a theoretical framework for relaxation processes in pattern recognition application to robust nonparametric contour generalization while various approaches are suggested in the literature to describe and generalize relaxation processes concerning to several objectives the wider problem addressed here is to find the best suited relaxation process for a given assignment problem or better still to construct a task dependent relaxation process for this we develop a general framework for the theoretical foundations of relaxation processes in pattern recognition the resulting structure enables 1 a description of all known relaxation processes in general terms and 2 the design of task dependent relaxation processes we show that the well known standard relaxation formulas verify our approach referring to the common problem of generating a generalized description of a contour we demonstrate the applicability of the suggested generalization in detail important characteristics of the constructed task dependent relaxation process are 1 the independency of the segmentation from any parameters 2 the invariance to geometric transformations 3 the simplicity and 4 efficiency

a differential complex for poisson manifolds construction du complexe canonique d une variete de poisson homologie canonique des varietes symplectiques application a l homologie de hochschild des algebres non commutatives

relaxation by hopfield network in stereo image matching abstract this paper outlines a relaxation approach using the hopfield neural network for solving the global stereovision matching problem the primitives used are edge segments the similarity smoothness and uniqueness constraints are transformed into the form of an energy function whose minimum value corresponds to the best solution of the problem we combine two methods a optimization relaxation 1 and b relaxation merit 2 with the above three constraints mapped in an energy function the main contribution is made 1 by applying a learning strategy in the similarity constraint and 2 by introducing specific conditions to overcome the violation of the smoothness constraint and to avoid the serious problem arising from the required fixation of a disparity limit so we improve the stereovision matching process a better performance of the proposed method is illustrated with a comparative analysis against a classical relaxation method

analysis of quantization error in line based stereo matching abstract quantization error generated by the quantization process of an image is inherent in computer vision because especially in stereo vision the quantization error in 2d digital images results in position errors in a reconstructed 3d scene it is necessary to analyze stochastically quantization error in stereo vision in this paper an analysis of the probability density function pdf of quantization error in line based stereo matching is presented it is shown that the theoretical pdfs of quantization errors of the reconstructed 3d point positions in line based stereo matching show general forms compared to those of the conventional error analysis in pixel based stereo matching computer simulations are observed to support the theoretical pdfs

comutations underlying the measuremnt of visual motion abstract the organization of movement in a changing image provides a valuable source of information for analyzing the environment in terms of objects their motion in space and their three dimensional structure a description of this movement is not provided to our visual system directly however it must be inferred from the pattern of changing intensity that reaches the eye this paper examines the problem of motion measurement which we formulate as the computation of an instantaneous two dimensional velocity field initial motion measurements occur at the location of significant intensity changes as suggested by marr and ullman 1 these measurements provide only one component of velocity and must be integrated to compute the two dimensional velocity field a fundamental problem for this integration is that motion is not determined uniquely from the changing image an additional constraint of smoothness of the velocity field is formulated based on the physical assumption that surfaces are generally smooth allowing the computation of a unique solution a theoretical analysis of the conditions under which this computation yields the correct velocity field suggests that the solution is physically plausible empirical studies show the results to be consistent with human motion perception

poisson co homology of polynomial poisson algebras in dimension four sklyanin s case abstract in this paper we compute the poisson co homology of a polynomial poisson structure given by two casimir polynomial functions which define a complete intersection with an isolated singularity

fast and accurate computation of bessel functions with large complex order and argument abstract a fast and highly accurate computational scheme to compute a product of bessel functions with large complex order and argument is of utmost importance in some problems in physics involving cylindrical configurations since these products can occur in the kernel of multiple integrals and are subject to mutual cancellations speed and accuracy of their numerical computation are key moreover the order and argument can vary over a vast range of several orders of magnitude to deliver a high relative accuracy 10 11 over the entire range we use the integral representations of the bessel functions and introduce a deformation into steepest descent paths the numerical computation is accelerated by three orders of magnitude if these paths are replaced by well chosen piecewise linear segments while maintaining the set relative accuracy

twisted poincare duality between poisson homology and poisson cohomology abstract a version of the twisted poincare duality is proved between the poisson homology and cohomology of a polynomial poisson algebra with values in an arbitrary poisson module the duality is achieved by twisting the poisson module structure in a canonical way which is constructed from the modular derivation in the case that the poisson structure is unimodular the twisted poincare duality reduces to the poincare duality in usual sense the main result generalizes the work of launois and richard 8 for the quadratic poisson structures and zhu 25 for the linear poisson structures

some experiments in relaxation image matching using corner features abstract a relaxation method based on patterns of local features is used to find matches between pairs of images or subimages that differ in position or orientation a local operator is applied to the two images to detect two sets of corners c1 cm and d1 dn each of them characterized by position orientation contrast and sharpness of the angle for each pair ci dj a figure of merit is computed and a relaxation process is used to iteratively adjust these figures of merit based on the merits of other pairs in approximately corresponding positions after a few iterations of this process good matches pairs having much better merit than their next best choices are clustered yielding sets of transformation parameters shift vectors or rotation angles under which many corners correspond this method has yielded good results for tv images of objects such as tools and industrial parts as well as for aerial images of terrain

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

correlation coefficient based fast template matching through partial elimination partial computation elimination techniques are often used for fast template matching at a particular search location computations are prematurely terminated as soon as it is found that this location cannot compete with an already known best match location due to the nonmonotonic growth pattern of the correlation based similarity measures partial computation elimination techniques have been traditionally considered inapplicable to speed up these measures in this paper we show that partial elimination techniques may be applied to a correlation coefficient by using a monotonic formulation and we propose basic mode and extended mode partial correlation elimination algorithms for fast template matching the basic mode algorithm is more efficient on small template sizes whereas the extended mode is faster on medium and larger templates we also propose a strategy to decide which algorithm to use for a given data set to achieve a high speedup elimination algorithms require an initial guess of the peak correlation value we propose two initialization schemes including a coarse to fine scheme for larger templates and a two stage technique for small and medium sized templates our proposed algorithms are exact i e having exhaustive equivalent accuracy and are compared with the existing fast techniques using real image data sets on a wide variety of template sizes while the actual speedups are data dependent in most cases our proposed algorithms have been found to be significantly faster than the other algorithms

robust contour decomposition using a constant curvature criterion the problem of decomposing an extended boundary or contour into simple primitives is addressed with particular emphasis on laplacian of gaussian zero crossing contours a technique is introduced for partitioning such contours into constant curvature segments a nonlinear blip filter matched to the impairment signature of the curvature computation process an overlapped voting scheme and a sequential contiguous segment extraction mechanism are used this technique is insensitive to reasonable changes in algorithm parameters and robust to noise and minor viewpoint induced distortions in the contour shape such as those encountered between stereo image pairs the results vary smoothly with the data and local perturbations induce only local changes in the result robustness and insensitivity are experimentally verified

on an integral related to biaxially anisotropic media an integral arising in certain studies of theoretical electromagnetics is evaluated and its properties are discussed in some detail the integral has three integer two real and one complex parameter the integrand involves a product of bessel functions of different argument and order several generalizations are discussed

gerstenhaber algebras and bv algebras in poisson geometry the purpose of this paper is to establish an explicit correspondence between various geometric structures on a vector bundle with some well known algebraic structures such as gerstenhaber algebras and bv algebras some applications are discussed in particular we find an explicit connection between the koszul brylinski operator and the modular class of a poisson manifold as a consequence we prove that poisson homology is isomorphic to poisson cohomology for unimodular poisson structures

matching two perspective views a computational approach to image matching is described it uses multiple attributes associated with each image point to yield a generally overdetermined system of constraints taking into account possible structural discontinuities and occlusions in the algorithm implemented intensity edgeness and cornerness attributes are used in conjunction with the constraints arising from intraregional smoothness field continuity and discontinuity and occlusions to compute dense displacement fields and occlusion maps along the pixel grids the intensity edgeness and cornerness are invariant under rigid motion in the image plane in order to cope with large disparities a multiresolution multigrid structure is employed coarser level edgeness and cornerness measures are obtained by blurring the finer level measures the algorithm has been tested on real world scenes with depth discontinuities and occlusions a special case of two view matching is stereo matching where the motion between two images is known the algorithm can be easily specialized to perform stereo matching using the epipolar constraint

detection of intensity changes with subpixel accuracy using laplacian gaussian masks we present a system that takes a gray level image as input locates edges with subpixel accuracy and links them into lines edges are detected by finding zero crossings in the convolution of the image with laplacian of gaussian log masks the implementation differs markedly from m i t s as we decompose our masks exactly into a sum of two separable filters instead of the usual approximation by a difference of two gaussians dog subpixel accuracy is obtained through the use of the facet model 1 we also note that the zero crossings obtained from the full resolution image using a space constant for the gaussian and those obtained from the 1 n resolution image with 1 n pixel accuracy and a space constant of n for the gaussian are very similar but the processing times are very different finally these edges are grouped into lines using the technique described in 2

relaxation matching techniques a comparison many different relaxation schemes have been proposed for image analysis tasks we have developed a general matching procedure for comparing semantic network descriptions of images and we have implemented a variety of relaxation techniques an automatic segmentation and description system is used to produce the image representations so that the matching procedures must cope with variations in feature values missing objects and possible multiple matches this environment is used to test different relaxation matching schemes under a variety of conditions the best performance of those we compared in terms of the number of iterations and the number of errors is for the gradient based optimization approach of faugeras and price the related optimization approach of hummel and zucker performed almost as well with differences primarily in difficult matches i e where much of the evidence is against the match for instance poor segmentations the product combination rule proposed by peleg was extremely fast indeed too fast to work when global context is needed the classical rosenfeld hummel and zucker method is included for historical comparisons and performed only adequately producing fewer correct matches and taking more iterations

poisson cohomology of the affine plane abstract we compute the poisson cohomology of homogeneous poisson structures on the plane the singular locus of such a poisson structure consists of a family of lines passing through o and we show how the dimensions of the first and second cohomology groups are related to the weight of o as a singular point of

optical flow with an intensity weighted smoothing matching algorithms which use image structure such as edges and junctions cannot perform well on unstructured images for such images global gradient based methods may be more appropriate some of the assumptions involved in applying discretized conservation equations such as the optical flow equation are discussed and an intensity weighted method of estimating dense displacement fields is presented which attempts to avoid some of the problems of the standard methods the only derivative required is the intensity gradient and the method includes procedures for automatic parameter evaluation the algorithm is expected to perform better than conventional algorithms on images without strong texture as is demonstrated on the test set of images

evaluation of the modified bessel function of the third kind of imaginary orders the evaluation of the modified bessel function of the third kind of purely imaginary order kia x is discussed we also present analogous results for the derivative the methods are based on the use of maclaurin series nonoscillatory integral representations asymptotic expansions and a continued fraction method depending on the ranges of x and a we discuss the range of applicability of the different approaches considered and conclude that power series the continued fraction method and the nonoscillatory integral representation can be used to accurately compute the function kia x in the range 0 a 200 0 x 100 using a similar scheme the derivative k ia x can also be computed within these ranges

poisson algebras in terms of non associative algebras poisson algebra is usually defined to be a commutative algebra together with a lie bracket and these operations are required to satisfy the leibniz rule we describe poisson structures in terms of a single bilinear operation this enables us to explore poisson algebras in the realm of non associative algebras we study their algebraic and cohomological properties their deformations as non associative algebras and settle the classification problem in low dimensions

on the foundations of relaxation labeling processes a large class of problems can be formulated in terms of the assignment of labels to objects frequently processes are needed which reduce ambiguity and noise and select the best label among several possible choices relaxation labeling processes are just such a class of algorithms they are based on the parallel use of local constraints between labels this paper develops a theory to characterize the goal of relaxation labeling the theory is founded on a definition of con sistency in labelings extending the notion of constraint satisfaction in certain restricted circumstances an explicit functional exists that can be maximized to guide the search for consistent labelings this functional is used to derive a new relaxation labeling operator when the restrictions are not satisfied the theory relies on variational cal culus it is shown that the problem of finding consistent labelings is equivalent to solving a variational inequality a procedure nearly identical to the relaxation operator derived under restricted circum stances serves in the more general setting further a local convergence result is established for this operator the standard relaxation labeling formulas are shown to approximate our new operator which leads us to conjecture that successful applications of the standard methods are explainable by the theory developed here observations about con vergence and generalizations to higher order compatibility relations are described

coulomb and bessel functions of complex arguments and order abstract the coulomb wavefunctions originally constructed for real 0 real and integer 0 are defined for and all complex we examine the complex continuation of a variety of series and continued fraction expansions for the coulomb functions and their logarithmic derivatives and then see how these expansions may be selectively combined to calculate both the regular and irregular functions and their derivatives the resulting algorithm 46 is a complex generalisation of steed s method 6 7 as it appears in the real procedure coulfg 10 complex whittaker confluent hypergeometric and bessel functions can also be calculated

surfaces from stereo integrating feature matching disparity estimation and contour detection an approach is described that integrates the processes of feature matching contour detection and surface interpolation to determine the three dimensional distance or depth of objects from a stereo pair of images integration is necessary to ensure that the detected surfaces are smooth surface interpolation takes into account detected occluding and ridge contours in the scene interpolation is performed within regions enclosed by these contours planar and quadratic patches are used as local models of the surface occluded regions in the image are identified and are not used for matching and interpolation a coarse to fine algorithm is presented that generates a multiresolution hierarchy of surface maps one at each level of resolution experimental results are given for a variety of stereo images

poisson co homology and isolated singularities abstract to each polynomial f x y z is associated a poisson structure on f 3 a surface and a poisson structure on this surface when is weight homogeneous with an isolated singularity we determine the poisson cohomology and homology of the two poisson varieties obtained

an investigation of smoothness constraints for the estimation of displacement vector fields from image sequences a mapping between one frame from an image sequence and the preceding or following frame can be represented as a displacement vector field in most situations the mere gray value variations do not provide sufficient information in order to estimate such a displacement vector field supplementary constraints are necessary for example the postulate that a displacement vector field varies smoothly as a function of the image position taken as a general requirement this creates difficulties at gray value transitions which correspond to occluding contours nagel therefore introduced the oriented smoothness requirement which restricts variations of the displacement vector field only in directions with small or no variation of gray values this contribution reports results of an investigation about how such an oriented smoothness constraint may be formulated and evaluated

lie poisson structure on some poisson lie groups poisson lie groups appeared in the work of drinfel d see e g drl dr2 as classical objects corresponding to quantum groups going in the other direction we may say that a poisson lie group is a group of symmetries of a phase space that are allowed to twist in a certain sense the symplectic or poisson structure the poisson structure on the group controls this twisting in a precise way quantizing both the phase space and the symmetries one may obtain a quantum group acting on a quantum phase space in recent work lu and ratiu lr used so called standard poisson structures on a compact semisimple lie group k and on its poisson dual k in order to give a new proof of the nonlinear convexity theorem of kostant ko their method is analogous to the famous symplectic proof of the linear convexity theorem given by atiyah a and guillemin and stemnberg gs the nonlinear convexity theorem like the linear one follows from a very general result on convexity of the image of the momentum map a gs however in lr it is applied not to a coadjoint orbit in t but to a symplectic leaf in k the main result of this paper is that the standard poisson structure on the poisson dual k to a compact semisimple poisson lie group k is actually isomorphic to the linear one on t this theorem seems to be related to some facts in the theory of quantum groups namely for generic q the universal enveloping algebra u t and its quantum deformation uq t are isomorphic as algebras though not as coalgebras of course since the quantum version is not cocommutative in particular there is a bijective correspondence between their representations a direct connection between our work and its quantum analogues though is still to be found the present work supplies a positive answer to question 5 1 in lr and strongly depends on that paper to simplify reading we keep the notations of lr wherever possible on one hand but give all necessary definitions on the other our work is also related to du in which the nonlinear convexity theorem is reduced to the linear one by a deformation argument not unlike the one that we use in 5 the paper is organized as follows in 2 we define poisson lie groups discuss

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

a computational framework and an algorithm for the measurement of visual the robust measurement of visual motion from digitized image sequences has been an important but difficult problem in computer vision this paper describes a hierarchical computational framework for the determination of dense displacement fields from a pair of images and an algorithm consist ent with that framework our framework is based on the separation of the image intensity information as well as the process of measuring motion according to scale the large scale intensity information is first used to obtain rough estimates of image motion which are then refined by using intensity information at smaller scales the estimates are in the form of displacement or velocity vectors for pixels and are accompanied by a direction dependent confidence measure a smoothness constraint is employed to propagate the measurements with high confidence to their neigboring areas where the confidences are low at all levels the computations are pixel parallel uniform across the image and based on information from a small neighborhood of a pixel for our algorithm the local displacement vectors are determind by mini mizing the sum of squared differences ssd of intensities the confidence measures are derived from the shape of the ssd surface and the smoothness constraint is cast in the form of energy minimization results of applying our algorithm to pairs of real images are included in addition to our own

determining optical flow optical flow cannot be computed locally since only one independent measurement is available from the image sequence at a point while the flow velocity has two components a second constraint is needed a method for finding the optical flow pattern is presented which assumes that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image an iterative implementation is shown which successfully computes the optical flow for a number of synthetic image sequences the algorithm is robust in that it can handle image sequences that are quantized rather coarsely in space and time it is also insensitive to quantization of brightness levels and additive noise examples are included where the assumption of smoothness is violated at singular points or along lines in the image

disparity maps for dynamic stereo abstract stereo matching algorithms often use regularization or relaxation methods to refine estimates of disparity in static images unfortunately the computational requirements of these iterative techniques often preclude their use in real time systems furthermore most real time stereo matching systems do not exploit the availability of a disparity map from the previous time step to compute the current disparity we propose two algorithms for correspondence determination in dynamic stereo image sequences using prior disparity maps to localize and to speed the search for matches the first method uses optical flow estimates in the stereo images to constrain the search space of feasible matchings the second method uses a heuristic search scheme to prune matching graphs without explicit feature tracking or optical flow computation both methods can be applied to existing matching algorithms to reduce their search space the resulting improvement in matching is demonstrated in sample images and is quantified through the mean square error of the computed disparity map compared to dense ground truth the proposed methods are shown to improve the matching speed decrease the latency of five different matching algorithms

bittracker a bitmap tracker for visual tracking under very general conditions this paper addresses the problem of visual tracking under very general conditions a possibly non rigid target whose appearance may drastically change over time general camera motion a 3d scene and no a priori information except initialization this is in contrast to the vast majority of trackers which rely on some limited model in which for example the target s appearance is known a priori or restricted the scene is planar or a pan tilt zoom camera is used their goal is to achieve speed and robustness but their limited context may cause them to fail in the more general case the proposed tracker works by approximating in each frame a pdf probability distribution function of the target s bitmap and then estimating the maximum a posteriori bitmap the pdf is marginalized over all possible motions per pixel thus avoiding the stage in which optical flow is determined this is an advantage over other general context trackers that do not use the motion cue at all or rely on the error prone calculation of optical flow using a gibbs distribution with respect to the first order neighborhood system yields a bitmap pdf whose maximization may be transformed into that of a quadratic pseudo boolean function the maximum of which is approximated via a reduction to a maximum flow problem many experiments were conducted to demonstrate that the tracker is able to track under the aforementioned general context

stereo correspondence using the hopfield neural network of a new energy function abstract this paper presents an approach using a hopfield neural network to the stereo correspondence problem for extracting the 3d structure of a scene the stereo correspondence problem can be defined in terms of finding a disparity map that satisfies three competing constraints similarity smoothness and uniqueness in order to solve the stereo correspondence problem using a hopfield neural network these constraints are transformed into the form of an energy function whose minimum value corresponds to the best solution of the problem on the hopfield network in the process of mapping the constraints into energy function the energy functions are derived so that the network ensures hopfield s convergence rule stereo correspondence then is carried out through the network evolving energy surface to find the minimum energy corresponding to the solution of the problem the examples for random dot stereograms and real images are shown in the experiment illustrating how the proposed network works

efficient registration of stereo images by matching graph descriptions of edge segments we present a new approach to the stereo matching problem images are individually described by aneighborhood graph of line segments coming from a polygonal approximation of the contours the matching process is defined as the exploration of the largest components of adisparity graph built from the descriptions of the two images and is performed by an efficient prediction and propagation technique this approach was tested on a variety of man made environments and it appears to be fast and robust enough for mobile robot navigation and three dimensional part positioning applications