some remarks on quasiconvexity and rank one convexity we explore some necessary conditions for quasiconvexity in an attempt to show that rank one convexity does not imply quasiconvexity when the target space for deformations is two dimensional an interesting construction is presented showing how rank one directions may fit with each other making the task harder than in higher dimensions

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

errors in variables modeling in optical flow estimation gradient based optical flow estimation methods typically do not take into account errors in the spatial derivative estimates the presence of these errors causes an errors in variables eiv problem moreover the use of finite difference methods to calculate these derivatives ensures that the errors are strongly correlated between pixels total least squares tls has often been used to address this eiv problem however its application in this context is flawed as tls implicitly assumes that the errors between neighborhood pixels are independent in this paper a new optical flow estimation method eivm is formulated to properly treat the eiv problem in optical flow eivm is based on sprent s 1966 procedure which allows the incorporation of a general eiv model in the estimation process in eivm the neighborhood size acts as a smoothing parameter due to the weights in the eivm objective function the effect of changing the neighborhood size is more complex than in other local model methods such as lucas and kanade 1981 these weights which are functions of the flow estimate can alter the effective size and orientation of the neighborhood in this paper we also present a data driven method for choosing the neighborhood size based on stein s unbiased risk estimators sure

polar codes for broadcast channels polar codes are introduced for discrete memoryless broadcast channels for m user deterministic broadcast channels polarization is applied to map uniformly random message bits from m independent messages to one codeword while satisfying broadcast constraints the polarization based codes achieve rates on the boundary of the private message capacity region for two user noisy broadcast channels polar implementations are presented for two information theoretic schemes 1 cover s superposition codes and 2 marton s codes due to the structure of polarization constraints on the auxiliary and channel input distributions are identified to ensure proper alignment of polarization indices in the multiuser setting the codes achieve rates on the capacity boundary of a few classes of broadcast channels e g binary input stochastically degraded the complexity of encoding and decoding is o n log n where n is the block length in addition polar code sequences obtain a stretched exponential decay of o 2 n beta of the average block error probability where 0 reproducible experiments for finite block lengths n 512 1024 2048 corroborate the theory

plateaus problem for parametric double integrals ii regularity at the boundary we establish global regularity of class h c 0 0 x z r r h throughout we also assume that there are numbers m1 m2 with 0 m1 m2 such that m1 z f x z m2 z for all x z r r d 1 2 s hildebrandt h von der mosel and that f x z is convex in z for any x r c suppose that is a closed rectifiable jordan curve in rn n 2 and let c be the nonempty class of surfaces x h1 2 b rn whose sobolev traces x b are continuous and monotonic mappings of b onto in section 2 of 8 we have proved that under the assumptions h d c there is a solution x of the plateau problem f min in c p satisfying the conformality relations xu xv xu xv 0 a e on b 1 1 a slightly weaker result was proved in 7 moreover it was shown in 7 and 8 respectively that every conformally parametrized minimizer x of f in c is of class c0 b rn c0 b rn m1 m2 and satisfies

polar codes for arbitrary dmcs and arbitrary macs polar codes are constructed for arbitrary channels by imposing an arbitrary quasi group structure on the input alphabet just as with usual polar codes the block error probability under successive cancellation decoding is o 2 n 1 2 epsilon where n is the block length encoding and decoding for these codes can be implemented with a complexity of o n log n it is shown that the same technique can be used to construct polar codes for arbitrary multiple access channels by using an appropriate abelian group structure although the symmetric sum capacity is achieved by this coding scheme some points in the symmetric capacity region may not be achieved in the case where the channel is a combination of linear channels we provide a necessary and sufficient condition characterizing the channels whose symmetric capacity region is preserved by the polarization process we also provide a sufficient condition for having a maximal loss in the dominant face

self calibration from image derivatives this study investigates the problem of estimating camera calibration parameters from image motion fields induced by a rigidly moving camera with unknown parameters where the image formation is modeled with a linear pinhole camera model the equations obtained show the flow to be separated into a component due to the translation and the calibration parameters and a component due to the rotation and the calibration parameters a set of parameters encoding the latter component is linearly related to the flow and from these parameters the calibration can be determined however as for discrete motion in general it is not possible to decouple image measurements obtained from only two frames into translational and rotational components geometrically the ambiguity takes the form of a part of the rotational component being parallel to the translational component and thus the scene can be reconstructed only up to a projective transformation in general for full calibration at least four successive image frames are necessary with the 3d rotation changing between the measurements the geometric analysis gives rise to a direct self calibration method that avoids computation of optical flow or point correspondences and uses only normal flow measurements new constraints on the smoothness of the surfaces in view are formulated to relate structure and motion directly to image derivatives and on the basis of these constraints the transformation of the viewing geometry between consecutive images is estimated the calibration parameters are then estimated from the rotational components of several flow fields as the proposed technique neither requires a special set up nor needs exact correspondence it is potentially useful for the calibration of active vision systems which have to acquire knowledge about their intrinsic parameters while they perform other tasks or as a tool for analyzing image sequences in large video databases

integral estimates for null lagrangians sobolev spaces of differential forms are studied lp projections onto exact forms are introduced as a tool to obtain integral estimates for null lagrangians new results on compensated compactness are given and mean coercive variational integrals are found existence of minima of certain mean coercive functionals is established

abelian group codes for channel coding and source coding in this paper we study the asymptotic performance of abelian group codes for the channel coding problem for arbitrary discrete finite alphabet memoryless channels as well as the lossy source coding problem for arbitrary discrete finite alphabet memoryless sources for the channel coding problem we find the capacity characterized in a single letter information theoretic form this simplifies to the symmetric capacity of the channel when the underlying group is a field for the source coding problem we derive the achievable rate distortion function that is characterized in a single letter information theoretic form when the underlying group is a field it simplifies to the symmetric rate distortion function we give several illustrative examples due to the nonsymmetric nature of the sources and channels considered our analysis uses a synergy of information theoretic and group theoretic tools

semicontinuity problems in the calculus of variations soit f r 3 r une fonction deux fois continument differentiable et pour u w 1 1 a b f u a b a b f x u x u x dx si f r n r m r nm r satisfait 1 f est mesurable en x continue en cs et 2 0 f x s a x c s p p ou p 1 a est une fonction localement sommable non negative et c une constante non negative alors la fonctionnelle f u a b est sequentiellement faiblement semi continue inferieurement sur w 1 p r m si et seulement si f x s est quasi convexe pour chaque s et presque chaque x

polar codes for q ary channels q 2 r we study polarization for nonbinary channels with input alphabet of size q 2r r 2 3 using arikan s polarizing kernel h2 we prove that the virtual channels that arise in the process of channel evolution converge to q ary channels with capacity 0 1 2 r bits as a result of this analysis we show that polar codes support reliable transmission over discrete memoryless channels with q ary input for all rates below the symmetric capacity of the channel this leads to an explicit transmission scheme for q ary channels the block error probability of decoding using successive cancellation behaves as exp n where n is the code length and is any constant less than 0 5

robust optic flow computation this paper formulates the optic flow problem as a set of over determined simultaneous linear equations it then introduces and studies two new robust optic flow methods the first technique is based on using the least median of squares lmeds to detect the outliers then the inlier group is solved using the least square technique the second method employs a new robust statistical method named the least median of squares orthogonal distances lmsod to identify the outliers and then uses total least squares to solve the optic flow problem the performance of both methods are studied by experiments on synthetic and real image sequences these methods outperform other published methods both in accuracy and robustness

construction of polar codes for arbitrary discrete memoryless channels it is known that polar codes can be efficiently constructed for binary input channels at the same time existing algorithms for general input alphabets are less practical because of high complexity we address the construction problem for the general case and analyze an algorithm that is based on successive reduction of the output alphabet size of the subchannels in each recursion step for this procedure we estimate the approximation error as o mu 1 q 1 where q is the input alphabet size and mu is the quantization parameter i e the maximum size of the subchannel output alphabet allowed by the algorithm the complexity of the code construction scales as o n mu 2 log mu where n is the length of the code we also show that if the polarizing operation relies on modulo q addition it is possible to merge subsets of output symbols without any loss in subchannel capacity performing this procedure before each approximation step results in a further speed up of the code construction and the resulting codes have smaller gap to capacity we also show that a similar acceleration can be attained for polar codes over finite field alphabets experimentation shows that the suggested construction algorithms can be used to construct long polar codes for alphabets of size q 16 and more with acceptable loss of the code rate for a variety of polarizing transforms

a relaxation theorem and its application to the equilibrium of gases keywords relaxed problem lower convex envelope gas equilibrium van der waal s equation reference caa article 1981 001doi 10 1007 bf00280643view record in web of science record created on 2008 11 25 modified on 2017 05 12

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

channel polarization through the lens of blackwell measures each memoryless binary input channel bic can be uniquely described by its blackwell measure which is a probability distribution on the unit interval 0 1 with mean 1 2 conversely any such probability distribution defines a bic the evolution of the blackwell measure under arikan s polar transform is derived for general bics and is analogous to density evolution as cited in the literature the present analysis emphasizes functional equations consequently the evolution of a variety of channel functionals is characterized including the symmetric capacity bhattacharyya parameter moments of information density hellinger affinity gallager s reliability function the hirschfeld gebelein renyi maximal correlation and the bayesian information gain the evolution of measure is specialized for symmetric bics according to their decomposition into binary symmetric sub channels bscs which simplifies iterative computations and the construction of polar codes it is verified that as a consequence of the blackwell sherman stein theorem all channel functionals text i f that can be expressed as an expectation of a convex function f with respect to the blackwell measure of a channel polarize in each iteration due to the polar transformation on the class of symmetric bics moreover for f either convex or non convex a necessary and sufficient condition is established to determine whether the random process associated with each text i f is a martingale submartingale or supermartingale represented via functional inequalities in terms of f this condition is numerically verifiable for all text i f and can generate analytical proofs to exhibit one such proof it is shown that the random process associated with the squared maximal correlation parameter is a supermartingale and converges almost surely on the unit interval 0 1

plateau s problem for parametric double integrals i existence and regularity in the interior we study plateau s problem for two dimensional parametric integrals f x b f x x u x v du dv the lagrangian f x z of which is positive definite and at least semi elliptic it turns out that there always exists a conformally parametrized minimizer any such minimizer x is seen to be holder continuous in the parameter domain b and continuous up to its boundary if f possesses a perfect dominance function g of class c 2 we can establish higher regularity of x in the interior in fact we prove x h 2 2 loc b r n c 1 b r n for some a 0 finally we discuss the existence of perfect dominance functions

quasi structured codes for multi terminal communications a new class of structured codes called quasi group codes qgcs is introduced a qgc is a subset of a group code in contrast with the group codes qgcs are not closed under group addition the parameters of the qgc can be chosen such that the size of mathcal c mathcal c is equal to any number between mathcal c and mathcal c 2 we analyze the performance of a specific class of qgcs this class of qgcs is constructed by assigning single letter distributions to the indices of the codewords in a group code then the qgc is defined as the set of codewords whose index is in the typical set corresponding to these single letter distributions the asymptotic performance limits of this class of qgcs are characterized using single letter information quantities corresponding covering and packing bounds are derived it is shown that the point to point channel capacity and optimal rate distortion function are achievable using qgcs coding strategies based on qgcs are introduced for three fundamental multi terminal problems the korner marton problem for modulo prime power sums computation over the multiple access channel mac and mac with distributed states for each problem a single letter achievable rate region is derived it is shown through examples that the coding strategies improve upon the previous strategies based on the unstructured codes linear codes and group codes

generalized partial orders for polar code bit channels we study partial orders pos for the synthesized bit channels of polar codes first we give an alternative proof of an existing po for bit channels with the same hamming weight and use the underlying idea to extend the bit channel ordering to some additional cases in particular the bit channel ordering for a given code block length is used to generate additional bit channel ordering relationships for larger block lengths generalizing previously known pos next we consider pos especially for the binary erasure channel bec we identify a symmetry property of the bhattacharyya parameters of complementary bit channel pairs on the bec and provide a condition for the alignment of polarized sets of bit channels for the bec and general binary input memoryless symmetric bms channels numerical examples and further properties about the pos for the bit channels with different hamming weights are provided to illustrate the new pos the bit channels with universal ordering positions which are independent of the channel erasure probability are verified for all of the code block lengths finally we show the threshold behavior of the bhattacharyya parameters of some bit channels by approximating the threshold values the corresponding value for a bit channel can be used to determine whether it is good or bad when the underlying channel is known

on rank one convex and polyconvex conformal energy functions with slow growth we make some remarks about rank one convex and polyconvex functions on the set of all real n n matrices that vanish on the subset k n consisting of all conformal matrices and grow like a power function at infinity we prove that every non negative rank one convex function that vanishes on k n and grows below a power of degree n 2 must vanish identically in odd dimensions n 3 we prove that every non negative polyconvex function that vanishes on k n must vanish identically if it grows below a power of degree n while in even dimensions such polyconvex functions can exist that also grow like a power of half dimension degree

point matching under large image deformations and illumination changes to solve the general point correspondence problem in which the underlying transformation between image patches is represented by a homography a solution based on extensive use of first order differential techniques is proposed we integrate in a single robust m estimation framework the traditional optical flow method and matching of local color distributions these distributions are computed with spatially oriented kernels in the 5d joint spatial color space the estimation process is initiated at the third level of a gaussian pyramid uses only local information and the illumination changes between the two images are also taken into account subpixel matching accuracy is achieved under large projective distortions significantly exceeding the performance of any of the two components alone as an application the correspondence algorithm is employed in oriented tracking of objects

achieving marton s region for broadcast channels using polar codes this paper presents polar coding schemes for the two user discrete memoryless broadcast channel dm bc which achieve marton s region with both common and private messages this is the best achievable rate region known to date and it is tight for all classes of two user dm bcs whose capacity regions are known to accomplish this task we first construct polar codes for both the superposition as well as binning strategy by combining these two schemes we obtain marton s region with private messages only finally we show how to handle the case of common information the proposed coding schemes possess the usual advantages of polar codes i e they have low encoding and decoding complexity and a superpolynomial decay rate of the error probability we follow the lead of goela abbe and gastpar who recently introduced polar codes emulating the superposition and binning schemes to align the polar indices for both schemes their solution involves some degradedness constraints that are assumed to hold between the auxiliary random variables and channel outputs to remove these constraints we consider the transmission of k blocks and employ a chaining construction that guarantees the proper alignment of the polarized indices the techniques described in this paper are quite general and they can be adopted to many other multiterminal scenarios whenever there polar indices need to be aligned

lusin type approximation of sobolev by lipschitz functions in gaussian and rcd k spaces abstract we establish new approximation results in the sense of lusin of sobolev functions by lipschitz ones in some classes of non doubling metric measure structures our proof technique relies upon estimates for heat semigroups and applies to gaussian and rcd k spaces as a consequence we obtain quantitative stability for regular lagrangian flows in gaussian settings

polar coded modulation a framework is proposed that allows for a joint description and optimization of both binary polar coding and 2m ary digital pulse amplitude modulation pam schemes for the latter the multilevel coding mlc approach as well as bit interleaved coded modulation bicm are considered the conceptual equivalence of polar coding and multilevel coding is covered in detail based on an alternative characterization of the channel polarization phenomenon rules for the optimum choice of the labeling in coded modulation schemes employing polar codes are developed simulation results regarding the error performance of the proposed schemes on the awgn channel are included

null lagrangians weak continuity and variational problems of arbitrary order abstract we consider the problem of minimizing integral functionals of the form i u f x k u x dx where r p u r and k u denotes the set of all partial derivatives of u with orders k the method is based on a characterization of null lagrangians l ku depending only on derivatives of order k applications to elasticity and other theories of mechanics are given

vardohus codes polar codes based on castle curves kernels in this paper we show some applications of algebraic curves to the construction of kernels of polar codes over a discrete memoryless channel which is symmetric w r t the field operations we will also study the minimum distance of the polar codes proposed their duals and the exponents of the matrices used for defining them all the restrictions that we make to our curves will be accomplished by the so called castle curves

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

polar codes characterization of exponent bounds and constructions polar codes were recently introduced by arikan they achieve the symmetric capacity of arbitrary binary input discrete memoryless channels under a low complexity successive cancellation decoding scheme the original polar code construction is closely related to the recursive construction of reed muller codes and is based on the 2 2 matrix 1 0 1 1 it was shown by arikan telatar that this construction achieves an error exponent of 1 2 i e that for sufficiently large blocklengths the error probability decays exponentially in the square root of the blocklength it was already mentioned by arikan that in principle larger matrices can be used to construct polar codes in this paper it is first shown that any l l matrix none of whose column permutations is upper triangular polarizes binary input memoryless channels the exponent of a given square matrix is characterized upper and lower bounds on achievable exponents are given using these bounds it is shown that there are no matrices of size smaller than 15 15 with exponents exceeding 1 2 further a general construction based on bch codes which for large i achieves exponents arbitrarily close to 1 is given at size 16 16 this construction yields an exponent greater than 1 2

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

computing optical flow with physical models of brightness variation although most optical flow techniques presume brightness constancy it is well known that this constraint is often violated producing poor estimates of image motion this paper describes a generalized formulation of optical flow estimation based on models of brightness variations that are caused by time dependent physical processes these include changing surface orientation with respect to a directional illuminant motion of the illuminant and physical models of heat transport in infrared images with these models we simultaneously estimate the 2d image motion and the relevant physical parameters of the brightness change model the estimation problem is formulated using total least squares with confidence bounds on the parameters experiments in four domains with both synthetic and natural inputs show how this formulation produces superior estimates of the 2d image motion

estimation of the velocity field of two dimensional deformable motion abstract for a deformable motion the velocities of neighboring points are different in general the traditional smoothness constraints which minimize the spatial derivatives of the velocity are not applicable a new way is proposed to integrate the motion fundamental constraint and the deformation linear constraint an iterative algorithm based on the maximum a posteriori map estimation criterion is proposed to estimate the velocity field of a two dimensional 2d deformable motion based on the statistical approach the relative weights of the two constraints used in the estimation process can be represented by a single parameter methods to avoid the critical problem of determining the region size for which the linear constraint holds are discussed the constraint propagation property is also used to overcome this problem by assuming that the flow field is analytic a promising application for optical flow techniques is to visualize the 2d heart motion quantitatively the 2d echocardiographic images taken by the short axis view are used in the experiments to study the performance of the proposed algorithm the results of using the method proposed by horn and schunck are also given for comparison

approximately universal codes over slow fading channels performance of reliable communication over a coherent slow fading multiple input multiple output mimo channel at high signal to noise ratio snr is succinctly captured as a fundamental tradeoff between diversity and multiplexing gains this paper studies the problem of designing codes that optimally tradeoff the diversity and multiplexing gains the main contribution is a precise characterization of codes that are universally tradeoff optimal i e they optimally tradeoff the diversity and multiplexing gains for every statistical characterization of the fading channel this characterization is referred to as approximate universality the approximation is in the connection between error probability and outage capacity with diversity and multiplexing gains respectively the characterization of approximate universality is then used to construct new coding schemes as well as to show optimality of several schemes proposed in the space time coding literature

channel polarization a method for constructing capacity achieving codes for symmetric binary input memoryless channels a method is proposed called channel polarization to construct code sequences that achieve the symmetric capacity i w of any given binary input discrete memoryless channel b dmc w the symmetric capacity is the highest rate achievable subject to using the input letters of the channel with equal probability channel polarization refers to the fact that it is possible to synthesize out of n independent copies of a given b dmc w a second set of n binary input channels wn i 1 les i les n such that as n becomes large the fraction of indices i for which i wn i is near 1 approaches i w and the fraction for which i wn i is near 0 approaches 1 i w the polarized channels wn i are well conditioned for channel coding one need only send data at rate 1 through those with capacity near 1 and at rate 0 through the remaining codes constructed on the basis of this idea are called polar codes the paper proves that given any b dmc w with i w 0 and any target rate r i w there exists a sequence of polar codes cfrn nges1 such that cfrn has block length n 2n rate ges r and probability of block error under successive cancellation decoding bounded as pe n r les o n 1 4 independently of the code rate this performance is achievable by encoders and decoders with complexity o n logn for each

source and channel polarization over finite fields and reed solomon matrices polarization phenomenon over any finite field fq with size q being a power of a prime is considered this problem is a generalization of the original proposal of channel polarization by arikan for the binary field as well as its extension to a prime field by sasoglu telatar and arikan in this paper a necessary and sufficient condition of a matrix over a finite field fq is shown under which any source and channel are polarized furthermore the result of the speed of polarization for the binary alphabet obtained by arikan and telatar is generalized to arbitrary finite field it is also shown that the asymptotic error probability of polar codes is improved by using the reed solomon matrices which can be regarded as a natural generalization of the 2 2 binary matrix used in the original proposal by arikan