a local algorithm for the computation of image velocity via constructive interference of global fourier components a novel fourier based technique for local motion detection from image sequences is proposed in this method the instantaneous velocities of local image points are inferred directly from the global 3d fourier components of the image sequence this is done by selecting those velocities for which the superposition of the corresponding fourier gratings leads to constructive interference at the image point hence image velocities can be assigned locally even though position is computed from the phases and amplitudes of global fourier components spanning the whole image sequence that have been filtered based on the motion constraint equation reducing certain aperture effects typically arising from windowing in other methods regularization is introduced for sequences having smooth flow fields aperture effects and their effect on optic flow regularization are investigated in this context the algorithm is tested on both synthetic and real image sequences and the results are compared to those of other local methods finally we show that other motion features i e motion direction can be computed using the same algorithmic framework without requiring an intermediate representation of local velocity which is an important characteristic of the proposed method

on the estimation of optical flow relations between different approaches and some new results abstract a common basis is suggested for the optical flow estimation approaches of nagel 1983 haralick and lee 1983 and tretiak and pastor 1984 based on a discussion of these approaches an exact solution for the system of partial differential equations proposed by horn and schunck 1981 is given at gray value corners and extrema the insight gained by this solution results in a modification of the oriented smoothness approach of nagel 1983 which thereby becomes considerably simpler in addition the optical flow estimation approach of hildreth 1983 1984 can be shown to represent a kind of special case of this modified oriented smoothness approach in a more direct manner than discussed in nagel 1984

a harmonic retrieval framework for discontinuous motion estimation motion discontinuities arise when there are occlusions or multiple moving objects in the scene that is imaged conventional regularization techniques use smoothness constraints but are not applicable to motion discontinuities in this paper we show that discontinuous or multiple motion estimation can be viewed as a multicomponent harmonic retrieval problem from this viewpoint a number of established techniques for harmonic retrieval ran be applied to solve the challenging problem of discontinuous or multiple motion compared with existing techniques the resulting algorithm is not iterative which not only implies computational efficiency but also obviates concerns regarding convergence or local minima it also adds flexibility to spatio temporal techniques which have suffered from lack of explicit modeling of discontinuous motion experimental verification of our framework on both synthetic data as well as real image data is provided

computing optical flow via variational techniques defined as the apparent motion in a sequence of images the optical flow is very important in the computer vision community where its accurate estimation is necessary for many applications it is o

some comments on fourier analysis uncertainty and modeling investigation of the problem of simultaneously concentrating a function and its fourier transform has led to some interesting special functions that have widespread applications in engineering they provide a means of proving a rigorous version of an engineering folk theorem called the 2wt theorem many generalizations of these ideas seem to possess a similar elegant mathematical structure a brief descriptive review is given of these developments

quaternion collaborative and sparse representation with application to color face recognition collaborative representation based classification crc and sparse rc src have recently achieved great success in face recognition fr previous crc and src are originally designed in the real setting for grayscale image based fr they separately represent the color channels of a query color image and ignore the structural correlation information among the color channels to remedy this limitation in this paper we propose two novel rc methods for color fr namely quaternion crc qcrc and quaternion src qsrc using quaternion ell 1 minimization by modeling each color image as a quaternionic signal they naturally preserve the color structures of both query and gallery color images while uniformly coding the query channel images in a holistic manner despite the empirical success of crc and src on fr a few theoretical results are developed to guarantee their effectiveness another purpose of this paper is to establish the theoretical guarantee for qcrc and qsrc under mild conditions comparisons with competing methods on benchmark real world databases consistently show the superiority of the proposed methods for both color fr and reconstruction

a new technique for velocity estimation of large moving objects a technique for motion estimation of large moving objects is presented this technique is based on analyzing the hartley transform spectrum of the image sequence directly instead of using it to compute other transforms in this technique the fast hartley transform fht is applied to the image sequence and followed by a peak detection procedure the location of the peak is related to the velocity of the moving object dividing the temporal frequency f sub p corresponding to the detected peak by the corresponding spatial frequency k sub p gives the velocity of the moving object the fourier spectrum for a spatial frequency of k sub p is then computed this is followed by a peak detection of the fourier spectrum to validate the previous results and find the direction of the velocity of the moving object this method is faster than other techniques based on the fourier transform

robust optical flow estimation based on a sparse motion trajectory set this paper presents an approach to the problem of estimating a dense optical flow field the approach is based on a multiframe irregularly spaced motion trajectory set where each trajectory describes the motion of a given point as a function of time from this motion trajectory set a dense flow field is estimated using a process of interpolation a set of localized motion models are estimated with each pixel labeled as belonging to one of the motion models a markov random field framework is adopted allowing the incorporation of contextual constraints to encourage region like structures the approach is compared with a number of conventional optical flow estimation algorithms taken over a number of real and synthetic sequences results indicate that the method produces more accurate results for sequences with known ground truth flow also applying the method to real sequences with unknown flow results in lower dfd for all of the sequences tested

state space realizations and monomial equivalence for convolutional codes we will study convolutional codes with the help of state space realizations it will be shown that two such minimal realizations belong to the same code if and only if they are equivalent under the full state feedback group this result will be used in order to prove that two codes with positive forney indices are monomially equivalent if and only if they share the same adjacency matrix the adjacency matrix is an invariant of the code obtained via a minimal state space realization and counts in a detailed way the weights of all possible outputs it contains full information about the weights of the codewords in the given code

quasi cyclic unit memory convolutional codes unit memory convolutional codes with generator matrices which are composed of circulant submatrices are introduced this structure facilitates the analysis of efficient search for good codes equivalences among such codes and some of the basic structural properties are discussed in particular catastrophic encoders and minimal encoders are characterized and dual codes treated further various distance measures are discussed and a number of good codes some of which result from efficient computer search and some of which result from known block codes are presented

generalized union bound for space time codes gallager s second bounding technique also known as the generalized union bound is employed to derive a new upper bound on the error probability of space time codes stcs with maximum likelihood ml decoding on quasi static rayleigh fading channels the new bound is distinguished by two characteristics unlike the classical union bound the new bound is rapidly convergent and is only a few decibels away from simulation results and compared with gallager s first bound it has better computational efficiency and numerical stability hence the new bound is a useful tool for performance analysis and computer search of good stcs moreover the correlation between fading coefficients is easily accommodated by the new bound the application of the new bound to convolutional coding on block fading channels is also demonstrated and an improved version is derived for the bit error probability of maximum a posteriori probability decoding

on the flux phase conjecture at half filling an improved proof we present a simplification of lieb s proof of the flux phase conjecture for interacting fermion systems such as the hubbard model at half filling on a general class of graphs the main ingredient is a procedure which transforms a class of fermionic hamiltonians into reflection positive form the method can also be applied to other problems which we briefly illustrate with two examples concerning the t v model and an extended falicov kimball model

a differential equation approach to the computation of the fourier transform of the images of translating objects the frequency domain analysis of constant velocity motion has proven useful in a number of different contexts ranging from television signal processing to computer vision this work considers the frequency domain analysis of a generalization of such simple dynamics which includes the effect of acceleration and its time derivatives of any order in the frequency domain the contribution due to the object s shape and the contribution due to translation terms are clearly separated motion information in the frequency domain is given by functions characterized by a family of differential equations such differential equations are introduced in the work and their solutions are exemplified in order to compute the frequency domain motion contributions for simplicity the results are presented for the case of translations but they apply equally well to rotations

estimation of motions in color image sequences using hypercomplex fourier transforms although the motion estimation problem has been extensively studied most of the proposed estimation approaches deal mainly with monochrome videos the most usual way to apply them also in color image sequences is to process each color channel separately a different more sophisticated approach is to process the color channels in a ldquoholisticrdquo manner using quaternions as proposed by ell and sangwine in this paper we extend standard spatiotemporal fourier based approaches to handle color image sequences using the hypercomplex fourier transform we show that translational motions are manifested as energy concentration along planes in the hypercomplex 3d fourier domain and we describe a methodology to estimate the motions based on this property furthermore we compare the three channels separately approach with our approach and we show that the computational effort can be reduced by a factor of 1 3 using the hypercomplex fourier transform also we propose a simple accompanying method to extract the moving objects in the hypercomplex fourier domain our experimental results on synthetic and natural images verify our arguments throughout the paper

hierarchical construction of orientation and velocity selective filters as a step towards the early measurement of visual primitives the authors outline design criteria for the extraction of orientation and velocity information and present a variety of tools useful in the construction of simple linear filters a hierarchical parallel processing scheme is used in which nodes compute a weighted sum of inputs from within a small spatio temporal neighborhood the resulting scheme is easily analyzed and provides mechanisms sensitive to narrow ranges of both image velocity and orientation the hierarchical approach in combination with separability in the first levels yields an efficient implementation

estimation of motion from sequential images using integral constraints abstract a novel method for estimating nonuniform motion from sequential images is presented which is based on integral brightness constancy constraints the equations which transform arbitrary integrals between sequential images are expressed as a function of the displacement field and intensity changes the apparent displacement field is then computed by iterative projections onto the solution space of each linearized transformation equation some properties of this technique are demonstrated on a synthetic image pair realistic motion estimation is also demonstrated using sequential tagged cine magnetic resonance images

the frequency structure of one dimensional occluding image signals we present a theoretical investigation of the frequency structure of 1d occluding image signals we show that image signal occlusion contains relevant information which is most easily extractable from its representation in the frequency domain for instance the occluding and occluded signal velocities may be identified as such and translucency phenomena may be understood in the terms of this theoretical investigation in addition it is found that the structure of occluding 1d signals is invariant under constant and linear models of signal velocity this theoretical framework can be used to describe the exact frequency structure of non fourier motion and bridges the gap between such visual phenomena and their understanding in the frequency domain

optical flow using spatiotemporal filters a model is presented consonant with current views regarding the neurophysiology and psychophysics of motion perception that combines the outputs of a set of spatiotemporal motion energy filters to estimate image velocity a parallel implementation computes a distributed representation of image velocity a measure of image flow uncertainty is formulated preliminary results indicate that this uncertainty measure may be used to recognize ambiguity due to the aperture problem the model appears to deal with the aperture problem as well as the human visual system since it extracts the correct velocity for some patterns that have large differences in contrast at different spatial orientations

error probability for digital transmission over nonlinear channels with application to tcm the computation of upper and lower bounds to error probability in digital transmission over nonlinear channels with a finite memory is considered by using orthogonal volterra series the authors derive a canonical representation for discrete nonlinear systems based on a linear convolutional code and a memoryless mapper this representation shows that finite memory discrete nonlinear systems can be analyzed in much the same way as tcm trellis coded modulation schemes in particular tcm over nonlinear channels can be analyzed a technique is derived that expresses an upper bound to error probability based on the computation of the transfer of a state diagram with n branches and whose branch labels are matrices rather than scalars some examples of its application are given in particular error bounds are derived for nonlinear tcm schemes and for tcm schemes operating on nonlinear channels

on joint source and channel coding using trellis coded cpm analytical bounds on the channel distortion joint source and channel coding jscc using trellis coded quantization tcq in conjunction with trellis coded continuous phase modulation cpm is studied the channel is assumed to be the additive white gaussian noise awgn channel analytical bounds on the channel distortion for the investigated systems with maximum likelihood sequence detection mlsd are developed the bounds are based on the transfer function technique which was modified and generalized to include continuous amplitude discrete time signals for a memoryless uniform source the constructed bounds for the investigated systems are shown to be asymptotically tight for increasing channel signal to noise ratio snr values for a memoryless nonuniform source the constructed bounds are not as tight as the one for the uniform source however it still can be used as an indication to how the system performs it is concluded that the minimum euclidean distance of the system alone is not enough to evaluate the performance of the considered systems the number of error events having minimum euclidean distance and the total distortion caused by those error events also affect the asymptotic performance this work provides an analysis tool for the investigated systems the analysis method is very general it may be applied to any trellis based jscc schemes

convolutional codes with maximum distance profile abstract maximum distance profile codes are characterized by the property that two trajectories which start at the same state and proceed to a different state will have the maximum possible minimum distance from each other relative to any other convolutional code of the same rate and degree in this paper we use methods from systems theory to characterize maximum distance profile codes algebraically the main result shows that maximum distance profile codes form a generic set inside the variety which parametrizes the set of convolutional codes of a fixed rate and a fixed degree

spatiotemporal wavelets a group theoretic construction for motion estimation and tracking this paper presents a new group theoretic perspective for signal and image analysis it addresses the problem of motion analysis and trajectory determination the construction exploits the properties of motion parameters to be structured in lie algebras and lie groups the motion models are provided by the group structure which carries an entire theoretical build up this theoretical construction is based on a natural association of lie group representations minimum mean squared error estimations and variational principles of optimality these concepts naturally provide a corresponding association of tools based on continuous wavelet transforms kalman filters and lagrangians these tools result in highly parallelizable algorithms based on ffts gradients and dynamic programming the core of the construction is made of spatiotemporal continuous wavelets that are tuned to the motion parameters to perform motion estimation the motion parameters consist of scale orientation location velocity acceler

performance of space time codes gallager bounds and weight enumeration since the standard union bound for space time codes may diverge in quasi static fading channels the limit before average lba technique has been exploited to derive tight performance bounds however it suffers from the computational burden arising from a multidimensional integral in this paper efficient bounding techniques for space time codes are developed in the framework of gallager bounds two closed form upper bounds the ellipsoidal bound and the spherical bound are proposed that come close to simulation results within a few tenths of a decibel in addition two novel methods of weight enumeration operating on a further reduced state diagram are presented which in conjunction with the bounding techniques give a thorough treatment of performance bounds for space time codes

psychophysical and computational studies towards a theory of human stereopsis psychophysical studies are described which pose a strong challenge to models of human stereopsis based on the processing of disparity information within independent spatial frequency tuned binocular channels these studies support instead the proposal that the processes of human binocular combination integrally relate the extraction of disparity information with the construction of raw primal sketch assertions this proposal implies global binocular combination rules using principles of figural continuity and cross channel correspondence to disambiguate local matches found independently within spatial frequency channels exploratory small scale computational experiments with stereo algorithms based on these rules are described and found to be successful in dealing with a variety of stereo inputs the constraints presented by objects which are exploited by these algorithms are discussed

hypercomplex correlation techniques for vector images correlation techniques have been applied to almost every area of signal processing over the past century yet their use has in general been limited to scalar signals while there have been implementations in multichannel applications these can be characterized as a combination of single channel processes true vector correlation techniques with global and interchannel measures have only recently been demonstrated and are still in their infancy by comparison this paper describes our work on vector correlation based on the use of hypercomplex fourier transforms and presents for the first time a unified theory behind the information contained in the peak of a vector correlation response by using example applications for color images we also demonstrate some of the practical implications together with our latest results

efficient computation of trellis code generating functions for trellis codes generating function techniques provide the distance spectrum and a union bound on bit error rate the computation of the generating function of a trellis code may be separated into two stages the first stage reduces the number of states as much as possible using low complexity approaches the second stage produces the generating function from the reduced state diagram through some form of matrix inversion which has a relatively high complexity in this paper we improve on the amount of state reduction possible during the low complexity first stage we also show that for a trellis code that is a linear convolutional code followed by a signal mapper the number of states may always be reduced from n sup 2 to n sup 2 n 2 1 using low complexity techniques finally we analytically compare the complexity of various matrix inversion techniques and verify through simulation that the two stage approach we propose has the lowest complexity in an example the new technique produced the union bound in about half the time required by the best algorithm already in the literature

reduced state representations for trellis codes using constellation symmetry this paper presents a symmetry based technique for trellis code state diagram reduction that has more general applicability than the quasi regularity technique of rouanne et al and zehavi et al for trellis codes using standard constellations and labelings for a 2 sup spl nu x state trellis code the new technique reduces the 2 sup 2 spl nu x state diagram to 2 sup spl nu x spl nu q state diagram where 0 spl les spl nu sub q spl les spl nu sub x the particular value of spl nu sub q depends on the constellation labeling and the convolutional encoder for standard rate k k 1 set partitioned trellis codes spl nu sub q 0 and the overall number of states is the same with the new technique as with quasi regularity for codes that are not quasi regular and thus not amenable to the quasi regularity technique the new technique often provides some improvement when spl nu sub q spl nu sub x for 8 phase shift keying trellis codes the new technique always yields spl nu sub q 0

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

on the computation of weight enumerators for convolutional codes performance bounds for maximum likelihood decoding of convolutional codes over memoryless channels are commonly measured using the distance weight enumerator t x y also referred to as the transfer function of the code this paper presents an efficient iterative method to obtain t x y called the state reduction algorithm the algorithm is a systematic technique to simplify signal flow graphs that algebraically manipulate the symbolic adjacency matrix associated with the convolutional code next the algorithm is modified to compute the first few terms of the series expansion of t 1 y and spl part t x y spl part x sub x 1 the distance spectra without first computing the complete t x y

how can we speed up matrix multiplication due to the new algebraic methods of algorithm design recently it became possible to perform multiplication and inversion of n times n matrices using o n 2 496 rather than o n 3 arithmetical operations consequently algorithms for several other computational problems of linear algebra and combinatorics have been accelerated the major ideas and techniques that have led to that progress are surveyed

on minimality of convolutional ring encoders convolutional codes are considered with code sequences modeled as semi infinite laurent series it is well known that a convolutional code c over a finite group g has a minimal trellis representation that can be derived from code sequences it is also well known that for the case that g is a finite field any polynomial encoder of c can be algebraically manipulated to yield a minimal polynomial encoder whose controller canonical realization is a minimal trellis in this paper we seek to extend this result to the finite ring case g bbzpr by introducing a so called ldquo p encoderrdquo we show how to manipulate a polynomial encoding scheme of a noncatastrophic convolutional code over bbzpr to produce a particular type of p encoder ldquominimal p encoderrdquo whose controller canonical realization is a minimal trellis with nonlinear features the minimum number of trellis states is then expressed as p gamma where gamma is the sum of the row degrees of the minimal p encoder in particular we show that any convolutional code over bbzpr admits a delay free p encoder which implies the novel result that delay freeness is not a property of the code but of the encoder just as in the field case we conjecture that a similar result holds with respect to catastrophicity i e any catastrophic convolutional code over bbzpr admits a noncatastrophic p encoder

note on the one dimensional holstein hubbard model the one dimensional holstein hubbard model is studied we show the uniqueness of the ground state and the ordering of energy levels

estimation of multiple accelerated motions using chirp fourier transform and clustering motion estimation in the spatiotemporal domain has been extensively studied and many methodologies have been proposed which however cannot handle both time varying and multiple motions extending previously published ideas we present an efficient method for estimating multiple linearly time varying motions it is shown that the estimation of accelerated motions is equivalent to the parameter estimation of superpositioned chirp signals from this viewpoint one can exploit established signal processing tools such as the chirp fourier transform it is shown that accelerated motion results in energy concentration along planes in the 4 d space spatial frequencies temporal frequency chirp rate using fuzzy c planes clustering we estimate the plane motion parameters the effectiveness of our method is verified on both synthetic as well as real sequences and its advantages are highlighted

on the performance evaluation of trellis codes generating function techniques for analyzing the error event and the bit error probabilities for trellis codes are considered the conventional state diagram approach for linear codes where the number of states is equal to the number of trellis states cannot be applied directly to arbitrary trellis codes and instead a state diagram where the number of states is equal to the square of the number of trellis states must be used it is shown that for an interesting class of trellis codes a modified generating function can be defined for which the number of states em is equal to the number of trellis states the class of codes considered includes trellis codes of rate r n 1 n based upon set partitioning whenever the first partition breaks the signal constellation into two subsets which have the same configuration matrix i e the same ordered set of mutual distances the complexity of calculating this modified generating function is the same as for the ordinary generating function of a convolutional code with the same number of trellis states bounds on the performance of some interesting codes are given based upon this 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

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

learning intermediate level representations of form and motion from natural movies we present a model of intermediate level visual representation that is based on learning invariances from movies of the natural environment the model is composed of two stages of processing an early feature representation layer and a second layer in which invariances are explicitly represented invariances are learned as the result of factoring apart the temporally stable and dynamic components embedded in the early feature representation the structure contained in these components is made explicit in the activities of second layer units that capture invariances in both form and motion when trained on natural movies the first layer produces a factorization or separation of image content into a temporally persistent part representing local edge structure and a dynamic part representing local motion structure consistent with known response properties in early visual cortex area v1 this factorization linearizes statistical dependencies among the first layer units making them learnable by the second layer the second layer units are split into two populations according to the factorization in the first layer the form selective units receive their input from the temporally persistent part local edge structure and after training result in a diverse set of higher order shape features consisting of extended contours multiscale edges textures and texture boundaries the motion selective units receive their input from the dynamic part local motion structure and after training result in a representation of image translation over different spatial scales and directions in addition to more complex deformations these representations provide a rich description of dynamic natural images and testable hypotheses regarding intermediate level representation in visual cortex

two dimensional matched filtering for motion estimation in this work we describe a frequency domain technique for the estimation of multiple superimposed motions in an image sequence the least squares optimum approach involves the computation of the three dimensional 3 d fourier transform of the sequence followed by the detection of one or more planes in this domain with high energy concentration we present a more efficient algorithm based on the properties of the radon transform and the two dimensional 2 d fast fourier transform which can sacrifice little performance for significant computational savings we accomplish the motion detection and estimation by designing appropriate matched filters the performance is demonstrated on two image sequences

hypercomplex fourier transforms of color images fourier transforms are a fundamental tool in signal and image processing yet until recently there was no definition of a fourier transform applicable to color images in a holistic manner in this paper hypercomplex numbers specifically quaternions are used to define a fourier transform applicable to color images the properties of the transform are developed and it is shown that the transform may be computed using two standard complex fast fourier transforms the resulting spectrum is explained in terms of familiar phase and modulus concepts and a new concept of hypercomplex axis a method for visualizing the spectrum using color graphics is also presented finally a convolution operational formula in the spectral domain is discussed

uniform distance and error probability properties of tcm schemes the class of uniform trellis coded modulation tcm techniques is defined and simple explicit conditions for uniformity are derived uniformity is shown to depend on the metric properties of the two subconstellations resulting from the first step in set partitioning as well as on the assignment of binary labels to channel symbols the uniform distance property and uniform error property which are both derived from uniformity but are not equivalent are discussed the derived concepts are extended to encompass transmission over a not necessarily gaussian memoryless channel in which the metric used for detection may not be maximum likelihood an appropriate distance measure is defined that generalizes the euclidean distance it is proved that uniformity of a tcm scheme can also be defined under this new distance the results obtained are shown to hold for channels with phase offset or independent amplitude only fading examples are included to illustrate the applicability of the results

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

recursive estimation of 3d motion and surface structure from local affine flow parameters a recursive structure from motion algorithm based on optical flow measurements taken from an image sequence is described it provides estimates of surface normal in addition to 3d motion and depth the measurements are affine motion parameters which approximate the local flow fields associated with near planar surface patches in the scene these are integrated over time to give estimates of the 3d parameters using an extended kalman filter this also estimates the camera focal length and so the 3d estimates are metric the use of parametric measurements means that the algorithm is computationally less demanding than previous optical flow approaches and the recursive filter builds in a degree of noise robustness results of experiments on synthetic and real image sequences demonstrate that the algorithm performs well

geometrically uniform codes a signal space code c is defined as geometrically uniform if for any two code sequences in c there exists an isometry that maps one sequence into the other while leaving the code c invariant geometrical uniformity a strong kind of symmetry implies such properties as a the distance profiles from code sequences in c to all other code sequences are all the same and b all voronoi regions of code sequences in c have the same shape it is stronger than ungerboeck zehavi wolf symmetry or calderbank sloane regularity nonetheless most known good classes of signal space codes are shown to be generalized coset codes and therefore geometrically uniform including a lattice type trellis codes based on lattice partitions lambda lambda such that z sup n lambda lambda 4z sup n is a lattice partition chain and b phase shift keying psk type trellis codes based on up to four way partitions of a 2 sup n psk signal set

recognition and velocity computation of large moving objects in images two one dimensional time sequences are generated from the projections of the two dimensional sequence on the x and y axes then the two dimensional fast fourier transform for the generated time sequences is computed a peak in the spectrum for the selected spatial frequency is detected the temporal frequency at which the peak is detected gives an estimate of the velocity of the moving object analytical formulations for large moving objects in a time sequence with zero background are presented an algorithm is given for velocity formulation

computation of component image velocity from local phase information we present a technique for the computation of 2d component velocity from image sequences initially the image sequence is represented by a family of spatiotemporal velocity tuned linear filters component velocity computed from spatiotemporal responses of identically tuned filters is expressed in terms of the local first order behavior of surfaces of constant phase justification for this definition is discussed from the perspectives of both 2d image translation and deviations from translation that are typical in perspective projections of 3d scenes the resulting technique is predominantly linear efficient and suitable for parallel processing moreover it is local in space time robust with respect to noise and permits multiple estimates within a single neighborhood promising quantiative results are reported from experiments with realistic image sequences including cases with sizeable perspective deformation

exact eigenspectrum of the symmetric simple exclusion process on the complete complete bipartite and related graphs we show that the infinitesimal generator of the symmetric simple exclusion process recast as a quantum spin ferromagnetic heisenberg model can be solved by elementary techniques on the complete complete bipartite and related multipartite graphs some of the resulting infinitesimal generators are formally identical to homogeneous as well as mixed higher spins models the degeneracies of the eigenspectra are described in detail and the clebsch gordan machinery needed to deal with the arbitrary spin s representations of the su 2 is briefly developed we mention in passing how our results fit within the related questions of a ferromagnetic ordering of energy levels and a conjecture according to which the spectral gaps of the random walk and the interchange process on finite simple graphs must be equal

on the weight distribution of convolutional codes detailed information about the weight distribution of a convolutional code is given by the adjacency matrix of the state diagram associated with a minimal realization of the code we will show that this matrix is an invariant of the code moreover it will be proven that codes with the same adjacency matrix have the same dimension and the same forney indices and finally that for one dimensional binary convolutional codes the adjacency matrix determines the code uniquely up to monomial equivalence

woven convolutional codes i encoder properties encoders for convolutional codes with large free distances can be constructed by combining several less powerful convolutional encoders this paper is devoted to constructions in which the constituent convolutional codes are woven together in a manner that resembles the structure of a fabric the general construction is called twill and it is described together with two special cases viz woven convolutional encoders with outer warp and with inner warp the woven convolutional encoders inherit many of their structural properties such as minimality and catastrophicity from their constituent encoders for all three types of woven convolutional codes upper and lower bounds on their free distances as well as lower bounds on the active distances of their encoders are derived

minimal grobner bases and the predictable leading monomial property abstract we focus on grobner bases for modules of univariate polynomial vectors over a ring we identify a useful property the predictable leading monomial plm property that is shared by minimal grobner bases of modules in f x q no matter what positional term order is used the plm property is useful in a range of applications and can be seen as a strengthening of the wellknown predictable degree property row reducedness a terminology introduced by forney in the 70 s because of the presence of zero divisors minimal grobner bases over a finite ring of the type z p r where p is a prime integer and r is an integer 1 do not necessarily have the plm property in this paper we show how to derive from an ordered minimal grobner basis a so called minimal grobner p basis that does have a plm property we demonstrate that minimal grobner p bases lend themselves particularly well to derive minimal realization parametrizations over z p r applications are in coding and sequences over z p r

ferromagnetic ordering of energy levels we study a natural conjecture regarding ferromagnetic ordering of energy levels in the heisenberg model which complements the lieb mattis theorem of 1962 for antiferromagnets for ferromagnetic heisenberg models the lowest energies in each subspace of fixed total spin are strictly ordered according to the total spin with the lowest i e the ground state belonging to the maximal total spin subspace our main result is a proof of this conjecture for the spin 1 2 heisenberg xxx and xxz ferromagnets in one dimension our proof has two main ingredients the first is an extension of a result of koma and nachtergaele which shows that monotonicity as a function of the total spin follows from the monotonicity of the ground state energy in each total spin subspace as a function of the length of the chain for the second part of the proof we use the temperley lieb algebra to calculate in a suitable basis the matrix elements of the hamiltonian restricted to each subspace of the highest weight vectors with a given total spin we then show that the positivity properties of these matrix elements imply the necessary monotonicity in the volume our method also shows that the first excited state of the xxx ferromagnet on any finite tree has one less than maximal total spin

quaternion bessel fourier moments and their invariant descriptors for object reconstruction and recognition in this paper the quaternion bessel fourier moments are introduced the significance of phase information in quaternion bessel fourier moments is investigated and an accurate estimation method for rotation angle is described furthermore a new set of invariant descriptors based on the magnitude and the phase information of quaternion bessel fourier moments is derived experimental results show that quaternion bessel fourier moments lead to better performance for color image reconstruction than the other quaternion orthogonal moments such as quaternion zernike moments quaternion pseudo zernike moments and quaternion orthogonal fourier mellin moments in addition the angles estimated by the proposed moments are more accurate than those obtained by using other quaternion orthogonal moments the proposed invariant descriptors show also better robustness to geometric and photometric transformations quaternion bessel fourier moments for color image reconstruction and recognition an accurate estimation method for rotation angle throughout quaternion moments the invariant descriptor using the moment magnitudes and phase coefficients

existence of neel order in some spin 1 2 heisenberg antiferromagnets the methods of dyson lieb and simon are extended to prove the existence of neel order in the ground state of the 3d spin 1 2 heisenberg antiferromagnet on the cubic lattice we also consider the spin 1 2 antiferromagnet on the cubic lattice with the coupling in one of the three lattice directions taken to be r times its value in the other two lattice directions we prove the existence of neel order for 0 16 r 1 for the 2d spin 1 2 model we give a series of inequalities which involve the two point function only at short distances and each of which would by itself imply neel order

multiple constraints to compute optical flow the computation of the optical flow field from an image sequence requires the definition of constraints on the temporal change of image features in this paper we consider the implications of using multiple constraints in the computational schema in the first step it is shown that differential constraints correspond to an implicit feature tracking therefore the best results either in terms of measurement accuracy and speed in the computation are obtained by selecting and applying the constraints which are best tuned to the particular image feature under consideration considering also multiple image points not only allows us to obtain a locally better estimate of the velocity field but also to detect erroneous measurements due to discontinuities in the velocity field moreover by hypothesizing a constant acceleration motion model also the derivatives of the optical flow are computed several experiments are presented from real image sequences