mean curvature flow with triple junctions in higher space dimensions we consider mean curvature flow of n dimensional surface clusters at n 1 dimensional triple junctions an angle condition is required which in the symmetric case reduces to the well known 120 angle condition using a novel parametrization of evolving surface clusters and a new existence and regularity approach for parabolic equations on surface clusters we show local well posedness by a contraction argument in parabolic holder spaces

label propagation and higher order constraint based segmentation of fluid associated regions in retinal sd oct images the segmentation of the fluid associated region in the retina plays an important role in the treatment of retinal diseases such as diabetic retinopathy dr and age related macular degeneration amd the existing methods for the detection of the fluid region generally suffer from the limitation of the segmentation accuracy and the expensive time costs to overcome these problems in this paper we propose an interactive segmentation method for the fluid associated region in three dimensional 3 d spectral domain optical coherence tomography sd oct retinal imaging in which only a few seeds in one sd oct slice are needed after which the algorithm finishes the segmentation automatically to improve the segmentation accuracy the higher order constraint is introduced into the conventional markov random field mrf framework to impose the superpixel consistency to maintain temporal coherence of the 3 d sd oct slices the labeling information is propagated slice by slice via a proposed motion estimation based algorithm the proposed higher order based energy function can be efficiently solved by the max flow algorithm on a specified graph with several auxiliary nodes experiments on 28 sd oct cubes demonstrate the competitiveness of the proposed method compared with the state of the art methods

optimal surface segmentation in volumetric images a graph theoretic approach efficient segmentation of globally optimal surfaces representing object boundaries in volumetric data sets is important and challenging in many medical image analysis applications we have developed an optimal surface detection method capable of simultaneously detecting multiple interacting surfaces in which the optimality is controlled by the cost functions designed for individual surfaces and by several geometric constraints defining the surface smoothness and interrelations the method solves the surface segmentation problem by transforming it into computing a minimum s hbox t cut in a derived arc weighted directed graph the proposed algorithm has a low order polynomial time complexity and is computationally efficient it has been extensively validated on more than 300 computer synthetic volumetric images 72 ct scanned data sets of different sized plexiglas tubes and tens of medical images spanning various imaging modalities in all cases the approach yielded highly accurate results our approach can be readily extended to higher dimensional image segmentation

convergence of dziuk s linearly implicit parametric finite element method for curve shortening flow convergence of dziuk s fully discrete linearly implicit parametric finite element method for curve shortening flow on the plane still remains open since it was proposed in 1991 though the correspo

young measure solutions of a class of forward backward diffusion equations abstract this paper is devoted to young measure solutions of a class of forward backward diffusion equations inspired by the idea from a recent work of demoulini we first discuss the regular case by introducing the young measure solutions and prove the existence for such solutions and then approximate the extreme case by the approach of regularization and establish the existence of young measure solutions in the class of functions with bounded variation

non parametric radially symmetric mean curvature flow with a free boundary we study the mean curvature flow of radially symmetric graphs with prescribed contact angle on a fixed smooth hypersurface in euclidean space in this paper we treat two distinct problems the first problem has a free neumann boundary only while the second has two disjoint boundaries a free neumann boundary and a fixed dirichlet height we separate the two problems and prove that under certain initial conditions we have either long time existence followed by convergence to a minimal surface or finite maximal time of existence at the end of which the graphs develop a curvature singularity we also give a rate of convergence for the singularity

a second order stabilization method for linearizing and decoupling nonlinear parabolic systems a new time discretization method for strongly nonlinear parabolic systems is constructed by combining the fully explicit two step backward difference formula and a second order stabilization of wav

double grow up and global convergence of solutions for a parabolic prescribed mean curvature problem abstract the paper is concerned with a parabolic mean curvature type problem with a varying parameter we study large time behavior of global solutions for different ranges of and initial data and present some new asymptotic results about global convergence and infinite time blow up in particular it is shown that for suitable ranges of parameter and initial data there exists a double grow up phenomenon the solution itself blows up at every interior point and its gradient blows up at the boundary of the domain as t we also establish an interesting connection between global convergence and the non classical solution of the associated stationary problem if initial data are smaller than the non classical solution then the solutions must decay to zero in c 1 norm as t

globally minimal surfaces by continuous maximal flows in this paper we address the computation of globally minimal curves and surfaces for image segmentation and stereo reconstruction we present a solution simulating a continuous maximal flow by a novel system of partial differential equations existing methods are either grid biased graph based methods or suboptimal active contours and surfaces the solution simulates the flow of an ideal fluid with isotropic velocity constraints velocity constraints are defined by a metric derived from image data an auxiliary potential function is introduced to create a system of partial differential equations it is proven that the algorithm produces a globally maximal continuous flow at convergence and that the globally minimal surface may be obtained trivially from the auxiliary potential the bias of minimal surface methods toward small objects is also addressed an efficient implementation is given for the flow simulation the globally minimal surface algorithm is applied to segmentation in 2d and 3d as well as to stereo matching results in 2d agree with an existing minimal contour algorithm for planar images results in 3d segmentation and stereo matching demonstrate that the new algorithm is robust and free from grid bias

some aspects of the dynamic of v h h abstract we consider the evolution of a surface t according to the equation v h h where v is the normal velocity of t h is the sum of the two principal curvatures and h is the average of h on t we study the case where t intersects orthogonally a fixed surface and discuss some aspects of the dynamics of t under the assumption that the volume of the region enclosed between t and is small we show that in this case if 0 is near a hemisphere t keeps its almost hemispherical shape and slides on crawling approximately along orbits of the tangential gradient h of the sum h of the two principal curvatures of we also show that if p is a nondegenerate zero of h and a 0 is sufficiently small then there is a surface of constant mean curvature which is near a hemisphere of radius a with center near p and intersects orthogonally

linearized fe approximations to a nonlinear gradient flow we study fully discrete linearized galerkin finite element approximations to a nonlinear gradient flow applications of which can be found in many areas due to the strong nonlinearity of the equation existing analyses for implicit schemes require certain restrictions on the time step and no analysis has been explored for linearized schemes this paper focuses on the unconditionally optimal l 2 error estimate of a linearized scheme the key to our analysis is an iterated sequence of time discrete elliptic equations and a rigorous analysis of its solution we prove the w 1 infty boundedness of the solution of the time discrete system and the corresponding finite element solution based on a more precise estimate of elliptic pdes in w 2 2 epsilon 1 and h 2 epsilon 2 and a physical feature of the gradient dependent diffusion coefficient numerical examples are provided to support our theoretical analysis

the dirichlet problem for the minimal surface system in arbitrary dimensions and codimensions let be a bounded c2 domain in n and m be a continuous map the dirichlet problem for the minimal surface system asks whether there exists a lipschitz map f m with f and with the graph of f a minimal submanifold in n m for m 1 the dirichlet problem was solved more than 30 years ago by jenkins and serrin 12 for any mean convex domains and the solutions are all smooth this paper considers the dirichlet problem for convex domains in arbitrary codimension m we prove that if m satisfies 8n sup d2 2 sup d 1 then the dirichlet problem for is solvable in smooth maps here is the diameter of such a condition is necessary in view of an example of lawson and osserman 13 in order to prove this result we study the associated parabolic system and solve the cauchy dirichlet problem with as initial data 2003 wiley periodicals inc

an optimal algorithm for approximate nearest neighbor searching fixed dimensions consider a set of s of n data points in real d dimensional space r d where distances are measured using any minkowski metric in nearest neighbor searching we preprocess s into a data structure so that given any query point q r d is the closest point of s to q can be reported quickly given any positive real e data point p is a 1 e approximate nearest neighbor of q if its distance from q is within a factor of 1 e of the distance to the true nearest neighbor we show that it is possible to preprocess a set of n points in r d in o dn log n time and o dn space so that given a query point q r d and e 0 a 1 e approximate nearest neighbor of q can be computed in o c d e log n time where c d e d 1 6d e d is a factor depending only on dimension and e in general we show that given an integer k 1 1 e approximations to the k nearest neighbors of q can be computed in additional o kd log n time

mean curvature flow of entire graphs in a half space with a free boundary we study the mean curvature flow of graphs with prescribed contact angle on a fixed smooth hyperplane in euclidean space we obtain long time existence and convergence to a self similar solution of the mean curvature flow orthogonal to the fixed hyperplane

a convergent evolving finite element algorithm for mean curvature flow of closed surfaces a proof of convergence is given for semi and full discretizations of mean curvature flow of closed two dimensional surfaces the numerical method proposed and studied here combines evolving finite elements whose nodes determine the discrete surface like in dziuk s method and linearly implicit backward difference formulae for time integration the proposed method differs from dziuk s approach in that it discretizes huisken s evolution equations for the normal vector and mean curvature and uses these evolving geometric quantities in the velocity law projected to the finite element space this numerical method admits a convergence analysis in the case of finite elements of polynomial degree at least two and backward difference formulae of orders two to five the error analysis combines stability estimates and consistency estimates to yield optimal order h 1 norm error bounds for the computed surface position velocity normal vector and mean curvature the stability analysis is based on the matrix vector formulation of the finite element method and does not use geometric arguments the geometry enters only into the consistency estimates numerical experiments illustrate and complement the theoretical results

non parametric mean curvature evolution with boundary conditions soit un domaine borne de r n n 2 de frontiere lisse et soit a l operateur de surface minimale donne par a d i a i p a i p i 1 p 2 1 2 on considere des surfaces dont la vitesse en direction de leur normale unite est egale a la courbure moyenne on etudie l equation d evolution qui en resulte u 1 du 2 1 2 au 0 dans 0 t

isogeometric analysis of geometric partial differential equations abstract we consider the numerical approximation of geometric partial differential equations pdes defined on surfaces in the 3d space in particular we focus on the geometric pdes deriving from the minimization of an energy functional by l 2 gradient flow we analyze two energy functionals the area which leads to the mean curvature flow a nonlinear second order pde and the willmore energy leading to the willmore flow a nonlinear fourth order pde we consider surfaces represented by single patch tensor product nurbs and discretize the pdes by means of nurbs based isogeometric analysis in the framework of the galerkin method to approximate the high order geometric pdes we use high order continuous nurbs basis functions for the time discretization of the nonlinear geometric pdes we use backward differentiation formulas bdf with extrapolation of the geometric quantities involved in the weak formulation of the problem in this manner we solve a linear problem at each time step we report numerical results concerning the mean curvature and willmore flows on different geometries of interest and we show the accuracy and efficiency of the proposed approximation scheme

broadband multilevel fast multipole algorithm based on an approximate diagonalization of the green s function we present a broadband multilevel fast multipole algorithm mlfma for fast and efficient solutions of three dimensional multiscale problems involving large objects with dense discretizations the proposed solver is based on the approximate diagonalization of the green s function using scaled spherical and plane waves leading to stable interaction computations for arbitrarily short distances in terms of wavelength despite contradictory requirements on the scaling factor that limit the accuracy of the diagonalization the resulting low frequency scheme is extremely stable and easy to plug into conventional mlfma implementations by simply extending built in tree structures converting them into broadband solvers without needing dense programming efforts accuracy and efficiency of the broadband mlfma are demonstrated on canonical problems as well as on multiscale problems that cannot be solved efficiently via standard implementations of mlfma

on the strong maximum principle and the large time behavior of generalized mean curvature flow with the neumann boundary condition abstract a generalized mean curvature flow is considered in a cylindrical domain under the right angle boundary condition its large time behavior is studied by analyzing the level set equation of the flow when the initial hypersurface is not necessarily graph like for a convex domain it is shown that the solution of the level set equation converges to a function whose level sets are perpendicular to the lateral boundary of the domain as time tends to infinity when the initial data is constant outside some bounded set for this purpose a version of the strong maximum principle is established for the level set minimal surface equation although the equation is degenerate

algorithms for computing motion by mean curvature we propose a finite element algorithm for computing the motion of a surface moving by mean curvature the algorithm uses the level set formulation so that changes in topology of the surface can be accommodated stability is deduced by showing that the discrete solutions satisfy both l infty and w 1 1 bounds existence of discrete solutions and connections with brakke flows are established some numerical examples and application to related problems such as the phase field equations are also presented

a finite element method for surface diffusion the parametric case surface diffusion is a fourth order highly nonlinear geometric driven motion of a surface with normal velocity proportional to the surface laplacian of mean curvature we present a novel variational formulation for parametric surfaces with or without boundaries the method is semi implicit requires no explicit parametrization and yields a linear system of elliptic pde to solve at each time step we next develop a finite element method propose a schur complement approach to solve the resulting linear systems and show several significant simulations some with pinch off in finite time we introduce a mesh regularization algorithm which helps prevent mesh distortion and discuss the use of time and space adaptivity to increase accuracy while reducing complexity

a nondirective plane wave mlfma stable at low frequencies a novel method called the nondirective stable plane wave multilevel fast multipole algorithm nspwmlfma is presented to evaluate the low frequency lf interactions that cannot be handled by the multilevel fast multipole algorithm mlfma it is well known that the mlfma cannot be used for lf interactions since it suffers from numerical instability contrary to current techniques the proposed technique is not based on the spectral representation of the green function instead the addition theorem of the mlfma is manipulated into a form that allows numerically stable translations along the z axis the translation operator for these translations is derived in closed form a qr based method is devised to allow stable translations in all the other directions interpolations and anterpolations are also provided allowing a full multilevel algorithm since the nspwmlfma is based on the same mathematical foundations as the mlfma it requires limited adaptations to existing mlfma codes the fact that a qr is needed limits this algorithm to lf interactions however a coupling with the mlfma is straightforward allowing the easy construction of a broadband algorithm the dc limit of the algorithm is also presented and it is shown that the algorithm remains valid for static problems finally it is shown that the error introduced in the different steps of the algorithm is controllable and a single level vectorial version of the algorithm is applied to a generic scattering application to demonstrate its validity

efficient fast multipole method for low frequency scattering the solution of the helmholtz and maxwell equations using integral formulations requires to solve large complex linear systems a direct solution of those problems using a gauss elimination is practical only for very small systems with few unknowns the use of an iterative method such as gmres can reduce the computational expense most of the expense is then computing large complex matrix vector products the cost can be further reduced by using the fast multipole method which accelerates the matrix vector product for a linear system of size n the use of an iterative method combined with the fast multipole method reduces the total expense of the computation to n log n there exist two versions of the fast multipole method one which is based on a multipole expansion of the interaction kernel exp ikr r and which was first proposed by v rokhlin and another based on a plane wave expansion of the kernel first proposed by w c chew in this paper we propose a third approach the stable plane wave expansion spw fmm which has a lower computational expense than the multipole expansion and does not have the accuracy and stability problems of the plane wave expansion the computational complexity is n log n as with the other methods

a wideband fast multipole method for the helmholtz kernel this work presents a new fast multipole method fmm based on plane wave expansions pwfmm combining the advantages of the low and high frequency formulations we revisit the method of greengard etal 1998 devoted to the low frequency regime and based on the splitting of the greens function into a propagative and an evanescent part more precisely we give an explicit formula of the filtered translation function for the propagative part we derive a new formula for the evanescent part and we provide a new interpolation algorithm at all steps we check the accuracy of the method by providing error estimates these theoretical developments are used to propose a wideband fmm based entirely on plane wave expansions the numerical efficiency and accuracy of this broadband pwfmm are illustrated with a numerical example

on rotationally symmetric mean curvature flow the evolutionary motion of surfaces by their mean curvature has been studied by several authors from different points of view a measure theoretic approach is studied by k a brakke b the classical parametric problem is studied by g huisken hl non parametric mean curvature evolution with boundary conditions is treated in h2 for a detailed discussion see h3 we restrict our attention to the case in which the initial surface has rotational symmetry we shall show that under suitable initial conditions the solution degenerates in the sense that its curvature develops a singularity at exactly one point this confirms numerical results of the first author d for general surfaces in r3 see also the work of m a grayson gl p 286 g2 the proofs rely on the parabolic maximum principle the second author is gratefully indebted to s angencnt for bringing the problem to his attention and for pointing out the resemblance to so called quenching problems this research was financially via sfb 256 and sfb 123

computation and storage of the bianisotropic scalar green s function and its derivatives a set of algorithms is proposed for the accurate and efficient computation and storage of the bianisotropic scalar green s function the computation is based on an expansion of the green s function into chebyshev polynomials the analytical properties of these polynomials are exploited to allow the accurate computation of the derivatives of the green s function as well as the green s function itself for lossy materials the proposed computation strategy is provably robust in addition a multilevel storage scheme with a favorable complexity based on the chebyshev polynomial expansion is proposed for the storage of the expansion coefficients numerical results showcase the accuracy and computational complexity of the proposed algorithms

flow by mean curvature of convex surfaces into spheres the motion of surfaces by their mean curvature has been studied by brakke 1 from the viewpoint of geometric measure theory other authors investigated the corresponding nonparametric problem 2 5 9 a reason for this interest is that evolutionary surfaces of prescribed mean curvature model the behavior of grain boundaries in annealing pure metal in this paper we take a more classical point of view consider a compact uniformly convex w dimensional surface m mo without boundary which is smoothly imbedded in r let mo be represented locally by a diffeomorphism

an algorithm for evolutionary surfaces an algorithm is presented which allows to split the calculation of the mean curvature flow of surfaces with or without boundary into a series of poisson problems on a series of surfaces this gives a new method to solve plateau s problem forh surfaces

the heat flow in nonlinear hodge theory we study the nonlinear hodge systemd 0 and 2 0 for an exterior form on a compact oriented riemannian manifold m where q is a given positive function the solutions are called harmonic forms they are the stationary points on cohomology classes of the functional e me 2 dm with e q q 2 the codifferential of a form is defined as 1 with 2 we evolve a given closed form 0 by the nonlinear heat flow system d for a time dependent exterior form x t on m this system is the differential of the normalized gradient flow u for e with 0 du under a technical assumption on the function 2 q q q we show that the nonlinear heat flow system d with initial condition 0 0 has a unique solution for all times which converges to a harmonic form in the cohomology class of 0 this yields a nonlinear hodge theorem that every cohomology class of m has a unique harmonic representative

automatic liver segmentation based on shape constraints and deformable graph cut in ct images liver segmentation is still a challenging task in medical image processing area due to the complexity of the liver s anatomy low contrast with adjacent organs and presence of pathologies this investigation was used to develop and validate an automated method to segment livers in ct images the proposed framework consists of three steps 1 preprocessing 2 initialization and 3 segmentation in the first step a statistical shape model is constructed based on the principal component analysis and the input image is smoothed using curvature anisotropic diffusion filtering in the second step the mean shape model is moved using thresholding and euclidean distance transformation to obtain a coarse position in a test image and then the initial mesh is locally and iteratively deformed to the coarse boundary which is constrained to stay close to a subspace of shapes describing the anatomical variability finally in order to accurately detect the liver surface deformable graph cut was proposed which effectively integrates the properties and inter relationship of the input images and initialized surface the proposed method was evaluated on 50 ct scan images which are publicly available in two databases sliver07 and 3dircadb the experimental results showed that the proposed method was effective and accurate for detection of the liver surface

a low frequency efie mlfma solver based on approximate diagonalization of green s function the low frequency fast multipole algorithm lffma based on the approximate diagonalization of green s function for the electric field integral equation efie is proposed for open and complex structures with high accuracy moreover the multiresolution preconditioner is employed to the mixed potential form of efie with rwg basis functions for stability herein a triangle grouping scheme is adopted for the scalar potential so that the accuracy of the lffma can be guaranteed furthermore the computational resources can be reduced largely since part of the radiation pattern of vector potential can share one of the scalar potentials by taking advantage of some mathematical deductions

graph cuts and efficient n d image segmentation combinatorial graph cut algorithms have been successfully applied to a wide range of problems in vision and graphics this paper focusses on possibly the simplest application of graph cuts segmentation of objects in image data despite its simplicity this application epitomizes the best features of combinatorial graph cuts methods in vision global optima practical efficiency numerical robustness ability to fuse a wide range of visual cues and constraints unrestricted topological properties of segments and applicability to n d problems graph cuts based approaches to object extraction have also been shown to have interesting connections with earlier segmentation methods such as snakes geodesic active contours and level sets the segmentation energies optimized by graph cuts combine boundary regularization with region based properties in the same fashion as mumford shah style functionals we present motivation and detailed technical description of the basic combinatorial optimization framework for image segmentation via s t graph cuts after the general concept of using binary graph cut algorithms for object segmentation was first proposed and tested in boykov and jolly 2001 this idea was widely studied in computer vision and graphics communities we provide links to a large number of known extensions based on iterative parameter re estimation and learning multi scale or hierarchical approaches narrow bands and other techniques for demanding photo video and medical applications

contracting convex hypersurfaces in riemannian manifolds by their mean curvature which shrink towards the center of the initial sphere in finite time it was shown in 3 that this behaviour is very typical if the initial hypersurface m o o r 1 is uniformly convex then the surfaces m t contract smoothly to a single point in finite time and the shape of the surfaces becomes spherical at the end of the contraction if the ambient space n is a general riemannian manifold the curvature of n will interfere with the mot ion of the surfaces m r we want to show here that the contract ion first to a small sphere and then to a single point is still

performing interpolation and anterpolation entirely by fast fourier transform in the 3 d multilevel fast multipole algorithm the fast multipole methods are used for solving a scalar acoustic or vector electromagnetic wave equation by integral equation methods with a large number of unknowns in this paper a new method is presented for performing interpolation and anterpolation in both spherical coordinates theta and phi by fft in the three dimensional 3 d multilevel fast multipole algorithm mlfma the key idea is to approximate functions on the unit sphere by truncated fourier series in two variables rather than by the usual spherical harmonics the proposed method is exact in interpolating and anterpolating and has the high numerical efficiency of fft the method is numerically compared to the method of performing interpolation and anterpolation using lagrangian interpolation which presently is probably the fastest method for those operations and the results suggest that the proposed new method is equally or more efficient depending on the desired accuracy

a mixed form fast multipole algorithm the fast multipole algorithm manifests in two very different forms at low frequencies and at mid frequencies each can operate in their respective regimes but are not tenable in the other regimes the paper reports on a way to factorize the green s function for fast algorithm using a mixed form the low frequency fast multipole algorithm lf fma will be used at low frequencies or the long wavelength regime and the multilevel fast multipole algorithm mlfma will be used for the mid frequencies or the shorter wavelength regime for object modeling where both long wavelength and wave physics are important we propose a mixed form fast multipole algorithm mf fma this algorithm has no low frequency break down and it can work seamlessly from static where circuit physics is important to dynamic where wave physics is important

a fully discrete numerical scheme for weighted mean curvature flow we analyze a fully discrete numerical scheme approximating the evolution of n dimensional graphs under anisotropic mean curvature the highly nonlinear problem is discretized by piecewise linear finite elements in space and semi implicitly in time the scheme is unconditionally stable und we obtain optimal error estimates in natural norms we also present numerical examples which confirm our theoretical results

convergence of a finite element method for non parametric mean curvature flow convergence for the spatial discretization by linear finite elements of the non parametric mean curvature flow is proved under natural regularity assumptions on the continuous solution asymptotic convergence is also obtained for the time derivative which is proportional to mean curvature an existence result for the continuous problem in adequate spaces is included

a low frequency stable plane wave addition theorem the multilevel fast multipole algorithm mlfma is a well known and very successful method for accelerating the matrix vector products required for the iterative solution of helmholtz problems the mlfma has an important drawback namely its inability to handle scattering problems with a lot of subwavelength detail due to the low frequency lf breakdown of the mlfma there is a need to extend the mlfma to lf since alternative methods are less efficient multipole methods or hard to implement spectral methods in this paper a new addition theorem will be developed that does not suffer from an lf breakdown instead it suffers from a high frequency hf breakdown the new method relies on a novel set of distributions the so called pseudospherical harmonics closely related to the spherical harmonics these allow the discretization points and translation operators to be calculated in closed form hence the method presented in this paper allows the easy implementation of a method that is stable at lf furthermore a combination of the traditional mlfma and the new method allows for the construction of a broadband mlfma

constant mean curvature surfaces and mean curvature flow with non zero neumann boundary conditions on strictly convex domains abstract in this paper we study nonparametric surfaces over strictly convex bounded domains in r n which are evolving by the mean curvature flow with neumann boundary value we prove that solutions converge to the ones moving only by translation and we will prove the existence and uniqueness of the constant mean curvature equation with neumann boundary value on strictly convex bounded domains

three dimensional segmentation of fluid associated abnormalities in retinal oct probability constrained graph search graph cut an automated method is reported for segmenting 3 d fluid associated abnormalities in the retina so called symptomatic exudate associated derangements sead from 3 d oct retinal images of subjects suffering from exudative age related macular degeneration in the first stage of a two stage approach retinal layers are segmented candidate sead regions identified and the retinal oct image is flattened using a candidate sead aware approach in the second stage a probability constrained combined graph search graph cut method refines the candidate seads by integrating the candidate volumes into the graph cut cost function as probability constraints the proposed method was evaluated on 15 spectral domain oct images from 15 subjects undergoing intravitreal anti vegf injection treatment leave one out evaluation resulted in a true positive volume fraction tpvf false positive volume fraction fpvf and relative volume difference ratio rvdr of 86 5 1 7 and 12 8 respectively the new graph cut graph search method significantly outperformed both the traditional graph cut and traditional graph search approaches p 0 01 p 0 04 and has the potential to improve clinical management of patients with choroidal neovascularization due to exudative age related macular degeneration