fast joint estimation of silhouettes and dense 3d geometry from multiple images we propose a probabilistic formulation of joint silhouette extraction and 3d reconstruction given a series of calibrated 2d images instead of segmenting each image separately in order to construct a 3d surface consistent with the estimated silhouettes we compute the most probable 3d shape that gives rise to the observed color information the probabilistic framework based on bayesian inference enables robust 3d reconstruction by optimally taking into account the contribution of all views we solve the arising maximum a posteriori shape inference in a globally optimal manner by convex relaxation techniques in a spatially continuous representation for an interactively provided user input in the form of scribbles specifying foreground and background regions we build corresponding color distributions as multivariate gaussians and find a volume occupancy that best fits to this data in a variational sense compared to classical methods for silhouette based multiview reconstruction the proposed approach does not depend on initialization and enjoys significant resilience to violations of the model assumptions due to background clutter specular reflections and camera sensor perturbations in experiments on several real world data sets we show that exploiting a silhouette coherency criterion in a multiview setting allows for dramatic improvements of silhouette quality over independent 2d segmentations without any significant increase of computational efforts this results in more accurate visual hull estimation needed by a multitude of image based modeling approaches we made use of recent advances in parallel computing with a gpu implementation of the proposed method generating reconstructions on volume grids of more than 20 million voxels in up to 4 41 seconds

a kam theorem for hamiltonian partial differential equations with unbounded perturbations we establish an abstract infinite dimensional kam theorem dealing with unbounded perturbation vector field which could be applied to a large class of hamiltonian pdes containing the derivative x in the perturbation especially in this range of application lie a class of derivative nonlinear schrodinger equations with dirichlet boundary conditions and perturbed benjamin ono equation with periodic boundary conditions so kam tori and thus quasi periodic solutions are obtained for them

structured prediction dual extragradient and bregman projections we present a simple and scalable algorithm for maximum margin estimation of structured output models including an important class of markov networks and combinatorial models we formulate the estimation problem as a convex concave saddle point problem that allows us to use simple projection methods based on the dual extragradient algorithm nesterov 2003 the projection step can be solved using dynamic programming or combinatorial algorithms for min cost convex flow depending on the structure of the problem we show that this approach provides a memory efficient alternative to formulations based on reductions to a quadratic program qp we analyze the convergence of the method and present experiments on two very different structured prediction tasks 3d image segmentation and word alignment illustrating the favorable scaling properties of our algorithm

maximal flow through a domain in place of flows on a discrete network we study flows described by a vector field x y in a plane domain the analogue of the capacity constraint is c x y and the strength of sources and sinks is n f on the boundary and div f in the interior we show that the largest the maximal flow is determined by the minimal cut as in the discrete case the dual problem has a 0 1 solution given by the characteristic function of the minimal cut for the continuous problem the argument depends on the coarea formula for functions of bounded variation

multi view stereo reconstruction and scene flow estimation with a global image based matching score we present a new variational method for multi view stereovision and non rigid three dimensional motion estimation from multiple video sequences our method minimizes the prediction error of the shape and motion estimates both problems then translate into a generic image registration task the latter is entrusted to a global measure of image similarity chosen depending on imaging conditions and scene properties rather than integrating a matching measure computed independently at each surface point our approach computes a global image based matching score between the input images and the predicted images the matching process fully handles projective distortion and partial occlusions neighborhood as well as global intensity information can be exploited to improve the robustness to appearance changes due to non lambertian materials and illumination changes without any approximation of shape motion or visibility moreover our approach results in a simpler more flexible and more efficient implementation than in existing methods the computation time on large datasets does not exceed thirty minutes on a standard workstation finally our method is compliant with a hardware implementation with graphics processor units our stereovision algorithm yields very good results on a variety of datasets including specularities and translucency we have successfully tested our motion estimation algorithm on a very challenging multi view video sequence of a non rigid scene

enhancing multiple point geostatistical modeling 1 graph theory and pattern adjustment in recent years higher order geostatistical methods have been used for modeling of a wide variety of large scale porous media such as groundwater aquifers and oil reservoirs their popularity stems from their ability to account for qualitative data and the great flexibility that they offer for conditioning the models to hard quantitative data which endow them with the capability for generating realistic realizations of porous formations with very complex channels as well as features that are mainly a barrier to fluid flow one group of such models consists of pattern based methods that use a set of data points for generating stochastic realizations by which the large scale structure and highly connected features are reproduced accurately the cross correlation based simulation ccsim algorithm proposed previously by the authors is a member of this group that has been shown to be capable of simulating multimillion cell models in a matter of a few cpu seconds the method is however sensitive to pattern s specifications such as boundaries and the number of replicates in this paper the original ccsim algorithm is reconsidered and two significant improvements are proposed for accurately reproducing large scale patterns of heterogeneities in porous media first an effective boundary correction method based on the graph theory is presented by which one identifies the optimal cutting path surface for removing the patchiness and discontinuities in the realization of a porous medium next a new pattern adjustment method is proposed that automatically transfers the features in a pattern to one that seamlessly matches the surrounding patterns the original ccsim algorithm is then combined with the two methods and is tested using various complex two and three dimensional examples it should however be emphasized that the methods that we propose in this paper are applicable to other pattern based geostatistical simulation methods

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

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

multiview stereo via volumetric graph cuts and occlusion robust photo consistency this paper presents a volumetric formulation for the multiview stereo problem which is amenable to a computationally tractable global optimization using graph cuts our approach is to seek the optimal partitioning of 3d space into two regions labeled as object and empty under a cost functional consisting of the following two terms 1 a term that forces the boundary between the two regions to pass through photo consistent locations and 2 a ballooning term that inflates the object region to take account of the effect of occlusion on the first term we use an occlusion robust photo consistency metric based on normalized cross correlation which does not assume any geometric knowledge about the reconstructed object the globally optimal 3d partitioning can be obtained as the minimum cut solution of a weighted graph

gradient flows for optimizing triangular mesh based surfaces applications to 3d reconstruction problems dealing with visibility this article tackles the problem of using variational methods for evolving 3d deformable surfaces we give an overview of gradient descent flows when the shape is represented by a triangular mesh based surface and we detail the gradients of two generic energy functionals which embody a number of energies used in mesh processing and computer vision in particular we show how to rigorously account for visibility in the surface optimization process we present different applications including 3d reconstruction from multiple views for which the visibility is fundamental the gradient correctly takes into account the visibility changes that occur when a surface moves this forces the contours generated by the reconstructed surface to match with the apparent contours in the input images

boundary detection by constrained optimization a statistical framework is used for finding boundaries and for partitioning scenes into homogeneous regions the model is a joint probability distribution for the array of pixel gray levels and an array of labels in boundary finding the labels are binary zero or one representing the absence or presence of boundary elements in partitioning the label values are generic two labels are the same when the corresponding scene locations are considered to belong to the same region the distribution incorporates a measure of disparity between certain spatial features of block pairs of pixel gray levels using the kolmogorov smirnov nonparametric measures of difference between the distributions of these features the number of model parameters is minimized by forbidding label configurations which are assigned probability zero the maximum a posteriori estimator of boundary placements and partitionings is examined the forbidden states introduce constraints into the calculation of these configurations stochastic relaxation methods are extended to accommodate constrained optimization

deformations of special legendrian submanifolds in sasaki einstein manifolds in this paper we study the deformation theory of submanifolds characterized by a system of differential forms and provide a criterion for deformations of such submanifolds to be unobstructed we apply this deformation theory to special legendrian submanifolds in sasaki einstein manifolds in general special legendrian deformations have the obstruction however we show that the deformation space of special legendrian submanifolds is the intersection of two larger smooth deformation spaces of different types we also prove that any special legendrian submanifold admits smooth deformations which are not special legendrian deformations given by harmonic 1 forms

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

a linear framework for region based image segmentation and inpainting involving curvature penalization we present the first method to handle curvature regularity in region based image segmentation and inpainting that is independent of initialization to this end we start from a new formulation of length based optimization schemes based on surface continuation constraints and discuss the connections to existing schemes the formulation is based on a cell complex and considers basic regions and boundary elements the corresponding optimization problem is cast as an integer linear program we then show how the method can be extended to include curvature regularity again cast as an integer linear program here we are considering pairs of boundary elements to reflect curvature moreover a constraint set is derived to ensure that the boundary variables indeed reflect the boundary of the regions described by the region variables we show that by solving the linear programming relaxation one gets reasonably close to the global optimum and that curvature regularity is indeed much better suited in the presence of long and thin objects compared to standard length regularity

on reducibility of schrodinger equations with quasiperiodic in time potentials we prove that a linear d dimensional schrodinger equation with an x periodic and t quasiperiodic potential reduces to an autonomous equation for most values of the frequency vector the reduction is made by means of a non autonomous linear transformation of the space of x periodic functions this transformation is a quasiperiodic function of t

segmentation given partial grouping constraints we consider data clustering problems where partial grouping is known a priori we formulate such biased grouping problems as a constrained optimization problem where structural properties of the data define the goodness of a grouping and partial grouping cues define the feasibility of a grouping we enforce grouping smoothness and fairness on labeled data points so that sparse partial grouping information can be effectively propagated to the unlabeled data considering the normalized cuts criterion in particular our formulation leads to a constrained eigenvalue problem by generalizing the rayleigh ritz theorem to projected matrices we find the global optimum in the relaxed continuous domain by eigendecomposition from which a near global optimum to the discrete labeling problem can be obtained effectively we apply our method to real image segmentation problems where partial grouping priors can often be derived based on a crude spatial attentional map that binds places with common salient features or focuses on expected object locations we demonstrate not only that it is possible to integrate both image structures and priors in a single grouping process but also that objects can be segregated from the background without specific object knowledge

a theory of shape by space carving in this paper we consider the problem of computing the 3d shape of an unknown arbitrarily shaped scene from multiple photographs taken at known but arbitrarily distributed viewpoints by studying the equivalence class of all 3d shapes that reproduce the input photographs we prove the existence of a special member of this class the photo hull that 1 can be computed directly from photographs of the scene and 2 subsumes all other members of this class we then give a provably correct algorithm called space carving for computing this shape and present experimental results on complex real world scenes the approach is designed to 1 capture photorealistic shapes that accurately model scene appearance from a wide range of viewpoints and 2 account for the complex interactions between occlusion parallax shading and their view dependent effects on scene appearance

a reduction theorem for time dependent schrodinger operator with finite differentiable unbounded perturbation in this paper we consider the time dependent schrodinger operator with a temporal quasi periodic perturbation which is some function of class cl for any l 100 3n 2 1 by using the kam technique we establish a reduction theorem for the above operator and prove that the invariant tori of the nearly integrable hamiltonian system with unbounded small perturbation are linearly stable both for d d 1 and the limiting case d d 1

power watershed a unifying graph based optimization framework in this work we extend a common framework for graph based image segmentation that includes the graph cuts random walker and shortest path optimization algorithms viewing an image as a weighted graph these algorithms can be expressed by means of a common energy function with differing choices of a parameter q acting as an exponent on the differences between neighboring nodes introducing a new parameter p that fixes a power for the edge weights allows us to also include the optimal spanning forest algorithm for watershed in this same framework we then propose a new family of segmentation algorithms that fixes p to produce an optimal spanning forest but varies the power q beyond the usual watershed algorithm which we term the power watershed in particular when q 2 the power watershed leads to a multilabel scale and contrast invariant unique global optimum obtained in practice in quasi linear time placing the watershed algorithm in this energy minimization framework also opens new possibilities for using unary terms in traditional watershed segmentation and using watershed to optimize more general models of use in applications beyond image segmentation

floquet hamiltonians with pure point spectrum we consider floquet hamiltonians of the type k f i partial t h 0 beta v omega t whereh0 a selfadjoint operator acting in a hilbert space has simple discrete spectrume1 0 for a given 0 t v t is 2 periodic andr times strongly continuously differentiable as a bounded operator on and are real parameters and the periodic boundary condition is imposed in time we show roughly that providedr is large enough small enough and non resonant then the spectrum ofkf is pure point the method we use relies on a successive application of the adiabatic treatment due to howland and the kam type iteration settled by bellissard and extended by combescure both tools are revisited adjusted and at some points slightly simplified

sar image regularization with fast approximate discrete minimization synthetic aperture radar sar images like other coherent imaging modalities suffer from speckle noise the presence of this noise makes the automatic interpretation of images a challenging task and noise reduction is often a prerequisite for successful use of classical image processing algorithms numerous approaches have been proposed to filter speckle noise markov random field mrf modelization provides a convenient way to express both data fidelity constraints and desirable properties of the filtered image in this context total variation minimization has been extensively used to constrain the oscillations in the regularized image while preserving its edges speckle noise follows heavy tailed distributions and the mrf formulation leads to a minimization problem involving nonconvex log likelihood terms such a minimization can be performed efficiently by computing minimum cuts on weighted graphs due to memory constraints exact minimization although theoretically possible is not achievable on large images required by remote sensing applications the computational burden of the state of the art algorithm for approximate minimization namely the alpha expansion is too heavy specially when considering joint regularization of several images we show that a satisfying solution can be reached in few iterations by performing a graph cut based combinatorial exploration of large trial moves this algorithm is applied to joint regularization of the amplitude and interferometric phase in urban area sar images

moser s theorem for lower dimensional tori moser s c version of kolmogorov s theorem on the persistence of maximal quasi periodic solutions for nearly integrable hamiltonian system is extended to the persistence of non maximal quasi periodic solutions corresponding to lower dimensional elliptic tori of any dimension n between one and the number of degrees of freedom the theorem is proved for hamiltonian

a super resolution framework for high accuracy multiview reconstruction we present a variational framework to estimate super resolved texture maps on a 3d geometry model of a surface from multiple images given the calibrated images and the reconstructed geometry the proposed functional is convex in the super resolution texture using a conformal atlas of the surface we transform the model from the curved geometry to the flat charts and solve it using state of the art and provably convergent primal dual algorithms in order to improve image alignment and quality of the texture we extend the functional to also optimize for a normal displacement map on the surface as well as the camera calibration parameters since the sub problems for displacement and camera parameters are non convex we revert to relaxation schemes in order to robustly estimate a minimizer via sequential convex programming experimental results confirm that the proposed super resolution framework allows to recover textured models with significantly higher level of detail than the individual input images

reducibility for wave equations of finitely smooth potential with periodic boundary conditions abstract in the present paper the reducibility is derived for the wave equations with finitely smooth and time quasi periodic potential subject to periodic boundary conditions more exactly the linear wave equation u t t u x x m u e v 0 t u x x v t x u 0 x r 2 z can be reduced to a linear hamiltonian system with a constant coefficient operator which is of pure imaginary point spectrum set where v is finitely smooth in t x quasi periodic in time t with diophantine frequency r n and v 0 is finitely smooth and quasi periodic in time t with diophantine frequency r n moreover it is proved that the corresponding wave operator possesses the property of pure point spectra and zero lyapunov exponent

continuous global optimization in multiview 3d reconstruction in this article we introduce a new global optimization method to the field of multiview 3d reconstruction while global minimization has been proposed in a discrete formulation in form of the maxflow mincut framework we suggest the use of a continuous convex relaxation scheme specifically we propose to cast the problem of 3d shape reconstruction as one of minimizing a spatially continuous convex functional in qualitative and quantitative evaluation we demonstrate several advantages of the proposed continuous formulation over the discrete graph cut solution firstly geometric properties such as weighted boundary length and surface area are represented in a numerically consistent manner the continuous convex relaxation assures that the algorithm does not suffer from metrication errors in the sense that the reconstruction converges to the continuous solution as the spatial resolution is increased moreover memory requirements are reduced allowing for globally optimal reconstructions at higher resolutions we study three different energy models for multiview reconstruction which are based on a common variational template unifying regional volumetric terms and on surface photoconsistency the three models use data measurements at increasing levels of sophistication while the first two approaches are based on a classical silhouette based volume subdivision the third one relies on stereo information to define regional costs furthermore this scheme is exploited to compute a precise photoconsistency measure as opposed to the classical estimation all three models are compared on standard data sets demonstrating their advantages and shortcomings for the third one which gives the most accurate results a more exhaustive qualitative and quantitative evaluation is presented

optimal approximations by piecewise smooth functions and associated variational problems abstract this reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision in computer vision a fundamental problem is to appropriately decompose the domain r of a function g x y of two variables this problem starts by describing the physical situation which produces images assume that a three dimensional world is observed by an eye or camera from some point p and that g1 rho represents the intensity of the light in this world approaching the point sub 1 from a direction rho if one has a lens at p focusing this light on a retina or a film in both cases a plane domain r in which we may introduce coordinates x y then let g x y be the strength of the light signal striking r at a point with coordinates x y g x y is essentially the same as sub 1 rho possibly after a simple transformation given by the geometry of the imaging syste the function g x y defined on the plane domain r will be called an image what sort of function is g the light reflected off the surfaces si of various solid objects o sub i visible from p will strike the domain r in various open subsets r sub i when one object o1 is partially in front of another object o2 as seen from p but some of object o2 appears as the background to the sides of o1 then the open sets r1 and r2 will have a common boundary the edge of object o1 in the image defined on r and one usually expects the image g x y to be discontinuous along this boundary jhd

multi view performance capture of surface details this paper presents a novel approach to recover true fine surface detail of deforming meshes reconstructed from multi view video template based methods for performance capture usually produce a coarse to medium scale detail 4d surface reconstruction which does not contain the real high frequency geometric detail present in the original video footage fine scale deformation is often incorporated in a second pass by using stereo constraints features or shading based refinement in this paper we propose an alternative solution to this second stage by formulating dense dynamic surface reconstruction as a global optimization problem of the densely deforming surface our main contribution is an implicit representation of a deformable mesh that uses a set of gaussian functions on the surface to represent the initial coarse mesh and a set of gaussians for the images to represent the original captured multi view images we effectively find the fine scale deformations for all mesh vertices which maximize photo temporal consistency by densely optimizing our model to image consistency energy on all vertex positions our formulation yields a smooth closed form energy with implicit occlusion handling and analytic derivatives furthermore it does not require error prone correspondence finding or discrete sampling of surface displacement values we demonstrate our approach on a variety of datasets of human subjects wearing loose clothing and performing different motions we qualitatively and quantitatively demonstrate that our technique successfully reproduces finer detail than the input baseline geometry

generalized flows for optimal inference in higher order mrf map use of higher order clique potentials in mrf map problems has been limited primarily because of the inefficiencies of the existing algorithmic schemes we propose a new combinatorial algorithm for computing optimal solutions to 2 label mrf map problems with higher order clique potentials the algorithm runs in time o 2 kn 3 in the worst case k is size of clique and n is the number of pixels a special gadget is introduced to model flows in a higher order clique and a technique for building a flow graph is specified based on the primal dual structure of the optimization problem the notions of the capacity of an edge and a cut are generalized to define a flow problem we show that in this flow graph when the clique potentials are submodular the max flow is equal to the min cut which also is the optimal solution to the problem we show experimentally that our algorithm provides significantly better solutions in practice and is hundreds of times faster than solution schemes like dual decomposition 1 trws 2 and reduction 3 4 5 the framework represents a significant advance in handling higher order problems making optimal inference practical for medium sized cliques

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

level set methods an overview and some recent results the level set method was devised by s osher and j a sethian 1988 j comput phys 79 12 49 as a simple and versatile method for computing and analyzing the motion of an interface in two or three dimensions bounds a possibly multiply connected region the goal is to compute and analyze the subsequent motion of under a velocity field v this velocity can depend on position time the geometry of the interface and the external physics the interface is captured for later time as the zero level set of a smooth at least lipschitz continuous function x t i e t x x t 0 is positive inside negative outside and is zero on t topological merging and breaking are well defined and easily performed in this review article we discuss recent variants and extensions including the motion of curves in three dimensions the dynamic surface extension method fast methods for steady state problems diffusion generated motion and the variational level set approach we also give a user s guide to the level set dictionary and technology and couple the method to a wide variety of problems involving external physics such as compressible and incompressible possibly reacting flow stefan problems kinetic crystal growth epitaxial growth of thin films vortex dominated flows and extensions to multiphase motion we conclude with a discussion of applications to computer vision and image processing

exact solution to median surface problem using 3d graph search and application to parameter space exploration in this paper we propose the generalized median surface problem and present an exact solution by applying a 3d graph search algorithm to our knowledge this is a novel class of median computation problem which has not been considered before in the literature in addition to the theoretic interest in median surface computation we also demonstrate its practical value by means of the task of parameter space exploration without ground truth which is an effective means of dealing with the difficult parameter selection problem for image segmentation we present a concrete application for artery boundary detection in sonography ultrasound imaging it will be shown that the median computation can not only avoid the parameter training but also potentially achieve results comparable with trained parameters the median based approach can thus be a good alternate particularly in situations with no ground truth available highlightsthis paper proposes the median surface problem an optimal graph search algorithm is applied to solve the problem efficiently experimental work is conducted to demonstrate its usability it can potentially be used for segmentation parameter exploration

the geometric complexity of special lagrangian t2 cones we prove a number of results on the geometric complexity of special lagrangian slg t2 cones in 3 every slg t2 cone has a fundamental integer invariant its spectral curve genus we prove that the spectral curve genus of an slg t2 cone gives a lower bound for its geometric complexity i e the area the stability index and the legendrian index of any slg t2 cone are all bounded below by explicit linearly growing functions of the spectral curve genus we prove that the cone on the clifford torus which has spectral curve genus zero in s5 is the unique slg t2 cone with the smallest possible legendrian index and hence that it is the unique stable slg t2 cone this leads to a classification of all rigid index 1 slg cone types in dimension three for cones with spectral curve genus two we give refined lower bounds for the area the legendrian index and the stability index one consequence of these bounds is that there exist s1 invariant slg torus cones of arbitrarily large area legendrian and stability indices we explain some consequences of our results for the programme due to joyce to understand the most common three dimensional isolated singularities of generic families of slg submanifolds in almost calabi yau manifolds

reducibility of quantum harmonic oscillator on rd with differential and quasi periodic in time potential abstract we improve the results in the following two aspects by grebert and paturel in 28 and prove that a linear schrodinger equation on r d with harmonic potential x 2 and small t quasiperiodic potential as i u t u x 2 u e v t x u 0 t x r r d reduces to an autonomous system for most values of the frequency vector r n firstly we assume the potential v is only in c t n h s r d with large enough secondly the condition on s is better than 28 as a consequence any solution of such a linear pde is almost periodic in time and remains bounded in some suitable sobolev norms

schrodinger operators in the twentieth century this paper reviews the past fifty years of work on spectral theory and related issues in nonrelativistic quantum mechanics

kam for the nonlinear schrodinger equation we consider the d dimensional nonlinear schrodinger equation under periodic boundary conditions i dot u delta u v x u ep frac p f p bar u x u bar u quad u u t x x in t d where v x sum hat v a e i sc a x is an analytic function with hat v real and f is a real analytic function in re u im u and x this equation is a popular model for the real nls equation where instead of the convolution term v u we have the potential term vu for ep 0 the equation is linear and has time quasi periodic solutions u u t x sum a in a hat u a e i a 2 hat v a t e i sc a x quad hat u a 0 where a is any finite subset of z d we shall treat omega a a 2 hat v a a ina as free parameters in some domain u subset r a this is a hamiltonian system in infinite degrees of freedom degenerate but with external parameters and we shall describe a kam theory which under general conditions will have the following consequence if ep is sufficiently small then there is a large subset u of u such that for all omega in u the solution u persists as a time quasi periodic solution which has all lyapounov exponents equal to zero and whose linearized equation is reducible to constant coefficients

spectrum for quantum duffing oscillator and small divisor equation with large variable coefficient by establishing a new estimate of the solutions for the small divisor equation with large variable coefficients and using the kam technique we prove a reduction theorem that entails the pure point nature of the floquet spectrum of the quantum duffing oscillator with a small perturbation temporal quasi periodic with nonresonant frequencies 2010 wiley periodicals inc

a variational approach to vesicle membrane reconstruction from fluorescence imaging biological applications like vesicle membrane analysis involve the precise segmentation of 3d structures in noisy volumetric data obtained by techniques like magnetic resonance imaging mri or laser scanning microscopy lsm dealing with such data is a challenging task and requires robust and accurate segmentation methods in this article we propose a novel energy model for 3d segmentation fusing various cues like regional intensity subdivision edge alignment and orientation information the uniqueness of the approach consists in the definition of a new anisotropic regularizer which accounts for the unbalanced slicing of the measured volume data and the generalization of an efficient numerical scheme for solving the arising minimization problem based on linearization and fixed point iteration we show how the proposed energy model can be optimized globally by making use of recent continuous convex relaxation techniques the accuracy and robustness of the presented approach are demonstrated by evaluating it on multiple real data sets and comparing it to alternative segmentation methods based on level sets although the proposed model is designed with focus on the particular application at hand it is general enough to be applied to a variety of different segmentation tasks

minimization of monotonically levelable higher order mrf energies via graph cuts a feature of minimizing images of submodular binary markov random field mrf energies is introduced using this novel feature the collection of minimizing images of levels of higher order monotonically levelable multilabel mrf energies is shown to constitute a monotone collection this implies that these minimizing binary images can be combined to give minimizing images of the multilabel mrf energies thanks to the graph cuts framework the mentioned class of binary mrf energies is known to be minimized by maximum flow computations on appropriately constructed graphs with the aid of these developments an exact and efficient algorithm to minimize monotonically levelable multilabel mrf energies of any order which is composed of a series of maximum flow computations is proposed and an application of the proposed algorithm to image denoising is given

new loss functions in bayesian imaging abstract unlike the development of more accurate prior distributions for use in bayesian imaging the design of more sensible estimators through loss functions has been neglected in the literature we discuss the design of loss functions with a local structure that depend only on a binary misclassification vector the proposed approach is similar to modeling with a markov random field the bayes estimate is calculated in a two step algorithm using markov chain monte carlo and simulated annealing algorithms we present simulation experiments with the ising model where the observations are corrupted with gaussian and flip noise

absolute continuity of the floquet spectrum for a nonlinearly forced harmonic oscillator we prove that the floquet spectrum of the time periodic schrodinger equation corresponding to a mildly nonlinear resonant forcing is purely absolutely continuous for suitably small

time quasi periodic unbounded perturbations of schrodinger operators and kam methods we eliminate by kam methods the time dependence in a class of linear differential equations in l2 subject to an unbounded quasi periodic forcing this entails the pure point nature of the floquet spectrum of the operator h0 ep t for e small here h0 is the one dimensional schrodinger operator p2 v v x x 2 for x the time quasi periodic perturbation p may grow as x 2 2 and the frequency vector is non resonant the proof extends to infinite dimensional spaces the result valid for quasiperiodically forced linear differential equations and is based on kuksin s estimate of solutions of homological equations with non constant coefficients