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

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

contour detection and hierarchical image segmentation this paper investigates two fundamental problems in computer vision contour detection and image segmentation we present state of the art algorithms for both of these tasks our contour detector combines multiple local cues into a globalization framework based on spectral clustering our segmentation algorithm consists of generic machinery for transforming the output of any contour detector into a hierarchical region tree in this manner we reduce the problem of image segmentation to that of contour detection extensive experimental evaluation demonstrates that both our contour detection and segmentation methods significantly outperform competing algorithms the automatically generated hierarchical segmentations can be interactively refined by user specified annotations computation at multiple image resolutions provides a means of coupling our system to recognition applications

correntropy properties and applications in non gaussian signal processing the optimality of second order statistics depends heavily on the assumption of gaussianity in this paper we elucidate further the probabilistic and geometric meaning of the recently defined correntropy function as a localized similarity measure a close relationship between correntropy and m estimation is established connections and differences between correntropy and kernel methods are presented as such correntropy has vastly different properties compared with second order statistics that can be very useful in non gaussian signal processing especially in the impulsive noise environment examples are presented to illustrate the technique

open questions concerning weiszfeld s algorithm for the fermat weber location problem the fermat weber location problem is to find a point in n that minimizes the sum of the weighted euclidean distances fromm given points in n a popular iterative solution method for this problem was first introduced by weiszfeld in 1937 in 1973 kuhn claimed that if them given points are not collinear then for all but a denumerable number of starting points the sequence of iterates generated by weiszfeld s scheme converges to the unique optimal solution we demonstrate that kuhn s convergence theorem is not always correct we then conjecture that if this algorithm is initiated at the affine subspace spanned by them given points the convergence is ensured for all but a denumerable number of starting points

robust guided image filtering using nonconvex potentials filtering images using a guidance signal a process called guided or joint image filtering has been used in various tasks in computer vision and computational photography particularly for noise reduction and joint upsampling this uses an additional guidance signal as a structure prior and transfers the structure of the guidance signal to an input image restoring noisy or altered image structure the main drawbacks of such a data dependent framework are that it does not consider structural differences between guidance and input images and that it is not robust to outliers we propose a novel sd for static dynamic filter to address these problems in a unified framework and jointly leverage structural information from guidance and input images guided image filtering is formulated as a nonconvex optimization problem which is solved by the majorize minimization algorithm the proposed algorithm converges quickly while guaranteeing a local minimum the sd filter effectively controls the underlying image structure at different scales and can handle a variety of types of data from different sensors it is robust to outliers and other artifacts such as gradient reversal and global intensity shift and has good edge preserving smoothing properties we demonstrate the flexibility and effectiveness of the proposed sd filter in a variety of applications including depth upsampling scale space filtering texture removal flash non flash denoising and rgb nir denoising

h k trichotomies and asymptotics of nonautonomous difference systems abstract discrete nonautonomous nonlinear systems possessing h k trichotomies are considered we specialize to the case of solutions moving inside and in a neighborhood of an invariant manifold of a special kind which we call h k hyperbolic the aulbach coppel knobloch transformation is then developed and used to state conditions for granting asymptotic equivalence of solutions our results generalize some of aulbach s results in which the manifold considered was made of stationary points and the system taken was autonomous

the equivalence of half quadratic minimization and the gradient linearization iteration a popular way to restore images comprising edges is to minimize a cost function combining a quadratic data fidelity term and an edge preserving possibly nonconvex regularization term mainly because of the latter term the calculation of the solution is slow and cumbersome half quadratic hq minimization multiplicative form was pioneered by geman and reynolds 1992 in order to alleviate the computational task in the context of image reconstruction with nonconvex regularization by promoting the idea of locally homogeneous image models with a continuous valued line process they reformulated the optimization problem in terms of an augmented cost function which is quadratic with respect to the image and separable with respect to the line process hence the name half quadratic since then a large amount of papers were dedicated to hq minimization and important results including edge preservation along with convex regularization and convergence have been obtained in this paper we show that hq minimization multiplicative form is equivalent to the most simple and basic method where the gradient of the cost function is linearized at each iteration step in fact both methods give exactly the same iterations furthermore connections of hq minimization with other methods such as the quasi newton method and the generalized weiszfeld s method are straightforward

behavior of solutions near manifolds of periodic solutions abstract consider an autonomous differential system x f x of dimension n that admits a k dimensional invariant manifold in x space represented by a k parameter family of periodic solutions then k characteristic multipliers of the corresponding variational equation are equal to 1 under the hypothesis that none of the remaining n k characteristic multipliers has modulus 1 the behavior of the solutions of x f x near is investigated the main results are the description of a neighborhood of in terms of stable and unstable manifolds and the statement that whenever a solution of x f x approaches the invariant manifold as t it tends to with asymptotic amplitude and phase

constrained restoration and the recovery of discontinuities the linear image restoration problem is to recover an original brightness distribution x sup 0 given the blurred and noisy observations y kx sup 0 b where k and b represent the point spread function and measurement error respectively this problem is typical of ill conditioned inverse problems that frequently arise in low level computer vision a conventional method to stabilize the problem is to introduce a priori constraints on x sup 0 and design a cost functional h x over images x which is a weighted average of the prior constraints regularization term and posterior constraints data term the reconstruction is then the image x which minimizes h a prominent weakness in this approach especially with quadratic type stabilizers is the difficulty in recovering discontinuities the authors therefore examine prior smoothness constraints of a different form which permit the recovery of discontinuities without introducing auxiliary variables for marking the location of jumps and suspending the constraints in their vicinity in this sense discontinuities are addressed implicitly rather than explicitly

deterministic edge preserving regularization in computed imaging many image processing problems are ill posed and must be regularized usually a roughness penalty is imposed on the solution the difficulty is to avoid the smoothing of edges which are very important attributes of the image in this paper we first give conditions for the design of such an edge preserving regularization under these conditions we show that it is possible to introduce an auxiliary variable whose role is twofold first it marks the discontinuities and ensures their preservation from smoothing second it makes the criterion half quadratic the optimization is then easier we propose a deterministic strategy based on alternate minimizations on the image and the auxiliary variable this leads to the definition of an original reconstruction algorithm called artur some theoretical properties of artur are discussed experimental results illustrate the behavior of the algorithm these results are shown in the field of 2d single photon emission tomography but this method can be applied in a large number of applications in image processing

a formula for the total variation of sbv functions abstract following some ideas of a recent paper by ambrosio bourgain brezis and figalli we prove a formula for the total variation of certain sbv functions without making use of the distributional derivatives

bmo type seminorms generating sobolev functions abstract in the recent literature certain bmo type seminorms provide characterizations of sobolev functions in the same order of ideas we obtain the norm of the gradient of a function in l p where r n n 1 and p 1 as limit of bmo type seminorms involving families of pairwise disjoint sets with all orientations the sets being not necessarily cubes or tessellation cells an analogous result is obtained when rotations are not allowed

depth video enhancement based on weighted mode filtering this paper presents a novel approach for depth video enhancement given a high resolution color video and its corresponding low quality depth video we improve the quality of the depth video by increasing its resolution and suppressing noise for that a weighted mode filtering method is proposed based on a joint histogram when the histogram is generated the weight based on color similarity between reference and neighboring pixels on the color image is computed and then used for counting each bin on the joint histogram of the depth map a final solution is determined by seeking a global mode on the histogram we show that the proposed method provides the optimal solution with respect to l1 norm minimization for temporally consistent estimate on depth video we extend this method into temporally neighboring frames simple optical flow estimation and patch similarity measure are used for obtaining the high quality depth video in an efficient manner experimental results show that the proposed method has outstanding performance and is very efficient compared with existing methods we also show that the temporally consistent enhancement of depth video addresses a flickering problem and improves the accuracy of depth video

bmo type seminorms from escher type tessellations abstract the paper is about a representation formula introduced by fusco moscariello and sbordone in 14 the formula permits to characterize the gradient norm of a sobolev function defined on the whole space as the limit of non local energies bmo type seminorms defined on tessellations of generated by cubic cells with arbitrary orientation we improve the main result in 14 in three different regards we give a new concise proof of the representation formula we analyze the case of a generic open subset and consider general tessellations of by means of cells more general than cubes again arbitrarily oriented inspired by the creative mind of the graphic artist m c escher

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

asymptotic integration of a system resulting from the perturbation of an h system z systems were introduced in lo with the intention of obtaining results about stability for a weakly stable system at least weaker than those given by exponential stability under some perturbations in this paper we get asymptotic formulae for these systems which state new results about asymptotic integration for nonlinear systems under general hypotheses moreover the corresponding results for linear systems give new insight about levinson s theorem on asymptotic integration in this way using the h systems we get a uniform treatment for the concept of stability and we verify that several classical theorems of stability take a precise form by the asymptotic formulae in section 2 we recall the definition and some properties of an h system and we state two new theorems about asymptotic behavior of solutions of perturbed h systems in section 3 some general results about asymptotic integration are given these results extend those given in lo in section 4 we apply the technique to the linear case finally in section 5 we show examples and applications and we study the emden fowler equation which originally does not satisfy the general hypothesis but can be transformed into one where they are satisfied 2 h systems let us consider the differential system

guided image filtering in this paper we propose a novel explicit image filter called guided filter derived from a local linear model the guided filter computes the filtering output by considering the content of a guidance image which can be the input image itself or another different image the guided filter can be used as an edge preserving smoothing operator like the popular bilateral filter 1 but it has better behaviors near edges the guided filter is also a more generic concept beyond smoothing it can transfer the structures of the guidance image to the filtering output enabling new filtering applications like dehazing and guided feathering moreover the guided filter naturally has a fast and nonapproximate linear time algorithm regardless of the kernel size and the intensity range currently it is one of the fastest edge preserving filters experiments show that the guided filter is both effective and efficient in a great variety of computer vision and computer graphics applications including edge aware smoothing detail enhancement hdr compression image matting feathering dehazing joint upsampling etc

incremental majorization minimization optimization with application to large scale machine learning majorization minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function these upper bounds are tight at the current estimate and each iteration monotonically drives the objective function downhill such a simple principle is widely applicable and has been very popular in various scientific fields especially in signal processing and statistics we propose an incremental majorization minimization scheme for minimizing a large sum of continuous functions a problem of utmost importance in machine learning we present convergence guarantees for nonconvex and convex optimization when the upper bounds approximate the objective up to a smooth error we call such upper bounds first order surrogate functions more precisely we study asymptotic stationary point guarantees for nonconvex problems and for convex ones we provide convergence rates for the expected objective function value we apply our scheme to composite optimization and obtain a new incremental proximal gradient algorithm with linear convergence rate for strongly convex functions our experiments show that our method is competitive with the state of the art for solving machine learning problems such as logistic regression when the number of training samples is large enough and we demonstrate its usefulness for sparse estimation with nonconvex penalties

fast global image smoothing based on weighted least squares this paper presents an efficient technique for performing a spatially inhomogeneous edge preserving image smoothing called fast global smoother focusing on sparse laplacian matrices consisting of a data term and a prior term typically defined using four or eight neighbors for 2d image our approach efficiently solves such global objective functions in particular we approximate the solution of the memory and computation intensive large linear system defined over a d dimensional spatial domain by solving a sequence of 1d subsystems our separable implementation enables applying a linear time tridiagonal matrix algorithm to solve d three point laplacian matrices iteratively our approach combines the best of two paradigms i e efficient edge preserving filters and optimization based smoothing our method has a comparable runtime to the fast edge preserving filters but its global optimization formulation overcomes many limitations of the local filtering approaches our method also achieves high quality results as the state of the art optimization based techniques but runs 10 30 times faster besides considering the flexibility in defining an objective function we further propose generalized fast algorithms that perform l norm smoothing 0 2 and support an aggregated robust data term for handling imprecise data constraints we demonstrate the effectiveness and efficiency of our techniques in a range of image processing and computer graphics applications

efficient nonlocal means for denoising of textural patterns this paper contributes two novel techniques in the context of image restoration by nonlocal filtering first we introduce an efficient implementation of the nonlocal means filter based on arranging the data in a cluster tree the structuring of data allows for a fast and accurate preselection of similar patches in contrast to previous approaches the preselection is based on the same distance measure as used by the filter itself it allows for large speedups especially when the search for similar patches covers the whole image domain i e when the filter is truly nonlocal however also in the windowed version of the filter the cluster tree approach compares favorably to previous techniques in respect of quality versus computational cost second we suggest an iterative version of the filter that is derived from a variational principle and is designed to yield nontrivial steady states it reveals to be particularly useful in order to restore regular textured patterns

a formula for the anisotropic total variation of sbv functions abstract the purpose of this paper is to present the relation between certain bmo type seminorms and the total variation of sbv functions following some ideas of 2 we give a representation formula of the total variation of sbv functions which does not make use of the distributional derivatives we consider an anisotropic variant of the bmo type seminorm introduced in 4 by using instead of cubes covering families made by translations of a given open bounded set with lipschitz boundary