a convex relaxation method for computing exact global solutions for multiplicative noise removal we propose a convex relaxation technique for computing global solutions for the nonconvex multiplicative noise model the method is based on functional lifting by introducing an additional dimension we employ a primal dual based gradient type algorithm in numerical implementations to overcome the nondifferentiability of the total variation term numerical results show that our algorithm is highly efficient furthermore global solutions of the original model can be obtained with no dependence on the initial guess

robust optical flow estimation based on a sparse motion trajectory set this paper presents an approach to the problem of estimating a dense optical flow field the approach is based on a multiframe irregularly spaced motion trajectory set where each trajectory describes the motion of a given point as a function of time from this motion trajectory set a dense flow field is estimated using a process of interpolation a set of localized motion models are estimated with each pixel labeled as belonging to one of the motion models a markov random field framework is adopted allowing the incorporation of contextual constraints to encourage region like structures the approach is compared with a number of conventional optical flow estimation algorithms taken over a number of real and synthetic sequences results indicate that the method produces more accurate results for sequences with known ground truth flow also applying the method to real sequences with unknown flow results in lower dfd for all of the sequences tested

spatially adapted total variation model to remove multiplicative noise multiplicative noise removal based on total variation tv regularization has been widely researched in image science in this paper inspired by the spatially adapted methods for denoising gaussian noise we develop a variational model which combines the tv regularizer with local constraints it is also related to a tv model with spatially adapted regularization parameters the automated selection of the regularization parameters is based on the local statistical characteristics of some random variable the corresponding subproblem can be efficiently solved by the augmented lagrangian method numerical examples demonstrate that the proposed algorithm is able to preserve small image details whereas the noise in the homogeneous regions is sufficiently removed as a consequence our method yields better denoised results than those of the current state of the art methods with respect to the signal to noise ratio values

multiplicative noise removal using variable splitting and constrained optimization multiplicative noise also known as speckle noise models are central to the study of coherent imaging systems such as synthetic aperture radar and sonar and ultrasound and laser imaging these models introduce two additional layers of difficulties with respect to the standard gaussian additive noise scenario 1 the noise is multiplied by rather than added to the original image 2 the noise is not gaussian with rayleigh and gamma being commonly used densities these two features of multiplicative noise models preclude the direct application of most state of the art algorithms which are designed for solving unconstrained optimization problems where the objective has two terms a quadratic data term log likelihood reflecting the additive and gaussian nature of the noise plus a convex possibly nonsmooth regularizer e g a total variation or wavelet based regularizer prior in this paper we address these difficulties by 1 converting the multiplicative model into an additive one by taking logarithms as proposed by some other authors 2 using variable splitting to obtain an equivalent constrained problem and 3 dealing with this optimization problem using the augmented lagrangian framework a set of experiments shows that the proposed method which we name midal multiplicative image denoising by augmented lagrangian yields state of the art results both in terms of speed and denoising performance

a variational approach to removing multiplicative noise this paper focuses on the problem of multiplicative noise removal we draw our inspiration from the modeling of speckle noise by using a map estimator we can derive a functional whose minimizer corresponds to the denoised image we want to recover although the functional is not convex we prove the existence of a minimizer and we show the capability of our model on some numerical examples we study the associated evolution problem for which we derive existence and uniqueness results for the solution we prove the convergence of an implicit scheme to compute the solution

optical flow estimation and moving object segmentation based on median radial basis function network various approaches have been proposed for simultaneous optical flow estimation and segmentation in image sequences in this study the moving scene is decomposed into different regions with respect to their motion by means of a pattern recognition scheme the inputs of the proposed scheme are the feature vectors representing still image and motion information each class corresponds to a moving object the classifier employed is the median radial basis function mrbf neural network an error criterion function derived from the probability estimation theory and expressed as a function of the moving scene model is used as the cost function each basis function is activated by a certain image region marginal median and median of the absolute deviations from the median mad estimators are employed for estimating the basis function parameters the image regions associated with the basis functions are merged by the output units in order to identify moving objects

a nonlinear primal dual method for total variation based image restoration we present a new method for solving total variation tv minimization problems in image restoration the main idea is to remove some of the singularity caused by the nondifferentiability of the quantity nabla u in the definition of the tv norm before we apply a linearization technique such as newton s method this is accomplished by introducing an additional variable for the flux quantity appearing in the gradient of the objective function which can be interpreted as the normal vector to the level sets of the image u our method can be viewed as a primal dual method as proposed by conn and overton a primal dual interior point method for minimizing a sum of euclidean norms preprint 1994 and andersen ph d thesis odense university denmark 1995 for the minimization of a sum of euclidean norms in addition to possessing local quadratic convergence experimental results show that the new method seems to be globally convergent

bayesian estimation of motion vector fields a stochastic approach to the estimation of 2d motion vector fields from time varying images is presented the formulation involves the specification of a deterministic structural model along with stochastic observation and motion field models two motion models are proposed a globally smooth model based on vector markov random fields and a piecewise smooth model derived from coupled vector binary markov random fields two estimation criteria are studied in the maximum a posteriori probability map estimation the a posteriori probability of motion given data is maximized whereas in the minimum expected cost mec estimation the expectation of a certain cost function is minimized both algorithms generate sample fields by means of stochastic relaxation implemented via the gibbs sampler two versions are developed one for a discrete state space and the other for a continuous state space the map estimation is incorporated into a hierarchical environment to deal efficiently with large displacements

precision tracking based on segmentation with optimal layering for imaging sensors in the authors previous work oron kumar and bar shalom 1993 they presented a method for precision tracking of a low observable target based on data obtained from imaging sensors the image was divided into several layers of gray level intensities and thresholded a binary image was obtained and grouped into clusters using image segmentation techniques using the centroid measurements of the clusters the probabilistic data association filter pdaf was employed for tracking the target centroid in this correspondence the division of the image into several layers of gray level intensities is optimized by minimizing the bayes risk this optimal layering of the image has the following properties 1 following the segmentation a closed form analytical expression is obtained for the noise variance of the centroid measurement based on a single frame 2 in comparison to the previous paper the measurement noise variance is smaller by at least a factor of 2 thus improving the performance of the tracker the usefulness of the method for practical applications is demonstrated by considering a sequence of real target images a moving car of about 20 pixels in size in a noisy urban environment where the measurement noise was calculated as having 0 32 pixel rms value filtering with the pdaf further reduces this by a factor of 1 6

multiplicative noise removal via using nonconvex regularizers based on total variation and wavelet frame abstract total variation based regularization and wavelet frame based regularization are two different methods for image restoration moreover nonconvex regularization has advantages over convex regularization for preserving edges in images in this paper a variational model consisting of two nonconvex regularizers based respectively on total variation and wavelet frame is proposed for multiplicative noise removal the proposed model combines the advantages of the nonconvex regularization and the hybrid regularization so it can more effectively preserve edges and details in images than any single regularization can the alternating minimization method is proposed to solve the novel model although the corresponding minimization problem is nonconvex the convexity of all subproblems is guaranteed under some mild conditions therefore we study the convergence property of the algorithm numerical experiments have proved that the proposed model with the corresponding algorithm outperforms some state of the art models in terms of the peak signal to noise ratio and the relative error of the restored images

median radial basis function neural network radial basis functions rbfs consist of a two layer neural network where each hidden unit implements a kernel function each kernel is associated with an activation region from the input space and its output is fed to an output unit in order to find the parameters of a neural network which embeds this structure we take into consideration two different statistical approaches the first approach uses classical estimation in the learning stage and it is based on the learning vector quantization algorithm and its second order statistics extension after the presentation of this approach we introduce the median radial basis function mrbf algorithm based on robust estimation of the hidden unit parameters the proposed algorithm employs the marginal median for kernel location estimation and the median of the absolute deviations for the scale parameter estimation a histogram based fast implementation is provided for the mrbf algorithm the theoretical performance of the two training algorithms is comparatively evaluated when estimating the network weights the network is applied in pattern classification problems and in optical flow segmentation

fast linearized alternating direction minimization algorithm with adaptive parameter selection for multiplicative noise removal owing to the edge preserving ability and low computational cost of the total variation tv variational models with the tv regularizer have been widely investigated in the field of multiplicative noise removal the key points of the successful application of these models lie in the optimal selection of the regularization parameter which balances the data fidelity term with the tv regularizer the efficient algorithm to compute the solution in this paper we propose two fast algorithms based on the linearized technique which are able to estimate the regularization parameter and recover the image simultaneously in the iteration step of the proposed algorithms the regularization parameter is adjusted by a special discrepancy function defined for multiplicative noise the convergence properties of the proposed algorithms are proved under certain conditions and numerical experiments demonstrate that the proposed algorithms overall outperform some state of the art methods in the psnr values and computational time

robust processing of optical flow of fluids this paper proposes a new approach coupling physical models and image estimation techniques for modelling the movement of fluids the fluid flow is characterized by turbulent movement and dynamically changing patterns which poses challenges to existing optical flow estimation methods the proposed methodology which relies on navier stokes equations is used for processing fluid optical flow by using a succession of stages such as advection diffusion and mass conservation a robust diffusion step jointly considering the local data geometry and its statistics is embedded in the proposed framework the diffusion kernel is gaussian with the covariance matrix defined by the local second derivatives such an anisotropic kernel is able to implicitly detect changes in the vector field orientation and to diffuse accordingly a new approach is developed for detecting fluid flow structures such as vortices the proposed methodology is applied on artificially generated vector fields as well as on various image sequences

fixed point continuation for ell_1 minimization methodology and convergence we present a framework for solving the large scale ell 1 regularized convex minimization problem min x 1 mu f x our approach is based on two powerful algorithmic ideas operator splitting and continuation operator splitting results in a fixed point algorithm for any given scalar mu continuation refers to approximately following the path traced by the optimal value of x as mu increases in this paper we study the structure of optimal solution sets prove finite convergence for important quantities and establish q linear convergence rates for the fixed point algorithm applied to problems with f x convex but not necessarily strictly convex the continuation framework motivated by our convergence results is demonstrated to facilitate the construction of practical algorithms

proximal linearized alternating direction method for multiplicative denoising multiplicative noise naturally appears in coherent imaging systems such as synthetic aperture radar due to the edge preserving feature of total variation tv variational models with tv regularization show good performance for multiplicative denoising recently proposed augmented lagrangian frameworks with the gauss seidel method are efficient for solving multiplicative denoising variational models with tv but recent algorithms based on the augmented lagrangian require inner iterations or an inverse involving the laplacian operator at each iteration in this paper we propose efficient algorithms for tv regularized convex variational models our proposed algorithms do not require any inner iteration or the inverse involving the laplacian operator by using a linearization scheme and a proximal function we establish global convergence under a lipschitz continuous assumption on the gradient of the fidelity term when a correction step is used numerical results show that our proposed algorithms overall

primal dual algorithm based on gauss seidel scheme with application to multiplicative noise removal due to the strong edge preserving ability and low computational cost the total variation tv regularization has been developed as one promising approach to solve the multiplicative denoising problem in recent years many efficient algorithms have been proposed for computing the numerical solution of tv based convex variational models among these methods the linearized augmented lagrangian algorithm alm and the primal dual hybrid gradient pdhg algorithm are two of the most effective and most widely used techniques in this paper inspired by the connection of the alm and pdhg algorithms we develop an improved primal dual algorithm for multiplicative noise removal in the proposed algorithm an auxiliary variable which is updated by the gauss seidel scheme is introduced to accelerate the original primal dual framework the global convergence property of the proposed algorithm is also investigated numerical experiments on the multiplicative denoising show that the proposed algorithm outperforms the current state of the art methods

prediction and tracking of moving objects in image sequences we employ a prediction model for moving object velocity and location estimation derived from bayesian theory the optical flow of a certain moving object depends on the history of its previous values a joint optical flow estimation and moving object segmentation algorithm is used for the initialization of the tracking algorithm the segmentation of the moving objects is determined by appropriately classifying the unlabeled and the occluding regions segmentation and optical flow tracking is used for predicting future frames

visual tracking in high dimensional state space by appearance guided particle filtering in this paper we propose a new approach appearance guided particle filtering agpf for high degree of freedom visual tracking from an image sequence this method adopts some known attractors in the state space and integrates both appearance and motion transition information for visual tracking a probability propagation model based on these two types of information is derived from a bayesian formulation and a particle filtering framework is developed to realize it experimental results demonstrate that the proposed method is effective for high degree of freedom visual tracking problems such as articulated hand tracking and lip contour tracking

rigid body segmentation and shape description from dense optical flow under weak perspective we present an algorithm for identifying and tracking independently moving rigid objects from optical flow some previous attempts at segmentation via optical flow have focused on finding discontinuities in the flow field while discontinuities do indicate a change in scene depth they do not in general signal a boundary between two separate objects the proposed method uses the fact that each independently moving object has a unique epipolar constraint associated with its motion thus motion discontinuities based on self occlusion can be distinguished from those due to separate objects the use of epipolar geometry allows for the determination of individual motion parameters for each object as well as the recovery of relative depth for each point on the object the algorithm assumes an affine camera where perspective effects are limited to changes in overall scale no camera calibration parameters are required a kalman filter based approach is used for tracking motion parameters with time

alternating minimization algorithm for speckle reduction with a shifting technique speckles multiplicative noise in synthetic aperture radar sar make it difficult to interpret the observed image due to the edge preserving feature of total variation tv variational models with tv regularization have attracted much interest in reducing speckles algorithms based on the augmented lagrangian function have been proposed to efficiently solve speckle reduction variational models with tv regularization however these algorithms require inner iterations or inverses involving the laplacian operator at each iteration in this paper we adapt tseng s alternating minimization algorithm with a shifting technique to efficiently remove the speckle without any inner iterations or inverses involving the laplacian operator the proposed method is very simple and highly parallelizable therefore it is very efficient to despeckle huge size sar images numerical results show that our proposed method outperforms the state of the art algorithms for speckle reduction variational models with a tv regularizer in terms of central processing unit time