fundamental principles on learning new features for effective dense matching in dense matching including stereo matching and optical flow nearly all existing approaches are based on simple features such as gray or rgb color gradient or simple transformations like census to calculate matching costs these features do not perform well in complex scenes that may involve radiometric changes noises overexposure and or textureless regions various problems may appear such as wrong matching at the pixel or region level flattening breaking of edges and or even entire structural collapse in this paper we propose two fundamental principles based on the consistency and the distinctiveness of features we show that almost all existing problems in dense matching are caused by features that violate one or both of these principles to systematically learn good features for dense matching we develop a general multi objective optimization based on these two principles and apply convolutional neural networks to find new features that lie on the pareto frontier by using two frame optical flow and stereo matching as applications our experimental results show that the features learned can significantly improve the performance of state of the art approaches based on the kitti benchmarks our method ranks first on the two stereo benchmarks and is the best among existing two frame optical flow algorithms on flow benchmarks

constrained kp hierarchy and bi hamiltonian structures the kakomtsev petviashvili kp hierarchy is considered together with the evolutions of eigenfunctions and adjoint eigenfunctions constraining the kp flows in terms of squared eigenfunctions one obtains 1 1 dimensional integrable equations with scattering problems given by pseudo differential lax operators the bi hamiltonian nature of these systems is shown by a systematic construction of two general poisson brackets on the algebra of associated lax operators gauge transformations provide miura links to modified equations these systems are constrained flows of the modified kp hierarchy for which again a general description of their bi hamiltonian nature is given the gauge transformations are shown to be poisson maps relating the bi hamiltonian structures of the constrained kp hierarchy and the modified kp hierarchy the simplest realization of this scheme yields the akns hierarchy and its miura link to the kaup broer hierarchy

classical r matrix theory for bi hamiltonian field systems this is a survey of the application of the classical r matrix formalism to the construction of infinite dimensional integrable hamiltonian field systems the main point is the study of bi hamiltonian structures appropriate constructions on poisson noncommutative and loop algebras as well as the central extension procedure are presented the theory is developed for 1 1 and 2 1 dimensional field and lattice soliton systems as well as hydrodynamic systems the formalism presented contains sufficiently many proofs and important details to make it self contained and complete the general theory is applied to several infinite dimensional lie algebras in order to construct both dispersionless and dispersive soliton integrable field systems

integrable equations on time scales integrable systems are usually given in terms of functions of continuous variables on r in terms of functions of discrete variables on z and recently in terms of functions of q variables on kq we formulate the gel fand dikii gd formalism on time scales by using the delta differentiation operator and find more general integrable nonlinear evolutionary equations in particular they yield integrable equations over integers difference equations and over q numbers q difference equations we formulate the gd formalism also in terms of shift operators for all regular discrete time scales we give a method allowing to construct the recursion operators for integrable systems on time scales finally we give a trace formula on time scales and then construct infinitely many conserved quantities casimirs of the integrable systems on time scales

positive definite completions of partial hermitian matrices abstract the question of which partial hermitian matrices some entries specified some free may be completed to positive definite matrices is addressed it is shown that if the diagonal entries are specified and principal minors composed of specified entries are positive then if the undirected graph of the specified entries is chordal a positive definite completion necessarily exists furthermore if this graph is not chordal then examples exist without positive definite completions in case a positive definite completion exists there is a unique matrix in the class of all positive definite completions whose determinant is maximal and this matrix is the unique one whose inverse has zeros in those positions corresponding to unspecified entries in the original partial hermitian matrix additional observations regarding positive definite completions are made

high dimensional camera shake removal with given depth map camera motion blur is drastically nonuniform for large depth range scenes and the nonuniformity caused by camera translation is depth dependent but not the case for camera rotations to restore the blurry images of large depth range scenes deteriorated by arbitrary camera motion we build an image blur model considering 6 degrees of freedom dof of camera motion with a given scene depth map to make this 6d depth aware model tractable we propose a novel parametrization strategy to reduce the number of variables and an effective method to estimate high dimensional camera motion as well the number of variables is reduced by temporal sampling motion function which describes the 6 dof camera motion by sampling the camera trajectory uniformly in time domain to effectively estimate the high dimensional camera motion parameters we construct the probabilistic motion density function pmdf to describe the probability distribution of camera poses during exposure and apply it as a unified constraint to guide the convergence of the iterative deblurring algorithm specifically pmdf is computed through a back projection from 2d local blur kernels to 6d camera motion parameter space and robust voting we conduct a series of experiments on both synthetic and real captured data and validate that our method achieves better performance than existing uniform methods and nonuniform methods on large depth range scenes

decomposition in conic optimization with partially separable structure decomposition techniques for linear programming are difficult to extend to conic op timization problems with general nonpolyhedral convex cones because the conic inequalities introduce an additional nonlinear coupling between the variables however in many applications the convex cones have a partially separable structure that allows them to be characterized in terms of simpler lower dimensional cones the most important example is sparse semidefinite programming with a chordal sparsity pattern here partial separability derives from the clique decomposition theorems that characterize positive semidefinite and positive semidefinite completable matrices with chordal sparsity patterns the paper describes a decomposition method that exploits partial separability in conic linear optimization the method is based on spingarn s method for equality constrained convex optimization combined with a fast interior point method for evaluating proximal operators

the r matrix approach to integrable systems on time scales a general unifying framework for integrable soliton like systems on time scales is introduced the r matrix formalism is applied to the algebra of differential operators in terms of which one can construct an infinite hierarchy of commuting vector fields the theory is illustrated by two infinite field integrable hierarchies on time scales which are differential counterparts of kp and mkp the difference counterparts of akns and kaup broer soliton systems are constructed as related finite field restrictions

r matrices and higher poisson brackets for integrable systems the tri hamiltonian nature of lax equations is revealed starting with an r matrix on an associative algebra g equipped with a trace form there are g compatible poisson brackets with linear quadratic and cubic dependence on the coordinates the invariant functions casimir functions on g are in involution relative to these brackets they yield a hierarchy of integrable tri hamiltonian lax equations the results can be applied to solvable pde s such as the korteweg de vries equation as well as to finite integrable systems such as the toda lattice in these cases the poisson structures considered here turn out to be abstract versions of the first 3 hamiltonian operators of these equations obtained by their well known recursion operators

symmetrical dense optical flow estimation with occlusions detection traditional techniques of dense optical flow estimation do not generally yield symmetrical solutions the results will differ if they are applied between images i 1 and i 2 or between images i 2 and i 1 in this work we present a method to recover a dense optical flow field map from two images while explicitely taking into account the symmetry across the images as well as possible occlusions in the flow field the idea is to consider both displacements vectors from i 1 to i 2 and i 2 to i 1 and to minimise an energy functional that explicitely encodes all those properties this variational problem is then solved using the gradient flow defined by the euler lagrange equations associated to the energy to prove the importance of the concepts of symmetry and occlusions for optical flow computation we have extended a classical approach to handle those experiments clearly show the added value of these properties to improve the accuracy of the computed flows figures appear in color in the online version of this paper

darboux transformations on a space scale abstract using the time space scale calculus introduced by hilger we describe a darboux transformation for partial differential equations on a space scale and extend the classical theorems of darboux and crum to this setting as an application we use the lax equation to deduce a system of korteweg de vries equations on a space scale and obtain a solution to this system by using the darboux transformation

bi hamiltonian structures for integrable systems on regular time scales a construction of the bi hamiltonian structures for integrable systems on regular time scales is presented the trace functional on an algebra of pseudodifferential operators valid on an arbitrary regular time scale is introduced the linear poisson tensors and the related hamiltonians are derived the quadratic poisson tensors are given by the use of the recursion operators of the lax hierarchies the theory is illustrated by differential counterparts of ablowitz kaup newell segur and kaup broer hierarchies

exploiting sparsity in linear and nonlinear matrix inequalities via positive semidefinite matrix completion a basic framework for exploiting sparsity via positive semidefinite matrix completion is presented for an optimization problem with linear and nonlinear matrix inequalities the sparsity characterized with a chordal graph structure can be detected in the variable matrix or in a linear or nonlinear matrix inequality constraint of the problem we classify the sparsity in two types the domain space sparsity d space sparsity for the symmetric matrix variable in the objective and or constraint functions of the problem which is required to be positive semidefinite and the range space sparsity r space sparsity for a linear or nonlinear matrix inequality constraint of the problem four conversion methods are proposed in this framework two for exploiting the d space sparsity and the other two for exploiting the r space sparsity when applied to a polynomial semidefinite program sdp these conversion methods enhance the structured sparsity of the problem called the correlative sparsity as a result the resulting polynomial sdp can be solved more effectively by applying the sparse sdp relaxation preliminary numerical results on the conversion methods indicate their potential for improving the efficiency of solving various problems

r matrix approach to lattice integrable systems an r matrix formalism is applied to the construction of the integrable lattice systems and their bi hamiltonian structure miura like gauge transformations between the hierarchies are also investigated in the end the ladder of linear maps between generated hierarchies is established and described

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

light field reconstruction using shearlet transform in this article we develop an image based rendering technique based on light field reconstruction from a limited set of perspective views acquired by cameras our approach utilizes sparse representation of epipolar plane images epi in shearlet transform domain the shearlet transform has been specifically modified to handle the straight lines characteristic for epi the devised iterative regularization algorithm based on adaptive thresholding provides high quality reconstruction results for relatively big disparities between neighboring views the generated densely sampled light field of a given 3d scene is thus suitable for all applications which require light field reconstruction the proposed algorithm compares favorably against state of the art depth image based rendering techniques and shows superior performance specifically in reconstructing scenes containing semi transparent objects

discriminability limits in spatio temporal stereo block matching disparity estimation is a fundamental task in stereo imaging and is a well studied problem recently methods have been adapted to the video domain where motion is used as a matching criterion to help disambiguate spatially similar candidates in this paper we analyze the validity of the underlying assumptions of spatio temporal disparity estimation and determine the extent to which motion aids the matching process by analyzing the error signal for spatio temporal block matching under the sum of squared differences criterion and treating motion as a stochastic process we determine the probability of a false match as a function of image features motion distribution image noise and number of frames in the spatio temporal patch this performance quantification provides insight into when spatio temporal matching is most beneficial in terms of the scene and motion and can be used as a guide to select parameters for stereo matching algorithms we validate our results through simulation and experiments on stereo video

consistent depth maps recovery from a video sequence this paper presents a novel method for recovering consistent depth maps from a video sequence we propose a bundle optimization framework to address the major difficulties in stereo reconstruction such as dealing with image noise occlusions and outliers different from the typical multi view stereo methods our approach not only imposes the photo consistency constraint but also explicitly associates the geometric coherence with multiple frames in a statistical way it thus can naturally maintain the temporal coherence of the recovered dense depth maps without over smoothing to make the inference tractable we introduce an iterative optimization scheme by first initializing the disparity maps using a segmentation prior and then refining the disparities by means of bundle optimization instead of defining the visibility parameters our method implicitly models the reconstruction noise as well as the probabilistic visibility after bundle optimization we introduce an efficient space time fusion algorithm to further reduce the reconstruction noise our automatic depth recovery is evaluated using a variety of challenging video examples

depth estimation using a sliding camera image based 3d reconstruction technology is widely used in different fields the conventional algorithms are mainly based on stereo matching between two or more fixed cameras and high accuracy can only be achieved using a large camera array which is very expensive and inconvenient in many applications another popular choice is utilizing structure from motion methods for arbitrarily placed camera s however due to too many degrees of freedom its computational cost is heavy and its accuracy is rather limited in this paper we propose a novel depth estimation algorithm using a sliding camera system by analyzing the geometric properties of the camera system we design a camera pose initialization algorithm that can work satisfyingly with only a small number of feature points and is robust to noise for pixels corresponding to different depths an adaptive iterative algorithm is proposed to choose optimal frames for stereo matching which can take advantage of continuously pose changing imaging and save the time consumption amazingly too the proposed algorithm can also be easily extended to handle less constrained situations such as using a camera mounted on a moving robot or vehicle experimental results on both synthetic and real world data have illustrated the effectiveness of the proposed algorithm

extracting view dependent depth maps from a collection of images stereo correspondence algorithms typically produce a single depth map in addition to the usual problems of occlusions and textureless regions such algorithms cannot model the variation in scene or object appearance with respect to the viewing position in this paper we propose a new representation that overcomes the appearance variation problem associated with an image sequence rather than estimating a single depth map we associate a depth map with each input image or a subset of them our representation is motivated by applications such as view interpolation and depth based segmentation for model building or layer extraction we describe two approaches to extract such a representation from a sequence of images the first approach which is more classical computes the local depth map associated with each chosen reference frame independently the novelty of this approach lies in its combination of shiftable windows temporal selection and graph cut optimization the second approach simultaneously optimizes a set of self consistent depth maps at multiple key frames since multiple depth maps are estimated simultaneously visibility can be modeled explicitly and disparity consistency imposed across the different depth maps results which include a difficult specular scene example show the effectiveness of our approach

positive semidefinite matrices with a given sparsity pattern abstract this paper concerns the cone of positive semidefinite matrices which have zeros in prescribed entries one of the main purposes is to obtain information and if possible describe the ranks of external matrices in such cones in terms of the pattern of prescribed zeros in particular we study those patterns for which the ranks of extremal matrices are less than a given number

stereo matching using belief propagation in this paper we formulate the stereo matching problem as a markov network and solve it using bayesian belief propagation the stereo markov network consists of three coupled markov random fields that model the following a smooth field for depth disparity a line process for depth discontinuity and a binary process for occlusion after eliminating the line process and the binary process by introducing two robust functions we apply the belief propagation algorithm to obtain the maximum a posteriori map estimation in the markov network other low level visual cues e g image segmentation can also be easily incorporated in our stereo model to obtain better stereo results experiments demonstrate that our methods are comparable to the state of the art stereo algorithms for many test cases

consistent binocular depth and scene flow with chained temporal profiles we propose a depth and image scene flow estimation method taking the input of a binocular video the key component is motion depth temporal consistency preservation making computation in long sequences reliable we tackle a number of fundamental technical issues including connection establishment between motion and depth structure consistency preservation in multiple frames and long range temporal constraint employment for error correction we address all of them in a unified depth and scene flow estimation framework our main contributions include development of motion trajectories which robustly link frame correspondences in a voting manner rejection of depth motion outliers through temporal robust regression novel edge occurrence map estimation and introduction of anisotropic smoothing priors for proper regularization

extensions and contractions of the lie algebra ofq pseudodifferential symbols on the circle abstract we construct cocycles on the lie algebra of pseudo and q pseudodifferential symbols of one variable and on their close relatives the sine algebra and the poisson algebra on two torus a quantum godbillon vey cocycle on pseudo differential operators appears in this construction as a natural generalization of the gelfand fuchs 3 cocycle on periodic vector fields a nontrivial embedding of the virasoro algebra into a completion of q pseudodifferential symbols is proposed we describe q analogs of the kp and kdv hierarchies admitting an infinite number of conserved charges as well as q deformed gelfand dickey structures

variational principles surface evolution pdes level set methods and the stereo problem we present a novel geometric approach for solving the stereo problem for an arbitrary number of images spl ges 2 it is based upon the definition of a variational principle that must be satisfied by the surfaces of the objects in the scene and their images the euler lagrange equations that are deduced from the variational principle provide a set of partial differential equations pdes that are used to deform an initial set of surfaces which then move toward the objects to be detected the level set implementation of these pdes potentially provides an efficient and robust way of achieving the surface evolution and to deal automatically with changes in the surface topology during the deformations i e to deal with multiple objects results of an implementation of our theory also dealing with occlusion and visibility are presented on synthetic and real images

a multiple baseline stereo a stereo matching method that uses multiple stereo pairs with various baselines generated by a lateral displacement of a camera to obtain precise distance estimates without suffering from ambiguity is presented matching is performed simply by computing the sum of squared difference ssd values the ssd functions for individual stereo pairs are represented with respect to the inverse distance and are then added to produce the sum of ssds this resulting function is called the sssd in inverse distance it is shown that the sssd in inverse distance function exhibits a unique and clear minimum at the correct matching position even when the underlying intensity patterns of the scene include ambiguities or repetitive patterns the authors first define a stereo algorithm based on the sssd in inverse distance and present a mathematical analysis to show how the algorithm can remove ambiguity and increase precision experimental results with real stereo images are presented to demonstrate the effectiveness of the algorithm

the sine gordon equation on time scales abstract we formulate and discuss integrable analogue of the sine gordon equation on arbitrary time scales this unification contains the sine gordon equation discrete sine gordon equation and the hirota equation doubly discrete sine gordon equation as special cases we present the lax pair check compatibility conditions and construct the darboux backlund transformation finally we obtain a soliton solution on arbitrary time scale the solution is expressed by the so called cayley exponential function

visual modeling with a hand held camera in this paper a complete system to build visual models from camera images is presented the system can deal with uncalibrated image sequences acquired with a hand held camera based on tracked or matched features the relations between multiple views are computed from this both the structure of the scene and the motion of the camera are retrieved the ambiguity on the reconstruction is restricted from projective to metric through self calibration a flexible multi view stereo matching scheme is used to obtain a dense estimation of the surface geometry from the computed data different types of visual models are constructed besides the traditional geometry and image based approaches a combined approach with view dependent geometry and texture is presented as an application fusion of real and virtual scenes is also shown

matrices attaining the minimum semidefinite rank of a chordal graph every positive semidefinite matrix whose graph g is chordal may be represented as a sum of rank 1 positive semidefinite matrices whose graphs are subgraphs of g we show that if the matrix is of minimum rank then this representation is unique this result is used to give a full characterization of the completely positive matrices of minimum rank with a given chordal graph every such matrix is shown to have a unique easily computable minimal rank 1 representation and cp rank equal to its rank we also characterize all chordal graphs with the property that every minimum rank doubly nonnegative matrix realization of the graph is completely positive

large occlusion stereo a method for solving the stereo matching problem in the presence of large occlusion is presented a data structure the disparity space image is defined to facilitate the description of the effects of occlusion on the stereo matching process and in particular on dynamic programming dp solutions that find matches and occlusions simultaneously we significantly improve upon existing dp stereo matching methods by showing that while some cost must be assigned to unmatched pixels sensitivity to occlusion cost and algorithmic complexity can be significantly reduced when highly reliable matches or ground control points are incorporated into the matching process the use of ground control points eliminates both the need for biasing the process towards a smooth solution and the task of selecting critical prior probabilities describing image formation finally we describe how the detection of intensity edges can be used to bias the recovered solution such that occlusion boundaries will tend to be proposed along such edges reflecting the observation that occlusion boundaries usually cause intensity discontinuities

functional representations of integrable hierarchies we consider a general framework for integrable hierarchies in lax form and derive certain universal equations from which functional representations of particular hierarchies such as kp discrete kp mkp akns i e formulations in terms of functional equations are systematically and quite easily obtained the formalism genuinely applies to hierarchies where the dependent variables live in a noncommutative typically matrix algebra the obtained functional representations can be understood as noncommutative analogues of fay identities for the kp hierarchy

cuts matrix completions and graph rigidity this paper brings together several topics arising in distinct areas polyhedral combinatorics in particular cut and metric polyhedra matrix theory and semidefinite programming in particular completion problems for positive semidefinite matrices and euclidean distance matrices distance geometry and structural topology in particular graph realization and rigidity problems cuts and metrics provide the unifying theme indeed cuts can be encoded as positive semidefinite matrices this fact underlies the approximative algorithm for max cut of goemans and williamson and both positive semidefinite and euclidean distance matrices yield points of the cut polytope or cone after applying the functions 1 arccos or when fixing the dimension in the euclidean distance matrix completion problem we find the graph realization problem and the related question of unicity of realization which leads to the question of graph rigidity our main objective here is to present in a unified setting a number of results and questions concerning matrix completion graph realization and rigidity problems these problems contain indeed very interesting questions relevant to mathematical programming and we believe that research in this area could yield to cross fertilization between the various fields involved

chordal decomposition in operator splitting methods for sparse semidefinite programs we employ chordal decomposition to reformulate a large and sparse semidefinite program sdp either in primal or dual standard form into an equivalent sdp with smaller positive semidefinite psd constraints in contrast to previous approaches the decomposed sdp is suitable for the application of first order operator splitting methods enabling the development of efficient and scalable algorithms in particular we apply the alternating direction method of multipliers admm to solve decomposed primal and dual standard form sdps each iteration of such admm algorithms requires a projection onto an affine subspace and a set of projections onto small psd cones that can be computed in parallel we also formulate the homogeneous self dual embedding hsde of a primal dual pair of decomposed sdps and extend a recent admm based algorithm to exploit the structure of our hsde the resulting hsde algorithm has the same leading order computational cost as those for the primal or dual problems only with the advantage of being able to identify infeasible problems and produce an infeasibility certificate all algorithms are implemented in the open source matlab solver cdcs numerical experiments on a range of large scale sdps demonstrate the computational advantages of the proposed methods compared to common state of the art solvers

a direct proof for the matrix decomposition of chordal structured positive semidefinite matrices agler helton mccullough and rodman proved that a graph is chordal if and only if any positive semidefinite psd symmetric matrix whose nonzero entries are specified by a given graph can be decomposed as a sum of psd matrices corresponding to the maximal cliques this decomposition is recently exploited to solve positive semidefinite programming efficiently their proof is based on a characterization for psd matrix completion of a chordal structured matrix due to grone johnson sa and wolkowicz this note gives a direct and simpler proof for the result of agler et al which leads to an alternative proof of grone et al

cyclic homology of differential operators the virasoro algebra and a q analogue we show how methods from cyclic homology give easily an explicit 2 cocycle on the lie algebra of differential operators of the circle such that restricts to the cocycle defining the virasoro algebra the same methods yield also aq analogue of as well as an infinite family of linearly independent cocycles arising when the complex parameterq is a root of unity we use an algebra ofq difference operators andq analogues of koszul and the rham complexes to construct these quantum cocycles

the visual hull concept for silhouette based image understanding many algorithms for both identifying and reconstructing a 3 d object are based on the 2 d silhouettes of the object in general identifying a nonconvex object using a silhouette based approach implies neglecting some features of its surface as identification clues the same features cannot be reconstructed by volume intersection techniques using multiple silhouettes of the object this paper addresses the problem of finding which parts of a nonconvex object are relevant for silhouette based image understanding for this purpose the geometric concept of visual hull of a 3 d object is introduced this is the closest approximation of object s that can be obtained with the volume intersection approach it is the maximal object silhouette equivalent to s i e which can be substituted for s without affecting any silhouette only the parts of the surface of s that also lie on the surface of the visual hull can be reconstructed or identified using silhouette based algorithms the visual hull depends not only on the object but also on the region allowed to the viewpoint two main viewing regions result in the external and internal visual hull in the former case the viewing region is related to the convex hull of s in the latter it is bounded by s the internal visual hull also admits an interpretation not related to silhouettes algorithms for computing visual hulls are presented and their complexity analyzed in general the visual hull of a 3 d planar face object turns out to be bounded by planar and curved patches

integrable discrete systems on r and related dispersionless systems a general framework for integrable discrete systems on r in particular containing lattice soliton systems and their q deformed analogs is presented the concept of regular grain structures on r generated by discrete one parameter groups of diffeomorphisms in terms of which one can define algebra of shift operators is introduced two integrable hierarchies of discrete chains together with bi hamiltonian structures and their continuous limits are constructed the inverse problem based on the deformation quantization scheme is considered

image coding using depth blurring for aesthetically acceptable distortion we introduce the concept of depth based blurring to achieve an aesthetically acceptable distortion when reducing the bitrate in image coding the proposed depth based blurring is a prefiltering that reduces high frequency components by mimicking the limited depth of field effect that occurs in cameras to cope with the challenge of avoiding intensity leakage at the boundaries of objects when blurring at different depth levels we introduce a selective blurring algorithm that simulates occlusion effects as occur in natural blurring the proposed algorithm can handle any number of blurring and occlusion levels subjective experiments show that the proposed algorithm outperforms foveation filtering which is the dominant approach for bitrate reduction by space variant prefiltering