multiscale tikhonov total variation image restoration using spatially varying edge coherence exponent edge preserving regularization using partial differential equation pde based methods although extensively studied and widely used for image restoration still have limitations in adapting to local structures we propose a spatially adaptive multiscale variable exponent based anisotropic variational pde method that overcomes current shortcomings such as over smoothing and staircasing artifacts while still retaining and enhancing edge structures across scale our innovative model automatically balances between tikhonov and total variation tv regularization effects using scene content information by incorporating a spatially varying edge coherence exponent map constructed using the eigenvalues of the filtered structure tensor the multiscale exponent model we develop leads to a novel restoration method that preserves edges better and provides selective denoising without generating artifacts for both additive and multiplicative noise models mathematical analysis of our proposed method in variable exponent space establishes the existence of a minimizer and its properties the discretization method we use satisfies the maximum minimum principle which guarantees that artificial edge regions are not created extensive experimental results using synthetic and natural images indicate that the proposed multiscale tikhonov tv mttv and dynamical mttv methods perform better than many contemporary denoising algorithms in terms of several metrics including signal to noise ratio improvement and structure preservation promising extensions to handle multiplicative noise models and multichannel imagery are also discussed

fuzzy contextual contrast enhancement this paper presents contrast enhancement algorithms based on fuzzy contextual information of the images we introduce fuzzy similarity index and fuzzy contrast factor to capture the neighborhood characteristics of a pixel a new histogram using fuzzy contrast factor of each pixel is developed and termed the fuzzy dissimilarity histogram fdh a cumulative distribution function is formed with normalized values of an fdh and used as a transfer function to obtain the contrast enhanced image the algorithm gives good contrast enhancement and preserves the natural characteristic of the image in order to develop a contextual intensity transfer function we introduce a fuzzy membership function based on fuzzy similarity index and coefficient of variation of the image the contextual intensity transfer function is designed using the fuzzy membership function to achieve final contrast enhanced image the overall algorithm is referred as the fuzzy contextual contrast enhancement algorithm the proposed algorithms are compared with the conventional and the state of the art contrast enhancement algorithms the quantitative and visual assessment of the results is performed the results of quantitative measures are statistically analyzed using t test the exhaustive experimentation and analysis show the proposed algorithm efficiently enhances contrast and yields in natural visual quality images

duality for a class of nondifferentiable mathematical programming problems abstract two dual problems are proposed for the minimax problem minimize maxy y x y subject to g x 0 a duality theorem is established for each dual problem it is revealed that these problems are intimately related to a class of nondifferentiable programming problems

active contours without edges we propose a new model for active contours to detect objects in a given image based on techniques of curve evolution mumford shah 1989 functional for segmentation and level sets our model can detect objects whose boundaries are not necessarily defined by the gradient we minimize an energy which can be seen as a particular case of the minimal partition problem in the level set formulation the problem becomes a mean curvature flow like evolving the active contour which will stop on the desired boundary however the stopping term does not depend on the gradient of the image as in the classical active contour models but is instead related to a particular segmentation of the image we give a numerical algorithm using finite differences finally we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable also the initial curve can be anywhere in the image and interior contours are automatically detected

complex short pulse and coupled complex short pulse equations abstract in the present paper we propose a complex short pulse equation and a coupled complex short equation to describe ultra short pulse propagation in optical fibers they are integrable due to the existence of lax pairs and infinite number of conservation laws furthermore we find their multi soliton solutions in terms of pfaffians by virtue of hirota s bilinear method one and two soliton solutions are investigated in details showing favorable properties in modeling ultra short pulses with a few optical cycles especially same as the coupled nonlinear schrodinger equation there is an interesting phenomenon of energy redistribution in soliton interactions it is expected that for the ultra short pulses the complex and coupled complex short pulses equation will play the same roles as the nonlinear schrodinger equation and coupled nonlinear schrodinger equation

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

on nonlinear programming in complex spaces abstract the present approach is based essentially on theorems of the alternative which are exploited mainly in real spaces in this paper only finite dimensional spaces are considered making use of separation arguments and of the one to one correspondence between c n and r 2 n both the real and the complex case can be considered from the same point of view then optimality conditions are established both when the objective function is expressed in terms of real and imaginary parts and when it is expressed in terms of the real part only

propagation of ultra short optical pulses in cubic nonlinear media abstract we derive a partial differential equation that approximates solutions of maxwell s equations describing the propagation of ultra short optical pulses in nonlinear media and which extends the prior analysis of alterman and rauch phys lett a 264 2000 390 diffractive nonlinear geometric optics for short pulses preprint 2002 we discuss non rigorously conditions under which this approximation should be valid but the main contributions of this paper are 1 an emphasis on the fact that the model equation for short pulse propagation may depend on the details of the optical susceptibility in the wavelength regime under consideration 2 a numerical comparison of solutions of this model equation with solutions of the full nonlinear partial differential equation 3 a local well posedness result for the model equation and 4 a proof that in contrast to the nonlinear schrodinger equation which models slowly varying wavetrains this equation has no smooth pulse solutions which propagate with fixed shape and speed

large scale weakly supervised object localization via latent category learning localizing objects in cluttered backgrounds is challenging under large scale weakly supervised conditions due to the cluttered image condition objects usually have large ambiguity with backgrounds besides there is also a lack of effective algorithm for large scale weakly supervised localization in cluttered backgrounds however backgrounds contain useful latent information e g the sky in the aeroplane class if this latent information can be learned object background ambiguity can be largely reduced and background can be suppressed effectively in this paper we propose the latent category learning lcl in large scale cluttered conditions lcl is an unsupervised learning method which requires only image level class labels first we use the latent semantic analysis with semantic object representation to learn the latent categories which represent objects object parts or backgrounds second to determine which category contains the target object we propose a category selection strategy by evaluating each category s discrimination finally we propose the online lcl for use in large scale conditions evaluation on the challenging pascal visual object class voc 2007 and the large scale imagenet large scale visual recognition challenge 2013 detection data sets shows that the method can improve the annotation precision by 10 over previous methods more importantly we achieve the detection precision which outperforms previous results by a large margin and can be competitive to the supervised deformable part model 5 0 baseline on both data sets

multi soliton multi breather and higher order rogue wave solutions to the complex short pulse equation abstract in the present paper we are concerned with the general analytic solutions to the complex short pulse csp equation including soliton breather and rogue wave solutions with the aid of a generalized darboux transformation we construct the n bright soliton solution in a compact determinant form the n breather solution including the akhmediev breather and a general higher order rogue wave solution the first and second order rogue wave solutions are given explicitly and analyzed the asymptotic analysis is performed rigorously for both the n soliton and the n breather solutions all three forms of the analytical solutions admit either smoothed cusped or looped type ones for the csp equation depending on the parameters it is noted that due to the reciprocal hodograph transformation the rogue wave solution to the csp equation can be a smoothed cusponed or a looped one which is different from the rogue wave solution found so far

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

integrable discretizations and numerical simulation for a modified coupled integrable dispersionless equation abstract in this paper we propose an integrable semi discrete and full discrete analogues of the modified coupled integrable dispersionless mcid equation that was derived recently as a two component generalization of cid equation the key of the integrable discretization is to find the relation between the mcid equation and the sine gordon equation we complete the integrable discrete analogues based on the discrete sine gordon equation numerical simulation of one soliton two soliton and breather solution are conducted based on the integrable semi discrete scheme we also present the casorati determinant solution in parametric form of n soliton solutions for the semi discrete analogue of the mcid equation we show that the continuum limit of the full discrete mcid equation leads to the semi discrete mcid equation

on the impact of anisotropic diffusion on edge detection content aware edge preserving smoothing techniques have gained visibility in recent years however they have had a rather limited impact on the edge detection literature compared to content unaware linear techniques often based on gaussian filters in this work we focus on anisotropic diffusion covering its initial definition by perona and malik and subsequent extensions a visual case study is used to illustrate their features we perform a quantitative evaluation of the performance of the canny method for edge detection when substituting linear gaussian smoothing filters by anisotropic diffusion highlightsreviewing the main trends in anisotropic diffusion identifying the practical scenarios on which anisotropic diffusion fails quantifying the improvement of edge detection when anisitropic diffusion is applied

the short pulse hierarchy we study a new hierarchy of equations containing the short pulse equation which describes the evolution of very short pulses in nonlinear media and the elastic beam equation which describes nonlinear transverse oscillations of elastic beams under tension we show that the hierarchy of equations is integrable we obtain the two compatible hamiltonian structures we construct an infinite series of both local and nonlocal conserved charges a lax description is presented for both systems for the elastic beam equations we also obtain a nonstandard lax representation

trace inference curvature consistency and curve detection an approach is described for curve inference that is based on curvature information the inference procedure is divided into two stages a trace inference stage which is the subject of the present work and a curve synthesis stage it is shown that recovery of the trace of a curve requires estimating local models for the curve at the same time and that tangent and curvature information are sufficient these make it possible to specify powerful constraints between estimated tangents to a curve in terms of a neighborhood relationship called cocircularity and between curvature estimates in terms of a curvature consistency relation because all curve information is quantized special care must be taken to obtain accurate estimates of trace points tangents and curvatures this issue is addressed specifically to the introduction of a smoothness constraint and a maximum curvature constraint the procedure is applied to two types of images artificial images designed to evaluate curvature and noise sensitivity and natural images

a multiphase level set framework for image segmentation using the mumford and shah model we propose a new multiphase level set framework for image segmentation using the mumford and shah model for piecewise constant and piecewise smooth optimal approximations the proposed method is also a generalization of an active contour model without edges based 2 phase segmentation developed by the authors earlier in t chan and l vese 1999 in scale space 99 m nilsen et al eds lncs vol 1682 pp 141 151 and t chan and l vese 2001 ieee ip 10 2 266 277 the multiphase level set formulation is new and of interest on its own by construction it automatically avoids the problems of vacuum and overlaps it needs only log n level set functions for n phases in the piecewise constant cases it can represent boundaries with complex topologies including triple junctionss in the piecewise smooth case only two level set functions formally suffice to represent any partition based on the four color theorem finally we validate the proposed models by numerical results for signal and image denoising and segmentation implemented using the osher and sethian level set method

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

revisiting graph construction for fast image segmentation abstract in this paper we propose a simple but effective method for fast image segmentation we re examine the locality preserving character of spectral clustering by constructing a graph over image regions with both global and local connections our novel approach to build graph connections relies on two key observations 1 local region pairs that co occur frequently will have a high probability to reside on a common object 2 spatially distant regions in a common object often exhibit similar visual saliency which implies their neighborship in a manifold we present a novel energy function to efficiently conduct graph partitioning based on multiple high quality partitions we show that the generated eigenvector histogram based representation can automatically drive effective unary potentials for a hierarchical random field model to produce multi class segmentation sufficient experiments on the bsds500 benchmark large scale pascal voc and coco datasets demonstrate the competitive segmentation accuracy and significantly improved efficiency of our proposed method compared with other state of the arts

optimality conditions for a nondifferentiable minimax programming in complex spaces abstract in this paper we study a nondifferentiable minimax programming in complex spaces we establish the kuhn tucker type necessary optimality conditions and prove the existence theorem for optimality in complex programming under generalized convexity

a self adaptive moving mesh method for the camassa holm equation a self adaptive moving mesh method is proposed for the numerical simulations of the camassa holm equation it is an integrable scheme in the sense that it possesses the exact n soliton solution it is named a self adaptive moving mesh method because the non uniform mesh is driven and adapted automatically by the solution once the non uniform mesh is evolved the solution is determined by solving a tridiagonal linear system due to these two superior features of the method several test problems give very satisfactory results even if by using a small number of grid points

feedback and surround modulated boundary detection edges are key components of any visual scene to the extent that we can recognise objects merely by their silhouettes the human visual system captures edge information through neurons in the visual cortex that are sensitive to both intensity discontinuities and particular orientations the classical approach assumes that these cells are only responsive to the stimulus present within their receptive fields however recent studies demonstrate that surrounding regions and inter areal feedback connections influence their responses significantly in this work we propose a biologically inspired edge detection model in which orientation selective neurons are represented through the first derivative of a gaussian function resembling double opponent cells in the primary visual cortex v1 in our model we account for four kinds of receptive field surround i e full far iso and orthogonal orientation whose contributions are contrast dependant the output signal from v1 is pooled in its perpendicular direction by larger v2 neurons employing a contrast variant centre surround kernel we further introduce a feedback connection from higher level visual areas to the lower ones the results of our model on three benchmark datasets show a big improvement compared to the current non learning and biologically inspired state of the art algorithms while being competitive to the learning based methods

non parametric blur map regression for depth of field extension real camera systems have a limited depth of field dof which may cause an image to be degraded due to visible misfocus or too shallow dof in this paper we present a blind deblurring pipeline able to restore such images by slightly extending their dof and recovering sharpness in regions slightly out of focus to address this severely ill posed problem our algorithm relies first on the estimation of the spatially varying defocus blur drawing on local frequency image features a machine learning approach based on the recently introduced regression tree fields is used to train a model able to regress a coherent defocus blur map of the image labeling each pixel by the scale of a defocus point spread function a non blind spatially varying deblurring algorithm is then used to properly extend the dof of the image the good performance of our algorithm is assessed both quantitatively using realistic ground truth data obtained with a novel approach based on a plenoptic camera and qualitatively with real images

the design and use of steerable filters the authors present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters allowing one to adaptively steer a filter to any orientation and to determine analytically the filter output as a function of orientation steerable filters may be designed in quadrature pairs to allow adaptive control over phase as well as orientation the authors show how to design and steer the filters and present examples of their use in the analysis of orientation and phase angularly adaptive filtering edge detection and shape from shading one can also build a self similar steerable pyramid representation the same concepts can be generalized to the design of 3 d steerable filters

efficient graph based image segmentation this paper addresses the problem of segmenting an image into regions we define a predicate for measuring the evidence for a boundary between two regions using a graph based representation of the image we then develop an efficient segmentation algorithm based on this predicate and show that although this algorithm makes greedy decisions it produces segmentations that satisfy global properties we apply the algorithm to image segmentation using two different kinds of local neighborhoods in constructing the graph and illustrate the results with both real and synthetic images the algorithm runs in time nearly linear in the number of graph edges and is also fast in practice an important characteristic of the method is its ability to preserve detail in low variability image regions while ignoring detail in high variability regions

l_ 0 regularized image downscaling in this paper we propose a novel l 0 regularized optimization framework for image downscaling the optimization is driven by two l 0 regularized priors the first prior gradient ratio prior is based on the observation that the number of edges in the downscaled image is approximately inverse square proportional to the downscaling factor by introducing l 0 norm sparsity to the gradient ratio the downscaled image is able to preserve the most salient edges as well as the visual perception of the original image the second prior downsampling prior is to constrain the downsampling matrix so that pixels of the downscaled image are estimated according to those optimal neighboring pixels extensive experiments on the urban100 and bsds500 data sets show that the proposed algorithm achieves superior performance over the state of the arts in terms of both quality and robustness

activity representation with motion hierarchies complex activities e g pole vaulting are composed of a variable number of sub events connected by complex spatio temporal relations whereas simple actions can be represented as sequences of short temporal parts in this paper we learn hierarchical representations of activity videos in an unsupervised manner these hierarchies of mid level motion components are data driven decompositions specific to each video we introduce a spectral divisive clustering algorithm to efficiently extract a hierarchy over a large number of tracklets i e local trajectories we use this structure to represent a video as an unordered binary tree we model this tree using nested histograms of local motion features we provide an efficient positive definite kernel that computes the structural and visual similarity of two hierarchical decompositions by relying on models of their parent child relations we present experimental results on four recent challenging benchmarks the high five dataset patron perez et al high five recognising human interactions in tv shows 2010 the olympics sports dataset niebles et al modeling temporal structure of decomposable motion segments for activity classification 2010 the hollywood 2 dataset marszalek et al actions in context 2009 and the hmdb dataset kuehne et al hmdb a large video database for human motion recognition 2011 we show that per video hierarchies provide additional information for activity recognition our approach improves over unstructured activity models baselines using other motion decomposition algorithms and the state of the art

clustering via geometric median shift over riemannian manifolds the mean shift algorithms have been successfully applied to many areas such as data clustering feature analysis and image segmentation however they still have two limitations one is that they are ineffective in clustering data with low dimensional manifolds because of the use of the euclidean distance for calculating distances the other is that they sometimes produce poor results for data clustering and image segmentation this is because a mean may not be a point in a data set in order to overcome the two limitations we propose a novel approach for the median shift over riemannian manifolds that uses the geometric median and geodesic distances unlike the mean the geometric median of a data set is one of points in the set compared to the euclidean distance the geodesic distances can better describe data points distributed on riemannian manifolds based on these two facts we first present a novel density function that characterizes points on a manifold with the geodesic distance the shift of the geometric median over the riemannian manifold is derived from maximizing this density function after this we present an algorithm for geometric median shift over riemannian manifolds together with theoretical proofs of its correctness extensive experiments have demonstrated that our method outperforms the state of the art algorithms in data clustering image segmentation and noise filtering on both synthetic data sets and real image databases

an integrable coupled short pulse equation an integrable coupled short pulse csp equation is proposed for the propagation of ultra short pulses in optical fibers based on two sets of bilinear equations to a two dimensional toda lattice linked by a backlund transformation and an appropriate hodograph transformation the proposed csp equation is derived meanwhile its n soliton solutions are given by the casorati determinant in a parametric form the properties of one and two soliton solutions are investigated in detail same as the short pulse equation the two soliton solution turns out to be a breather type if the wave numbers are complex conjugate we also illustrate an example of soliton breather interaction

symmetric duality for mathematical programming in complex spaces with f convexity abstract under f convexity f concavity f pseudoconvexity f pseudoconcavity appropriate duality results for a pair of wolfe and mond weir type symmetric dual nonlinear programming problems in complex spaces are established these results are then used to develop second order f convexity f concavity second order f pseudoconvexity f pseudoconcavity and appropriate second order symmetric dual nonlinear programming problems in complex spaces

complementary saliency driven co segmentation with region searching and hierarchical constraint foreground histogram consistency is a commonly used global constraint for co segmentation problems however scale target posture as well as the viewpoint changes usually make it hard to guarantee the absolute consistency of histogram in this paper we formulate a unified framework by incorporating the local region searching strategy and hierarchical constraint with the global scale invariant framework additionally complementary saliency is adopted to reduce the unreliable prediction brought by single saliency estimation method such automatic foreground inferring strategy also shows good compatibility and interaction with the new unified co segmentation framework the comparison experiments conducted on the public datasets demonstrate the good performance of the proposed method

a multiscale algorithm for image segmentation by variational method most segmentation algorithms are composed of several procedures split and merge small region elimination boundary smoothing each depending on several parameters the introduction of an energy to minimize leads to a drastic reduction of these parameters the authors prove that the most simple segmentation tool the region merging algorithm made according to the simplest energy is enough to compute a local energy minimum belonging to a compact class and to achieve the job of most of the tools mentioned above the authors explain why merging in a variational framework leads to a fast multiscale multichannel algorithm with a pyramidal structure the obtained algorithm is o n ln n where n is the number of pixels of the picture this fast algorithm is applied to make grey level and texture segmentation and experimental results are shown

an active contour model based on local fitted images for image segmentation active contour models are popular and widely used for a variety of image segmentation applications with promising accuracy but they may suffer from limited segmentation performances due to the presence of intensity inhomogeneity to overcome this drawback a novel region based active contour model based on two different local fitted images is proposed by constructing a novel local hybrid image fitting energy which is minimized in a variational level set framework to guide the evolving of contour curves toward the desired boundaries the proposed model is evaluated and compared with several typical active contour models to segment synthetic and real images with different intensity characteristics experimental results demonstrate that the proposed model outperforms these models in terms of accuracy in image segmentation

optimality and duality for minmax problems involving arcwise connected and generalized arcwise connected functions abstract in this paper we establish necessary optimality conditions for a static minmax programming problem of the form min max y y x y subject tog x 0 in terms of the right derivatives of the functions with respect to the same arc various theorems giving sufficient optimality conditions are proved a mond weir type dual is proposed and duality results are established under arcwise connectedness and generalized arcwise connectedness assumptions

separability criteria for the evaluation of boundary detection benchmarks there exist a significant number of benchmarks for evaluating the performance of boundary detection algorithms most of them relying on some sort of comparison of the automatically generated boundaries with human labeled ones such benchmarks are composed of a representative image data set as well as a comparison measure on the universe of boundary images despite many such data sets and measures have been proposed there is no clear way of knowing which combinations of them are the most suitable for the task in this paper we introduce four criteria that allow for a sensible evaluation of the performance of a comparison measure on a given data set the criteria mimic the way in which humans understand boundary images as well as their ability to recognize the underlying scenes these criteria can as a final goal quantify the ability of the boundary detection benchmarks to evaluate the performance of boundary detection methods either edge based or segmentation based

curvature filters efficiently reduce certain variational energies in image processing the rapid approximate solution of variational problems involving generic data fitting terms is often of practical relevance for example in real time applications variational solvers based on diffusion schemes or the euler lagrange equations are too slow and restricted in the types of data fitting terms here we present a filter based approach to reduce variational energies that contain generic data fitting terms but are restricted to specific regularizations our approach is based on reducing the regularization part of the variational energy while guaranteeing non increasing total energy this is applicable to regularization dominated models where the data fitting energy initially increases while the regularization energy initially decreases we present fast discrete filters for regularizers based on gaussian curvature mean curvature and total variation these pixel local filters can be used to rapidly reduce the energy of the full model we prove the convergence of the resulting iterative scheme in a greedy sense and we show several experiments to demonstrate applications in image processing problems involving regularization dominated variational models

geodesic saliency of watershed contours and hierarchical segmentation the watershed is one of the latest segmentation tools developed in mathematical morphology in order to prevent its oversegmentation the notion of dynamics of a minimum based on geodesic reconstruction has been proposed in this paper we extend the notion of dynamics to the contour arcs this notion acts as a measure of the saliency of the contour contrary to the dynamics of minima our concept reflects the extension and shape of the corresponding object in the image this representation is also much more natural because it is expressed in terms of partitions of the plane i e segmentations a hierarchical segmentation process is then derived which gives a compact description of the image containing all the segmentations one can obtain by the notion of dynamics by means of a simple thresholding finally efficient algorithms for computing the geodesic reconstruction as well as the dynamics of contours are presented

evaluation of hierarchical watersheds this paper aims to understand the practical features of hierarchies of morphological segmentations namely the quasi flat zones hierarchy and watershed hierarchies and to evaluate their potential in the context of natural image analysis we propose a novel evaluation framework for the hierarchies of partitions designed to capture various aspects of those representations precision of their regions and contours possibility to extract high quality horizontal cuts and optimal non horizontal cuts for image segmentation and the ease of finding a set of regions representing a semantic object this framework is used to assess and to optimize hierarchies with respect to the possible pre and post processing steps we show that used in conjunction with a state of the art contour detector watershed hierarchies are competitive with the complex state of the art methods for hierarchy construction in particular the proposed framework allows us to identify a watershed hierarchy based on a novel extinction value the number of parent nodes that outperforms the other hierarchies of morphological segmentations this coupled with the fact that watershed hierarchies satisfy clear global optimality properties and can be efficiently computed on large data make them valuable candidates for various computer vision tasks

a variational framework for multiregion pairwise similarity based image segmentation variational cost functions that are based on pairwise similarity between pixels can be minimized within level set framework resulting in a binary image segmentation in this paper we extend such cost functions and address multi region image segmentation problem by employing a multi phase level set framework for multi modal images cost functions become more complicated and relatively difficult to minimize we extend our previous work proposed for background foreground separation to the segmentation of images in more than two regions we also demonstrate an efficient implementation of the curve evolution which reduces the computational time significantly finally we validate the proposed method on the berkeley segmentation data set by comparing its performance with other segmentation techniques

regularized tree partitioning and its application to unsupervised image segmentation in this paper we propose regularized tree partitioning approaches we study normalized cut ncut and average cut acut criteria over a tree forming two approaches 1 normalized tree partitioning ntp and 2 average tree partitioning atp we give the properties that result in an efficient algorithm for ntp and atp in addition we present the relations between the solutions of ntp and atp over the maximum weight spanning tree of a graph and ncut and acut over this graph to demonstrate the effectiveness of the proposed approaches we show its application to image segmentation over the berkeley image segmentation data set and present qualitative and quantitative comparisons with state of the art methods

nonsmooth invex functions and sufficient optimality conditions in this paper the various definitions of nonsmooth invex functions are gathered in a general scheme by means of the concept of k directional derivative characterizations of nonsmooth k invexity are derived as well as results concerning constrained optimization without any assumption of convexity of the k directional derivatives

normalized cut based saliency detection by adaptive multi level region merging existing salient object detection models favor over segmented regions upon which saliency is computed such local regions are less effective on representing object holistically and degrade emphasis of entire salient objects as a result the existing methods often fail to highlight an entire object in complex background toward better grouping of objects and background in this paper we consider graph cut more specifically the normalized graph cut ncut for saliency detection since the ncut partitions a graph in a normalized energy minimization fashion resulting eigenvectors of the ncut contain good cluster information that may group visual contents motivated by this we directly induce saliency maps via eigenvectors of the ncut contributing to accurate saliency estimation of visual clusters we implement the ncut on a graph derived from a moderate number of superpixels this graph captures both intrinsic color and edge information of image data starting from the superpixels an adaptive multi level region merging scheme is employed to seek such cluster information from ncut eigenvectors with developed saliency measures for each merged region encouraging performance is obtained after across level integration experiments by comparing with 13 existing methods on four benchmark datasets including msra 1000 sod sed and cssd show the proposed method ncut saliency results in uniform object enhancement and achieves comparable better performance to the state of the art methods

category specific object segmentation via unsupervised discriminant shape category specific object segmentation has been a long standing research topic in pattern recognition this paper presents an unsupervised discriminant shape uds to address category specific object segmentation by incorporating the proposed shape prior into an intuitive energy minimization framework recently based on the region proposal methods deep convolutional neural networks cnns provide access to candidate segments in categories of interest from images however the segments obtained from bottom up proposals tend to undershoot or overshoot objects and are easily classified into one specific class to address this problem we propose an unsupervised discriminant projection based clustering algorithm udc to obtain more precise shape prior to guide the segmentation and the class specific proposals are clustered based on their projections onto the discriminant projection direction based on the set of proposals we then obtain the prior information of foreground uds with an easy voting scheme the derived uds prior is finally utilized in the subsequent energy minimizing formulation based figure ground segmentation we conduct extensive and comprehensive evaluations on the msrc object discovery fashionista and pascal s datasets demonstrating the effectiveness and robustness of the uds based segmentation highlightsa novel unsupervised discriminant shape is proposed for segmenting images an unsupervised discriminant clustering method is built for precise shape prior our model can produce reliable segmentation for category specific objects evaluations on 4 datasets demonstrate the effectiveness of our method

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

optimality and duality for complex nondifferentiable fractional programming abstract both parametric and nonparametric necessary and sufficient optimality conditions are established for a class of complex nondifferentiable fractional programming problems containing generalized convex functions subsequently these optimality criteria are utilized as a basis for constructing one parametric and two other parameter free dual models with appropriate duality theorems

parametric duality on minimax programming involving generalized convexity in complex space in this paper we employ generalized convexity of complex functions to establish several sufficient optimality conditions for minimax programming in complex spaces using such criteria we constitute a parametrical dual and establish the weak strong and strict converse duality theorems in the framework

correctness of local probability propagation in graphical models with loops graphical models such as bayesian networks and markov networks represent joint distributions over a set of variables by means of a graph when the graph is singly connected local propagation rules of the sort proposed by pearl 1988 are guaranteed to converge to the correct posterior probabilities recently a number of researchers have empirically demonstrated good performance of these same local propagation schemes on graphs with loops but a theoretical understanding of this performance has yet to be achieved for graphical models with a single loop we derive an analytical relationship between the probabilities computed using local propagation and the correct marginals using this relationship we show a category of graphical models with loops for which local propagation gives rise to provably optimal maximum a posteriori assignments although the computed marginals will be incorrect we also show how nodes can use local information in the messages they receive in order to correct their computed marginals we discuss how these results can be extended to graphical models with multiple loops and show simulation results suggesting that some properties of propagation on single loop graphs may hold for a larger class of graphs specifically we discuss the implication of our results for understanding a class of recently proposed error correcting codes known as turbo codes

monocular extraction of 2 1d sketch using constrained convex optimization this paper presents an approach to estimating the 2 1d sketch from monocular low level visual cues we use a low level segmenter to partition the image into regions and then estimate their 2 1d sketch subject to figure ground and similarity constraints between neighboring regions the 2 1d sketch assigns a depth ordering to image regions which are expected to correspond to objects and surfaces in the scene this is cast as a constrained convex optimization problem and solved within the optimization transfer framework the optimization objective takes into account the curvature and convexity of parts of region boundaries appearance and spatial layout properties of regions our new optimization transfer algorithm admits a closed form expression of the duality gap and thus allows explicit computation of the achieved accuracy the algorithm is efficient with quadratic complexity in the number of constraints between image regions quantitative and qualitative results on challenging real world images of berkeley segmentation geometric context and stanford make3d datasets demonstrate our high accuracy efficiency and robustness

radial projection an efficient update rule for relaxation labeling relaxation labeling uses contextual information for finding consistent labelings of graphs although relaxation labeling is parallel and iterative the complexity of updating with standard rules is too costly for practical implementation a description is given of a computationally more efficient updating rule that utilizes radial projection instead of normal projection to avoid the complexities incurred by previous update rules when boundaries to the labeling space are encountered this reduction in complexity is achieved by first restricting support vectors to the positive quadrant and then using radial projection onto the constraint instead of normal projection crucial order information is conserved through smooth convergence towards the optimum and a rate of convergence proportional to the magnitudes of the support functions

complex minimax programming under generalized convexity we establish the kuhn tucker type sufficient optimality conditions for complex minimax programming under generalized invex functions subsequently we apply these optimality criteria to formulate two dual models we also establish weak strong and strict converse duality theorems

2d segmentation using a robust active shape model with the em algorithm statistical shape models have been extensively used in a wide range of applications due to their effectiveness in providing prior shape information for object segmentation problems the most popular method is the active shape model asm however accurately fitting the shape model to an object boundary under a cluttered environment is a challenging task under such assumptions the model is often attracted toward invalid observations outliers leading to meaningless estimates of the object boundary in this paper we propose a novel algorithm that improves the robustness of asm in the presence of outliers the proposed framework assumes that both type of observations valid observations and outliers are detected in the image a new strategy is devised for treating the data in different ways depending on the observations being considered as valid or invalid the proposed algorithm assigns a different weight to each observation the shape parameters are recursively updated using the expectation maximization method allowing a correct and robust fit of the shape model to the object boundary in the image two estimation criteria are considered 1 the maximum likelihood criterion and 2 the maximum a posteriori criterion that use priors for the unknown parameters the methods are tested with synthetic and real images comprising medical images of the heart and image sequences of the lips the results are promising and show that this approach is robust in the presence of outliers leading to a significant improvement over the standard asm and other state of the art methods

multi region active contours with a single level set function segmenting an image into an arbitrary number of coherent regions is at the core of image understanding many formulations of the segmentation problem have been suggested over the past years these formulations include among others axiomatic functionals which are hard to implement and analyze and graph based alternatives which impose a non geometric metric on the problem we propose a novel method for segmenting an image into an arbitrary number of regions using an axiomatic variational approach the proposed method allows to incorporate various generic region appearance models while avoiding metrication errors in the suggested framework the segmentation is performed by level set evolution yet contrarily to most existing methods here multiple regions are represented by a single non negative level set function the level set function evolution is efficiently executed through the voronoi implicit interface method for multi phase interface evolution the proposed approach is shown to obtain accurate segmentation results for various natural 2d and 3d images comparable to state of the art image segmentation algorithms

a new generalised α scale spaces quadrature filters abstract the scale spaces is a recent theory that open new possibilities of phase based image processing it is a parameterised class 0 1 of linear scale space representations which allows a continuous connection beyond the well known gaussian scale space 1 in this paper we make use of this unified representation to derive new families of band pass quadrature filters built from derivatives and difference of the scale space generating kernels this construction leads to generalised kernel filters including the commonly known families derived from the gaussian and the poisson kernels the properties of each family are first studied and then experiments on one and two dimensional signals are shown to exemplify how the suggested filters can be used for edge detection this work is complemented by an experimental evaluation which demonstrates that the new proposed filters are a good alternative to the commonly used log gabor filter

an integrable semi discretization of the camassa holm equation and its determinant solution an integrable semi discretization of the camassa holm ch equation is presented the keys of its construction are bilinear forms and determinant structure of solutions of the ch equation determinant formulas of n soliton solutions of the continuous and semi discrete camassa holm equations are presented based on determinant formulas we can generate multi soliton multi cuspon and multi soliton cuspon solutions numerical computations using the integrable semi discrete camassa holm equation are performed it is shown that the integrable semi discrete camassa holm equation gives very accurate numerical results even in the cases of cuspon cuspon and soliton cuspon interactions the numerical computation for an initial value condition which is not an exact solution is also presented

optimality and duality for nonsmooth multiobjective fractional programming problems involving exponential v r invexity abstract this paper is to study a subdifferentiable multiobjective fractional programming problem under exponential v r invexity we establish sufficient optimality conditions for multiobjective fractional programming problems involving exponential v r invex lipschitz functions by optimality conditions the parametric dual model is formulated consequently the duality theorems are proved so that the optimal values of the duality problems are equal to the primary problem under the framework of exponential v r invexity for the lipschitz function

necessary and sufficient conditions for minimax fractional programming we establish the necessary and sufficient optimality conditions for a class of nondifferentiable minimax fractional programming problems solving generalized convex functions subsequently we apply the optimality conditions to formulate one parametric dual problem and we prove weak duality strong duality and strict converse duality theorems

optimality and duality for the multiobjective fractional programming with the generalized f ρ convexity abstract a class of multiobjective fractional programmings mfp are first formulated where the involved functions are local lipschitz and clarke subdifferentiable in order to deduce our main results we give the definitions of the generalized f convex class about the clarke subgradient under the above generalized convexity assumption the alternative theorem is obtained and some sufficient and necessary conditions for optimality are also given related to the properly efficient solution for the problems finally we formulate the two dual problems md and md1 corresponding to mfp and discuss the week strong and reverse duality

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

joint occlusion boundary detection and figure ground assignment by extracting common fate fragments in a back projection scheme occlusion boundary detection and figure ground assignment are among the fundamental challenges for the real world visual pattern recognition applications such as 3d spatial understanding robotic navigation and object search we attack these challenges by extracting an intermediate level image video representation namely common fate fragments a common fate fragment is composed of both over segmented region and edge fragments physically it exists as a coupled edge region fragment bound with dynamic information common fate fragment candidates are generated by an integrated line region growing process which does not require complete object segmentation or closed object boundary extraction to identify common fate fragments from these extracted candidates we introduce a back projection verification scheme that can circumvent the notoriously difficult task of direct motion estimation on boundaries this allows occlusion detection and figure ground labeling to be jointly conducted within a simple but effective hypothesize and test framework we test the proposed method on youtube motion boundaries ymb data set and two benchmark data sets the cmu and berkeley motion data sets even though the idea of the proposed method is simple and transparent promising experimental results are observed occlusion boundary and figure ground segmentation are studied in a gestalt based low level approach experiments on occlusion boundary benchmarks demonstrate the power of this mid level non learning based approach

integrable semi discretization of a multi component short pulse equation in the present paper we mainly study the integrable semi discretization of a multi component short pulse equation first we briefly review the bilinear equations for a multi component short pulse equation proposed by matsuno j math phys 52 123702 2011 and reaffirm its n soliton solution in terms of pfaffians then by using a backlund transformation of the bilinear equations and defining a discrete hodograph reciprocal transformation an integrable semi discrete multi component short pulse equation is constructed meanwhile its n soliton solution in terms of pfaffians is also proved

integrable discretizations of the short pulse equation in this paper we propose integrable semi discrete and full discrete analogues of the short pulse sp equation the key construction is the bilinear form and determinant structure of solutions of the sp equation we also give the determinant formulas of n soliton solutions of the semi discrete and full discrete analogues of the sp equations from which the multi loop and multi breather solutions can be generated in the continuous limit the full discrete sp equation converges to the semi discrete sp equation and then to the continuous sp equation based on the semi discrete sp equation an integrable numerical scheme i e a self adaptive moving mesh scheme is proposed and used for the numerical computation of the short pulse equation

optimality conditions for nondifferentiable minimax fractional programming with complex variables we show that a minimax fractional programming problem is equivalent to a minimax nonfractional parametric problem for a given parameter in complex space we establish the necessary and sufficient optimality conditions of nondifferentiable minimax fractional programming problem with complex variables under generalized convexities

contextual and variational contrast enhancement this paper proposes an algorithm that enhances the contrast of an input image using interpixel contextual information the algorithm uses a 2 d histogram of the input image constructed using a mutual relationship between each pixel and its neighboring pixels a smooth 2 d target histogram is obtained by minimizing the sum of frobenius norms of the differences from the input histogram and the uniformly distributed histogram the enhancement is achieved by mapping the diagonal elements of the input histogram to the diagonal elements of the target histogram experimental results show that the algorithm produces better or comparable enhanced images than four state of the art algorithms

contour and texture analysis for image segmentation this paper provides an algorithm for partitioning grayscale images into disjoint regions of coherent brightness and texture natural images contain both textured and untextured regions so the cues of contour and texture differences are exploited simultaneously contours are treated in the intervening contour framework while texture is analyzed using textons each of these cues has a domain of applicability so to facilitate cue combination we introduce a gating operator based on the texturedness of the neighborhood at a pixel having obtained a local measure of how likely two nearby pixels are to belong to the same region we use the spectral graph theoretic framework of normalized cuts to find partitions of the image into regions of coherent texture and brightness experimental results on a wide range of images are shown

duality for a class of nondifferentiable mathematical programming problems in complex space craven and mond 1 have given fritz john type necessary conditions for a class of nonlinear programming problems in complex space over polyhedral cones here we derive the necessary and sufficient conditions for the static minimax problems in complex space which are extensions of the corresponding real space conditions of 4 these conditions are then used to extend some duality results of 2 for a general class of nondifferentiable programming problems to complex space over arbitrary polyhedral cones the complex minimax problem that we consider seeks to choose e so e c g c e s which minimizes

weakly supervised part proposal segmentation from multiple images weakly supervised local part segmentation is challenging due to the difficulty of modeling multiple local parts from image level prior in this paper we propose a new weakly supervised local part proposal segmentation method based on the observation that local parts will keep fixed along the object pose variations hence the local part can be segmented by capturing object pose variations based on such observation a new local part proposal segmentation model is proposed three aspects such as shape similarity based cosegmentation shape matching based part detection and segmentation and graph matching based part assignment are considered a part segmentation energy function is first proposed four terms such as mrf based single image segmentation term shape feature based foreground consistency term ncuts based part segmentation term and two order graphs matching based part consistency term are contained then a three sub minimization based energy minimization method is proposed to accomplish approximation solution finally we verify our method based on three image data sets pascal voc 2008 part data set ucb bird data set and cat dog data set and one video data set ucf sports data set the experimental results demonstrate a better segmentation performance compared with the existing object cosegmentation and part proposal generation methods

duality for nondifferentiable minimax programming in complex spaces abstract employing the optimality necessary and sufficient conditions of a nondifferentiable minimax programming problem in complex spaces we formulate a one parametric dual and a parameter free dual problems on both dual problems we establish three duality theorems weak strong and strict converse duality theorem and prove that there is no duality gap between the two dual problems with respect to the primal problem under some generalized convexities of complex functions in the complex programming problem

efficient graph based search for object detection in this paper we focus on the object localization problem in images given a single hand drawn example as the object model we propose a novel framework for shape based object detection and recognition which we formulate as a graph based search problem in our method we first propose five preprocessing procedures to reduce the irrelevant edge fragments in cluttered real images that often occur in edge detection then we build a graph to represent the edge images therefore our goal is to find the group of adjacent nodes in the graph that match well to the model contours finally we present a new evaluation method to verify the candidate hypotheses we did experiments on the ethz shape classes dataset and the inria horses dataset experimental results demonstrate that the proposed method achieves not only accurate object detection but also precise contour localization in cluttered real images comparisons with other recent template based matching methods further demonstrate the effectiveness and efficiency of the proposed method

dct inspired feature transform for image retrieval and reconstruction scale invariant feature transform sift is effective for representing images in computer vision tasks as one of the most resistant feature descriptions to common image deformations however two issues should be addressed first feature description based on gradient accumulation is not compact and contains redundancies second multiple orientations are often extracted from one local region and therefore produce multiple descriptions which is not good for memory efficiency to resolve these two issues this paper introduces a novel method to determine the dominant orientation for multiple orientation cases named discrete cosine transform dct intrinsic orientation and a new dct inspired feature transform dift in each local region it first computes a unique dct intrinsic orientation via dct matrix and rotates the region accordingly and then describes the rotated region with partial dct matrix coefficients to produce an optimized low dimensional descriptor we test the accuracy and robustness of dift on real image matching afterward extensive applications performed on public benchmarks for visual retrieval show that using dct intrinsic orientation achieves performance on a par with sift but with only 60 of its features replacing the sift description with dift reduces dimensions from 128 to 32 and improves precision image reconstruction resulting from dift is presented to show another of its advantages over sift

sledge sequential labeling of image edges for boundary detection our goal is to detect boundaries of objects or surfaces occurring in an arbitrary image we present a new approach that discovers boundaries by sequential labeling of a given set of image edges a visited edge is labeled as on or off a boundary based on the edge s photometric and geometric properties and evidence of its perceptual grouping with already identified boundaries we use both local gestalt cues e g proximity and good continuation and the global helmholtz principle of non accidental grouping a new formulation of the helmholtz principle is specified as the entropy of a layout of image edges for boundary discovery we formulate a new policy iteration algorithm called sledge training of sledge is iterative in each training image sledge labels a sequence of edges which induces loss with respect to the ground truth these sequences are then used as training examples for learning sledge in the next iteration such that the total loss is minimized for extracting image edges that are input to sledge we use our new low level detector it finds salient pixel sequences that separate distinct textures within the image on the benchmark berkeley segmentation datasets 300 and 500 our approach proves robust and effective we outperform the state of the art both in recall and precision for different input sets of image edges

solitary wave solutions of the short pulse equation an exact nonsingular solitary wave solution of the schafer wayne short pulse equation is derived from the breather solution of the sine gordon equation by means of a transformation between these two integrable equations

salient closed boundary extraction with ratio contour we present ratio contour a novel graph based method for extracting salient closed boundaries from noisy images this method operates on a set of boundary fragments that are produced by edge detection boundary extraction identifies a subset of these fragments and connects them sequentially to form a closed boundary with the largest saliency we encode the gestalt laws of proximity and continuity in a novel boundary saliency measure based on the relative gap length and average curvature when connecting fragments to form a closed boundary this new measure attempts to remove a possible bias toward short boundaries we present a polynomial time algorithm for finding the most salient closed boundary we also present supplementary preprocessing steps that facilitate the application of ratio contour to real images we compare ratio contour to two closely related methods for extracting closed boundaries elder and zucker s method based on the shortest path algorithm and williams and thornber s method based on spectral analysis and a strongly connected components algorithm this comparison involves both theoretic analysis and experimental evaluation on both synthesized data and real images

integrable discretizations and self adaptive moving mesh method for a coupled short pulse equation in the present paper integrable semi discrete and fully discrete analogues of a coupled short pulse csp equation are constructed the key to the construction are the bilinear forms and determinant structure of the solutions of the csp equation we also construct n soliton solutions for the semi discrete and fully discrete analogues of the csp equations in the form of casorati determinants in the continuous limit we show that the fully discrete csp equation converges to the semi discrete csp equation then further to the continuous csp equation moreover the integrable semi discretization of the csp equation is used as a self adaptive moving mesh method for numerical simulations the numerical results agree with the analytical results very well

unsupervised joint salient region detection and object segmentation this paper presents a novel unsupervised algorithm to detect salient regions and to segment out foreground objects from background in contrast to previous unidirectional saliency based object segmentation methods in which only the detected saliency map is used to guide the object segmentation our algorithm mutually exploits detection segmentation cues from each other to achieve this goal an initial saliency map is generated by the proposed segmentation driven low rank matrix recovery model such a saliency map is exploited to initialize object segmentation model which is formulated as energy minimization of markov random field mutually the quality of saliency map is further improved by the segmentation result and serves as a new guidance for the object segmentation the optimal saliency map and the final segmentation are achieved by jointly optimizing the defined objective functions extensive evaluations on msra b and pascal 1500 datasets demonstrate that the proposed algorithm achieves the state of the art performance for both the salient region detection and the object segmentation

complex minimax programming under generalized type i functions we establish the kuhn tucker type sufficient optimality conditions for complex minimax programming under generalized type i and related functions subsequently we apply these optimality criteria to formulate two dual models we also establish weak strong and strict converse duality theorems