bubble stabilization of linear finite element methods for nonlinear evolutionary convection diffusion equations abstract a spatial stabilization via bubble functions of linear finite element methods for nonlinear evolutionary convection diffusion equations is discussed the method of lines with supg discretization in space leads to numerical schemes that are not only difficult to implement when considering nonlinear evolutionary equations but also do not produce satisfactory results the method we propose can be seen as an alternative to this kind of methods once the numerical approximation belonging to a linear finite element space enriched with bubble functions is obtained the bubble part is discarded the linear part is shown to give a stabilized approximation to the solution being approached the bubble functions are deduced using a linear steady convection diffusion model in such a way that the linear part of the approximation to the linear steady model after static condensation of bubbles reproduces the supg method in the convection dominated regime however for the nonlinear evolutionary equations we consider in the paper the method we propose is not equivalent to the supg method some numerical experiments are provided in the paper to show the efficiency of the procedure

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

parameter estimation in geometric process with weibull distribution we consider geometric process gp when the distribution of the first occurrence time of an event is assumed to be weibull explicit estimators of the parameters in gp are derived by using the method of modified maximum likelihood mml proposed by tiku 24 asymptotic distributions and consistency properties of these estimators are obtained we show that our estimators are more efficient than the widely used modified moment mm estimators via monte carlo simulation study further two real life examples are given at the end of the paper

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

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

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

stability of the supg finite element method for transient advection diffusion problems implicit time integration coupled with supg discretization in space leads to additional terms that provide consistency and improve the phase accuracy for convection dominated flows recently it has been suggested that for small courant numbers these terms may dominate the streamline diffusion term ostensibly causing destabilization of the supg method while consistent with a straightforward finite element stability analysis this contention is not supported by computational experiments and contradicts earlier von neumann stability analyses of the semidiscrete supg equations this prompts us to re examine finite element stability of the fully discrete supg equations a careful analysis of the additional terms reveals that regardless of the time step size they are always dominated by the consistent mass matrix consequently supg cannot be destabilized for small courant numbers numerical results that illustrate our conclusions are reported

postprocessing finite element methods for the navier stokes equations the fully discrete case an accuracy enhancing postprocessing technique for finite element discretizations of the navier stokes equations is analyzed the technique had been previously analyzed only for semidiscretizations and fully discrete methods are addressed in the present paper we show that the increased spatial accuracy of the postprocessing procedure is not affected by the errors arising from any convergent time stepping procedure further refined bounds are obtained when the time stepping procedure is either the backward euler method or the two step backward differentiation formula

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

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

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

an adaptive finite element method for evolutionary convection dominated problems abstract we present an adaptive finite element method for evolutionary convection diffusion problems the algorithm is based on an a posteriori indicator of the size of the oscillations displayed by the finite element approximation the procedure is able to refine or coarsen dynamically the mesh adjusting it automatically to evolving layers the method produces nearly non oscillatory approximations in the convection dominated regime we check the performance of the adaptive method with some numerical experiments

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

local variation as a statistical hypothesis test the goal of image oversegmentation is to divide an image into several pieces each of which should ideally be part of an object one of the simplest and yet most effective oversegmentation algorithms is known as local variation lv felzenszwalb and huttenlocher in efficient graph based image segmentation ijcv 59 2 167 181 2004 in this work we study this algorithm and show that algorithms similar to lv can be devised by applying different statistical models and decisions thus providing further theoretical justification and a well founded explanation for the unexpected high performance of the lv approach some of these algorithms are based on statistics of natural images and on a hypothesis testing decision we denote these algorithms probabilistic local variation plv the best plv algorithm which relies on censored estimation presents state of the art results while keeping the same computational complexity of the lv algorithm

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

the asymptotics of maximum likelihood and related estimators based on type ii censored data abstract some simple procedures are provided for establishing the asymptotic normality and uniform strong convergence of a class of functions that arise in the context of estimating parameters from a type ii censored sample these lead to an elementary yet rigorous treatment of the asymptotic properties of maximum likelihood estimators based on type ii censored data further applications include the treatment of asymptotics of some modified maximum likelihood mml estimators in particular conditions are provided for the consistency and limiting normality of the mml estimators of mehrotra and nanda and the asymptotic efficiencies of these estimators are evaluated

consistent supg method for transient transport problems stability and convergence we consider the time space discretization of the transient advection equation discretization in space is performed by the streamline upwind petrov galerkin method and in time we use an a stable finite difference operator the formulation is strongly consistent in the sense that the time derivative is included in the stabilization term uniform stability of the general formulation is proved under a regularity condition on data or a moderate inverse cfl condition that allows for optimal choices of the discretization parameters both the backward euler method bdf1 the crank nicolson scheme and the second order backward differentiation formula bdf2 enter the framework and quasi optimal convergence is proved for these schemes

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

coupling stabilized finite element methods with finite difference time integration for advection diffusion reaction problems abstract we present some numerical schemes for the unsteady advection diffusion reaction linear problem in one space dimension we investigate two possible different ways of combining the discretization in time and in space where the sequence of the discretizations is interchanged discretization in time is performed by using the crank nicolson finite difference scheme while for the space discretization we consider three classical stabilized finite element schemes and the more recent link cutting bubble strategy proposed in f brezzi g hauke l d marini g sangalli link cutting bubbles for the stabilization of convection diffusion reaction problems math models methods appl sci 13 2003 445 461 numerical experiments are presented to assess and valuate the capabilities of the proposed methods an l 1 error analysis of the link cutting bubble strategy for solving the steady problem is included

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

synergy between object recognition and image segmentation using the expectation maximization algorithm in this work we formulate the interaction between image segmentation and object recognition in the framework of the expectation maximization em algorithm we consider segmentation as the assignment of image observations to object hypotheses and phrase it as the e step while the m step amounts to fitting the object models to the observations these two tasks are performed iteratively thereby simultaneously segmenting an image and reconstructing it in terms of objects we model objects using active appearance models aams as they capture both shape and appearance variation during the e step the fidelity of the aam predictions to the image is used to decide about assigning observations to the object for this we propose two top down segmentation algorithms the first starts with an oversegmentation of the image and then softly assigns image segments to objects as in the common setting of em the second uses curve evolution to minimize a criterion derived from the variational interpretation of em and introduces aams as shape priors for the m step we derive aam fitting equations that accommodate segmentation information thereby allowing for the automated treatment of occlusions apart from top down segmentation results we provide systematic experiments on object detection that validate the merits of our joint segmentation and recognition approach

an approach toward fast gradient based image segmentation in this paper we present and investigate an approach to fast multilabel color image segmentation using convex optimization techniques the presented model is in some ways related to the well known mumford shah model but deviates in certain important aspects the optimization problem has been designed with two goals in mind the objective function should represent fundamental concepts of image segmentation such as incorporation of weighted curve length and variation of intensity in the segmented regions while allowing transformation into a convex concave saddle point problem that is computationally inexpensive to solve this paper introduces such a model the nontrivial transformation of this model into a convex concave saddle point problem and the numerical treatment of the problem we evaluate our approach by applying our algorithm to various images and show that our results are competitive in terms of quality at unprecedentedly low computation times our algorithm allows high quality segmentation of megapixel images in a few seconds and achieves interactive performance for low resolution images fig 1

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

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

finite element methods for linear hyperbolic problems abstract we give a survey of some recent work by the authors on finite element methods for convectiondiffusion problems and first order linear hyperbolic problems

on finite element methods for 3d time dependent convection diffusion reaction equations with small diffusion the paper studies finite element methods for the simulation of time dependent convection diffusion reaction equations with small diffusion the supg method a sold method and two types of fem fct methods the methods are assessed in particular with respect to the size of the spurious oscillations in the computed solutions at a 3d example with nonhomogeneous dirichlet boundary conditions and homogeneous neumann boundary conditions

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

finite element methods with symmetric stabilization for the transient convection diffusion reaction equation we consider implicit and semi implicit time stepping methods for finite element approximations of singularly perturbed parabolic problems or hyperbolic problems we are interested in problems where the advection dominates and stability is obtained using a symmetric weakly consistent stabilization operator in the finite element method several a stable time discretizations are analyzed and shown to lead to unconditionally stable and optimally convergent schemes in particular we show that the contribution from the stabilization leading to an extended matrix pattern may be extrapolated from previous time steps and hence handled explicitly without loss of stability and accuracy a fully explicit treatment of the stabilization term is obtained under a cfl condition

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

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

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

stabilization of galerkin finite element approximations to transient convection diffusion problems a postprocessing technique to improve galerkin finite element approximations to linear evolutionary convection reaction diffusion equations is considered a steady convection reaction diffusion problem with data based on the computed standard galerkin approximation is solved at any fixed time the postprocessing approximation is obtained using the supg method over the same galerkin finite element space error bounds for the method are obtained in the convection dominated regime the numerical experiments we present show a substantial reduction of spurious oscillations achieved by means of this procedure

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

modified maximum likelihood method for the robust estimation of system parameters from very noisy data abstract when experiments are conducted there is always a chance of the occurrence of large measurement errors outliers common identification methods like generalized least squares maximum likelihood etc may not converge in these situations due to the presence of outliers here we present a method for the robust estimation of system parameters based on the censoring of data and employing the maximum likelihood estimation several simulated examples show that the modified maximum likelihood method works well in situations where other methods failed

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

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

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

higher order finite element approximation of systems of convection diffusion reaction equations with small diffusion in this work we study numerically the performance properties of a class of approximation schemes for systems of convection diffusion reaction models with small diffusion a coupling of the equations by first order and zero order terms is admitted higher order conforming finite element methods are applied to minimize the effects of numerical diffusion and artificial mixing of species to reduce spurious oscillations close to sharp layers or interfaces streamline upwind petrov galerkin stabilization and shock capturing as an additional stabilization in the crosswind direction are used in applications of practical interest the reliability and accuracy of the approach is demonstrated

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

local symmetry detection in natural images using a particle filtering approach in this paper we propose an algorithm to detect smooth local symmetries and contours of ribbon like objects in natural images the detection is formulated as a spatial tracking task using a particle filtering approach extracting one part of a structure at a time using an adaptive local geometric model the method can detect straight reflection symmetries in perfectly symmetrical objects as well as smooth local symmetries in curved elongated objects in addition the proposed approach jointly estimates spine and contours making it possible to generate back ribbon objects experiments for local symmetry detection have been conducted on a recent extension of the berkeley segmentation data sets we also show that it is possible to retrieve specific geometrical objects using intuitive prior structural information

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

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

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

hierarchical image segmentation using correlation clustering in this paper we apply efficient implementations of integer linear programming to the problem of image segmentation the image is first grouped into superpixels and then local information is extracted for each pair of spatially adjacent superpixels given local scores on a map of several hundred superpixels we use correlation clustering to find the global segmentation that is most consistent with the local evidence we show that although correlation clustering is known to be np hard finding the exact global solution is still feasible by breaking the segmentation problem down into subproblems each such sub problem can be viewed as an automatically detected image part we can further accelerate the process by using the cutting plane method which provides a hierarchical structure of the segmentations the efficiency and improved performance of the proposed method is compared to several state of the art methods and demonstrated on several standard segmentation data sets

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100