feature matching in stereo images encouraging uniform spatial distribution finding feature correspondences between a pair of stereo images is a key step in computer vision for 3d reconstruction and object recognition in practice a larger number of correct correspondences and a higher percentage of correct matches are beneficial previous researches show that the spatial distribution of correspondences are also very important especially for fundamental matrix estimation so far no existing feature matching method considers the spatial distribution of correspondences in our research we develop a new algorithm to find good correspondences in all the three aspects mentioned i e larger number of correspondences higher percentage of correct correspondences and better spatial distribution of correspondences our method consists of two processes an adaptive disparity smoothing filter to remove false correspondences based on the disparities of neighboring correspondences and a matching exploration algorithm to find more correspondences according to the spatial distribution of correspondences so that the correspondences are as uniformly distributed as possible in the images to find correspondences correctly and efficiently we incorporate the cheirality constraint under an epipole polar transformation together with the epipolar constraint to predict the potential location of matching point experiments demonstrate that our method performs very well on both the number of correct correspondences and the percentage of correct correspondences and the obtained correspondences are also well distributed over the image space highlightswe propose a feature matching method incorporating epipolar geometry estimation uniformly distributed correspondences improve epipolar geometry estimation we propose an adaptive weighted median filter for removing false correspondences good results are obtained on both epipolar geometry estimation and correspondences

oscillatory and asymptotic behavior of certain functional differential equations some new criteria for the oscillatory and asymptotic behavior of odd order functional equations of the form x n t p t x n 1 t q t f x g t are established

mosaicing on adaptive manifolds image mosaicing is commonly used to increase the visual field of view by pasting together many images or video frames existing mosaicing methods are based on projecting all images onto a predetermined single manifold a plane is commonly used for a camera translating sideways a cylinder is used for a panning camera and a sphere is used for a camera which is both panning and tilting while different mosaicing methods should therefore be used for different types of camera motion more general types of camera motion such as forward motion are practically impossible for traditional mosaicing a new methodology to allow image mosaicing in more general cases of camera motion is presented mosaicing is performed by projecting thin strips from the images onto manifolds which are adapted to the camera motion while the limitations of existing mosaicing techniques are a result of using predetermined manifolds the use of more general manifolds overcomes these limitations

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

self calibration under the cayley framework the cayley framework here is meant to tackle the vision problems under the infinite cayley transformation ict its main advantage lies in its numerical stability in this work the stratified self calibration under the cayley framework is investigated it is well known that the main difficulty of the stratified self calibration in multiple view geometry is to upgrade a projective reconstruction to an affine one in other words to estimate the unknown 3 vector of the plane at infinity called the normal vector to our knowledge without any prior knowledge about the scene or the camera motion the only available constraint on a moving camera with constant intrinsic parameters is the well known modulus constraint in the literature do other kinds of constraints exist if yes what they are how could they be used in this work such questions will be systematically investigated under the cayley framework our key contributions include 1 the original projective expression of the ict is simplified and a new projective expression is derived to make the upgrade easier from a projective reconstruction to a metric reconstruction 2 the constraints on the normal vector are systematically investigated for two views two constraints on the normal vector are derived one of them is the well known modulus constraint while the other is a new inequality constraint there are only these two constraints for two views for three views besides the constraints for two views two groups of new constraints are derived and each of them contains three constraints in other words there are 12 constraints in total for three views 3 based on our projective expression and these constraints a stratified cayley algorithm and a total cayley algorithm are proposed for the metric reconstruction from images it is experimentally shown that they both improve significantly the numerical stability of the classical algorithms compared with the global optimal algorithm under the infinite homography framework the cayley algorithms have comparable calibration accuracy but substantially reduce the computational load

weak convergence for random weighting estimation of smoothed quantile processes this paper presents a new random weighting method for smoothed quantile processes a theory is established for random weighting estimation of smoothed quantile processes it proves the weak convergence of the random weighting estimation error experiments and comparison analysis demonstrate that the proposed random weighting method can effectively estimate statistics and the achieved accuracy and convergence speed are much higher than those of the bootstrap method

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

on the oscillation of certain functional differential equations via comparison methods abstract several new criteria for the oscillation of the functional differential equations of the form d dt 1 a n 1 t d dt 1 a n 2 t d dt 1 a 1 t d dt x t q t f x g t 0 are established in this paper

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

growth in gaussian elimination for weighing matrices w n n 1 abstract we consider the values for large minors of a skew hadamard matrix or conference matrix w of order n and find that maximum n n minor equals to n 1 n 2 maximum n 1 n 1 minor equals to n 1 n 2 1 maximum n 2 n 2 minor equals to 2 n 1 n 2 2 and maximum n 3 n 3 minor equals to 4 n 1 n 2 3 this leads us to conjecture that the growth factor for gaussian elimination ge of completely pivoted cp skew hadamard or conference matrices and indeed any cp weighing matrix of order n and weight n 1 is n 1 and that the first and last few pivots are 1 2 2 3 or 4 n 1 or n 1 2 n 1 2 n 1 for n 14 we show the unique w 6 5 has a single pivot pattern and the unique w 8 7 has at least two pivot structures we give two pivot patterns for the unique w 10 9

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

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

oscillation theorems for certain functional differential equations abstract some new criteria for the oscillation of functional differential equations with a middle term of the form x n t p t x n 1 t h h t x g t are presented

stereo using monocular cues within the tensor voting framework we address the fundamental problem of matching in two static images the remaining challenges are related to occlusion and lack of texture our approach addresses these difficulties within a perceptual organization framework considering both binocular and monocular cues initially matching candidates for all pixels are generated by a combination of matching techniques the matching candidates are then embedded in disparity space where perceptual organization takes place in 3d neighborhoods and thus does not suffer from problems associated with scanline or image neighborhoods the assumption is that correct matches produce salient coherent surfaces while wrong ones do not matching candidates that are consistent with the surfaces are kept and grouped into smooth layers thus we achieve surface segmentation based on geometric and not photometric properties surface overextensions which are due to occlusion can be corrected by removing matches whose projections are not consistent in color with their neighbors of the same surface in both images finally the projections of the refined surfaces on both images are used to obtain disparity hypotheses for unmatched pixels the final disparities are selected after a second tensor voting stage during which information is propagated from more reliable pixels to less reliable ones we present results on widely used benchmark stereo pairs

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

a new feature extractor invariant to intensity rotation and scaling of color images this paper proposes a new method for extracting the invariant features of an image based on the concept of principal component analysis and a competitive learning algorithm the proposed algorithm can be applied to binary gray level or colored texture images with a size greater than 256x256 pixels in addition to translation scaling and rotation invariant extraction the extraction of a feature invariant to color intensity can be implemented by using this method in our experiment the proposed method shows the capability to differentiate images having the same shape but different colored textures the experimental results report the effectiveness of this technique and its performance as measured by recognition accuracy rate and computational time these results are also compared with those obtained by classical techniques

oscillatory and asymptotic behavior of delay differential equations with a nonlinear damping term in this paper we study the oscillatory and asymptotic behavior of the solutions of delay differential equations of the form x n t f t x t x t 0 n even by comparing with certain differential equations of the same or lower order whose behavior is known the obtained criteria can be applied to the delay differential equation x n t q t x t x t sign x t 0 n even where and are positive constants

an eigenvalue approach evaluating minors for weighing matrices w n n 1 abstract in the present paper we concentrate our study on the evaluation of minors for weighing matrices w n n 1 theoretical proofs concerning their minors up to the order of n 4 n 4 are derived introducing an eigenvalue approach a general theorem specifying the analytical form of any n l n l minor is developed an application to the growth problem for weighing matrices is given

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

theory and practice of projective rectification this paper gives a new method for image rectification the process of resampling pairs of stereo images taken from widely differing viewpoints in order to produce a pair of matched epipolar projections these are projections in which the epipolar lines run parallel with the x axis and consequently disparities between the images are in the x direction only the method is based on an examination of the fundamental matrix of longuet higgins which describes the epipolar geometry of the image pair the approach taken is consistent with that advocated by faugeras 1992 of avoiding camera calibration the paper uses methods of projective geometry to determine a pair of 2d projective transformations to be applied to the two images in order to match the epipolar lines the advantages include the simplicity of the 2d projective transformation which allows very fast resampling as well as subsequent simplification in the identification of matched points and scene reconstruction

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

on the growth problem for skew and symmetric conference matrices abstract koukouvinos et al c koukouvinos m mitrouli j seberry growth in gaussian elimination for weighing matrices w n n 1 linear algebra appl 306 2000 189 202 conjectured that the growth factor for gaussian elimination of any completely pivoted weighing matrix of order n and weight n 1 is n 1 and that the first and last few pivots are 1 2 2 3 or 4 n 1 or n 1 2 n 1 2 n 1 for n 14 in the present paper we study the growth problem for skew and symmetric conference matrices an algorithm for extending a k k matrix with elements 0 1 to a skew and symmetric conference matrix of order n is described by using this algorithm we show that the unique w 8 7 has two pivot structures we also prove that the unique w 10 9 has three pivot patterns

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

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

estimation of f matrix and image rectification by double quaternion fundamental matrix or f matrix is one of the most important and elemental tools in the field of computer vision in conventional methods for estimating the f matrix an eight point algorithm is adopted first an approximate f matrix is calculated by a linear solver using at least eight corresponding pairs since this linear optimization method excludes an essential property the rank 2 constraint a method based on a singular value decomposition svd is applied to impose the constraint this last step with svd however provides additional noise in the f matrix several methods introduce parameterizations taking into account the rank 2 constraint and optimized nonlinearly without svd in this paper we propose a novel parameterization for the nonlinear optimization which includes this constraint we adopt double quaternion dq and a scalar as the parameter set experimental results show that the nonlinear optimization with our parameterization is competitive with other parameterization methods moreover through the proposed parameterization we can obtain two transformations for the two input images these transformations lead to a novel method to estimate epipolar lines and to rectify the image pairs this rectification method can deal with any image pairs in the same manner whether the epipoles are inside or outside the images

stereo effect of image converted from planar research on planar to stereo image conversion has significant theoretical and practical implications for image processing in this paper we use a method which segments an image into sub blocks to perform this kind of conversion parameters such as random variables are used for conversion control we use two quantitative criteria cross entropy and root mean square error to evaluate the stereo effect furthermore the stereo effect that the random variables create is discussed the results of the experiment show that i when all random variables have the same distribution different values of these random variables only slightly affect the stereo effect and ii when different distributions are applied to the random variables the cross entropies or root mean square errors are slightly different which indicates different distributions have a small influence on the stereo effect generally we recommend normal distribution for better stereo effect in most cases

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

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

oscillation criteria for certain nth order differential equations with deviating arguments abstract oscillation criteria for nth order differential equations with deviating arguments of the form x n 1 t 1 x n 1 t f t x g t 0 n even are established where g c t0 r f c t0 r r and 0 is a constant

oscillations caused by several retarded and advanced arguments in this paper we study the oscillatory behavior of equations of the forms y t i 1npiy t i 0 and y t i 1npiy t i 0 where piand i i 1 2 n are positive constants we prove that each one of the following conditions 1 pi i1 e for some i i 1 2 n 2 i 1npi 1 e where min 1 2 n 3 i 1npi 1 n i 1n i 1 e or 4 1 n i 1n pi i 1 2 21 e implies that every solution of and oscillates a generalization in the case where the coefficientspi i 1 2 n are positive and continuous functions is also presented

applications of a direct algorithm for the rectification of uncalibrated images an algorithm for the rectification of uncalibrated images is presented and applied to a variety of cases the algorithm generates the rectifying transformations directly from the geometrical relationship between the images using any three correspondences in the images to define a reference plane a small set of correspondences is used to calculate an initial rectification additional correspondences are introduced semi automatically by correlating regions of the rectified images since the rectified images of surfaces in the reference plane have no relative distortion features can be matched very accurately by correlation allowing small changes in disparity to be detected in the 3 d reconstruction of an architectural scene differences in depth are resolved to about 0 001 of the distance from camera to subject

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

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

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

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

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

łukasiewicz transform and its application to compression and reconstruction of digital images we define the lukasiewicz transform as a residuated map and a homomorphism between semimodules over the semiring reducts of an mv algebra then we describe the lukasiewicz transform based ltb algorithm for image processing demonstrating its applicability

introducing quaternion multi valued neural networks with numerical examples abstract this paper introduces a new quaternion multi valued neural network architecture and demonstrates its potential with numerical examples of multi channel prediction and classification a variety of real valued learning structures have been introduced in prior literature an important example is the multilayer perceptron neural network which forms the underlying basis for modern deep learning architectures however in multidimensional information processing problems real valued learning structures perform suboptimally due to distortion of inter channel relationships a natural way to represent multidimensional data is using quaternions a four dimensional associative normed division algebra over the real numbers that allows for the multiplication and division of points in three dimensional space this paper introduces quaternion multi valued neural networks which perform nonlinear operations on the three dimensional phase of quaternion data points as shown with two numerical examples the proposed quaternion multi valued neural network outperforms existing learning structures particularly in cases where limited training data is available

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

oscillation of certain functional differential equations sufficient conditions are presented for all bounded solutions of the linear system of delay differential equations 1 m 1 frac d m y i t dt m sum limits j 1 n q ij y j t h jj 0 text m geqslant 1 i 1 2 n to be oscillatory where qije hjj 0 i j 1 2 n also we study the oscillatory behavior of all bounded solutions of the linear system of neutral differential equations 1 m 1 frac d m dt m y i t cy i t g sum limits j 1 n q ij y j t h 0 where c g and h are real constants and i 1 2 n

oscillation theorems for nth order delay differential equations abstract oscillation criteria are obtained for a class of functional differential equations including the generalized emden fowler equation x n q t x g t sgn x g t 0 0 as a special case the purpose of this paper is to extend and improve known fundamental oscillation criteria for superlinear sublinear and linear differential equations with retarded arguments

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

efficient stereoscopic ranging via stochastic sampling of match quality we present an efficient method that computes dense stereo correspondences by stochastically sampling match quality values nonexhaustive sampling facilitates the use of quality metrics that take unique values at noninteger disparities depth estimates are iteratively refined with a stochastic cooperative search by perturbing the estimates sampling match quality and reweighting and aggregating the perturbations the approach gains significant efficiencies when applied to video where initial estimates are seeded using information from the previous pair in a novel application of the z buffering algorithm this significantly reduces the number of search iterations required we present a quantitative accuracy evaluation wherein the proposed method outperforms a microcanonical annealing approach by barnard and a cooperative approach by zitnick and kanade while using fewer match quality evaluations than either the approach is shown to have more attractive memory usage and scaling than alternatives based on exhaustive sampling

oscillation of even order linear functional differential equations with deviating arguments of mixed type where n is even p 0 co r and g o 00 r are continuous p t 0 g t is nondecreasing and cm g t 03 by a proper solution of eq 1 we mean a function x tx 00 r which satisfies 1 for all sufficiently large t and sup lx t j t t 0 for any t tx we make the standing hypothesis that 1 does possess proper solutions a proper solution is called oscillatory if it has arbitrarily large zeros otherwise it is called nonoscillatory if x t is a nonoscillatory solution of l then there exist an even integer 1 e 0 2 n and a t tx such that

evaluation of minors associated to weighing matrices in the present paper we focus our research on calculating minors of weighing matrices of order n and weight n k denoted by w n n k we provide analytical determinant computations counting techniques for specifying the existence of certain submatrices inside a w n n k and an algorithm for computing the n j n j minors of a w n n k which is realized with the notion of symbolic manipulation these results are valid of general n the ideas presented in this work can be used as the fundamental basis on which the calculation of minors of other weighing matrices and in general of orthogonal matrices can be developed an application of the derived formulas to an interesting problem of numerical analysis the growth problem is also presented

on various eigen fuzzy sets and their application to image reconstruction in this study we formulate and solve a problem of image reconstruction using eigen fuzzy sets treating images as fuzzy relations we propose two algorithms of generating eigen fuzzy sets that are used in the reconstruction process the first one corresponds to a convex combination of eigen fuzzy set equations i e fuzzy relational equations involving convex combination of max min and min max compositions in the case of the first algorithm various eigen fuzzy sets can be generated by changing the parameter controlling the convex combination of the corresponding equations the second algorithm generates various eigen fuzzy sets with respect to the original fuzzy relation using a permutation matrix a thorough comparison of the proposed algorithms and a conventional algorithm which reconstructs an image using the greatest and smallest eigen fuzzy sets is presented as well in the experiments 10 000 artificial images of size 5x5 pixels the approximation error in the case of the first second algorithm is decreased to 68 2 97 9 of that of the conventional algorithm respectively furthermore through the experimentation using real images extracted from standard image database sidba it is confirmed that the approximation error of the first algorithm is decreased to 41 5 of that of the conventional one

the oscillation of higher order differential equations with deviating arguments in this paper some new criteria for the oscillation of higher order functional differential equations of the form lnx t f t x g t 0 n is even are established some of our results are obtained via comparing it with second order ordinary linear and first order delay differential equations the oscillation of this equation when n is odd is also considered then we shall use the obtained results to study the oscillatory behavior of the neutral functional differential equations of the form ln x t c t x t f t x g t 0 n is even and the damped functional differential equations of the type lnx t h t x g t ddtx h t 0 n is even the obtained results extend improve and correlate a number of existing criteria

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

determining the epipolar geometry and its uncertainty a review two images of a single scene object are related by the epipolar geometry which can be described by a 3 3 singular matrix called the essential matrix if images internal parameters are known or the fundamental matrix otherwise it captures all geometric information contained in two images and its determination is very important in many applications such as scene modeling and vehicle navigation this paper gives an introduction to the epipolar geometry and provides a complete review of the current techniques for estimating the fundamental matrix and its uncertainty a well founded measure is proposed to compare these techniques projective reconstruction is also reviewed the software which we have developed for this review is available on the internet

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

a new class of zernike moments for computer vision applications a modified direct method for the computation of the zernike moments is presented in this paper the presence of many factorial terms in the direct method for computing the zernike moments makes their computation process a very time consuming task although the computational power of the modern computers is impressively increasing the calculation of the factorial of a big number is still an inaccurate numerical procedure the main concept of the present paper is that by using stirling s approximation formula for the factorial and by applying some suitable mathematical properties a novel factorial free direct method can be developed the resulted moments are not equal to those computed by the original direct method but they are a sufficiently accurate approximation of them besides their variability does not affect their ability to describe uniquely and distinguish the objects they represent this is verified by pattern recognition simulation examples

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

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

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

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

motion from point matches multiple of solutions in this paper we study the multiplicity of solutions of the motion problem given n point matches between two frames how many solutions are there to the motion problem we show that the maximum number of solutions is 10 when 5 point matches are available this settles a question that has been around in the computer vision community for a while we follow two tracks we show that the two approaches are compatible and yield the same result we then describe a computer implementation of the second approach that uses maple a language for symbolic computation the program allows us to compute exactly the solutions for any configuration of 5 points some experiments are described

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