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

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

on the numerical solution of two point boundary value problems abstract this paper presents a new numerical method for the solution of linear two point boundary value problems of ordinary differential equations after reducing the differential equation to a second kind integral equation the latter are discretized via a high order nystrom scheme a somewhat involved analytical apparatus is then constructed which allows for the solution of the discrete system using o n dot p2 operations where n is the number of nodes on the interval and p is the desired order of convergence thus the advantages of the integral equation formulation small condition number insensitivity to boundary layers insensitivity to end point singularities etc are retained while achieving a computational efficiency previously available only to finite difference or finite element methods keywords two point boundary value problems integral equations chebyshev polynomials approximation theory

monotone enclosure for a class of discrete boundary value problems without monotone nonlinearities abstract a new concept of a pair of upper and lower solutions is introduced for a class of discrete boundary value problems without monotone nonlinearities some comparison results are established an existence and enclosing theorem for the solutions is given in terms of upper and lower solutions a new monotone iterative scheme is proposed the numerical example is given

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

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

computational methods for discrete boundary value problems ii abstract for a given nonlinear discrete system together with nonlinear boundary conditions we use newton s iterative scheme and provide sufficient conditions for its convergence to the unique solution then the computational aspects of this iterative method on a floating point system are discussed this includes necessary and sufficient conditions for the convergence of the approximate newton s method an oscillatory state and the stopping criterion to make the analysis widely applicable all the results are proved component wise

a fast level set method for propagating interfaces a method is introduced to decrease the computational labor of the standard level set method for propagating interfaces the fast approach uses only points close to the curve at every time step we describe this new algorithm and compare its efficiency and accuracy with the standard level set approach

bi exponential edge preserving smoother edge preserving smoothers need not be taxed by a severe computational cost we present in this paper a lean algorithm that is inspired by the bi exponential filter and preserves its structure a pair of one tap recursions by a careful but simple local adaptation of the filter weights to the data we are able to design an edge preserving smoother that has a very low memory and computational footprint while requiring a trivial coding effort we demonstrate that our filter a bi exponential edge preserving smoother or beeps has formal links with the traditional bilateral filter on a practical side we observe that the beeps also produces images that are similar to those that would result from the bilateral filter but at a much reduced computational cost the cost per pixel is constant and depends neither on the data nor on the filter parameters not even on the degree of smoothing

a general framework for low level vision we introduce a new geometrical framework based on which natural flows for image scale space and enhancement are presented we consider intensity images as surfaces in the x i space the image is thereby a two dimensional 2 d surface in three dimensional 3 d space for gray level images and 2 d surfaces in five dimensions for color images the new formulation unifies many classical schemes and algorithms via a simple scaling of the intensity contrast and results in new and efficient schemes extensions to multidimensional signals become natural and lead to powerful denoising and scale space algorithms

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

the structure of locally orderless images we propose a representation of images in which a global but not a local topology is defined the topology is restricted to resolutions up to the extent of the local region of interest roi although the roi s may contain many pixels there is no spatial order on the pixels within the roi the only information preserved is the histogram of pixel values within the roi s this can be considered as an extreme case of a textel texture element image the histogram is the limit of texture where the spatial order has been completely disregarded we argue that locally orderless images are ubiquitous in perception and the visual arts formally the orderless images are most aptly described by three mutually intertwined scale spaces the scale parameters correspond to the pixellation inner scale the extent of the roi s outer scale and the resolution in the histogram tonal scale we describe how to construct locally orderless images how to render them and how to use them in a variety of local and global image processing operations

discriminative saliency propagation with sink points salient object detection is still very challenging especially in images with complex or cluttered background in this paper we present an efficient and discriminative framework to address it in specially a discriminative similarity metric is first proposed by measuring the chi square distance in a new constructed feature space then we apply it to calculate a background based coarse saliency map by introducing distribution prior to remove foreground noises in the image boundaries based on manifold ranking a robust saliency propagation mechanism is further developed to highlight salient object and simultaneously suppress background region by setting appropriate sink points finally several simple refinement techniques are utilized to generate pixel wise and smooth saliency maps extensive experimental results show the superior performance of the proposed method in terms of different evaluation metrics in addition the proposed framework can be also applied to the existing saliency propagation methods for significant performance boosting we also believe that it is a good choice for subsequent applications based on the achieved high performance and acceptable computational overhead a discriminative similarity metric is proposed to distinguish similar regions we propose an efficient distribution guided background based weak saliency method a discriminative propagation mechanism is developed to optimize coarse saliency maps several new refinements are utilized to enhance the visual quality of the output we make a good balance between saliency detection accuracy and computational cost

channel smoothing efficient robust smoothing of low level signal features in this paper we present a new and efficient method to implement robust smoothing of low level signal features b spline channel smoothing this method consists of three steps encoding of the signal features into channels averaging of the channels and decoding of the channels we show that linear smoothing of channels is equivalent to robust smoothing of the signal features if we make use of quadratic b splines to generate the channels the linear decoding from b spline channels allows the derivation of a robust error norm which is very similar to tukey s biweight error norm we compare channel smoothing with three other robust smoothing techniques nonlinear diffusion bilateral filtering and mean shift filtering both theoretically and on a 2d orientation data smoothing task channel smoothing is found to be superior in four respects it has a lower computational complexity it is easy to implement it chooses the global minimum error instead of the nearest local minimum and it can also be used on nonlinear spaces such as orientation space

recovering relative depth from low level features without explicit t junction detection and interpretation this work presents a novel computational model for relative depth order estimation from a single image based on low level local features that encode perceptual depth cues such as convexity concavity inclusion and t junctions in a quantitative manner considering information at different scales these multi scale features are based on a measure of how likely is a pixel to belong simultaneously to different objects interpreted as connected components of level sets and hence to be occluded in some of them providing a hint on the local depth order relationships they are directly computed on the discrete image data in an efficient manner without requiring the detection and interpretation of edges or junctions its behavior is clarified and illustrated for some simple images then the recovery of the relative depth order on the image is achieved by global integration of these local features applying a non linear diffusion filtering of bilateral type the validity of the proposed features and the integration approach is demonstrated by experiments on real images and comparison with state of the art monocular depth estimation techniques

susan a new approach to low level image processing this paper describes a new approach to low level image processing in particular edge and corner detection and structure preserving noise reduction non linear filtering is used to define which parts of the image are closely related to each individual pixel each pixel has associated with it a local image region which is of similar brightness to that pixel the new feature detectors are based on the minimization of this local image region and the noise reduction method uses this region as the smoothing neighbourhood the resulting methods are accurate noise resistant and fast details of the new feature detectors and of the new noise reduction method are described along with test results

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

some recent developments of numerov s method abstract this paper is a survey of some recent developments of numerov s method for solving nonlinear two point boundary value problems the survey consists of three different parts the existence uniqueness of a solution computational algorithm for computing a solution and some extensions of numerov s method the sufficient conditions for the existence and uniqueness of a solution are presented some of them are best possible various iterative methods are reviewed including picard s iterative method modified newton s iterative method monotone iterative method and accelerated monotone iterative method in particular two more direct monotone iterative methods are presented to save computational work each of these iterative methods not only gives a computational algorithm for computing a solution but also leads to an existence and uniqueness theorem the estimate on the rate of convergence of the iterative sequence is given the extensions of numerov s method to a coupled problem and a general problem are addressed the numerical results are presented to validate the theoretical analysis

speeding up the bilateral filter a joint acceleration way computational complexity of the brute force implementation of the bilateral filter bf depends on its filter kernel size to achieve the constant time bf whose complexity is irrelevant to the kernel size many techniques have been proposed such as 2d box filtering dimension promotion and shiftability property although each of the above techniques suffers from accuracy and efficiency problems previous algorithm designers were used to take only one of them to assemble fast implementations due to the hardness of combining them together hence no joint exploitation of these techniques has been proposed to construct a new cutting edge implementation that solves these problems jointly employing five techniques kernel truncation best n term approximation as well as previous 2d box filtering dimension promotion and shiftability property we propose a unified framework to transform bf with arbitrary spatial and range kernels into a set of 3d box filters that can be computed in linear time to the best of our knowledge our algorithm is the first method that can integrate all these acceleration techniques and therefore can draw upon one another s strong point to overcome deficiencies the strength of our method has been corroborated by several carefully designed experiments in particular the filtering accuracy is significantly improved without sacrificing the efficiency at running time

parametrized multicriteria optimization order continuity of the marginal multifunctions abstract two notions of continuity of multifunctions are introduced which take into account the order of the value space they reduce to the usual lower and upper semicontinuity if the multifunction is a real valued function we apply these notions to optimization problems and obtain generalizations of classical scalar results

diffusion tensors for processing sheared and rotated rectangles image restoration and simplification methods that respect important features such as edges play a fundamental role in digital image processing however known edge preserving methods like common nonlinear diffusion methods tend to round vertices for large diffusion times in this paper we adapt the diffusion tensor for anisotropic diffusion to avoid this effects in images containing rotated and sheared rectangles respectively in this context we propose a new method for estimating rotation angles and shear parameters based on the so called structure tensor further we show how the knowledge of appropriate diffusion tensors can be used in variational models numerical examples including orientation estimation denoising and segmentation demonstrate the good performance of our methods

fast domain decomposition for global image smoothing edge preserving smoothing eps can be formulated as minimizing an objective function that consists of data and regularization terms at the price of high computational cost this global eps approach is more robust and versatile than a local one that typically has a form of weighted averaging in this paper we introduce an efficient decomposition based method for global eps that minimizes the objective function of l 2 data and possibly non smooth and non convex regularization terms in linear time different from previous decomposition based methods which require solving a large linear system our approach solves an equivalent constrained optimization problem resulting in a sequence of 1 d sub problems this enables applying fast linear time solver for weighted least squares and l 1 smoothing problems an alternating direction method of multipliers algorithm is adopted to guarantee fast convergence our method is fully parallelizable and its runtime is even comparable to the state of the art local eps approaches we also propose a family of fast majorization minimization algorithms that minimize an objective with non convex regularization terms experimental results demonstrate the effectiveness and flexibility of our approach in a range of image processing and computational photography applications

an o 1 disparity refinement method for stereo matching disparity refinement is the final step but also the timing bottleneck of stereo matching due to its high computational complexity weighted media filter refinement method and non local refinement method are two typical refinement methods with o n computational complexity for each pixel where n indicates the maximum disparity this paper presents an o 1 disparity refinement method based on belief aggregation and belief propagation the aggregated belief which means the possibility of correct disparity value is efficiently computed on a minimum spanning tree first and then the belief aggregation is fast performed on another minimum spanning tree in two sequential passes first from leaf nodes to root then from root to leaf nodes only 2 additions and 4 multiplications are required for each pixel at all disparity levels so the computational complexity is o 1 performance evaluation on middlebury data sets shows that the proposed method has good performances both in accuracy and speed we proposed an o 1 disparity refinement method for each pixel speed evaluation shows constant result due to o 1 computational complexity accuracy evaluation shows better performance than 2 typical refinement methods

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

stability of efficient sets continuity of mobile polarities whenever for every x e d such that a x afi xo for i 1 2 n one hash x fi x for each i pareto optimization is also referred to as uecror multi objecfiue or multi criteria optimization multi objective maximization problems 0 1 have been nowadays extended to the situations where f is a mapping from x to a set y equipped with a transitive relation 2 this relation is frequently called a preference consider first the image a f d of the constraint d an element y of a is called 3 efficient up to indifference or in the broad sense if for every y e a y z y implies y 5 yo it is said to be strongly z eficient or efficient in the narrow sense if for each y e a y 2 y implies y y the two notions coincide for antisymmetric transitive relations we shall be primarily concerned with efficient points in the broad sense the set of efficient points of a with respect to 7 will be denoted by max a max z a and that of strongly efficient points by max a an element of y is called an efficient value of 0 1 if it is an efficient point of f d an element x0 of d is a solution of 0 1 if f xo is an efficient point of f d we shall use the latter s to denote the set of solutions of 0 1

dasc robust dense descriptor for multi modal and multi spectral correspondence estimation establishing dense correspondences between multiple images is a fundamental task in many applications however finding a reliable correspondence between multi modal or multi spectral images still remains unsolved due to their challenging photometric and geometric variations in this paper we propose a novel dense descriptor called dense adaptive self correlation dasc to estimate dense multi modal and multi spectral correspondences based on an observation that self similarity existing within images is robust to imaging modality variations we define the descriptor with a series of an adaptive self correlation similarity measure between patches sampled by a randomized receptive field pooling in which a sampling pattern is obtained using a discriminative learning the computational redundancy of dense descriptors is dramatically reduced by applying fast edge aware filtering furthermore in order to address geometric variations including scale and rotation we propose a geometry invariant dasc gi dasc descriptor that effectively leverages the dasc through a superpixel based representation for a quantitative evaluation of the gi dasc we build a novel multi modal benchmark as varying photometric and geometric conditions experimental results demonstrate the outstanding performance of the dasc and gi dasc in many cases of dense multi modal and multi spectral correspondences

fundamental relationship between bilateral filtering adaptive smoothing and the nonlinear diffusion equation in this paper the relationship between bilateral filtering and anisotropic diffusion is examined the bilateral filtering approach represents a large class of nonlinear digital image filters we first explore the connection between anisotropic diffusion and adaptive smoothing and then the connection between adaptive smoothing and bilateral filtering previously adaptive smoothing was considered to be an inconsistent approximation to the nonlinear diffusion equation we extend adaptive smoothing to make it consistent thus enabling a unified viewpoint that relates nonlinear digital image filters and the nonlinear diffusion equation

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

accelerated monotone iterative methods for a boundary value problem of second order discrete equations abstract an accelerated monotone iterative method for a boundary value problem of second order discrete equations is presented this method leads to an existence comparison theorem as well as a computational algorithm for the solutions the monotone property of the iterations gives improved upper and lower bounds of the solution in each iteration and the rate of convergence of the iterations is either quadratic or nearly quadratic depending on the property of the nonlinear function some numerical results are presented to illustrate the monotone convergence of the iterative sequences and the rate of convergence of the iterations

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

constant time median and bilateral filtering this paper formulates both the median filter and bilateral filter as a cost volume aggregation problem whose computational complexity is independent of the filter kernel size unlike most of the previous works the proposed framework results in a general bilateral filter that can have arbitrary spatial 1 1 and arbitrary range filter kernels this bilateral filter takes about 3 5 s to exactly filter a one megapixel 8 bit grayscale image on a 3 2 ghz intel core i7 cpu in practice the intensity range and spatial domain can be downsampled to improve the efficiency this compression can maintain very high accuracy e g 40 db but over 100 times 100 faster

relative reductive structure aware regression filter abstract structure aware image smoothing is a challenging and significant technique to remedy the limitation of current edge preserving smoothing filters for extracting the prominent structures to improve the technique we propose a novel structure aware filter via bilateral kernel regression with a variational structure kernel descriptor first the relative reductive texture decomposition is applied to construct the structure kernel descriptor then the descriptor is incorporated into the bilateral kernel regression to achieve an expected structure preservation output algorithmically a close form numerically iterative solver is exploited to achieve the efficient and effective implementation at last some experimental self evaluations and visual applications are presented to demonstrate that our method leads to better performance than the state of the art solutions

orientation guided geodesic weighting for patchmatch based stereo matching we propose an orientation guided geodesic weighting oggw strategy for local stereo matching we propose a method of cost volume filtering combining a multipoint lpa method with our oggw strategy we propose a patchmatch filter with curved surface fitting pmf cs to obtain a disparity map with sub pixel accuracy recently patchmatch based methods for local stereo matching are experiencing great progress with the use of compact and over segmented regions that have similar intensities or colors using patches as support regions this paper proposes an orientation guided geodesic weighting oggw strategy to search for an approximate shortest path from a support pixel in the patch to a pixel of interest along a guided orientation the oggw is computed by accumulating intensity differences or color dissimilarities between connected pixels along the path after obtaining matching cost updates by model fitting the oggw is used for weighted averaging on the updated costs to obtain a filtered cost volume in addition a new filtering method that combines the patchmatch filter with curved surface fitting pmf cs is presented in this paper curved surface fitting along with outliers removal is carried out to seek for a reliable regression model for estimating the disparities on a patch and to achieve a disparity map with sub pixel accuracy we conduct a number of experiments to evaluate the performances of oggw and pmf cs on cost volume filtering and disparity estimation experimental results show that our algorithm produces accurate stereo matching results and outperforms the current state of the art patchmatch based methods

stereo correspondence with compact windows via minimum ratio cycle one of the earliest and still widely used methods for dense stereo correspondence is based on matching windows of pixels the main difficulty of this method is choosing a window of appropriate size and shape small windows may lack sufficient intensity variation for reliable matching while large windows smooth out disparity discontinuities we propose an algorithm to choose a window size and shape by optimizing over a large class of compact windows the word compact is used informally to reflect the fact that the ratio of perimeter to area of our windows is small we believe that this is the first area based method which efficiently constructs nonrectangular windows fast optimization over compact windows is achieved via the minimum ratio cycle algorithm for graphs the algorithm has only a few parameters which are easy to fix

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

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

stability results for ekeland s e variational principle and cone extremal solutions given x a banach space and f x a a proper lower semicontinuous function which is bounded from below the ekeland s e variational principle asserts the existence of a point xi in x which we call e extremal with respect to f which satisfies fu fxi e u xi for all u x u xi by using set convergence notions kuratowski painleve mosco bounded hausdorff and their epigraphical versions we study the semi continuity properties of the mapping which to f associates e ext f the set of such e extremal points the key for the geometrical understanding of such properties is to consider the equivalent phelps extremization principle which given a closed set d in x and a partial ordering with respect to a pointed cone associates the set of elements of d maximal with respect to this order direct or potential applications are given in various fields multicriteria optimization numerical algorithmic calculus of variations

on discrete boundary value problems arising in transport phenomena for the discrete boundary value problems arising in transport processes we provide comparison results these results are used to develop monotone iterative methods for the construction of the maximal and minimal solutions in a sector the advantage of this technique is that the successive approximations are the solutions of the initial and terminal value problems numerical illustration showing the sharpness as well the importance of the obtained results is also included

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

monotone iterative methods for a general class of discrete boundary value problems abstract in this paper we shall offer comparison results as well as monotone iterative schemes for the construction of solutions to a very general class of discrete boundary value problems the discrete system we consider includes in particular the n th order prototype systems finite as well as infinite discrete delay equations and discrete integral equations further the boundary conditions we consider include the initial terminal periodic and transport type problems numerical examples illustrating the usefulness of the proposed schemes to a variety of boundary value problems are also included

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

parallel monotone iterative relaxation methods for a class of two dimensional discrete boundary value problems abstract a parallel monotone iterative relaxation method for a class of two dimensional discrete boundary value problems is established and the sequence of iterations is shown to converge monotonically either from above or below to a solution of the problem this monotone convergence results yields a parallel computational algorithm as well as an existence comparison result for the solutions to compute the sequence of iterations the thomas algorithm can be used in the same fashion as for one dimensional problem the existence and comparison results of the upper and lower solutions are given the local as well as global existence uniqueness of the solution are obtained the global convergence of the iterations is investigated and the influence of the parameters on the rate of convergence of the iterations is analyzed numerical results are given to corroborate the analytical results

revisiting the relationship between adaptive smoothing and anisotropic diffusion with modified filters anisotropic diffusion has been known to be closely related to adaptive smoothing and discretized in a similar manner this paper revisits a fundamental relationship between two approaches it is shown that adaptive smoothing and anisotropic diffusion have different theoretical backgrounds by exploring their characteristics with the perspective of normalization evolution step size and energy flow based on this principle adaptive smoothing is derived from a second order partial differential equation pde not a conventional anisotropic diffusion via the coupling of fick s law with a generalized continuity equation where a source or sink exists which has not been extensively exploited we show that the source or sink is closely related to the asymmetry of energy flow as well as the normalization term of adaptive smoothing it enables us to analyze behaviors of adaptive smoothing such as the maximum principle and stability with a perspective of a pde ultimately this relationship provides new insights into application specific filtering algorithm design by modeling the source or sink in the pde we introduce two specific diffusion filters the robust anisotropic diffusion and the robust coherence enhancing diffusion as novel instantiations which are more robust against the outliers than the conventional filters

fusion of median and bilateral filtering for range image upsampling we present a new upsampling method to enhance the spatial resolution of depth images given a low resolution depth image from an active depth sensor and a potentially high resolution color image from a passive rgb camera we formulate it as an adaptive cost aggregation problem and solve it using the bilateral filter the formulation synergistically combines the median and bilateral filters thus it better preserves the depth edges and is more robust to noise numerical and visual evaluations on a total of 37 middlebury data sets demonstrate the effectiveness of our method a real time high resolution depth capturing system is also developed using commercial active depth sensor based on the proposed upsampling method

fast bilateral filtering for denoising large 3d images a fast implementation of bilateral filtering is presented which is based on an optimal expansion of the filter kernel into a sum of factorized terms these terms are computed by minimizing the expansion error in the mean square error sense this leads to a simple and elegant solution in terms of eigenvectors of a square matrix in this way the bilateral filter is applied through computing a few gaussian convolutions for which very efficient algorithms are readily available moreover the expansion functions are optimized for the histogram of the input image leading to improved accuracy it is shown that this further optimization it made possible by removing the commonly deployed constrain of shiftability of the basis functions experimental validation is carried out in the context of digital rock imaging results on large 3d images of rock samples show the superiority of the proposed method with respect to other fast approximations of bilateral filtering

compressive bilateral filtering this paper presents an efficient constant time bilateral filter that produces a near optimal performance tradeoff between approximate accuracy and computational complexity without any complicated parameter adjustment called a compressive bilateral filter cblf the constant time means that the computational complexity is independent of its filter window size although many existing constant time bilateral filters have been proposed step by step to pursue a more efficient performance tradeoff they have less focused on the optimal tradeoff for their own frameworks it is important to discuss this question because it can reveal whether or not a constant time algorithm still has plenty room for improvements of performance tradeoff this paper tackles the question from a viewpoint of compressibility and highlights the fact that state of the art algorithms have not yet touched the optimal tradeoff the cblf achieves a near optimal performance tradeoff by two key ideas 1 an approximate gaussian range kernel through fourier analysis and 2 a period length optimization experiments demonstrate that the cblf significantly outperforms state of the art algorithms in terms of approximate accuracy computational complexity and usability

hashed nonlocal means for rapid image filtering denoising algorithms can alleviate the trade off between noise level and acquisition time that still exists for certain image types nonlocal means a recently proposed technique outperforms other methods in removing noise while retaining image structure albeit at prohibitive computational cost modifications have been proposed to reduce the cost but the method is still too slow for practical filtering of 3d images this paper proposes a hashed approach to explicitly represent two summed frequency hash functions of local descriptors patches utilizing all available image data unlike other approaches the hash spaces are discretized on a regular grid so primarily linear operations are used the large memory requirements are overcome by recursing the hash spaces additional speed gains are obtained by using a marginal linear interpolation method careful choice of the patch features results in high computational efficiency at similar accuracies the proposed approach can filter a 3d image in less than a minute versus 15 minutes to 3 hours for existing nonlocal means methods

automatic estimation and removal of noise from a single image image denoising algorithms often assume an additive white gaussian noise awgn process that is independent of the actual rgb values such approaches cannot effectively remove color noise produced by today s ccd digital camera in this paper we propose a unified framework for two tasks automatic estimation and removal of color noise from a single image using piecewise smooth image models we introduce the noise level function nlf which is a continuous function describing the noise level as a function of image brightness we then estimate an upper bound of the real nlf by fitting a lower envelope to the standard deviations of per segment image variances for denoising the chrominance of color noise is significantly removed by projecting pixel values onto a line fit to the rgb values in each segment then a gaussian conditional random field gcrf is constructed to obtain the underlying clean image from the noisy input extensive experiments are conducted to test the proposed algorithm which is shown to outperform state of the art denoising algorithms

efficient and robust specular highlight removal a robust and effective specular highlight removal method is proposed in this paper it is based on a key observation the maximum fraction of the diffuse colour component in diffuse local patches in colour images changes smoothly the specular pixels can thus be treated as noise in this case this property allows the specular highlights to be removed in an image denoising fashion an edge preserving low pass filter e g the bilateral filter can be used to smooth the maximum fraction of the colour components of the original image to remove the noise contributed by the specular pixels recent developments in fast bilateral filtering techniques enable the proposed method to run over 200 times faster than state of the art techniques on a standard cpu and differentiates it from previous work

large occlusion stereo a method for solving the stereo matching problem in the presence of large occlusion is presented a data structure the disparity space image is defined to facilitate the description of the effects of occlusion on the stereo matching process and in particular on dynamic programming dp solutions that find matches and occlusions simultaneously we significantly improve upon existing dp stereo matching methods by showing that while some cost must be assigned to unmatched pixels sensitivity to occlusion cost and algorithmic complexity can be significantly reduced when highly reliable matches or ground control points are incorporated into the matching process the use of ground control points eliminates both the need for biasing the process towards a smooth solution and the task of selecting critical prior probabilities describing image formation finally we describe how the detection of intensity edges can be used to bias the recovered solution such that occlusion boundaries will tend to be proposed along such edges reflecting the observation that occlusion boundaries usually cause intensity discontinuities

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

tree filtering efficient structure preserving smoothing with a minimum spanning tree we present a new efficient edge preserving filter tree filter to achieve strong image smoothing the proposed filter can smooth out high contrast details while preserving major edges which is not achievable for bilateral filter like techniques tree filter is a weighted average filter whose kernel is derived by viewing pixel affinity in a probabilistic framework simultaneously considering pixel spatial distance color intensity difference as well as connectedness pixel connectedness is acquired by treating pixels as nodes in a minimum spanning tree mst extracted from the image the fact that an mst makes all image pixels connected through the tree endues the filter with the power to smooth out high contrast fine scale details while preserving major image structures since pixels in small isolated region will be closely connected to surrounding majority pixels through the tree while pixels inside large homogeneous region will be automatically dragged away from pixels outside the region the tree filter can be separated into two other filters both of which turn out to have fast algorithms we also propose an efficient linear time mst extraction algorithm to further improve the whole filtering speed the algorithms give tree filter a great advantage in low computational complexity linear to number of image pixels and fast speed it can process a 1 megapixel 8 bit image at 0 25 s on an intel 3 4 ghz core i7 cpu including the construction of mst the proposed tree filter is demonstrated on a variety of applications

parametrized multicriteria optimization continuity and closedness of optimal multifunctions this paper studies continuity properties of the marginal multifunction and solution multifunction for optimization problems with respect to a preorder relation among others we present a number of results which are generalizations to multicriteria problems of theorems due to c berge w hogan t tanino and y sawaragi

global color sparseness and a local statistics prior for fast bilateral filtering the property of smoothing while preserving edges makes the bilateral filter a very popular image processing tool however its non linear nature results in a computationally costly operation various works propose fast approximations to the bilateral filter however the majority does not generalize to vector input as is the case with color images we propose a fast approximation to the bilateral filter for color images the filter is based on two ideas first the number of colors which occur in a single natural image is limited we exploit this color sparseness to rewrite the initial non linear bilateral filter as a number of linear filter operations second we impose a statistical prior to the image values that are locally present within the filter window we show that this statistical prior leads to a closed form solution of the bilateral filter finally we combine both ideas into a single fast and accurate bilateral filter for color images experimental results show that our bilateral filter based on the local prior yields an extremely fast bilateral filter approximation but with limited accuracy which has potential application in real time video filtering our bilateral filter which combines color sparseness and local statistics yields a fast and accurate bilateral filter approximation and obtains the state of the art results

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

stereo matching with nonlinear diffusion one of the central problems in stereo matching and other image registration tasks is the selection of optimal window sizes for comparing image regions this paper addresses this problem with some novel algorithms based on iteratively diffusing support at different disparity hypotheses and locally controlling the amount of diffusion based on the current quality of the disparity estimate it also develops a novel bayesian estimation technique which significantly outperforms techniques based on area based matching ssd and regular diffusion we provide experimental results on both synthetic and real stereo image pairs