounds many of the classification algorithms developed in the machine learning literature including the support vector machine and boosting can be viewed as minimum contrast methods that minimize a convex surrogate of the 0 1 loss function the convexity makes these algorithms computationally efficient the use of a surrogate however has statistical consequences that must be balanced against the computational virtues of convexity to study these issues we provide a general quantitative relationship between the risk as assessed using the 0 1 loss and the risk as assessed using any nonnegative surrogate loss function we show that this relationship gives nontrivial upper bounds on excess risk under the weakest possible condition on the loss function that it satisfies a pointwise form of fisher consistency for classification the relationship is based on a simple variational transformation of the loss function that is easy to compute in many applications we also present a refined version of this result in the

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

motion tracking as a constrained optimization problem in this paper we pose the problem of tracking of a varying number of points through an image sequence as a multi objective optimization problem with additional hard constraints one of the objectives is to find smooth tracks based on second order motion characteristics optimized over several frames the corresponding optimization algorithm we present is a sequential heuristic search algorithm that adequately prunes the search tree in such a way that its exponential order remains low when the algorithm is compared to other tracking algorithms it turns out that the proposed algorithm is easier to tune and generally more efficient and more accurate

a realization theory for perspective systems with applications to parameter estimation problems in machine vision in this paper we introduce and study a linear dynamical system with a perspective observation function the study of these systems has been shown to be useful in motion and shape estimation problems in machine vision we introduce the notion of perspective observability and obtain under a special case a necessary and sufficient condition that would guarantee observability of the initial condition of the linear dynamical system up to a one parameter magnitude scaling subsequently a new realization theory is introduced which is useful for studying linear systems with perspective observation our main result is to show that parameters can be recovered up to orbits of a suitable perspective group a new rescaling algorithm is described to identify parameters up to orbits of the perspective system the identification problem is further analyzed in detail for various problems that are of interest in machine vision

a diffusion mechanism for obstacle detection from size change information a mechanism fur the visual detection of obstacles is presented a new immediacy measure representing the imminence of collision between an object and a moving observer is defined a diffusion process on the image domain whose initial condition is determined by the motion field normal to the object s boundary is shown to converge asymptotically to the immediacy measure a network of locally connected cells derived from a finite difference approximation of the diffusion equation estimates the immediacy measure from normal velocity and boundary information provided by a motion measurement and segmentation stage the algorithm s performance on real image sequences is demonstrated

kernel type estimators for the extreme value index a large part of the theory of extreme value index estimation is developed for positive extreme value indices the best known estimator of a positive extreme value index is probably the hill estimator this estimator belongs to the category of moment estimators but can also be interpreted as a quasi maximum likelihood estimator it has been generalized to a kernel type estimator but this kernel type estimator can similarly to the hill estimator only be used for the estimation of positive extreme value indices in the present paper we introduce kernel type estimators which can be used for estimating the extreme value index over the whole positive and negative range we present a number of results on their distributional behavior and compare their performance with the performance of other estimators such as moment type estimators for the whole range and the quasi maximum likelihood estimator based on the generalized pareto distribution we also discuss an automatic bandwidth selection method and introduce a kernel estimator for a second order parameter controlling the speed of convergence

on some simple estimates of an exponent of regular variation summary we present a class of simple estimates of an exponent of regular variation unlike those proposed recently by de haan and resnick 1980 ours converge at an algebraic rather than a logarithmic rate and unlike those considered by teugels 1980 their form does not depend on the unknown exponent

optimal rates of convergence for estimates of the extreme value index hall and welsh established the best attainable rate of convergence for estimates of a positive extreme value index y under a certain second order condition implying that the distribution function of the maximum of n random variables converges at an algebraic rate to the pertaining extreme value distribution as a first generalization we obtain a surprisingly sharp bound on the estimation error if y is still assumed to be positive but the rate of convergence of the maximum may be nonalgebraic this result allows a more accurate evaluation of the asymptotic performance of an estimator for y than the hall and welsh theorem for example it is proved that the hill and the pickands estimators achieve the optimal rate but only the hill estimator attains the sharp bound finally an analogous result is derived for a general not necessarily positive extreme value index in this situation it turns out that location invariant estimators show the best performance 1 introduction consider n i i d random variables r v s whose distribution function d f f belongs to the weak domain of attraction of an extreme value d f

vehicle type motion estimation from multi frame images a model for vehicle type motion which assumes that the motion is a rotation around an axis through the vehicle center followed by a forward translation along the main axis of the vehicle is proposed when the rotation and the amplitude of translation are constant this type of motion is shown to be equivalent to a constant camera centered motion this indicates that a constant motion in the conventional camera centered model which is commonly considered to be artificial can in fact be a reasonable model in real life it is shown that a constant vehicle type motion can be interpreted as a constant screw motion a linear algorithm for estimating constant vehicle type motion is presented and experiments using real scene images are included as an extension vehicle type motion with constant rotation and constantly accelerated translation is discussed

multiple rank multi linear svm for matrix data classification matrices or more generally multi way arrays tensors are common forms of data that are encountered in a wide range of real applications how to classify this kind of data is an important research topic for both pattern recognition and machine learning in this paper by analyzing the relationship between two famous traditional classification approaches i e svm and stm a novel tensor based method i e multiple rank multi linear svm mrmlsvm is proposed different from traditional vector based and tensor based methods multiple rank left and right projecting vectors are employed to construct decision boundary and establish margin function we reveal that the rank of transformation can be regarded as a tradeoff parameter to balance the capacity of learning and generalization in essence we also proposed an effective approach to solve the proposed non convex optimization problem the convergence behavior initialization computational complexity and parameter determination problems are analyzed compared with vector based classification methods mrmlsvm achieves higher accuracy and has lower computational complexity compared with traditional supervised tensor based methods mrmlsvm performs better for matrix data classification promising experimental results on various kinds of data sets are provided to show the effectiveness of our method highlightswe have proposed a novel method i e mrmlsvm for matrix data classification we have revealed the essence of mrmlsvm from the view of learning theory we have provided an effective way to solve the proposed non convex problem our proposed approach is a common model and mrmlsvm is just an instance

on the algorithmic implementation of multiclass kernel based vector machines in this paper we describe the algorithmic implementation of multiclass kernel based vector machines our starting point is a generalized notion of the margin to multiclass problems using this notion we cast multiclass categorization problems as a constrained optimization problem with a quadratic objective function unlike most of previous approaches which typically decompose a multiclass problem into multiple independent binary classification tasks our notion of margin yields a direct method for training multiclass predictors by using the dual of the optimization problem we are able to incorporate kernels with a compact set of constraints and decompose the dual problem into multiple optimization problems of reduced size we describe an efficient fixed point algorithm for solving the reduced optimization problems and prove its convergence we then discuss technical details that yield significant running time improvements for large datasets finally we describe various experiments with our approach comparing it to previously studied kernel based methods our experiments indicate that for multiclass problems we attain state of the art accuracy

rigidity checking of 3d point correspondences under perspective projection an algorithm is described which rapidly verifies the potential rigidity of three dimensional point correspondences from a pair of two dimensional views under perspective projection the output of the algorithm is a simple yes or no answer to the question could these corresponding points from two views be the projection of a rigid configuration potential applications include 3d object recognition from a single previous view and correspondence matching for stereo or motion over widely separated views the rigidity checking problem is different from the structure from motion problem because it is often the case that two views cannot provide an accurate structure from motion estimate due to ambiguity and ill conditioning whereas it is still possible to give an accurate yes no answer to the rigidity question rigidity checking verifies point correspondences using 3d recovery equations as a matching condition the proposed algorithm improves upon other methods that fall under this approach because it works with as few as six corresponding points under full perspective projection handles correspondences from widely separated views makes full use of the disparity of the correspondences and is integrated with a linear algorithm for 3d recovery due to kontsevich 1993 results are given for experiments with synthetic and real image data a complete implementation of this algorithm is being made publicly available

paraperspective affine it is shown that the set of all paraperspective images with arbitrary reference point and the set of affine images of a 3 d object are identical consequently all uncalibrated paraperspective images of an object can be constructed from a 3 d model of the object by applying an affine transformation to the model and every affine image of the object represents some uncalibrated paraperspective image of the object it follows that the paraperspective images of an object can be expressed as linear combinations of any two non degenerate images of the object when the image position of the reference point is given the parameters of the affine transformation and likewise the coefficients of the linear combinations satisfy two quadratic constraints conversely when the values of parameters are given the image position of the reference point is determined by solving a bi quadratic equation

estimating three dimensional motion parameters of a rigid planar patch we present a new direct method of estimating the three dimensional motion parameters of a rigid planar patch from two time sequential perspective views image frames first a set of eight pure parameters are defined these parameters can be determined uniquely from the two given image frames by solving a set of linear equations then the actual motion parameters are determined from these pure parameters by a method which requires the solution of a sixth order polynomial of one variable only and there exists a certain efficient algorithm for solving a sixth order polynomial aside from a scale factor for the translation parameters the number of real solutions never exceeds two in the special case of three dimensional translation the motion parameters can be expressed directly as some simple functions of the eight pure parameters thus only a few arithmetic operations are needed

a correlation relaxation labeling framework for computing optical flow template matching from a new perspective optical flow estimation is discussed based on a model for time varying images more general than that implied by horn and schunk 1981 the emphasis is on applications where low contrast imagery nonrigid or evolving object patterns movement as well as large interframe displacements are encountered template matching is identified as having advantages over point correspondence and the gradient based approach in dealing with such applications the two fundamental uncertainties in feature matching whether template matching or feature point correspondences are discussed correlation template matching procedures are established based on likelihood measurement a method for determining optical flow is developed by combining template matching and relaxation labeling a number of candidate displacements for each template and their respective likelihood measures are determined then relaxation labeling is employed to iteratively update each candidate s likelihood by requiring smoothness within a motion field real cloud images from satellites are used to test the method

retargeted least squares regression algorithm this brief presents a framework of retargeted least squares regression relsr for multicategory classification the core idea is to directly learn the regression targets from data other than using the traditional zero one matrix as regression targets the learned target matrix can guarantee a large margin constraint for the requirement of correct classification for each data point compared with the traditional least squares regression lsr and a recently proposed discriminative lsr models relsr is much more accurate in measuring the classification error of the regression model furthermore relsr is a single and compact model hence there is no need to train two class binary machines that are independent of each other the convex optimization problem of relsr is solved elegantly and efficiently with an alternating procedure including regression and retargeting as substeps the experimental evaluation over a range of databases identifies the validity of our method

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

epipolar line estimation and rectification for stereo image pairs the assumption that epipolar lines are parallel to image scan lines is made in many algorithms for stereo analysis if valid it enables the search for corresponding image features to be confined to one dimension and hence simplified an algorithm that generates a vertically aligned stereo pair by warped resampling is described the method uses grey scale image matching between the components of the stereo pair but confined to feature points

groupwise retargeted least squares regression in this brief we propose a new groupwise retargeted least squares regression grelsr model for multicategory classification the main motivation behind grelsr is to utilize an additional regularization to restrict the translation values of relsr so that they should be similar within same class by analyzing the regression targets of relsr we propose a new formulation of relsr where the translation values are expressed explicitly on the basis of the new formulation discriminative least squares regression can be regarded as a special case of relsr with zero translation values moreover a groupwise constraint is added to relsr to form the new grelsr model extensive experiments on various machine leaning data sets illustrate that our method outperforms the current state of the art approaches

acquiring linear subspaces for face recognition under variable lighting previous work has demonstrated that the image variation of many objects human faces in particular under variable lighting can be effectively modeled by low dimensional linear spaces even when there are multiple light sources and shadowing basis images spanning this space are usually obtained in one of three ways a large set of images of the object under different lighting conditions is acquired and principal component analysis pca is used to estimate a subspace alternatively synthetic images are rendered from a 3d model perhaps reconstructed from images under point sources and again pca is used to estimate a subspace finally images rendered from a 3d model under diffuse lighting based on spherical harmonics are directly used as basis images in this paper we show how to arrange physical lighting so that the acquired images of each object can be directly used as the basis vectors of a low dimensional linear space and that this subspace is close to those acquired by the other methods more specifically there exist configurations of k point light source directions with k typically ranging from 5 to 9 such that by taking k images of an object under these single sources the resulting subspace is an effective representation for recognition under a wide range of lighting conditions since the subspace is generated directly from real images potentially complex and or brittle intermediate steps such as 3d reconstruction can be completely avoided nor is it necessary to acquire large numbers of training images or to physically construct complex diffuse harmonic light fields we validate the use of subspaces constructed in this fashion within the context of face recognition

estimating tails of probability distributions we study the asymptotic properties of estimators of the tail of a distribution based on the excesses over a threshold a key idea is the use of pickands generalised pareto distribution and its fitting in most cases by the method of maximum likelihood the results cover all three limiting types of extreme value theory we propose a new estimator for an index of regular variation and show that it often performs better than hill s estimator we give new results for estimating the endpoint of a distribution extending earlier work by hall and by smith and weissman finally we give detailed results for the domain of attraction of exp e x and show that in most cases our proposed estimator is more efficient than two others one based on the exponential distribution and the other due to davis and resnick we also touch briefly on the problem of large deviations from a statistical point of view the results make extensive use of existing work on rates of convergence

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

msdlsr margin scalable discriminative least squares regression for multicategory classification in this brief we propose a new margin scalable discriminative least squares regression msdlsr model for multicategory classification the main motivation behind the msdlsr is to explicitly control the margin of dlsr model we first prove that the dlsr is a relaxation of the traditional l 2 support vector machine based on this fact we further provide a theorem on the margin of dlsr with this theorem we add an explicit constraint on dlsr to restrict the number of zeros of dragging values so as to control the margin of dlsr the new model is called msdlsr theoretically we analyze the determination of the margin and support vectors of msdlsr extensive experiments illustrate that our method outperforms the current state of the art approaches on various machine leaning and real world data sets

direct passive navigation in this correspondence we show how to recover the motion of an observer relative to a planar surface from image brightness derivatives we do not compute the optical flow as an intermediate step only the spatial and temporal brightness gradients at a minimum of eight points we first present two iterative schemes for solving nine nonlinear equations in terms of the motion and surface parameters that are derived from a least squares fomulation an initial pass over the relevant image region is used to accumulate a number of moments of the image brightness derivatives all of the quantities used in the iteration are efficiently computed from these totals without the need to refer back to the image we then show that either of two possible solutions can be obtained in closed form we first solve a linear matrix equation for the elements of a 3 3 matrix the eigenvalue decomposition of the symmetric part of the matrix is then used to compute the motion parameters and the plane orientation a new compact notation allows us to show easily that there are at most two planar solutions

finding the motion position and orientation of a planar patch in 3d space from scaled orthographic projection abstract for the time being many methods about how to solve the motion and structure of a rigid object in 3d space by using point or line correspondences have been widely researched in this paper the projected 2d image shapes of planar patches in 3d space are used as our basic image features we try to determine the motion parameters and plane equations of planar patches in 3d space from the relationships among their observed image shapes besides scaled orthographic projection is used instead of the original perspective projection because of its simpler and tractable mathematical formulas not only a closely approximate model to perspective projection it further solves the inherent depth indeterminacy which exists in orthographic projection moreover after applying a pre processing of rotation correction to the original image data our estimation result can achieve a better numerical solution than that without this pre processing simulation experiments show the excellence of our algorithms in estimating the motion parameters ambiguities indeterminacy and data degeneracy are also carefully discussed in this paper which provides some important insights to the problems

identification of riccati dynamics under perspective and orthographic observations the problem of identifying motion and shape parameters of a planar object undergoing a riccati motion from the associated optical flow generated on the image plane of a single ccd camera is studied the optical flow is generated by projecting feature points on the object onto the image plane via perspective and orthographic projections an important result we show is that under perspective projection the parameters of a specific riccati dynamics that extend the well known rigid motion can be identified up to choice of a sign the paper also discusses other riccati equations obtained from quadratic extension of a rigid motion and affine motion for each of the various motion models considered and for each of the two projection models we show that the extent to which motion and shape parameters can be recovered from optical flow can in fact be recovered from the linear approximation of the optical flow we also extend our analysis to a pair of cameras

what can be seen in a noisy optical flow field projected by a moving planar patch in 3d space abstract in this paper we would like to propose a brand new interpretation to the so called structure from motion sfm problem the optical flow field projected by a moving rigid planar patch in 3d space is our main consideration instead of just obtaining an explicit 3d motion pose solution like the old approaches did before we focus our attention on analyzing its error sensitivity uncertainty and ambiguity from another point of view our new method can handle the above error analysis easily as known well before the optical flow field projected by a 3d moving planar patch can be completely expressed by eight coefficients two for second order four for first order and two for zeroth order based on these flow coefficients easily determined by a linear regression method or other similar approaches the error sensitivity of 3d estimates can be analyzed quantitatively and qualitatively in a coarse to fine way the concepts of camera fixation and singular value decomposition svd play important roles in our analysis there are three goals for our experiments 1 to prove the correctness of the algorithms simulated image 2 to show the tendency of error sensitivity when the 3d poses of the target planar patch are varied in a controlled manner simulated image 3 to show that our analysis is workable in the real world application real world image

rigid body segmentation and shape description from dense optical flow under weak perspective we present an algorithm for identifying and tracking independently moving rigid objects from optical flow some previous attempts at segmentation via optical flow have focused on finding discontinuities in the flow field while discontinuities do indicate a change in scene depth they do not in general signal a boundary between two separate objects the proposed method uses the fact that each independently moving object has a unique epipolar constraint associated with its motion thus motion discontinuities based on self occlusion can be distinguished from those due to separate objects the use of epipolar geometry allows for the determination of individual motion parameters for each object as well as the recovery of relative depth for each point on the object the algorithm assumes an affine camera where perspective effects are limited to changes in overall scale no camera calibration parameters are required a kalman filter based approach is used for tracking motion parameters with time

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

statistics of extremes by oracle estimation we use the fitted pareto law to construct an accompanying approximation of the excess distribution function a selection rule of the location of the excess distribution function is proposed based on a stagewise lack of fit testing procedure our main result is an oracle type inequality for the kullback leibler loss

a review on egomotion by means of differential epipolar geometry applied to the movement of a mobile robot the estimation of camera egomotion is an old problem in computer vision since the 1980s many approaches based on both the discrete and the differential epipolar constraint have been proposed the discrete case is used mainly in self calibrated stereoscopic systems whereas the differential case deals with a single moving camera this article surveys several methods for 3d motion estimation unifying the mathematics convention which are then adapted to the common case of a mobile robot moving on a plane experimental results are given on synthetic data covering more than 0 5 million estimations these surveyed algorithms have been programmed and are available on the internet

geometrizing rates of convergence ii consider estimating a functional t f of an unknown distribution f in mathbf f from data x 1 cdots x n i i d f let omega varepsilon denote the modulus of continuity of the functional t over mathbf f computed with respect to hellinger distance for well behaved loss functions l t we show that inf t n sup mathbf f e fl t n t f is equivalent to l omega n 1 2 to within constants whenever t is linear and mathbf f is convex the same conclusion holds in three nonlinear cases estimating the rate of decay of a density estimating the mode and robust nonparametric regression we study the difficulty of testing between the composite infinite dimensional hypotheses h 0 t f leq t and h 1 t f geq t delta our results hold in the cases studied because the difficulty of the full infinite dimensional composite testing problem is comparable to the difficulty of the hardest simple two point testing subproblem

interpretation of conic motion and its applications the indeterminacy of conic motion is analyzed in terms of lie group theory it is shown that an image motion of a conic is associated with a group ofinvisible motions that do not cause a visible change of the conic all such groups are isomorphic to the group associated with a special conic called thestandard circle for which the group of invisible motions is the three dimensional lorentz group similar results are obtained forinvisible optical flows finally our analysis is extended toconic stereo the 3 d position and orientation of a conic in the scene are computed from two projections this algorithm also works with one camera if a circular pattern is projected from a light source

direct computation of qualitative 3 d shape and motion invariants structure from motion often refers to the computation of three dimensional structure from a matched sequence of images however a depth map of a surface is difficult to compute and may not be a good representation for storage and recognition given matched images it is shown that the sign of the normal curvature in a given direction at a given point in the image can be computed from a simple difference of slopes of line segments in one image using this result local surface patches can be classified as convex concave cylindrical hyperbolic saddle point or planar at the same time the translational component of the optical flow from which the focus of expansion can be computed is obtained

establishing motion correspondence using extended temporal scope this paper addresses the motion correspondence problem the problem of finding corresponding point measurements in an image sequence solely based on positional information the motion correspondence problem is most difficult when the target points are densely moving it becomes even harder when the point detection scheme is imperfect or when points are temporarily occluded available motion constraints should be exploited in order to rule out physically impossible assignments of measurements to point tracks the performance can be further increased by deferring the correspondence decisions that is by examining whether the consequences of candidate correspondences lead to alternate and better solutions in this paper we concentrate on the latter by introducing a scheme that extends the temporal scope over which the correspondences are optimized the consequent problem we are faced with is a multi dimensional assignment problem which is known to be np hard to restrict the consequent increase in computation time the candidate solutions are suitably ordered and then additional combined motion constraints are imposed experiments show the appropriateness of the proposed extension both with respect to performance as well as computational aspects