relative index theorems and supersymmetric scattering theory we discuss supersymmetric scattering theory and employ krein s theory of spectral shift functions to investigate supersymmetric scattering systems this is the basis for the derivation of relative index theorems on some classes of open manifolds as an example we discuss the de rham complex for obstacles in n and asymptotically flat manifolds it is shown that the absolute or relative euler characteristic of an obstacle in n may be obtained from scattering data for the laplace operator on forms with absolute or relative boundary conditions respectively in the case of asymptotically flat manifolds we obtain the chern gauss bonnet theorem for thel2 euler characteristic

comments on exact error performance of square orthogonal space time block coding with channel estimation in a recent paper garg et al present an expression for the exact decoding error probability dep of square orthogonal space time block codes ostbcs with imperfect channel estimation we show that their dep expression is only asymptotically correct and point out how to obtain the exact result for arbitrary signal to noise ratio

pixelwise adaptive blind optical flow assuming nonstationary statistics we address some of the major issues in optical flow within a new framework assuming nonstationary statistics for the motion field and for the errors problems addressed include the preservation of discontinuities model data errors outliers confidence measures and performance evaluation in solving these problems we assume that the statistics of the motion field and the errors are not only spatially varying but also unknown we thus derive a blind adaptive technique based on generalized cross validation for estimating an independent regularization parameter for each pixel our formulation is pixelwise and combines existing first and second order constraints with a new second order temporal constraint we derive a new confidence measure for an adaptive rejection of erroneous and outlying motion vectors and compare our results to other techniques in the literature a new performance measure is also derived for estimating the signal to noise ratio for real sequences when the ground truth is unknown

computing correspondences in a sequence of non rigid shapes abstract image correspondences are computed using a new relaxation technique applied to edge features each image is represented by a network of nodes connected by branches the nodes represent the locations of corners or other conspicuous points on the contours of the image the branches may be real image contours or imaginary lines drawn to link the nodes nodes in one image are matched to nodes in the next image using a measure of the length and angular separation between connecting branches an iterative relaxation scheme searches for consistency in the structure and relative motion of neighboring branches and nodes and rewards the matching probability of each node accordingly around 15 20 iterations are needed for convergence the matching process favors structural rigidity on a local scale while allowing global image to image deformations to occur as in the case of fluid motion examples are given as evidence that the algorithm can match patterns undergoing distortion rotation and scaling

optical flow computation using extended constraints several approaches for optical flow estimation use partial differential equations to model changes in image brightness throughout time a commonly used equation is the so called optical flow constraint ofc which assumes that the image brightness is stationary with respect to time more recently a different constraint referred to as the extended optical flow constraint eofc has been introduced which also contains the divergence of the flow field of image brightness there is no agreement in the literature about which of these constraints provides the best estimation of the velocity field two new solutions for optical flow computation are proposed which are based on an approximation of the constraint equations the two techniques have been used with both eofc and ofc constraint equations results achieved by using these solutions have been compared with several well known computational methods for optical flow estimation in different motion conditions estimation errors have also been measured and compared for different types of motion

motion based grouping of optical flow fields the extrapolation and subtraction technique the goal of three dimensional 3 d motion segmentation is to identify the image areas projected by different moving objects in 3 d space however many prevailing methods merely detected the discontinuity of optical flow field and usually considered these boundaries as that produced by different 3 d motions in fact the flow discontinuity can be generated either by two different 3 d motions or by the structural discontinuity on the same moving object the wrong identification causes several problems in 3 d motion estimation a simple method called the extrapolation and subtraction es technique is proposed to solve these problems the input image flow field is first partitioned into several functionally analytic regions each analytic region is assumed to be projected by a roughly planar patch moving in 3 d space based on the parameterization of these analytic flow fields the es technique provides a very simple and fast method to test the 3 d motion compatibility between two interested analytic flow fields

high energy asymptotics of the magnetic spectral shift function we consider the three dimensional schrodinger operators h0 and h where h0 i a 2 b a is a magnetic potential generating a constant magnetic field of strength b 0 and h h0 v where v l1 r3 r satisfies certain regularity conditions then the spectral shift function e h h0 for the pair of operators h h0 is well defined for energies e 2qb q z we study the asymptotic behavior of e h h0 as e e or r 0 b where or e 0 dist e 2bz r we obtain a weyl type formula lime e ore 1 2 e h h0 1 4 2 r3v x dx

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

analysis and efficient evaluation of the ber of ostbcs with imperfect channel estimation in arbitrarily correlated fading channels an analysis of the exact bit error rate ber performance of orthogonal space time block codes ostbcs with maximum likelihood detection in the presence of channel estimation errors is presented the possibly correlated coefficients of the multiple input multiple output mimo propagation channel are assumed to be affected by flat block fading and the transmitted symbols belong to a pulse amplitude modulation or quadrature amplitude modulation signal constellation for both square and nonsquare ostbcs we derive approximate and exact ber expressions irrespective of the distribution of the fading it is also shown how the exact expressions can be efficiently and accurately evaluated using numerical integration techniques their application to the arbitrarily correlated nakagami m fading channel is presented and an efficient importance sampling technique is derived as the high diversity order resulting from the application of ostbcs gives rise to small ber values the numerical evaluation of the presented ber expressions is much faster than straightforward monte carlo simulations ber results have shown the impact of both imperfect channel estimation and antenna correlation on the performance of mimo ostbc systems it is also shown that under highly correlated conditions antenna correlation is the major source of ber degradation

motion estimation based on multiple local constraints and nonlinear smoothing abstract a new algorithm for estimating motion from image sequences is presented initial motion estimates are determined based on a least squares solution to a set of independent linear constraints on the motion at a pixel these initial estimates are then improved by a nonlinear smoothing operation the results of this algorithm are compared with those obtained by the horn schunck algorithm on a number of image sequences

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

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

on edge detection edge detection is the process that attempts to characterize the intensity changes in the image in terms of the physical processes that have originated them a critical intermediate goal of edge detection is the detection and characterization of significant intensity changes this paper discusses this part of the edge detection problem to characterize the types of intensity changes derivatives of different types and possibly different scales are needed thus we consider this part of edge detection as a problem in numerical differentiation we show that numerical differentiation of images is an ill posed problem in the sense of hadamard differentiation needs to be regularized by a regularizing filtering operation before differentiation this shows that this part of edge detection consists of two steps a filtering step and a differentiation step following this perspective the paper discusses in detail the following theoretical aspects of edge detection 1 the properties of different types of filters with minimal uncertainty with a bandpass spectrum and with limited support are derived minimal uncertainty filters optimize a tradeoff between computational efficiency and regularizing properties 2 relationships among several 2 d differential operators are established in particular we characterize the relation between the laplacian and the second directional derivative along the gradient zero crossings of the laplacian are not the only features computed in early vision 3 geometrical and topological properties of the zero crossings of differential operators are studied in terms of transversality and morse theory

exact behavior of jost functions at low energy for schrodinger operators with central potential q r and angular momentum l the behavior of the jost function fl k as k 0 is investigated it is assumed that 0dr 1 r q r where 1 situations where q is integrable with 1 2 but not with 2 are of particular interest for potentials satisfying q r q0r 2 e 0 e 1 and l 0 the leading behavior of f0 k and the phase shift 0 k as k 0 is derived also comments are made on the differentiability properties of the jost solutions with respect to the variable k at k 0 for 1 levinson s theorem is proved thereby clarifying some questions raised recently by newton j math phys 27 2720 1986

scattering theory for one dimensional systems with dx v x 0 abstract low energy scattering for schrodinger operators of the type h v in l2 r with rdx v x 0 is considered the possibility of zero energy eigenstates of h is taken into account explicitly in particular a laurent expansion for the transition operator and recursion relations for its coefficients are provided and the leading behaviour of the scattering operator is given in all possible cases

regularization of optical flow with m band wavelet transform abstract the optical flow is an important tool for problems arising in the analysis of image sequences flow fields generated by various existing solving techniques are often noisy and partially incorrect especially near occlusions or motion boundaries therefore the additional information on the scene gained from a sequence of images is usually worse in this paper discrete wavelet transform has been adopted in order to enhance the reliability of optical flow estimation a generalization of the well known dyadic orthonormal wavelets to the case of the dilation scale factor m 2 with n vanishing moments has been used and it has proved to be a useful regularizing tool the advantages in the computations have been shown by experimental results performed on real image sequences

exact error performance of square orthogonal space time block coding with channel estimation consider a wireless communication system in flat fading with n transmit and m receive antennas using space time block coding where n spl times 1 code vectors are transmitted over l symbol intervals resulting in an n spl times l code matrix a least squares estimate lse as well as a minimum mean square estimate mmse of the m spl times n channel matrix is obtained from a sequence of pilot code vectors for the case of linear square i e with n l orthogonal codes over constant envelope constellations we obtain an expression for the exact decoding error probability dep for coherent maximum likelihood decoding we also find the coding gain for high average signal to noise ratio snr per diversity branch in the case of rayleigh fading a comparison between both channel estimation techniques is done in terms of the average pilot power to signal power ratio appspr it is found that mmse requires lower pilot power than lse for the same dep and the same average snr per diversity branch in addition the error performance with lse approaches that with mmse with an increase of average snr per branch or an increase of appspr

potential scattering in constant magnetic field spectral asymptotics and levinson formula the scattering problem related to the schrodinger operator with an external constant homogeneous magnetic field is considered the behaviour of the corresponding s matrix and resolvent operator near the landau thresholds is studied the large energy asymptotics of the resolvent operator are evaluated a levinson type formula is obtained it relates the number of bound states to the determinant of the scattering matrix in the scattering threshold

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

estimation of optical flow based on higher order spatiotemporal derivatives in interlaced and non interlaced image sequences abstract this contribution 1 investigates local differential techniques for estimating optical flow and its derivatives based on the brightness change constraint by using the tensor calculus representation we build the taylor expansion of the gray value derivatives as well as of the optical flow in a spatiotemporal neighborhood such a formulation provides a unifying framework for all existing local differential approaches and allows to derive new systems of equations for the estimation of the optical flow and of its derivatives we also tested various optical flow estimation approaches on real image sequences recorded by a calibrated camera which was fixed on the arm of a robot by moving the arm of the robot along a precisely defined trajectory we can determine the true displacement rate of scene surface elements projected into the image plane and compare it quantitatively with the results of different optical flow estimators since the optical flow estimators are based on gray value derivatives of up to fourth order we were forced to develop modified gaussian derivative filters to obtain acceptable estimates for the derivatives further we show quantitatively that these filters contribute to a much more robust optical flow estimation in addition successive lines of tv cameras have an offset in time due to the interlace technique we demonstrate the adaptation of filter kernels for estimating higher order spatiotemporal derivatives in interlaced image sequences

experiments in computing optical flow with the gradient based multiconstraint method abstract in this paper we present results on experiments in computing optical flow with the multiconstraint approach this approach relies on the gradient equation which relates spatial and temporal changes in the image to optical flow and the use of various image functions the experiments reported here are performed on camera acquired pictures and use feature operators to derive image functions from the original luminance function results indicate that this approach is promising

the accuracy of the computation of optical flow and of the recovery of motion parameters the accuracy and the dependence on parameters of a general scheme for the analysis of time varying image sequences are discussed the approach is able to produce vector fields from which it is possible to recover 3 d motion parameters such as time to collision and angular velocity the numerical stability of the computed optical flow and the dependence of the recovery of 3 d motion parameters on spatial and temporal filtering is investigated by considering optical flows computed on subsampled images or along single scanlines it is also possible to recover 3 d motion parameters from reduced optical flows an adequate estimate of time to collision can be obtained from sequences of images with spatial resolution reduced to 128 128 pixels or from sequences of single scanlines passing near the focus of expansion the use of kalman filtering increases the accuracy and the robustness of the estimation of motion parameters the proposed approach seems to be able to provide not only a theoretical background but also practical tools that are adequate for the analysis of time varying image sequences

computation and analysis of image motion a synopsis of current problems and methods the goal of this paper is to offer a structured synopsis of the problems in image motion computation and analysis and of the methods proposed exposing the underlying models and supporting assumptions a sufficient number of pointers to the literature will be given concentrating mostly on recent contributions emphasis will be on the detection measurement and segmentation of image motion tracking and deformable motion issues will be also addressed finally a number of related questions which could require more investigations will be presented

two dimensional scattering the number of bound states from scattering data relations are found between scattering data and the spectrum for the two dimensional schrodinger operator v x where v is a local noncentral potential in particular a two dimensional version of the levinson theorem is obtained this theorem gives the number of bound states in terms of the change in phase of the determinant of the scattering operator

optical flow estimation and the interaction between measurement errors at adjacent pixel positions in order to estimate both components of optical flow as well as their first spatio temporal derivatives it is postulated that the optical flow constraint equation ofce is valid in a spatio temporal neighborhood of pixels so far it has been tacitly assumed that the partial derivatives of the gray value distribution which are required for this approach at the pixel positions involved are independent from each other it is shown how dropping this assumption affects the estimation procedure based on well established approaches of estimation theory the insight gained thereby is used to develop an approach towards merging image regions based on the compatibility of optical flow estimates obtained within the regions considered for merger

multimodal estimation of discontinuous optical flow using markov random fields the estimation of dense velocity fields from image sequences is basically an ill posed problem primarily because the data only partially constrain the solution it is rendered especially difficult by the presence of motion boundaries and occlusion regions which are not taken into account by standard regularization approaches in this paper the authors present a multimodal approach to the problem of motion estimation in which the computation of visual motion is based on several complementary constraints it is shown that multiple constraints can provide more accurate flow estimation in a wide range of circumstances the theoretical framework relies on bayesian estimation associated with global statistical models namely markov random fields the constraints introduced here aim to address the following issues optical flow estimation while preserving motion boundaries processing of occlusion regions fusion between gradient and feature based motion constraint equations deterministic relaxation algorithms are used to merge information and to provide a solution to the maximum a posteriori estimation of the unknown dense motion field the algorithm is well suited to a multiresolution implementation which brings an appreciable speed up as well as a significant improvement of estimation when large displacements are present in the scene experiments on synthetic and real world image sequences are reported

optical flow from constraint lines parametrization abstract optical flow is a measure of the change of image brightness in a frame sequence and is commonly used as an approximation of the velocity field which is the perspective projection of the three dimensional 3d real velocity on the image plane one method for evaluating optical flow is based on the optical flow constraint ofc equation such an equation is associated with each image pixel under the assumption that in the immediate neighbourhood of a pixel the optical flow field is smooth the constraint equations in that neighbourhood should have a common solution least squares techniques are commonly used to derive the solution which typically is very sensitive to discontinuities a new method of evaluating the optical flow from the ofc equation is presented which performs well in the presence of discontinuities the method proposes to accumulate evidence from the solution of all pairs of constraints in each image segment to provide the most probable value for optical flow rather than adopting least squares techniques the proposed accumulation of evidence is performed using a variant of the hough transform the combinatorial hough transform experimental results under different types of motion are presented an efficient implementation of the algorithm is discussed on a highly parallel architecture

multiconstraint wiener based motion compensation using wavelet pyramids we have investigated an original motion estimation method that exploits several frequency subbands of wavelet pyramids using a multigrid multiconstraint strategy a recursive and iterative solution based on the wiener approach allows to take into account the reconstruction quality criterion that is crucial to image coding experiments show its performances in terms of compression ratio reconstruction quality and reduction of implementation complexity compared to a monoresolution case

matching three dimensional objects using silhouettes a method for matching three dimensional objects against a library of models from an observed sequence of silhouettes is presented in this correspondence based upon the observed silhouettes the three dimensional structure of the object is constructed and refined the principal moments and three primary silhouettes are computed for the constructed three dimensional objects to represent the aggregate and detailed structure parameters the adaptive matching technique requires that sufficient silhouettes be added to modify the structure of the unknown object until consistent and steady matching results are obtained the library for matching is based on three primary silhouettes of the model objects experiments conducted show a fast convergence to a consistent result may be achieved provided that a reasonable choice of silhouettes is made

the use of optical flow for the analysis of non rigid motions this paper analysis the 2d motion field on the image plane produced by the 3d motion of a plane undergoing simple deformations when the deformation can be represented by a planar linear vector field the projected vector field i e the 2d motion field of the deformation is at most quadratic this 2d motion field has one singular point with eigenvalues identical to those of the singular point describing the deformation as a consequence the nature of the singular point of the deformation is a projective invariant when the plane moves and experiences a linear deformation at the same time the associated 2d motion field is at most quadratic with at most 3 singular points in the case of a normal rototranslation i e when the angular velocity is normal to the plane and of a linear deformation the 2d motion field has one singular point and substantial information on the rigid motion and on the deformation can be recovered from it experiments with image sequences of planes moving and undergoing linear deformations show that the proposed analysis can provide accurate results in addition experiments with deformable objects such as water oil textiles and rubber show that the proposed approach can provide information on more general 3d deformations