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

shape estimation from shading defocus and correspondence using light field angular coherence light field cameras are quickly becoming commodity items with consumer and industrial applications they capture many nearby views simultaneously using a single image with a micro lens array thereby providing a wealth of cues for depth recovery defocus correspondence and shading in particular apart from conventional image shading one can refocus images after acquisition and shift one s viewpoint within the sub apertures of the main lens effectively obtaining multiple views we present a principled algorithm for dense depth estimation that combines defocus and correspondence metrics we then extend our analysis to the additional cue of shading using it to refine fine details in the shape by exploiting an all in focus image in which pixels are expected to exhibit angular coherence we define an optimization framework that integrates photo consistency depth consistency and shading consistency we show that combining all three sources of information defocus correspondence and shading outperforms state of the art light field depth estimation algorithms in multiple scenarios

absorbing boundary in one dimensional anomalous transport in this paper we study the space time probability distribution q x t of a random walk subject to an absorbing boundary at the origin x 0 for motion controlled by l evy flights and l evy walks characterized by the exponent ensuremath gamma we find that the method of images usually applicable to brownian motion may break down for l evy processes we calculate the distribution q x t to be at xg0 after time tg0 having started at the origin assuming that the boundary is effective at time tg0 we show that q x t depends on the details of the underlying process q x t ensuremath sim mathit x ensuremath gamma 2 mathit t 1 1 ensuremath gamma 1 ensuremath le ensuremath gamma ensuremath le 2 for small x while total survival is independent of the spatial realization of motion and displays a universal behavior we also discuss the related smoluchowski boundary condition problem

complementarity framework for non linear dynamic analysis of skeletal structures with softening plastic hinges in this paper we describe an algorithm for the incremental state update of elasto plastic systems with softening the algorithm uses a complementary pivoting technique and is based on casting the incremental state update as a complementarity problem in developing the algorithm we take advantage of the special features of solid and structural mechanics problems to achieve good computational performance and hence the ability to compute numerical solutions to practical size problems for example the notion of a tangent stiffness matrix arises numerical examples using models of skeletal structures are presented to demonstrate the practicability of the algorithm the numerical examples also raise some interesting questions about multiplicity of the solutions copyright 2010 john wiley sons ltd

linearly constrained global optimization a general solution algorithm with applications this paper presents an efficient enumerative approach to solve general linearly constrained optimization problems this class of optimization problems includes fractional nonlinear network models quadratic convex and non convex programs the unified approach is accomplished by converting the constrained optimization problem to an unconstrained optimization problem through a parametric representation of its feasible region the proposed solution algorithm consists of three phases in phase 1 it finds all interior critical points in phase 2 the parametric representation of the feasible region is constructed to identify any critical points on the edges and faces of the feasible region this is done by a modified version of an algorithm for finding the v representation of the polyhedron then in phase 3 the global optimal value of the objective function is found by evaluating the objective function at the critical points as well as at the vertices for an illustration of the algorithm and a comparison with the existing methods small size numerical examples are presented

adaptive support weight approach for correspondence search we present a new window based method for correspondence search using varying support weights we adjust the support weights of the pixels in a given support window based on color similarity and geometric proximity to reduce the image ambiguity our method outperforms other local methods on standard stereo benchmarks

unsupervised feature selection based on maximum information and minimum redundancy for hyperspectral images unsupervised feature selection plays an important role in hyperspectral image processing it is a very challenge issue to select an effective feature subset with the unavailability of class labels to select the features maximally preserving the information of original features a maximum joint mutual information mjmi criterion is defined since the high order distribution involved in mjmi is hard to calculate a maximum information and minimum redundancy mimr criterion is derived as the low order approximation of mjmi from information theory many classical unsupervised feature selection criteria can also be considered as the low order approximations of mjmi compared with them mimr requires more relaxed approximation condition moreover a new clonal selection algorithm csa in artificial immune system is devised to optimize the selected features with the guidance of mimr experimental results on several hyperspectral datasets demonstrate that the proposed method obtains better feature subsets compared with classical unsupervised feature selection methods a new mimr criterion is proposed for unsupervised feature selection mimr can select more informative and distinctive features many classical criteria and mimr can be unified into the same framework the theoretical advantage of mimr over many classical criteria is given feature selection problem is solved by combinatorial optimization with a new csa

a review of statistical approaches to level set segmentation integrating color texture motion and shape since their introduction as a means of front propagation and their first application to edge based segmentation in the early 90 s level set methods have become increasingly popular as a general framework for image segmentation in this paper we present a survey of a specific class of region based level set segmentation methods and clarify how they can all be derived from a common statistical framework region based segmentation schemes aim at partitioning the image domain by progressively fitting statistical models to the intensity color texture or motion in each of a set of regions in contrast to edge based schemes such as the classical snakes region based methods tend to be less sensitive to noise for typical images the respective cost functionals tend to have less local minima which makes them particularly well suited for local optimization methods such as the level set method we detail a general statistical formulation for level set segmentation subsequently we clarify how the integration of various low level criteria leads to a set of cost functionals we point out relations between the different segmentation schemes in experimental results we demonstrate how the level set function is driven to partition the image plane into domains of coherent color texture dynamic texture or motion moreover the bayesian formulation allows to introduce prior shape knowledge into the level set method we briefly review a number of advances in this domain

inertia controlling methods for general quadratic programming active set quadratic programming qp methods use a working set to define the search direction and multiplier estimates in the method proposed by fletcher in 1971 and in several subsequent mathematically equivalent methods the working set is chosen to control the inertia of the reduced hessian which is never permitted to have more than one nonpositive eigenvalue such methods will be called inertia controlling this paper presents an overview of a generic inertia controlling qp method including the equations satisfied by the search direction when the reduced hessian is positive definite singular and indefinite recurrence relations are derived that define the search direction and lagrange multiplier vector through equations related to the karush kuhn tucker system discussion is included of connections with inertia controlling methods that maintain an explicit factorization of the reduced hessian matrix

a hierarchical symmetric stereo algorithm using dynamic programming in this paper a new hierarchical stereo algorithm is presented the algorithm matches individual pixels in corresponding scanlines by minimizing a cost function several cost functions are compared the algorithm achieves a tremendous gain in speed and memory requirements by implementing it hierarchically the images are downsampled an optimal number of times and the disparity map of a lower level is used as offset disparity map at a higher level an important contribution consists of the complexity analysis of the algorithm it is shown that this complexity is independent of the disparityrange this result is also used to determine the optimal number of downsample levels this speed gain results in the ability to use more complex compute intensive cost functions that deliver high quality disparity maps another advantage of this algorithm is that cost functions can be chosen independent of the optimisation algorithm the algorithm in this paper is symmetric i e exactly the same matches are found if left and right image are swapped finally the algorithm was carefully implemented so that a minimal amount of memory is used it has proven its efficiency on large images with a high disparity range as well as its quality examples are given in this paper

a simplex algorithm for piecewise linear programming i derivation and proof the simplex method for linear programming can be extended to permit the minimization of any convex separable piecewise linear objective subject to linear constraints this three part paper develops and analyzes a general computationally practical simplex algorithm for piecewiselinear programming

feature augmentation for learning confidence measure in stereo matching confidence estimation is essential for refining stereo matching results through a post processing step this problem has recently been studied using a learning based approach which demonstrates a substantial improvement on conventional simple non learning based methods however the formulation of learning based methods that individually estimates the confidence of each pixel disregards spatial coherency that might exist in the confidence map thus providing a limited performance under challenging conditions our key observation is that the confidence features and resulting confidence maps are smoothly varying in the spatial domain and highly correlated within the local regions of an image we present a new approach that imposes spatial consistency on the confidence estimation specifically a set of robust confidence features is extracted from each superpixel decomposed using the gaussian mixture model and then these features are concatenated with pixel level confidence features the features are then enhanced through adaptive filtering in the feature domain in addition the resulting confidence map estimated using the confidence features with a random regression forest is further improved through k nearest neighbor based aggregation scheme on both pixel and superpixel level to validate the proposed confidence estimation scheme we employ cost modulation or ground control points based optimization in stereo matching experimental results demonstrate that the proposed method outperforms state of the art approaches on various benchmarks including challenging outdoor scenes

a basis deficiency allowing variation of the simplex method for linear programming h one of the most important and fundamental concepts in the simplex methodology basis is restricted to being a square matrix of the order exactly equal to the number of rows of the coefficient matrix such inflexibility might have been the source of too many zero steps taken by the simplex method in solving real world linear programming problems which are usually highly degen erate to dodge this difficulty we first generalize the basis to allow the deficient case characterized as one that has columns fewer than rows of the coefficient matrix variations of the primal and dual simplex procedures are then made and used to form a two phase method based on such a basis the number of whose columns varies dynamically in the solution process generally speaking the more degenerate a problem to be handled is the fewer columns the basis will have so thii renders the possibility of efficiently solving highly degenerate problems we also provide a valuable insight into the distinctive and favorable behavior of the proposed method by reporting our computational experiments 1998 elsevier science ltd all rights reserved

a fast approximation of the bilateral filter using a signal processing approach the bilateral filter is a nonlinear filter that smoothes a signal while preserving strong edges it has demonstrated great effectiveness for a variety of problems in computer vision and computer graphics and fast versions have been proposed unfortunately little is known about the accuracy of such accelerations in this paper we propose a new signal processing analysis of the bilateral filter which complements the recent studies that analyzed it as a pde or as a robust statistical estimator the key to our analysis is to express the filter in a higher dimensional space where the signal intensity is added to the original domain dimensions importantly this signal processing perspective allows us to develop a novel bilateral filtering acceleration using downsampling in space and intensity this affords a principled expression of accuracy in terms of bandwidth and sampling the bilateral filter can be expressed as linear convolutions in this augmented space followed by two simple nonlinearities this allows us to derive criteria for downsampling the key operations and achieving important acceleration of the bilateral filter we show that for the same running time our method is more accurate than previous acceleration techniques typically we are able to process a 2 megapixel image using our acceleration technique in less than a second and have the result be visually similar to the exact computation that takes several tens of minutes the acceleration is most effective with large spatial kernels furthermore this approach extends naturally to color images and cross bilateral filtering

a hybrid multiview stereo algorithm for modeling urban scenes we present an original multiview stereo reconstruction algorithm which allows the 3d modeling of urban scenes as a combination of meshes and geometric primitives the method provides a compact model while preserving details irregular elements such as statues and ornaments are described by meshes whereas regular structures such as columns and walls are described by primitives planes spheres cylinders cones and tori we adopt a two step strategy consisting first in segmenting the initial mesh based surface using a multilabel markov random field based model and second in sampling primitive and mesh components simultaneously on the obtained partition by a jump diffusion process the quality of a reconstruction is measured by a multi object energy model which takes into account both photo consistency and semantic considerations i e geometry and shape layout the segmentation and sampling steps are embedded into an iterative refinement procedure which provides an increasingly accurate hybrid representation experimental results on complex urban structures and large scenes are presented and compared to state of the art multiview stereo meshing algorithms

fractional laplacian in bounded domains the fractional laplacian operator ensuremath ensuremath ensuremath delta ensuremath alpha 2 appears in a wide class of physical systems including l evy flights and stochastic interfaces in this paper we provide a discretized version of this operator which is well suited to deal with boundary conditions on a finite interval the implementation of boundary conditions is justified by appealing to two physical models namely hopping particles and elastic springs the eigenvalues and eigenfunctions in a bounded domain are then obtained numerically for different boundary conditions some analytical results concerning the structure of the eigenvalue spectrum are also obtained

patchmatch filter edge aware filtering meets randomized search for visual correspondence though many tasks in computer vision can be formulated elegantly as pixel labeling problems a typical challenge discouraging such a discrete formulation is often due to computational efficiency recent studies on fast cost volume filtering based on efficient edge aware filters provide a fast alternative to solve discrete labeling problems with the complexity independent of the support window size however these methods still have to step through the entire cost volume exhaustively which makes the solution speed scale linearly with the label space size when the label space is huge or even infinite which is often the case for subpixel accurate stereo and optical flow estimation their computational complexity becomes quickly unacceptable developed to search approximate nearest neighbors rapidly the patchmatch method can significantly reduce the complexity dependency on the search space size but its pixel wise randomized search and fragmented data access within the 3d cost volume seriously hinder the application of efficient cost slice filtering this paper presents a generic and fast computational framework for general multi labeling problems called patchmatch filter pmf we explore effective and efficient strategies to weave together these two fundamental techniques developed in isolation i e patchmatch based randomized search and efficient edge aware image filtering by decompositing an image into compact superpixels we also propose superpixel based novel search strategies that generalize and improve the original patchmatch method further motivated to improve the regularization strength we propose a simple yet effective cross scale consistency constraint which handles labeling estimation for large low textured regions more reliably than a single scale pmf algorithm focusing on dense correspondence field estimation in this paper we demonstrate pmf s applications in stereo and optical flow our pmf methods achieve top tier correspondence accuracy but run much faster than other related competing methods often giving over 10 100 times speedup

on wolfe s method for resolving degeneracy in linearly constrained optimization wolfe j soc indust appl math 11 1963 pp 205 211 describes a novel and very useful method for resolving degeneracy in the simplex method for linear programming lp the simplicity and reliability of the method makes it an excellent choice in this author s opinion the method is described here in the context of an active set method asm format for lp the method solves recursively generated subproblems that are smaller than the original which contributes to efficiency data structures are described that enable the recursive aspect of the method to be implemented very easily with minimal storage overhead the method is extended to solve a general form of linearly constrained optimization problem that includes quadratic programming qp and allows simple bounds on the variables and both equation and inequality general linear constraints issues of round off error are discussed and heuristics are described that have proved to be very reliable in practice the method is further extended to qp pr

robust matching cost function for stereo correspondence using matching by tone mapping and adaptive orthogonal integral image real world stereo images are inevitably affected by radiometric differences including variations in exposure vignetting lighting and noise stereo images with severe radiometric distortion can have large radiometric differences and include locally nonlinear changes in this paper we first introduce an adaptive orthogonal integral image which is an improved version of an orthogonal integral image after that based on matching by tone mapping and the adaptive orthogonal integral image we propose a robust and accurate matching cost function that can tolerate locally nonlinear intensity distortion by using the adaptive orthogonal integral image the proposed matching cost function can adaptively construct different support regions of arbitrary shapes and sizes for different pixels in the reference image so it can operate robustly within object boundaries furthermore we develop techniques to automatically estimate the values of the parameters of our proposed function we conduct experiments using the proposed matching cost function and compare it with functions employing the census transform supporting local binary pattern and adaptive normalized cross correlation as well as a mutual information based matching cost function using different stereo data sets by using the adaptive orthogonal integral image the proposed matching cost function reduces the error from 21 51 to 15 73 in the middlebury data set and from 15 9 to 10 85 in the kitti data set as compared with using the orthogonal integral image the experimental results indicate that the proposed matching cost function is superior to the state of the art matching cost functions under radiometric variation

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

variational recursive joint estimation of dense scene structure and camera motion from monocular high speed traffic sequences we present an approach to jointly estimating camera motion and dense structure of a static scene in terms of depth maps from monocular image sequences in driver assistance scenarios at each instant of time only two consecutive frames are processed as input data of a joint estimator that fully exploits second order information of the corresponding optimization problem and effectively copes with the non convexity due to both the imaging geometry and the manifold of motion parameters additionally carefully designed gaussian approximations enable probabilistic inference based on locally varying confidence and globally varying sensitivity due to the epipolar geometry with respect to the high dimensional depth map estimation embedding the resulting joint estimator in an online recursive framework achieves a pronounced spatio temporal filtering effect and robustness we evaluate hundreds of images taken from a car moving at speed up to 100 km h and being part of a publicly available benchmark data set the results compare favorably with two alternative settings stereo based scene reconstruction and camera motion estimation in batch mode using multiple frames they however require a calibrated camera pair or storage for more than two frames which is less attractive from a technical viewpoint than the proposed monocular and recursive approach in addition to real data a synthetic sequence is considered which provides reliable ground truth

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

on the eigenvalues of certain canonical higher order ordinary differential operators abstract we consider the operator of taking the 2pth derivative of a function with zero boundary conditions for the function and its first p 1 derivatives at two distinct points our main result provides an asymptotic formula for the eigenvalues and resolves a question on the appearance of certain regular numbers in the eigenvalue sequences for p 1 and p 3

stereo matching using tree filtering matching cost aggregation is one of the oldest and still popular methods for stereo correspondence while effective and efficient cost aggregation methods typically aggregate the matching cost by summing averaging over a user specified local support region this is obviously only locally optimal and the computational complexity of the full kernel implementation usually depends on the region size in this paper the cost aggregation problem is re examined and a non local solution is proposed the matching cost values are aggregated adaptively based on pixel similarity on a tree structure derived from the stereo image pair to preserve depth edges the nodes of this tree are all the image pixels and the edges are all the edges between the nearest neighboring pixels the similarity between any two pixels is decided by their shortest distance on the tree the proposed method is non local as every node receives supports from all other nodes on the tree the proposed method can be naturally extended to the time domain for enforcing temporal coherence unlike previous methods the non local property guarantees that the depth edges will be preserved when the temporal coherency between all the video frames are considered a non local weighted median filter is also proposed based on the non local cost aggregation algorithm it has been demonstrated to outperform all local weighted median filters on disparity depth upsampling and refinement

properties of levy flights on an interval with absorbing boundaries we consider a l evy yer of orderthat starts from a point x0 on an interval 0 l with absorbing boundaries we 7nd a closed form expression for an arbitrary average quantity char acterizing the trajectory of the yer such as mean 7rst passage time average total path length probability to be absorbed by one of the boundaries using fractional di erential equations with a riesz kernel we 7nd exact analytical expressions for these quantities in the continuous limit we 7nd numerically the eigenfunctions and the eigenvalues of these equations we study how the results of monte carlo simulations of the l evy ights with di erent ight length distribu tions converge to the continuous approximations we show that if x0 is placed in the vicinity of absorbing boundaries the average total path length has a minimum near 1 corresponding to the cauchy distribution we discuss the relevance of these results to the problem of biological foraging and transmission of light through cloudy atmosphere c 2001 elsevier science b v all rights reserved

stereo matching with color weighted correlation hierarchical belief propagation and occlusion handling in this paper we formulate a stereo matching algorithm with careful handling of disparity discontinuity and occlusion the algorithm works with a global matching stereo model based on an energy minimization framework the global energy contains two terms the data term and the smoothness term the data term is first approximated by a color weighted correlation then refined in occluded and low texture areas in a repeated application of a hierarchical loopy belief propagation algorithm the experimental results are evaluated on the middlebury data sets showing that our algorithm is the top performer among all the algorithms listed there

random walks for image segmentation a novel method is proposed for performing multilabel interactive image segmentation given a small number of pixels with user defined or predefined labels one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the prelabeled pixels by assigning each pixel to the label for which the greatest probability is calculated a high quality image segmentation may be obtained theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits this algorithm is formulated in discrete space i e on a graph using combinatorial analogues of standard operators and principles from continuous potential theory allowing it to be applied in arbitrary dimension on arbitrary graphs

fast segmentation from blurred data in 3d fluorescence microscopy we develop a fast algorithm for segmenting 3d images from linear measurements based on the potts model or piecewise constant mumford shah model to that end we first derive suitable space discretizations of the 3d potts model which are capable of dealing with 3d images defined on non cubic grids our discretization allows us to utilize a specific splitting approach which results in decoupled subproblems of moderate size the crucial point in the 3d setup is that the number of independent subproblems is so large that we can reasonably exploit the parallel processing capabilities of the graphics processing units gpus our gpu implementation is up to 18 times faster than the sequential cpu version this allows to process even large volumes in acceptable runtimes as a further contribution we extend the algorithm in order to deal with non negativity constraints we demonstrate the efficiency of our method for combined image deconvolution and segmentation on simulated data and on real 3d wide field fluorescence microscopy data

newton methods for large scale linear inequality constrained minimization newton methods of the linesearch type for large scale minimization subject to linear inequality constraints are discussed the purpose of the paper is twofold i to give an active set type method with the ability to delete multiple constraints simultaneously and ii to give a relatively short general convergence proof for such a method it is also discussed how multiple constraints can be added simultaneously the approach is an extension of a previous work by the same authors for equality constrained problems it is shown how the search directions can be computed without the need to compute the reduced hessian of the objective function the convergence analysis states that every limit point of a sequence of iterates satisfies the second order necessary optimality conditions

a primal deficient basis simplex algorithm for linear programming abstract the standard basis which plays a fundamental role in simplex methodology was recently extended to include a deficient case with fewer columns than rows by taking advantage of primal degeneracy computational results have been favorable with dense implementations in this paper we propose a primal simplex algorithm using sparse lu factors of deficient bases amenable to real world linear programming problems which are often degenerate or even highly degenerate the algorithm would solve them with potentially improved stability compared to the simplex algorithm the proposed algorithm has been implemented and tested on a set of 50 netlib test problems as well as a set of 15 much larger real world problems including 8 kennington and 5 bpmpd problems it significantly outperformed minos 5 3 in terms of both iteration counts and run time in particular these results reveal that there is no inevitable correlation between an algorithm s inefficiency and degeneracy contradicting common belief

euler spiral for shape completion in this paper we address the curve completion problem e g the geometric continuation of boundaries of objects which are temporarily interrupted by occlusion also known as the gap completion or shape completion problem this problem is a significant element of perceptual grouping of edge elements and has been approached by using cubic splines or biarcs which minimize total curvature squared elastica as motivated by a physical analogy our approach is motivated by railroad design methods of the early 1900 s which connect two rail segments by transition curves and by the work of knuth on mathematical typography we propose that in using an energy minimizing solution completion curves should not penalize curvature as in elastica but curvature variation the minimization of total curvature variation leads to an euler spiral solution a curve whose curvature varies linearly with arclength the construction of this curve from a pair of points and tangents at these points is reduced to a nonlinear system of equations involving fresnel integrals whose solution relies on optimization from a suitable initial condition constrained to satisfy given boundary conditions since the choice of an appropriate initial curve is critical in this optimization we analytically derive an optimal solution in the class of biarc curves which is then used as the initial curve the resulting interpolations yield intuitive interpolation across gaps and occlusions and are extensible in contrast to scale invariant elastica in addition euler spiral segments can be used in other applications of curve completions e g modeling boundary segments between curvature extrema or skeletal branch geometry

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

pivot versus interior point methods pros and cons linear optimization lo is the fundamental problem of mathematical optimization it admits an enormous number of applications in economics engineering science and many other fields the three most significant classes of algorithms for solving lo problems are pivot ellipsoid and interior point methods because ellipsoid methods are not efficient in practice we will concentrate on the computationally successful simplex and primal dual interior point methods only and summarize the pros and cons of these algorithm classes

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

accurate stereo matching by two step energy minimization in stereo matching cost filtering methods and energy minimization algorithms are considered as two different techniques due to their global extent energy minimization methods obtain good stereo matching results however they tend to fail in occluded regions in which cost filtering approaches obtain better results in this paper we intend to combine both the approaches with the aim to improve overall stereo matching results we show that a global optimization with a fully connected model can be solved by cost filtering methods based on this observation we propose to perform stereo matching as a two step energy minimization algorithm we consider two markov random field mrf models 1 a fully connected model defined on the complete set of pixels in an image and 2 a conventional locally connected model we solve the energy minimization problem for the fully connected model after which the marginal function of the solution is used as the unary potential in the locally connected mrf model experiments on the middlebury stereo data sets show that the proposed method achieves the state of the arts results

joint histogram based cost aggregation for stereo matching this paper presents a novel method for performing efficient cost aggregation in stereo matching the cost aggregation problem is reformulated from the perspective of a histogram giving us the potential to reduce the complexity of the cost aggregation in stereo matching significantly differently from previous methods which have tried to reduce the complexity in terms of the size of an image and a matching window our approach focuses on reducing the computational redundancy that exists among the search range caused by a repeated filtering for all the hypotheses moreover we also reduce the complexity of the window based filtering through an efficient sampling scheme inside the matching window the tradeoff between accuracy and complexity is extensively investigated by varying the parameters used in the proposed method experimental results show that the proposed method provides high quality disparity maps with low complexity and outperforms existing local methods this paper also provides new insights into complexity constrained stereo matching algorithm design

stereo processing by semiglobal matching and mutual information this paper describes the semiglobal matching sgm stereo method it uses a pixelwise mutual information ml based matching cost for compensating radiometric differences of input images pixelwise matching is supported by a smoothness constraint that is usually expressed as a global cost function sgm performs a fast approximation by pathwise optimizations from all directions the discussion also addresses occlusion detection subpixel refinement and multibaseline matching additionally postprocessing steps for removing outliers recovering from specific problems of structured environments and the interpolation of gaps are presented finally strategies for processing almost arbitrarily large images and fusion of disparity images using orthographic projection are proposed a comparison on standard stereo images shows that sgm is among the currently top ranked algorithms and is best if subpixel accuracy is considered the complexity is linear to the number of pixels and disparity range which results in a runtime of just 1 2 seconds on typical test images an in depth evaluation of the ml based matching cost demonstrates a tolerance against a wide range of radiometric transformations finally examples of reconstructions from huge aerial frame and pushbroom images demonstrate that the presented ideas are working well on practical problems

robust multiview photometric stereo using planar mesh parameterization we propose a robust uncalibrated multiview photometric stereo method for high quality 3d shape reconstruction in our method a coarse initial 3d mesh obtained using a multiview stereo method is projected onto a 2d planar domain using a planar mesh parameterization technique we describe methods for surface normal estimation that work in the parameterized 2d space that jointly incorporates all geometric and photometric cues from multiple viewpoints using an estimated surface normal map a refined 3d mesh is then recovered by computing an optimal displacement map in the same 2d planar domain our method avoids the need of merging view dependent surface normal maps that is often required in conventional methods we conduct evaluation on various real world objects containing surfaces with specular reflections multiple albedos and complex topologies in both controlled and uncontrolled settings and demonstrate that accurate 3d meshes with fine geometric details can be recovered by our method

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

large displacement optical flow descriptor matching in variational motion estimation optical flow estimation is classically marked by the requirement of dense sampling in time while coarse to fine warping schemes have somehow relaxed this constraint there is an inherent dependency between the scale of structures and the velocity that can be estimated this particularly renders the estimation of detailed human motion problematic as small body parts can move very fast in this paper we present a way to approach this problem by integrating rich descriptors into the variational optical flow setting this way we can estimate a dense optical flow field with almost the same high accuracy as known from variational optical flow while reaching out to new domains of motion analysis where the requirement of dense sampling in time is no longer satisfied

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

a component wise analysis of constructible match cost functions for global stereopsis match cost functions are common elements of every stereopsis algorithm that are used to provide a dissimilarity measure between pixels in different images global stereopsis algorithms incorporate assumptions about the smoothness of the resulting distance map that can interact with match cost functions in unpredictable ways in this paper we present a large scale study on the relative performance of a structured set of match cost functions within several global stereopsis frameworks we compare 272 match cost functions that are built from component parts in the context of four global stereopsis frameworks with a data set consisting of 57 stereo image pairs at three different variances of synthetic sensor noise from our analysis we infer a set of general rules that can be used to guide derivation of match cost functions for use in global stereopsis algorithms

eigenproblems of large powers of the laplacian in bounded domains we present a method for computing the spectrum of large powers of the laplacian in a bounded domain restricting ourselves to the one and three dimensional cases since it does not seem possible to obtain information on the eigenvalues directly from the transcendental equation that gives the spectrum we introduce a wallis inspired method we obtain the expansion of the eigenfunction and the eigenvalues in power series where the inverse of the power at which the laplacian is raised plays the role of the small parameter we compare these eigenvalues to those obtained through a simple variational approach and remark that the latter offers an excellent approximation to the exact result

yet another cost aggregation over models in the recent decades we have witnessed the advent of local or non local filters for cost aggregation in stereo matching pushing the envelope of local methods to the degree of global methods while maintaining the efficiency a specific filter with a specific parameter setting may have a potential to best work for an image pair but may not guarantee equally good performance for other image pairs to address this problem we propose a mixture of experts model which applies a heterogeneous set of filters on the cost volume and adaptively combines the results we employ supervised learning to estimate per pixel mixing coefficients which are used to adaptively control the weight of the filter responses through experiments we show that the mixture model significantly reduces errors in disparity estimation and even outperforms the strategy of selecting the best per pixel filter from the pool of filters in the average sense

on the solution of highly degenerate linear programs the solution of scheduling problems often gives rise to highly degenerate linear programmes which cause significant computational difficulties for the revised simplex method wolfe s highly effective ad hoc method for overcoming the cycling or stalling problems associated with degeneracy is described here it is given a geometric interpretation in terms of finding a direction of recession for a reduced problem which is fundamental to a full understanding of the procedure an example of an aircrew scheduling problem is used to illustrate the effectiveness of the method

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

an efficient linear model and optimisation algorithm for multi site combined heat and power production abstract combined heat and power chp production is an important energy production technology which can help to improve the efficiency of energy production and to reduce the emission of co2 cost efficient operation of a chp system can be planned using an optimisation model based on hourly load forecasts a long term planning model decomposes into hourly models which can be formulated as linear programming lp problems such problems can be solved efficiently using the specialized power simplex algorithm however power simplex can only manage one heat and one power balance since heat cannot be transported over long distances power simplex applies only for local chp planning in this paper we formulate the hourly multi site chp planning problem with multiple heat balances as an lp model with a special structure we then develop the extended power simplex eps algorithm for solving such models efficiently even though the problem can be quite large as the number of demand sites increases eps demonstrates very good efficiency in test runs with realistic models eps is from 29 to 85 times faster than an efficient sparse simplex code using the product form of inverse pfi furthermore the relative efficiency of eps improves as the problem size grows

alignment by maximization of mutual information a new information theoretic approach is presented for finding the pose of an object in an image the technique does not require information about the surface properties of the object besides its shape and is robust with respect to variations of illumination in our derivation few assumptions are made about the nature of the imaging process as a result the algorithms are quite general and may foreseeably be used in a wide variety of imaging situations experiments are presented that demonstrate the approach registering magnetic resonance mr images aligning a complex 3d object model to real scenes including clutter and occlusion tracking a human head in a video sequence and aligning a view based 2d object model to real images the method is based on a formulation of the mutual information between the model and the image as applied here the technique is intensity based rather than feature based it works well in domains where edge or gradient magnitude based methods have difficulty yet it is more robust than traditional correlation additionally it has an efficient implementation that is based on stochastic approximation

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

near real time stereo matching using geodesic diffusion adaptive weight algorithms currently represent the state of the art in local stereo matching however due to their computational requirements these types of solutions are not suitable for real time implementation here we present a novel aggregation method inspired by the anisotropic diffusion technique used in image filtering the proposed aggregation algorithm produces results similar to adaptive weight solutions while reducing the computational requirements moreover near real time performance is demonstrated with a gpu implementation of the algorithm

the simplest examples where the simplex method cycles and conditions where expand fails to prevent cycling this paper introduces a class of linear programming examples that cause the simplex method to cycle and that are the simplest possible examples showing this behaviour the structure of examples from this class repeats after two iterations cycling is shown to occur for both the most negative reduced cost and steepest edge column selection criteria in addition it is shown that the expand anti cycling procedure of gill et al is not guaranteed to prevent cycling

a practical anti cycling procedure for linearly constrained optimization a procedure is described for preventing cycling in active set methods for linearly constrained optimization including the simplex method the key ideas are a limited acceptance of infeasibilities in all variables and maintenance of a working feasibility tolerance that increases over a long sequence of iterations the additional work per iteration is nominal and stalling cannot occur with exact arithmetic the method appears to be reliable based on computational results for the first 53 linear programming problems in thenetlib set

correctness prediction accuracy improvement and generalization of stereo matching using supervised learning machine learning has been instrumental in most areas of computer vision but has not been applied to the problem of stereo matching with similar frequency or success in this paper we present a supervised learning approach by defining a set of features that capture various forms of information about each pixel and then by using them to predict the correctness of stereo matches based on a random forest we show highly competitive results in predicting the correctness of matches and in confidence estimation which allows us to rank pixels according to the reliability of their assigned disparities moreover we show how these confidence values can be used to improve the accuracy of disparity maps by integrating them with an mrf based stereo algorithm this is an important distinction from current literature that has mainly focused on sparsification by removing potentially erroneous disparities to generate quasi dense disparity maps finally we demonstrate domain generalization of our method by applying classifiers to datasets different than those they were trained on with minimal loss of accuracy

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

gaussian field consensus a robust nonparametric matching method for outlier rejection abstract in this paper we propose a robust method called gaussian field consensus gfc for outlier rejection from given putative point set matching correspondences finding correct correspondences inliers is a key component in many computer vision and pattern recognition tasks and the goal of outlier mismatch rejection is to fit the transformation function that maps one feature point set to another our gfc starts by inputting a putative correspondence set which is contaminated by many outliers and the main task of our gfc is to identify the underlying true correspondences from outliers then we formulate this challenging problem by gaussian field nonparametric matching model which bases on the exponential distance loss and kernel method in a reproducing kernel hilbert space next we introduce a local linear constraint based on the regularization theory to preserve the topological structure of the feature points moreover the sparse approximation is used to reduce the search space in this way we can handle a large number of points easily finally we test the gfc method on several real image datasets in the presence of outliers where the experimental results show that our proposed method outperforms current state of the art methods in most test scenarios

a multiparametric quadratic programming algorithm with polyhedral computations based on nonnegative least squares model predictive control mpc is one of the most successful techniques adopted in industry to control multivariable systems under constraints on input and output variables to circumvent the main drawback of mpc i e the need to solve a quadratic program qp on line to compute the control action explicit mpc was proposed in the past to precompute the control law off line using multiparametric qp mpqp the resulting form of the mpc law is piecewise affine which is extremely easy to code can be computed online by simple arithmetic operations and requires a maximum number of iterations that can be exactly determined a priori on the other hand the offline computations to solve the mpqp problem require detecting emptiness full dimensionality and minimal hyperplane representations of polyhedra and other computational geometric operations while most of the existing methods solve such operations via linear programming the approach proposed in this paper relies on a nonnegative least squares nnls solver that is very simple to code and fast to execute in addition the new approach exploits qp duality to identify and construct critical regions and to handle degeneracy issues

numerical aspects in developing lp softwares lpako and lpabo we have developed two public domain linear programming programs for several years lpako and lpabo which can solve large scale sparse lp problems stably and fast in this paper several important numerical aspects which were considered in developing lpako and lpabo are presented common issues are scaling tolerances and presolving for the lpako lu factorization and pivoting rule are important aspects in case of lpabo cholesky factorization ordering and dense column handling are important in the end of this paper several issues to be considered in the future development are proposed

motion estimation based on mutual information and adaptive multi scale thresholding this paper proposes a new method of calculating a matching metric for motion estimation the proposed method splits the information in the source images into multiple scale and orientation subbands reduces the subband values to a binary representation via an adaptive thresholding algorithm and uses mutual information to model the similarity of corresponding square windows in each image a moving window strategy is applied to recover a dense estimated motion field whose properties are explored the proposed matching metric is a sum of mutual information scores across space scale and orientation this facilitates the exploitation of information diversity in the source images experimental comparisons are performed amongst several related approaches revealing that the proposed matching metric is better able to exploit information diversity generating more accurate motion fields

making progress during a stall in the simplex algorithm abstract all the standard methods for avoiding cycling in the simplex algorithm use row selection rules for resolving degeneracy the method proposed in this paper does not instead the gass saaty parametric method applied to the objective cost form is used to choose the incoming column the pivot row choice among blocking rows i e those tied for pivot is arbitrary a simple anticycling device is used which avoids dual degeneracy of the parametrized objective with probability one tests were run on nine highly degenerate practical test problems ranging in size from small to large using minos software the standard simplex method required 31 195 iterations of which 20 504 or 66 were blocked pivots using the parametric scheme required 13 812 iterations of which 67 were blocked the reduction in the number of iterations for this set of highly degenerate test problems was 56 the cpu time reduction was 48

primal and dual active set methods for convex quadratic programming computational methods are proposed for solving a convex quadratic program qp active set methods are defined for a particular primal and dual formulation of a qp with general equality constraints and simple lower bounds on the variables in the first part of the paper two methods are proposed one primal and one dual these methods generate a sequence of iterates that are feasible with respect to the equality constraints associated with the optimality conditions of the primal dual form the primal method maintains feasibility of the primal inequalities while driving the infeasibilities of the dual inequalities to zero the dual method maintains feasibility of the dual inequalities while moving to satisfy the primal inequalities in each of these methods the search directions satisfy a kkt system of equations formed from hessian and constraint components associated with an appropriate column basis the composition of the basis is specified by an active set strategy that guarantees the nonsingularity of each set of kkt equations each of the proposed methods is a conventional active set method in the sense that an initial primal or dual feasible point is required in the second part of the paper it is shown how the quadratic program may be solved as a coupled pair of primal and dual quadratic programs created from the original by simultaneously shifting the simple bound constraints and adding a penalty term to the objective function any conventional column basis may be made optimal for such a primal dual pair of shifted penalized problems the shifts are then updated using the solution of either the primal or the dual shifted problem an obvious application of this approach is to solve a shifted dual qp to define an initial feasible point for the primal or vice versa the computational performance of each of the proposed methods is evaluated on a set of convex problems from the cutest test collection

a linear programming decomposition focusing on the span of the nondegenerate columns abstract the improved primal simplex ips was recently developed by elhalaloui et al to take advantage of degeneracy when solving linear programs with the primal simplex it implements a dynamic constraint reduction based on the compatible columns i e those that belong to the span of a given subset of basic columns including the nondegenerate ones the identification of the compatible variables may however be computationally costly and a large number of linear programs are solved to enlarge the subset of basic variables in this article we first show how the positive edge criterion of raymond et al can be included in ips for a fast identification of the compatible variables our algorithm then proceeds through a series of reduction and augmentation phases until optimality is reached in a reduction phase we identify compatible variables and focus on them to make quick progress toward optimality during an augmentation phase we compute one greatest normalized improving direction and select a subset of variables that should be considered in the reduced problem compared with ips the linear program that is solved to find this direction involves the data of the original constraint matrix this new algorithm is tested over mittelmann s benchmark for linear programming and on instances arising from industrial applications the results show that the new algorithm outperforms the primal simplex of cplex on most highly degenerate instances in which a sufficient number of nonbasic variables are compatible in contrast ips has difficulties on the eleven largest mittelmann instances

average time spent by levy flights and walks on an interval with absorbing boundaries we consider a levy flyer of order alpha that starts from a point x 0 on an interval o l with absorbing boundaries we find a closed form expression for the average number of flights the flyer takes and the total length of the flights it travels before it is absorbed these two quantities are equivalent to the mean first passage times for levy flights and levy walks respectively using fractional differential equations with a riesz kernel we find exact analytical expressions for both quantities in the continuous limit we show that numerical solutions for the discrete levy processes converge to the continuous approximations in all cases except the case of alpha 2 and the cases of x 0 0 and x 0 l for alpha 2 when the second moment of the flight length distribution exists our result is replaced by known results of classical diffusion we show that if x 0 is placed in the vicinity of absorbing boundaries the average total length has a minimum at alpha 1 corresponding to the cauchy distribution we discuss the relevance of this result to the problem of foraging which has received recent attention in the statistical physics literature

pm pm patchmatch with potts model for object segmentation and stereo matching this paper presents a unified variational formulation for joint object segmentation and stereo matching which takes both accuracy and efficiency into account in our approach depth map consists of compact objects each object is represented through three different aspects 1 the perimeter in image space 2 the slanted object depth plane and 3 the planar bias which is to add an additional level of detail on top of each object plane in order to model depth variations within an object compared with traditional high quality solving methods in low level we use a convex formulation of the multilabel potts model with patchmatch stereo techniques to generate depth map at each image in object level and show that accurate multiple view reconstruction can be achieved with our formulation by means of induced homography without discretization or staircasing artifacts our model is formulated as an energy minimization that is optimized via a fast primal dual algorithm which can handle several hundred object depth segments efficiently performance evaluations in the middlebury benchmark data sets show that our method outperforms the traditional integer valued disparity strategy as well as the original patchmatch algorithm and its variants in subpixel accurate disparity estimation the proposed algorithm is also evaluated and shown to produce consistently good results for various real world data sets kitti benchmark data sets and multiview benchmark data sets

a survey and comparison of discrete and continuous multi label optimization approaches for the potts model we present a survey and a comparison of a variety of algorithms that have been proposed over the years to minimize multi label optimization problems based on the potts model discrete approaches based on markov random fields as well as continuous optimization approaches based on partial differential equations can be applied to the task in contrast to the case of binary labeling the multi label problem is known to be np hard and thus one can only expect near optimal solutions in this paper we carry out a theoretical comparison and an experimental analysis of existing approaches with respect to accuracy optimality and runtime aimed at bringing out the advantages and short comings of the respective algorithms systematic quantitative comparison is done on the graz interactive image segmentation benchmark this paper thereby generalizes a previous experimental comparison klodt et al 2008 from the binary to the multi label case

a phase 1 approach for the generalized simplex algorithm abstract a new simplex variant allowing basis deficiency has recently been proposed to attack the degeneracy 1 as a generalization of the simplex algorithm it uses a phase 1 procedure solving an auxiliary problem with piecewise linear sums of infeasibilities as its objective in this paper we develop another phase 1 approach that only introduces a single artificial variable unlike the former which needs a crash procedure to supply an initial basis the proposed phase 1 is able to get itself started from scratch with an artificial basis having a single column computational results with a set of standard test problems from netlib are also reported

insertion of 3 d primitives in mesh based representations towards compact models preserving the details we propose an original hybrid modeling process of urban scenes that represents 3 d models as a combination of mesh based surfaces and geometric 3 d primitives meshes describe details such as ornaments and statues whereas 3 d primitives code for regular shapes such as walls and columns starting from an 3 d surface obtained by multiview stereo techniques these primitives are inserted into the surface after being detected this strategy allows the introduction of semantic knowledge the simplification of the modeling and even correction of errors generated by the acquisition process we design a hierarchical approach exploring different scales of an observed scene each level consists first in segmenting the surface using a multilabel energy model optimized by expansion and then in fitting 3 d primitives such as planes cylinders or tori on the obtained partition where relevant experiments on real meshes depth maps and synthetic surfaces show good potential for the proposed approach

a randomized linear time algorithm to find minimum spanning trees we present a randomized linear time algorithm to find a minimum spanning tree in a connected graph with edge weights the algorithm uses random sampling in combination with a recently discovered linear time algorithm for verifying a minimum spanning tree our computational model is a unit cost random access machine with the restriction that the only operations allowed on edge weights are binary comparisons

the spectrum of large powers of the laplacian in bounded domains we present exact results for the spectrum of the nth power of the laplacian in a bounded domain we begin with the one dimensional case and show that the whole spectrum can be obtained in the limit of large n we also show that it is a useful numerical approach valid for any n finally we discuss implications of this work and present its possible extensions for non integer n and for 3d laplacian problems

a novel image representation via local frequency analysis for illumination invariant stereo matching in this paper we propose a novel image representation approach to tackle illumination variations in stereo matching problems images are mapped using their fourier transforms which are convolved with a set of monogenic filters frequency analysis is carried out at different scales to account for most image content the phase congruency and the local weighted mean phase angle are then computed over all the scales the original image is transformed into a new representation using these two mappings this representation is invariant to illumination and contrast variations more importantly it is generic and can be used with most sparse as well as dense stereo matching algorithms in addition sequential feature matching or tracking can also benefit from our approach in varying radiometric conditions we demonstrate the improvements introduced with our image mappings on well established data sets in the literature as well as on our own experimental scenarios that include high dynamic range imagery the experiments include both dense and sparse stereo and sequential matching algorithms where the latter is considered in the very challenging visual odometry framework