a three dimensional parabolic equation model that includes the effects of rough boundaries a three dimensional parabolic equation 3dpe model that handles wide propagation angles in depth narrow propagation angles in azimuth and rough boundaries is derived and solved numerically with the method of alternating directions a homogeneous boundary condition which is easily incorporated into the numerical solution of the 3dpe is applied at the ocean surface to approximate the effects of rough boundaries in terms of a reflection coefficient that depends on grazing angle calculations are presented to demonstrate the accuracy of the 3dpe and to demonstrate that horizontal coupling the effects due to the term involving azimuth derivatives can be important in shallow water previous work has focused on deep water applications the model is applied to problems involving rough boundaries and range dependence

an energy conserving parabolic equation for elastic media the accuracy of the parabolic equation pe method is improved for range dependent elastic media the energy conserving elastic pe is a generalization of the energy conserving acoustic pe a range dependent waveguide is approximated by a sequence of range independent regions a linear approximation is derived for the nonlinear condition corresponding to conservation of compressional energy flux at the vertical interfaces between range independent regions the rotated elastic pe is applied to generate reference solutions for demonstrating accuracy the energy conserving elastic pe is applied to solve problems involving the propagation of an interface wave along a sloping ocean bottom and a problem involving mode cutoff and coupling into shear wave beams in the ocean bottom the latter problem is analogous to a cutoff problem that was first solved with the acoustic pe f b jensen and w a kuperman j acoust soc am 67 1564 1566 1980

epipolar plane image analysis an approach to determining structure from motion we present a technique for building a three dimensional description of a static scene from a dense sequence of images these images are taken in such rapid succession that they form a solid block of data in which the temporal continuity from image to image is approximately equal to the spatial continuity in an individual image the technique utilizes knowledge of the camera motion to form and analyze slices of this solid these slices directly encode not only the three dimensional positions of objects but also such spatiotemporal events as the occlusion of one object by another for straight line camera motions these slices have a simple linear structure that makes them easier to analyze the analysis computes the three dimensional positions of object features marks occlusion boundaries on the objects and builds a three dimensional map of free space in our article we first describe the application of this technique to a simple camera motion and then show how projective duality is used to extend the analysis to a wider class of camera motions and object types that include curved and moving objects

a mapping approach for handling sloping interfaces a mapping approach for handling sloping interfaces in parabolic equation solutions is developed and tested at each range the medium is rigidly translated vertically so that a sloping interface becomes horizontal to simplify the approach the slope is assumed to be small and the extra terms that arise in the wave equation under the mapping are neglected the effects of these terms can be approximately accounted for by applying a leading order correction to the phase the mapping introduces variations in topography which are relatively easy to handle for the case of a pressure release boundary condition the accuracy of the approach is demonstrated for problems involving fluid sediments the approach should also be accurate for problems involving elastic sediments and should be useful for solving three dimensional problems involving variable topography

on a generalization of uniformly convex and related functions in this paper we define and study some subclasses of analytic functions by using the concept of k uniformly convexity several interesting properties coefficients and radius problems are investigated the behaviour of these classes under a certain integral operator is also studied we indicate the relevant connections of our results with various known ones

on certain applications of the hadamard product abstract in this paper we give an extension of the ozkan and altintas results o ozkan o altintas applications of differential subordination appl math lett 19 2006 728 734 on the inclusion relationships involving various subclasses of analytic and univalent functions defined in terms of linear operators we show that these classes are closed under convolution with convex functions

robust and dense depth estimation for light field images we propose a depth estimation method for light field images light field images can be considered as a collection of 2d images taken from different viewpoints arranged in a regular grid we exploit this configuration and compute the disparity maps between specific pairs of views this computation is carried out by a state of the art two view stereo method providing a nondense disparity estimation we propose a disparity interpolation method increasing the density and improving the accuracy of this initial estimate disparities obtained from several pairs of views are fused to obtain a unique and robust estimation finally different experiments on synthetic and real images show how the proposed method outperforms the state of the art results

the hardy space of analytic functions associated with certain one parameter families of integral operators abstract recently h m srivastava and s owa j math anal appl 118 1986 80 87 proved a number of results relevant to komatu s conjectures cf y komatu bull fac sci engrg chuo univ ser i math 22 1979 1 22 for a certain one parameter additive family of operators defined on analytic functions regular in the open unit disk the object of the present paper is to investigate several one parameter families of integral operators and to prove certain inclusion theorems involving the hardy space h p of analytic functions and the class of functions whose derivative has a positive real part an application involving a generalized hypergeometric function is also considered

geometric occlusion analysis in depth estimation using integral guided filter for light field image unlike traditional multi view images sampling in angular domain of light field images is distributed in different directions therefore an angular sampling image asi comprising of possible matching points extracted from each view is available for each point in this paper we analyze the geometric relationship between asis and reference sub aperture images and then prove the occlusion boundary similarity based on the geometric relationship in extreme cases we show that some points in asi have higher reliability than other points for depth calculation an integral guided filter is then built based on the sub aperture image to predict occlusion probabilities in asis the filter is independent of asis and has no requirement for high angular resolution so that it is easy to apply to the cost volume calculation we integrate the filter into our depth estimation framework and other state of the art depth estimation frameworks experimental results demonstrate that the proposed filter is more effective to occluded point detection in asis than other methods results from different data sets show that our method outperforms the existing state of the art depth estimation methods especially along occlusion boundaries

applications and time domain solution of higher order parabolic equations in underwater acoustics a higher order parabolic equation and the corresponding higher order time domain parabolic equation are derived from a pade series and solved numerically these models provide accurate solutions for problems involving very wide angle propagation e g propagation in the nearfield or over a hard ocean bottom propagation in domains in which sound speed variations are large e g propagation in deep water deep within the ocean bottom in high speed ocean bottoms and possibly of different wave types and propagation out to very long ranges the possibility of modeling elastic wave propagation with a similar approach is considered

a higher order parabolic equation for wave propagation in an ocean overlying an elastic bottom a higher order elastic parabolic equation hepe is derived for wave propagation in depth dependent and weakly range dependent fluid solid media galerkin s method is used to discretize the depth operators in the hepe within layers in which depth variations in the lame constants and density are continuous discontinuities in material properties are handled with centered differences for the interface conditions between layers the numerical solution of the hepe also involves the method of alternating directions and crank nicolson integration the hepe is applied to underwater wave propagation problems involving a water column over an elastic bottom including a weakly range dependent problem the accuracy of the hepe is demonstrated with benchmark calculations

coupling scattering from the sea surface to a one way marching propagation model via conformal mapping validation propagation models in underwater acoustics usually incorporate sea surface scattering effects in an ad hoc manner which in most cases requires making severe approximations in particular to include in a coherent manner in a marching acoustic propagation model the scattering that occurs at a rough sea surface poses a serious problem dozier j acoust soc am 75 1415 1432 1984 introduced a rigorous approach in the framework of the split step parabolic equation model which used a sequence of conformal mappings to flatten segments of the sea surface locally each conformal mapping preserved the elliptic form of the wave equation in each transformed space the parabolic approximation is made and the solution advanced one range step the method has the attractive feature of handling surface roughness within a propagation model in a mathematically consistent manner including refraction and multiple surface interactions when and where they occur in this work the technique developed by dozier is impleme

global boundary flattening transforms for acoustic propagation under rough sea surfaces this paper introduces a conformal transform of an acoustic domain under a one dimensional rough sea surface onto a domain with a flat top this non perturbative transform can include many hundreds of wavelengths of the surface variation the resulting two dimensional flat topped domain allows direct application of any existing acoustic propagation model of the helmholtz or wave equation using transformed sound speeds such a transform model combination applies where the surface particle velocity is much slower than sound speed such that the boundary motion can be neglected once the acoustic field is computed the bijective one to one and onto mapping permits the field interpolation in terms of the original coordinates the bergstrom method for inverse riemann maps determines the transform by iterated solution of an integral equation for a surface matching term rough sea surface forward scatter test cases provide verification of the method using a particular parabolic equation model of the helmholt

two parabolic equations for propagation in layered poro elastic media parabolic equation methods for fluid and elastic media are extended to layered poro elastic media including some shallow water sediments a previous parabolic equation solution for one model of range independent poro elastic media collins et al j acoust soc am 98 1645 1656 1995 does not produce accurate solutions for environments with multiple poro elastic layers first a dependent variable formulation for parabolic equations used with elastic media is generalized to layered poro elastic media an improvement in accuracy is obtained using a second dependent variable formulation that conserves dependent variables across interfaces between horizontally stratified layers furthermore this formulation expresses conditions at interfaces using no depth derivatives higher than first order this feature should aid in treating range dependence because convenient matching across interfaces is possible with discretized derivatives of first order in contrast to second order

higher order pade approximations for accurate and stable elastic parabolic equations with application to interface wave propagation higher order pade approximations are applied to derive accurate and stable parabolic equations for sound propagation in oceans bounded below by an elastic bottom or bounded above by ice cover accuracy is achieved by placing constraints on the derivatives of the pade approximations at the point corresponding to the reference wave number stability is achieved by requiring that the pade approximations map part of the lower left quadrant of the complex plane into the upper half of the complex plane elastic parabolic equations based on these pade series can handle problems involving compressional shear and interface waves very wide propagation angles and large depth variations and weak range variations in the seismoacoustic parameters a finite difference spectral solution is developed for generating reference solutions and starting fields the rotated elastic parabolic equation is used to investigate the accuracy of the elastic parabolic equation for range dependent problems

a single scattering correction for large contrasts in elastic layers the single scattering solution is implemented in a formulation that makes it possible to accurately handle solid solid interfaces with the parabolic equation method problems involving large contrasts across sloping stratigraphy can be handled by subdividing a vertical interface into a series of two or more scattering problems the approach can handle complex layering and is applicable to a large class of seismic problems the solution of the scattering problem is based on an iteration formula which has improved convergence in the new formulation and the transverse operator of the parabolic wave equation which is implemented efficiently in terms of banded matrices accurate solutions can often be obtained by using only one iteration

a scaled mapping parabolic equation for sloping range dependent environments parabolic equation solutions use various techniques for approximating range dependent interfaces one is a mapping approach m d collins et al j acoust soc am 107 1937 1942 2000 where at each range the domain is vertically translated so that sloping bathymetry becomes horizontal and range dependence is transferred to the upper surface in this paper a scaled mapping is suggested where the domain is vertically distorted so that both the bathymetry and upper surface are horizontal accuracy is demonstrated for problems involving fluid sediments generalizations of the approach should be useful for environments with layer thicknesses that vary with range

the flattened surface parabolic equation a simple surface flattening transformation is applied to the problem of underwater acoustic scattering from an irregular sea surface the flattened surface elliptic wave equation is factored to obtain a parabolic equation that has the same high angle capability as recent parabolic equation models the flattened surface parabolic equation contains an additional surface slope term but includes forward scattering from the irregular sea surface the transformation creates additional volume irregularities and irregularities in the water sediment interface that the range and depth mesh need to resolve the surface flattening transformation is easy to implement in a parabolic equation model it compares very well with results obtained using boundary integral equations an example is given of scattering at 400 hz from a sea surface with wave heights of 3 m or nearly a wavelength

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

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

the stabilized self starter a stability problem is eliminated from the self starter which is a parabolic equation technique for generating initial conditions the stability problem is associated with evanescent modes that correspond to nearly vertical propagation it causes the solution to break down at certain frequencies for problems involving relatively low attenuation the error is restricted to relatively short ranges unless the medium is strongly range dependent near the source the stability problem is eliminated by placing the pole of the smoothing operator in the self starter away from the eigenvalues of the depth operator

nonuniform depth grids in parabolic equation solutions the parabolic wave equation is solved using a finite difference solution in depth that involves a nonuniform grid the depth operator is discretized using galerkin s method with asymmetric hat functions examples are presented to illustrate that this approach can be used to improve efficiency for problems in ocean acoustics and seismo acoustics for shallow water problems accuracy is sensitive to the precise placement of the ocean bottom interface this issue is often addressed with the inefficient approach of using a fine grid spacing over all depth efficiency may be improved by using a relatively coarse grid with nonuniform sampling to precisely position the interface efficiency may also be improved by reducing the sampling in the sediment and in an absorbing layer that is used to truncate the computational domain nonuniform sampling may also be used to improve the implementation of a single scattering approximation for sloping fluid solid interfaces

conic regions and k uniform convexity abstract let k c denote a domain such that 1 k and k is a conic section with eccentricity equal to 1 k in this paper authors introduce the class of k uniformly convex functions k ucv with the property that the values of the expression 1 zf z f z lie inside the domain k necessary and sufficient conditions for membership in k ucv as well as sharp growth and distortion theorems for k uniformly convex functions are given the obtained results generalize the concept of uniform convexity due to a w goodman ann polon math 56 1991 87 92

a single scattering correction for the seismo acoustic parabolic equation an efficient single scattering correction that does not require iterations is derived and tested for the seismo acoustic parabolic equation the approach is applicable to problems involving gradual range dependence in a waveguide with fluid and solid layers including the key case of a sloping fluid solid interface the single scattering correction is asymptotically equivalent to a special case of a single scattering correction for problems that only have solid layers kusel et al j acoust soc am 121 808 813 2007 the single scattering correction has a simple interpretation conservation of interface conditions in an average sense that facilitated its generalization to problems involving fluid layers promising results are obtained for problems in which the ocean bottom interface has a small slope

applications of certain operators to the classes of analytic functions related with generalized conic domains let a be the class of functions f f z z n 2 a nz n which are analytic in the open unit disc e we use a linear operator closely related to the multiplier transformation to introduce and investigate certain subclasses of a which map e onto a generalized form of the conic domain several properties of these classes including some inclusion relations convolution and other class preserving operators are studied in particular we derive many known and new results as special cases applications of some results are also given

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

the problem of energy conservation in one way models it is shown that the standard stair step representation of a sloping bottom may result in significant prediction errors in fact current parabolic equation implementations are not energy conserving the problem is shown to derive from the approximate treatment of the interface conditions at vertical boundaries along the stair steps several improved interface conditions are proposed

peruse a numerical treatment of rough surface scattering for the parabolic wave equation scattering of underwater acoustic signals from real ocean surfaces often does not fit into any of the classical theoretical approaches to the problem thus the need for a numerical approach is clear a novel method is presented that uses a sequence of conformal mappings to locally flatten successive segments of the surface which is assumed piecewise linear and frozen in time each conformal mapping preserves the elliptic form of the reduced wave equation so that in each transformed space the parabolic approximation can be made and the solution advanced one range step using the split step fourier algorithm this peruse pe rough surface numerical method is validated by exhibiting classically predicted bragg angle peaks for single scatter of a plane wave from a sinusoidal surface for multiple rough surface scattering in surface ducts peruse results are analyzed by resolution in depth into the virtual modes of labianca j acoust soc am 53 1137 1147 1973 the resulting modal intensities are then

occlusion aware depth estimation for light field using multi orientation epis abstract epipolar plane images epis contain special linear structures that reflect the disparity of a 3d point and are widely used in light field depth estimation however previous epi based approaches only utilize horizontal and vertical epis to estimate local disparities and ignore diagonal directions in order to make full use of the regular grid light field images we develop a strategy to extract epipolar plane images in all available directions based on the multi orientation epis a specific epi in which the point is not occluded is found and used to calculate robust depth estimation we also design a novel framework to estimate the depth information which combines the local depth with edge orientation the multi orientation epis and optimal orientation selection are proved to be effective in detecting and excluding occlusions experimental results show that the proposed method outperforms state of the art depth estimation methods especially near occlusion boundaries

a split step pade solution for the parabolic equation method a split step pade solution is derived for the parabolic equation pe method higher order pade approximations are used to reduce both numerical errors and asymptotic errors e g phase errors due to wide angle propagation this approach is approximately two orders of magnitude faster than solutions based on pade approximations that account for asymptotic errors but not numerical errors in contrast to the split step fourier solution which achieves similar efficiency for some problems the split step pade solution is valid for problems involving very wide propagation angles large depth variations in the properties of the waveguide and elastic ocean bottoms the split step pade solution is practical for global scale problems

variational light field analysis for disparity estimation and super resolution we develop a continuous framework for the analysis of 4d light fields and describe novel variational methods for disparity reconstruction as well as spatial and angular super resolution disparity maps are estimated locally using epipolar plane image analysis without the need for expensive matching cost minimization the method works fast and with inherent subpixel accuracy since no discretization of the disparity space is necessary in a variational framework we employ the disparity maps to generate super resolved novel views of a scene which corresponds to increasing the sampling rate of the 4d light field in spatial as well as angular direction in contrast to previous work we formulate the problem of view synthesis as a continuous inverse problem which allows us to correctly take into account foreshortening effects caused by scene geometry transformations all optimization problems are solved with state of the art convex relaxation techniques we test our algorithms on a number of real world examples as well as our new benchmark data set for light fields and compare results to a multiview stereo method the proposed method is both faster as well as more accurate data sets and source code are provided online for additional evaluation

higher order paraxial wave equation approximations in heterogenous media a new family of paraxial wave equation approximations is derived these approximations are of higher order accuracy than the parabolic approximation and they can be applied to the same computationa

modeling rayleigh and stoneley waves and other interface and boundary effects with the parabolic equation an improved approach for handling boundaries interfaces and continuous depth dependence with the elastic parabolic equation is derived and benchmarked the approach is applied to model the propagation of rayleigh and stoneley waves depending on the choice of dependent variables the operator in the elastic wave equation may not factor or the treatment of interfaces may be difficult these problems are resolved by using a formulation in terms of the vertical displacement and the range derivative of the horizontal displacement these quantities are continuous across horizontal interfaces which permits the use of galerkin s method to discretize in depth this implementation extends the capability of the elastic parabolic equation to handle arbitrary depth dependence and should lead to improvements for range dependent problems

an approximation to the three dimensional parabolic equation method for acoustic propagation we have reported previously ralph n baer j acoust soc am 69 70 75 1981 on an algorithm based on the parabolic approximation to the reduced wave equation for the propagation of sound in three dimensions in the ocean we present here a simpler algorithm solve n two dimensional problems and combine the results to form an approximate three dimensional solution analytic and numerical results show that this n 2d approach is an excellent approximation to the original algorithm for realistic ocean environments even those where fronts and eddies are present provided redirection of energy in azimuth due to boundary interaction is not important we compare the two computer models based on these algorithms for several test cases by considering how they distribute energy spatially and by simulating the performance of a hypothetical horizontal array of hydrophones placed in the calculated complex valued acoustic fields in an example of propagation through a large and strong ocean eddy the n 2d metho

a self starter for the parabolic equation method an efficient method is developed for generating accurate starting fields for the parabolic equation pe method for both fluid and solid media the self starter which is constructed by solving a one dimensional boundary value problem bvp involving the pe operator is more efficient than the normal mode starter which requires the solution of a large number of similar bvps the self starter depends on the depth dependent properties of the medium and satisfies all interface and boundary conditions since the self starter is based on higher order parabolic approximations it is accurate for problems involving wide propagation angles large depth variations in the properties of the medium low frequencies interface waves and the continuous spectrum

continuous depth map reconstruction from light fields in this paper we investigate how the recently emerged photography technology the light field can benefit depth map estimation a challenging computer vision problem a novel framework is proposed to reconstruct continuous depth maps from light field data unlike many traditional methods for the stereo matching problem the proposed method does not need to quantize the depth range by making use of the structure information amongst the densely sampled views in light field data we can obtain dense and relatively reliable local estimations starting from initial estimations we go on to propose an optimization method based on solving a sparse linear system iteratively with a conjugate gradient method two different affinity matrices for the linear system are employed to balance the efficiency and quality of the optimization then a depth assisted segmentation method is introduced so that different segments can employ different affinity matrices experiment results on both synthetic and real light fields demonstrate that our continuous results are more accurate efficient and able to preserve more details compared with discrete approaches

a higher order energy conserving parabolic equqation for range dependent ocean depth sound speed and density outgoing solutions of the wave equation including parabolic equation pe and normal mode solutions are usually formulated so that pressure is continuous with range for range dependent problems the accuracy of normal mode solutions has been improved by conserving energy rather than maintaining continuity of pressure porter et al the problem of energy conservation in one way equations j acoust soc am 89 1058 1067 1991 this approach is applied to derive a higher order energy conserving pe that provides improved accuracy for problems involving large ocean bottom slopes and large range and depth variations in sound speed and density a special numerical approach and complex pade coefficients are applied to suppress gibbs oscillations the back propagated half space field an improved pe starter is applied to handle wide propagation angles reference solutions generated with a complex ray model and with the rotated pe are used for comparison

a new rough surface parabolic equation program for computing low frequency acoustic forward scattering from the ocean surface the parabolic equation acoustic propagation program ram has been extended to handle a rough air water interface treated as a series of stair steps because much finer vertical spacing may be needed to resolve the interface than to propagate a low frequency acoustic wave accurately in the rest of the domain an option to use one vertical spacing near the surface and a coarser one in the rest of the ocean has been implemented the necessary galerkin approximations of derivatives on an unequally spaced grid have been worked out using computer algebra the new program rrsfc is efficient enough to compute the frequency spectrum of the field scattered off a moving surface by treating the surface as a sequence of frozen surfaces a comparison of one such spectrum with actual ocean data is provided in order to make a more detailed assessment of the program both the depth dependent pressure for individual surfaces and the frequency spectrum for sequences of surfaces are compared with the results of numerically exact integral equation calculations for a few constant sound speed test cases

global stereo reconstruction under second order smoothness priors second order priors on the smoothness of 3d surfaces are a better model of typical scenes than first order priors however stereo reconstruction using global inference algorithms such as graph cuts has not been able to incorporate second order priors because the triple cliques needed to express them yield intractable nonsubmodular optimization problems this paper shows that inference with triple cliques can be effectively performed our optimization strategy is a development of recent extensions to alpha expansion based on the ldquo qpbordquo algorithm the strategy is to repeatedly merge proposal depth maps using a novel extension of qpbo proposal depth maps can come from any source for example frontoparallel planes as in alpha expansion or indeed any existing stereo algorithm with arbitrary parameter settings

depth estimation with occlusion modeling using light field cameras light field cameras have become widely available in both consumer and industrial applications however most previous approaches do not model occlusions explicitly and therefore fail to capture sharp object boundaries a common assumption is that for a lambertian scene a pixel will exhibit photo consistency which means all viewpoints converge to a single point when focused to its depth however in the presence of occlusions this assumption fails to hold making most current approaches unreliable precisely where accurate depth information is most important at depth discontinuities in this paper an occlusion aware depth estimation algorithm is developed the method also enables identification of occlusion edges which may be useful in other applications it can be shown that although photo consistency is not preserved for pixels at occlusions it still holds in approximately half the viewpoints moreover the line separating the two view regions occluded object versus occluder has the same orientation as that of the occlusion edge in the spatial domain by ensuring photo consistency in only the occluded view region depth estimation can be improved occlusion predictions can also be computed and used for regularization experimental results show that our method outperforms current state of the art light field depth estimation algorithms especially near occlusion boundaries

the coupled mode parabolic equation the coupled mode parabolic equation pe is a generalization of the adiabatic mode pe that includes mode coupling terms it is practical to apply this approach to large scale problems involving coupling of energy between both modes and azimuths the solution is expressed in terms of the normal modes and mode coefficients which satisfy coupled horizontal wave equations the coupled mode pe may be solved efficiently with the splitting method the first step is equivalent to solving the adiabatic mode pe over one range step the second step involves the integration of the coupling term the coupling mode pe solution conserves energy which is an important aspect of a range dependent propagation model the derivation of the coupled mode pe which involves completing the square of an operator is related to the derivation of an adiabatic mode pe that accounts for ambient flow examples are presented to illustrate the accuracy of the coupled mode pe