stability and evolution of the quiescent and travelling solitonic bubbles abstract we simulate numerically the dynamics of the bubble like solitons of the cubic quintic nonlinear schrodinger equation in agreement with earlier predictions slow moving bubbles have been observed to be unstable in contrast to rapid bubbles which stabilize above a certain critical velocity the empirical formula for the critical velocity has been confirmed to a high degree of accuracy based on the choice of some critical perturbation we derive an integral criterion for stability of kinks and bubbles of the general nonlinear schrodinger equation which provides an explanation of the appearance of the critical velocity finally we follow numerically the nonlinear evolution of the unstable bubbles in one two and three dimensions

minimizing energies with hierarchical costs computer vision is full of problems elegantly expressed in terms of energy minimization we characterize a class of energies with hierarchical costs and propose a novel hierarchical fusion algorithm hierarchical costs are natural for modeling an array of difficult problems for example in semantic segmentation one could rule out unlikely object combinations via hierarchical context in geometric model estimation one could penalize the number of unique model families in a solution not just the number of models a kind of hierarchical mdl criterion hierarchical fusion uses the well known expansion algorithm as a subroutine and offers a much better approximation bound in important cases

nonlinear schrodinger equations and sharp interpolation estimates a sharp sufficient condition for global existence is obtained for the nonlinear schrodinger equation begin array 20 c nls 2i phi t delta phi left phi right 2 sigma phi 0 x in mathbb r n t in mathbb r end array in the case 2 n this condition is in terms of an exact stationary solution nonlinear ground state of nls it is derived by solving a variational problem to obtain the best constant for classical interpolation estimates of nirenberg and gagliardo

minimizing nonsubmodular functions with graph cuts a review optimization techniques based on graph cuts have become a standard tool for many vision applications these techniques allow to minimize efficiently certain energy functions corresponding to pairwise markov random fields mrfs currently there is an accepted view within the computer vision community that graph cuts can only be used for optimizing a limited class of mrf energies e g submodular functions in this survey we review some results that show that graph cuts can be applied to a much larger class of energy functions in particular nonsubmodular functions while these results are well known in the optimization community to our knowledge they were not used in the context of computer vision and mrf optimization we demonstrate the relevance of these results to vision on the problem of binary texture restoration

exact optimization for markov random fields with convex priors we introduce a method to solve exactly a first order markov random field optimization problem in more generality than was previously possible the mrf has a prior term that is convex in terms of a linearly ordered label set the method maps the problem into a minimum cut problem for a directed graph for which a globally optimal solution can be found in polynomial time the convexity of the prior function in the energy is shown to be necessary and sufficient for the applicability of the method

computer simulation of wave collapses in the nonlinear schro dinger equation abstract the self tuning numerical scheme for simulation of collapse phenomena in the framework of the nonlinear schrodinger equation is developed the scheme allows to reach extremely high field amplitudes 2 0 2 10 15 without lack of validity numerical results are compared with analytical predictions

highly accurate optic flow computation with theoretically justified warping in this paper we suggest a variational model for optic flow computation based on non linearised and higher order constancy assumptions besides the common grey value constancy assumption also gradient constancy as well as the constancy of the hessian and the laplacian are proposed since the model strictly refrains from a linearisation of these assumptions it is also capable to deal with large displacements for the minimisation of the rather complex energy functional we present an efficient numerical scheme employing two nested fixed point iterations following a coarse to fine strategy it turns out that there is a theoretical foundation of so called warping techniques hitherto justified only on an experimental basis since our algorithm consists of the integration of various concepts ranging from different constancy assumptions to numerical implementation issues a detailed account of the effect of each of these concepts is included in the experimental section the superior performance of the proposed method shows up by significantly smaller estimation errors when compared to previous techniques further experiments also confirm excellent robustness under noise and insensitivity to parameter variations

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

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

stabilizing static output feedback receding horizon controls for linear discrete time invariant systems in this paper a stabilizing static output feedback receding horizon control rhc is proposed for linear discrete time invariant systems an inequality condition on the terminal weighting matrices is presented under which the closed loop stability of static output feedback receding horizon controls is guaranteed it is shown that the stabilizing static output feedback receding horizon control problem can be represented as a non linear minimization problem based on linear matrix inequalities lmis an algorithm for solving the presented non linear minimization problem is proposed in addition this result is extended to an arbitrary reference tracking problem that is one of the main features of receding horizon control finally the efficiency of the proposed algorithm is illustrated by numerical examples

3d scene flow estimation with a piecewise rigid scene model 3d scene flow estimation aims to jointly recover dense geometry and 3d motion from stereoscopic image sequences thus generalizes classical disparity and 2d optical flow estimation to realize its conceptual benefits and overcome limitations of many existing methods we propose to represent the dynamic scene as a collection of rigidly moving planes into which the input images are segmented geometry and 3d motion are then jointly recovered alongside an over segmentation of the scene this piecewise rigid scene model is significantly more parsimonious than conventional pixel based representations yet retains the ability to represent real world scenes with independent object motion it furthermore enables us to define suitable scene priors perform occlusion reasoning and leverage discrete optimization schemes toward stable and accurate results assuming the rigid motion to persist approximately over time additionally enables us to incorporate multiple frames into the inference to that end each view holds its own representation which is encouraged to be consistent across all other viewpoints and frames in a temporal window we show that such a view consistent multi frame scheme significantly improves accuracy especially in the presence of occlusions and increases robustness against adverse imaging conditions our method currently achieves leading performance on the kitti benchmark for both flow and stereo

continuous 3d label stereo matching using local expansion moves we present an accurate stereo matching method using local expansion moves based on graph cuts this new move making scheme is used to efficiently infer per pixel 3d plane labels on a pairwise markov random field mrf that effectively combines recently proposed slanted patch matching and curvature regularization terms the local expansion moves are presented as many alpha expansions defined for small grid regions the local expansion moves extend traditional expansion moves by two ways localization and spatial propagation by localization we use different candidate alpha labels according to the locations of local alpha expansions by spatial propagation we design our local alpha expansions to propagate currently assigned labels for nearby regions with this localization and spatial propagation our method can efficiently infer mrf models with a continuous label space using randomized search our method has several advantages over previous approaches that are based on fusion moves or belief propagation it produces submodular moves deriving a subproblem optimality it helps find good smooth piecewise linear disparity maps it is suitable for parallelization it can use cost volume filtering techniques for accelerating the matching cost computations even using a simple pairwise mrf our method is shown to have best performance in the middlebury stereo benchmark v2 and v3

eigenvalue cutoff in the cubic quintic nonlinear schrodinger equation using theoretical arguments we prove the numerically well known fact that the eigenvalues of all localized stationary solutions of the cubic quintic 2 1 dimensional nonlinear schr odinger equation exhibit an upper cutoff value the existence of the cutoff is inferred using gagliardo nirenberg and h older inequalities together with pohozaev identities we also show that in the limit of eigenvalues close to zero the eigenstates of the cubic quintic nonlinear schr odinger equation behave similarly to those of the cubic nonlinear schr odinger equation

fusion moves for markov random field optimization the efficient application of graph cuts to markov random fields mrfs with multiple discrete or continuous labels remains an open question in this paper we demonstrate one possible way of achieving this by using graph cuts to combine pairs of suboptimal labelings or solutions we call this combination process the fusion move by employing recently developed graph cut based algorithms so called qpbo graph cut the fusion move can efficiently combine two proposal labelings in a theoretically sound way which is in practice often globally optimal we demonstrate that fusion moves generalize many previous graph cut approaches which allows them to be used as building blocks within a broader variety of optimization schemes than were considered before in particular we propose new optimization schemes for computer vision mrfs with applications to image restoration stereo and optical flow among others within these schemes the fusion moves are used 1 for the parallelization of mrf optimization into several threads 2 for fast mrf optimization by combining cheap to compute solutions and 3 for the optimization of highly nonconvex continuous labeled mrfs with 2d labels our final example is a nonvision mrf concerned with cartographic label placement where fusion moves can be used to improve the performance of a standard inference method loopy belief propagation

a comparative study of energy minimization methods for markov random fields with smoothness based priors among the most exciting advances in early vision has been the development of efficient energy minimization algorithms for pixel labeling tasks such as depth or texture computation it has been known for decades that such problems can be elegantly expressed as markov random fields yet the resulting energy minimization problems have been widely viewed as intractable algorithms such as graph cuts and loopy belief propagation lbp have proven to be very powerful for example such methods form the basis for almost all the top performing stereo methods however the trade offs among different energy minimization algorithms are still not well understood in this paper we describe a set of energy minimization benchmarks and use them to compare the solution quality and runtime of several common energy minimization algorithms we investigate three promising methods graph cuts lbp and tree reweighted message passing in addition to the well known older iterated conditional mode icm algorithm our benchmark problems are drawn from published energy functions used for stereo image stitching interactive segmentation and denoising we also provide a general purpose software interface that allows vision researchers to easily switch between optimization methods the benchmarks code images and results are available at http vision middlebury edu mrf

discrete and continuous models for partitioning problems recently variational relaxation techniques for approximating solutions of partitioning problems on continuous image domains have received considerable attention since they introduce significantly less artifacts than established graph cut based techniques this work is concerned with the sources of such artifacts we discuss the importance of differentiating between artifacts caused by discretization and those caused by relaxation and provide supporting numerical examples moreover we consider in depth the consequences of a recent theoretical result concerning the optimality of solutions obtained using a particular relaxation method since the employed regularizer is quite tight the considered relaxation generally involves a large computational cost we propose a method to significantly reduce these costs in a fully automatic way for a large class of metrics including tree metrics thus generalizing a method recently proposed by strekalovskiy and cremers ieee conference on computer vision and pattern recognition pp 1905 1911 2011

grma generalized range move algorithms for the efficient optimization of mrfs markov random fields mrf have become an important tool for many vision applications and the optimization of mrfs is a problem of fundamental importance recently veksler and kumar et al proposed the range move algorithms which are some of the most successful optimizers instead of considering only two labels as in previous move making algorithms they explore a large search space over a range of labels in each iteration and significantly outperform previous move making algorithms however two problems have greatly limited the applicability of range move algorithms 1 they are limited in the energy functions they can handle i e only truncated convex functions 2 they tend to be very slow compared to other move making algorithms e g alpha expansion and alpha beta swap in this paper we propose two generalized range move algorithms grma for the efficient optimization of mrfs to address the first problem we extend the grmas to more general energy functions by restricting the chosen labels in each move so that the energy function is submodular on the chosen subset furthermore we provide a feasible sufficient condition for choosing these subsets of labels to address the second problem we dynamically obtain the iterative moves by solving set cover problems this greatly reduces the number of moves during the optimization we also propose a fast graph construction method for the grmas experiments show that the grmas offer a great speedup over previous range move algorithms while yielding competitive solutions

computational methods for parametric lq problems a survey iterative methods for finding the optimal constant feedback gains for parametric lq problems notably for optimal constant output feedback problems are surveyed the connections of several methods to loss function expansions are discussed with important implications to the understanding of their convergence properties especially the descent anderson moore method levine athans like methods and the newton method are considered convergence results are also included the initialization problem and the output feedback stabilization problem are also discussed furthermore it is shown that the concepts and methods surveyed in this paper are useful in solving many realistic generalized parametric lq problems as well notably so called robust parametric lq problems

stability and evolution of solitary waves in perturbed generalized nonlinear schrodinger equations in this paper we study the stability and evolution of solitary waves in perturbed generalized nonlinear schrodinger nls equations our method is based on the completeness of the bounded eigenstates of the associated linear operator in l2 space and a standard multiple scale perturbation technique unlike the adiabatic perturbation method our method details all instability mechanisms caused by perturbations of such equations and explicitly specifies when such instabilities will occur in particular our method uncovers the instability caused by bifurcation of nonzero discrete eigenvalues of the linearization operator as an example we consider the perturbed cubic quintic nls equation in detail and determine the stability regions of its solitary waves in the instability region we also specify where the solitary waves decay collapse develop movingfronts or evolve into a stable spatially localized and temporally periodic state the generalization of this method to other perturbed nonlinear wave systems is also discussed