manifold regularization a geometric framework for learning from labeled and unlabeled examples we propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution we focus on a semi supervised framework that incorporates labeled and unlabeled data in a general purpose learner some transductive graph learning algorithms and standard methods including support vector machines and regularized least squares can be obtained as special cases we use properties of reproducing kernel hilbert spaces to prove new representer theorems that provide theoretical basis for the algorithms as a result in contrast to purely graph based approaches we obtain a natural out of sample extension to novel examples and so are able to handle both transductive and truly semi supervised settings we present experimental evidence suggesting that our semi supervised algorithms are able to use unlabeled data effectively finally we have a brief discussion of unsupervised and fully supervised learning within our general framework

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

subpixel edge localization and the interpolation of still images in this paper we present a nonlinear interpolation scheme for still image resolution enhancement the algorithm is based on a source model emphasizing the visual integrity of detected edges and incorporates a novel edge fitting operator that has been developed for this application a small neighborhood about each pixel in the low resolution image is first mapped to a best fit continuous space step edge the bilevel approximation serves as a local template on which the higher resolution sampling grid can then be superimposed where disputed values in regions of local window overlap are averaged to smooth errors the result is an image of increased resolution with noticeably sharper edges and in all tried cases lower mean squared reconstruction error than that produced by linear techniques

active contour based visual tracking by integrating colors shapes and motions in this paper we present a framework for active contour based visual tracking using level sets the main components of our framework include contour based tracking initialization color based contour evolution adaptive shape based contour evolution for non periodic motions dynamic shape based contour evolution for periodic motions and the handling of abrupt motions for the initialization of contour based tracking we develop an optical flow based algorithm for automatically initializing contours at the first frame for the color based contour evolution markov random field theory is used to measure correlations between values of neighboring pixels for posterior probability estimation for adaptive shape based contour evolution the global shape information and the local color information are combined to hierarchically evolve the contour and a flexible shape updating model is constructed for the dynamic shape based contour evolution a shape mode transition matrix is learnt to characterize the temporal correlations of object shapes for the handling of abrupt motions particle swarm optimization is adopted to capture the global motion which is applied to the contour in the current frame to produce an initial contour in the next frame

progressive image denoising through hybrid graph laplacian regularization a unified framework recovering images from corrupted observations is necessary for many real world applications in this paper we propose a unified framework to perform progressive image recovery based on hybrid graph laplacian regularized regression we first construct a multiscale representation of the target image by laplacian pyramid then progressively recover the degraded image in the scale space from coarse to fine so that the sharp edges and texture can be eventually recovered on one hand within each scale a graph laplacian regularization model represented by implicit kernel is learned which simultaneously minimizes the least square error on the measured samples and preserves the geometrical structure of the image data space in this procedure the intrinsic manifold structure is explicitly considered using both measured and unmeasured samples and the nonlocal self similarity property is utilized as a fruitful resource for abstracting a priori knowledge of the images on the other hand between two successive scales the proposed model is extended to a projected high dimensional feature space through explicit kernel mapping to describe the interscale correlation in which the local structure regularity is learned and propagated from coarser to finer scales in this way the proposed algorithm gradually recovers more and more image details and edges which could not been recovered in previous scale we test our algorithm on one typical image recovery task impulse noise removal experimental results on benchmark test images demonstrate that the proposed method achieves better performance than state of the art algorithms

cross weighted moments and affine invariants for image registration and matching a framework for deriving a class of new global affine invariants for both object matching and positioning based on a novel concept of cross weighted moments with fractional weights is presented the fractional weight factor allows for a more flexible range to balance between the capability to discriminate between objects that differ only in small shape details and the sensitivity of small shape details to the presence of the noise moreover it makes it possible to arrive at low order zero order affine invariants that are more robust than those derived from higher order regular moments the affine transformation parameters are recovered from the zero and the first order cross weighted moments without requiring any feature point correspondence information the equations used to find the affine transformation parameters are linear algebraic the sensitivity of the cross weighted moment invariants to noise missing data and perspective effects is shown on real images

the approximation power of moving least squares a general method for near best approximations to functionals on r d using scattered data information is discussed the method is actually the moving least squares method presented by the backus gilbert approach it is shown that the method works very well for interpolation smoothing and derivatives approximations for the interpolation problem this approach gives mclain s method the method is near best in the sense that the local error is bounded in terms of the error of a local best polynomial approximation the interpolation approximation in r d is shown to be a c function and an approximation order result is proven for quasi uniform sets of data points

fast image interpolation via random forests this paper proposes a two stage framework for fast image interpolation via random forests firf the proposed firf method gives high accuracy as well as requires low computation the underlying idea of this proposed work is to apply random forests to classify the natural image patch space into numerous subspaces and learn a linear regression model for each subspace to map the low resolution image patch to high resolution image patch the firf framework consists of two stages stage 1 of the framework removes most of the ringing and aliasing artifacts in the initial bicubic interpolated image while stage 2 further refines the stage 1 interpolated image by varying the number of decision trees in the random forests and the number of stages applied the proposed firf method can realize computationally scalable image interpolation extensive experimental results show that the proposed firf 3 2 method achieves more than 0 3 db improvement in peak signal to noise ratio over the state of the art nonlocal autoregressive modeling narm method moreover the proposed firf 1 1 obtains similar or better results as narm while only takes its 0 3 computational time

c ondensation conditional density propagation forvisual tracking the problem of tracking curves in dense visual clutter is challenging kalman filtering is inadequate because it is based on gaussian densities which being unimo dal cannot represent simultaneous alternative hypotheses the condensation algorithm uses factored sampling previously applied to the interpretation of static images in which the probability distribution of possible interpretations is represented by a randomly generated set condensation uses learned dynamical models together with visual observations to propagate the random set over time the result is highly robust tracking of agile motion notwithstanding the use of stochastic methods the algorithm runs in near real time

segment adaptive gradient angle interpolation we introduce a new edge directed interpolator based on locally defined straight line approximations of image isophotes spatial derivatives of image intensity are used to describe the principal behavior of pixel intersecting isophotes in terms of their slopes the slopes are determined by inverting a tridiagonal matrix and are forced to vary linearly from pixel to pixel within segments image resizing is performed by interpolating along the approximated isophotes the proposed method can accommodate arbitrary scaling factors provides state of the art results in terms of psnr as well as other quantitative visual quality metrics and has the advantage of reduced computational complexity that is directly proportional to the number of pixels

a whittaker function of matrix argument abstract whittaker functions arise naturally in many topics in physical biological and social sciences such as input output situations in econometric problems storage consumption situations growth decay situations when dealing with bilinear forms in random variables and so on an account of some of these is available in mathai 1993 the matrix variate analogue is considered in this article a whittaker function of matrix argument is defined and several new results on this function are established in this paper complementing the results given earlier by mathai and pederzoli 1996 some of these generalize the corresponding results in the scalar variable case

tracking with occlusions via graph cuts this work presents a new method for tracking and segmenting along time interacting objects within an image sequence one major contribution of the paper is the formalization of the notion of visible and occluded parts for each object we aim at tracking these two parts assuming that the velocity of each object is driven by a dynamical law predictions can be used to guide the successive estimations separating these predicted areas into good and bad parts with respect to the final segmentation and representing the objects with their visible and occluded parts permit handling partial and complete occlusions to achieve this tracking a label is assigned to each object and an energy function representing the multilabel problem is minimized via a graph cuts optimization this energy contains terms based on image intensities which enable segmenting and regularizing the visible parts of the objects it also includes terms dedicated to the management of the occluded and disappearing areas which are defined on the areas of prediction of the objects the results on several challenging sequences prove the strength of the proposed approach

image interpolation by adaptive 2 d autoregressive modeling and soft decision estimation the challenge of image interpolation is to preserve spatial details we propose a soft decision interpolation technique that estimates missing pixels in groups rather than one at a time the new technique learns and adapts to varying scene structures using a 2 d piecewise autoregressive model the model parameters are estimated in a moving window in the input low resolution image the pixel structure dictated by the learnt model is enforced by the soft decision estimation process onto a block of pixels including both observed and estimated the result is equivalent to that of a high order adaptive nonseparable 2 d interpolation filter this new image interpolation approach preserves spatial coherence of interpolated images better than the existing methods and it produces the best results so far over a wide range of scenes in both psnr measure and subjective visual quality edges and textures are well preserved and common interpolation artifacts blurring ringing jaggies zippering etc are greatly reduced

a morphological approach to curvature based evolution of curves and surfaces we introduce new results connecting differential and morphological operators that provide a formal and theoretically grounded approach for stable and fast contour evolution contour evolution algorithms have been extensively used for boundary detection and tracking in computer vision the standard solution based on partial differential equations and level sets requires the use of numerical methods of integration that are costly computationally and may have stability issues we present a morphological approach to contour evolution based on a new curvature morphological operator valid for surfaces of any dimension we approximate the numerical solution of the curve evolution pde by the successive application of a set of morphological operators defined on a binary level set and with equivalent infinitesimal behavior these operators are very fast do not suffer numerical stability issues and do not degrade the level set function so there is no need to reinitialize it moreover their implementation is much easier since they do not require the use of sophisticated numerical algorithms we validate the approach providing a morphological implementation of the geodesic active contours the active contours without borders and turbopixels in the experiments conducted the morphological implementations converge to solutions equivalent to those achieved by traditional numerical solutions but with significant gains in simplicity speed and stability

image interpolation via regularized local linear regression the linear regression model is a very attractive tool to design effective image interpolation schemes some regression based image interpolation algorithms have been proposed in the literature in which the objective functions are optimized by ordinary least squares ols however it is shown that interpolation with ols may have some undesirable properties from a robustness point of view even small amounts of outliers can dramatically affect the estimates to address these issues in this paper we propose a novel image interpolation algorithm based on regularized local linear regression rllr starting with the linear regression model where we replace the ols error norm with the moving least squares mls error norm leads to a robust estimator of local image structure to keep the solution stable and avoid overfitting we incorporate the l2 norm as the estimator complexity penalty moreover motivated by recent progress on manifold based semi supervised learning we explicitly consider the intrinsic manifold structure by making use of both measured and unmeasured data points specifically our framework incorporates the geometric structure of the marginal probability distribution induced by unmeasured samples as an additional local smoothness preserving constraint the optimal model parameters can be obtained with a closed form solution by solving a convex optimization problem experimental results on benchmark test images demonstrate that the proposed method achieves very competitive performance with the state of the art interpolation algorithms especially in image edge structure preservation

a probabilistic exclusion principle for tracking multiple objects tracking multiple targets is a challenging problem especially when the targets are identical in the sense that the same model is used to describe each target in this case simply instantiating several independent 1 body trackers is not an adequate solution because the independent trackers tend to coalesce onto the best fitting target this paper presents an observation density for tracking which solves this problem by exhibiting a probabilistic exclusion principle exclusion arises naturally from a systematic derivation of the observation density without relying on heuristics another important contribution of the paper is the presentation of partitioned sampling a new sampling method for multiple object tracking partitioned sampling avoids the high computational load associated with fully coupled trackers while retaining the desirable properties of coupling

high resolution local structure constrained image upsampling with the development of ultra high resolution display devices the visual perception of fine texture details is becoming more and more important a method of high quality image upsampling with a low cost is greatly needed in this paper we propose a fast and efficient image upsampling method that makes use of high resolution local structure constraints the average local difference is used to divide a bicubic interpolated image into a sharp edge area and a texture area and these two areas are reconstructed separately with specific constraints for reconstruction of the sharp edge area a high resolution gradient map is estimated as an extra constraint for the recovery of sharp and natural edges for the reconstruction of the texture area a high resolution local texture structure map is estimated as an extra constraint to recover fine texture details these two reconstructed areas are then combined to obtain the final high resolution image the experimental results demonstrated that the proposed method recovered finer pixel level texture details and obtained top level objective performance with a low time cost compared with state of the art methods

tracking deforming objects using particle filtering for geometric active contours tracking deforming objects involves estimating the global motion of the object and its local deformations as a function of time tracking algorithms using kalman filters or particle filters have been proposed for finite dimensional representations of shape but these are dependent on the chosen parametrization and cannot handle changes in curve topology geometric active contours provide a framework which is parametrization independent and allow for changes in topology in the present work we formulate a particle filtering algorithm in the geometric active contour framework that can be used for tracking moving and deforming objects to the best of our knowledge this is the first attempt to implement an approximate particle filtering algorithm for tracking on a theoretically infinite dimensional state space

image interpolation via graph based bayesian label propagation in this paper we propose a novel image interpolation algorithm via graph based bayesian label propagation the basic idea is to first create a graph with known and unknown pixels as vertices and with edge weights encoding the similarity between vertices then the problem of interpolation converts to how to effectively propagate the label information from known points to unknown ones this process can be posed as a bayesian inference in which we try to combine the principles of local adaptation and global consistency to obtain accurate and robust estimation specially our algorithm first constructs a set of local interpolation models which predict the intensity labels of all image samples and a loss term will be minimized to keep the predicted labels of the available low resolution lr samples sufficiently close to the original ones then all of the losses evaluated in local neighborhoods are accumulated together to measure the global consistency on all samples moreover a graph laplacian based manifold regularization term is incorporated to penalize the global smoothness of intensity labels such smoothing can alleviate the insufficient training of the local models and make them more robust finally we construct a unified objective function to combine together the global loss of the locally linear regression square error of prediction bias on the available lr samples and the manifold regularization term it can be solved with a closed form solution as a convex optimization problem experimental results demonstrate that the proposed method achieves competitive performance with the state of the art image interpolation algorithms

particle filtering for large dimensional state spaces with multimodal observation likelihoods we study efficient importance sampling techniques for particle filtering pf when either a the observation likelihood ol is frequently multimodal or heavy tailed or b the state space dimension is large or both when the ol is multimodal but the state transition pdf stp is narrow enough the optimal importance density is usually unimodal under this assumption many techniques have been proposed but when the stp is broad this assumption does not hold we study how existing techniques can be generalized to situations where the optimal importance density is multimodal but is unimodal conditioned on a part of the state vector sufficient conditions to test for the unimodality of this conditional posterior are derived our result is directly extendable to testing for unimodality of any posterior the number of particles n to accurately track using a pf increases with state space dimension thus making any regular pf impractical for large dimensional tracking problems but in most such problems most of the state change occurs in only a few dimensions while the change in the rest of the dimensions is small using this property we propose to replace importance sampling from a large part of the state space whose conditional posterior is narrow enough by just tracking the mode of the conditional posterior this introduces some extra error but it also greatly reduces the importance sampling dimension the net effect is much smaller error for a given n especially when the available n is small an important class of large dimensional problems with multimodal ol is tracking spatially varying physical quantities such as temperature or pressure in a large area using a network of sensors which may be nonlinear and or may have nonnegligible failure probabilities improved performance of our proposed algorithms over existing pfs is demonstrated for this problem

on integral representations of the coulomb functions by dealing with a new integral representation for the irregular s wave coulomb function exact analytical expressions for the corresponding jost states in momentum space are constructed and their usefulness in studying the coulomb half shell scattering is demonstrated a supersymmetry inspired ladder operator relation is employed to derive higher partial wave generalization of the results presented some applications of the integral representation for the associated regular solution are also sought

a motion aligned auto regressive model for frame rate up conversion in this paper a motion aligned auto regressive maar model is proposed for frame rate up conversion where each pixel is interpolated as the average of the results generated by one forward maar fw maar model and one backward maar bw maar model in the fw maar model each pixel in the to be interpolated frame is generated as a linear weighted summation of the pixels within a motion aligned square neighborhood in the previous frame to derive more accurate interpolation weights the aligned actual pixels in the following frame are also estimated as a linear weighted summation of the newly interpolated pixels in the to be interpolated frame by the same weights consequently the backward aligned actual pixels in the following frame can be estimated as a weighted summation of the corresponding pixels within an enlarged square neighborhood in the previous frame the bw maar is performed likewise except that it is operated in the reverse direction a damping newton algorithm is then proposed to compute the adaptive interpolation weights for the fw maar and bw maar models extensive experiments demonstrate that the proposed maar model is able to achieve superior performance than the traditional frame interpolation methods such as mci obmc and aobmc and it is even better than star model for the most test sequences with moderate or large motions

some properties of matrix variate laplace transforms and matrix variate whittaker functions abstract some results on scalar variable laplace transforms are generalized to the matrix variate case then a matrix variate function is defined which can be interpreted as a matrix variate analogue of the univariate whittaker function several properties of this function which generalize the corresponding properties of univariate whittaker function are established an application of this function to statistical distribution theory is also given

deformotion deforming motion shape average and the joint registration and approximation of structures in images what does it mean for a deforming object to be moving how can we separate the overall motion a finite dimensional group action from the more general deformation a diffeomorphism in this paper we propose a definition of motion for a deforming object and introduce a notion of shape average as the entity that separates the motion from the deformation our definition allows us to derive novel and efficient algorithms to register non identical shapes using region based methods and to simultaneously approximate and align structures in greyscale images we also extend the notion of shape average to that of a moving average in order to track moving and deforming objects through time the algorithms we propose extend prior work on landmark based matching to smooth curves and involve the numerical integration of partial differential equations which we address within the framework of level set methods

a shape based approach to the segmentation of medical imagery using level sets we propose a shape based approach to curve evolution for the segmentation of medical images containing known object types in particular motivated by the work of leventon grimson and faugeras 2000 we derive a parametric model for an implicit representation of the segmenting curve by applying principal component analysis to a collection of signed distance representations of the training data the parameters of this representation are then manipulated to minimize an objective function for segmentation the resulting algorithm is able to handle multidimensional data can deal with topological changes of the curve is robust to noise and initial contour placements and is computationally efficient at the same time it avoids the need for point correspondences during the training phase of the algorithm we demonstrate this technique by applying it to two medical applications two dimensional segmentation of cardiac magnetic resonance imaging mri and three dimensional segmentation of prostate mri

joint segmentation and shape regularization with a generalized forward backward algorithm this paper presents a method for the simultaneous segmentation and regularization of a series of shapes from a corresponding sequence of images such series arise as time series of 2d images when considering video data or as stacks of 2d images obtained by slicewise tomographic reconstruction we first derive a model where the regularization of the shape signal is achieved by a total variation prior on the shape manifold the method employs a modified kendall shape space to facilitate explicit computations together with the concept of sobolev gradients for the proposed model we derive an efficient and computationally accessible splitting scheme using a generalized forward backward approach our algorithm treats the total variation atoms of the splitting via proximal mappings whereas the data terms are dealt with by gradient descent the potential of the proposed method is demonstrated on various application examples dealing with 3d data we explain how to extend the proposed combined approach to shape fields which for instance arise in the context of 3d t imaging modalities and show an application in this setup as well

evaluation of the spherical bessel transform of a whittaker function an application of a difference equation method a simple analytic expression for the spherical bessel transform of the zero range bound state wave function with the coulomb interaction present for the lth partial wave expressed as a whittaker function is obtained the result is given in terms of polynomials of degree l the exponential function and a simple hypergeometric function which is independent of l transformations of this latter function are derived in terms of more rapidly convergent series the method presented has much wider application since it relies essentially only on the existence of differential difference equations for the functions involved and the solution of the inhomogeneous difference and differential equations satisfied by the transform

geodesic active contours and level sets for the detection and tracking of moving objects this paper presents a new variational framework for detecting and tracking multiple moving objects in image sequences motion detection is performed using a statistical framework for which the observed interframe difference density function is approximated using a mixture model this model is composed of two components namely the static background and the mobile moving objects one both components are zero mean and obey laplacian or gaussian law this statistical framework is used to provide the motion detection boundaries additionally the original frame is used to provide the moving object boundaries then the detection and the tracking problem are addressed in a common framework that employs a geodesic active contour objective function this function is minimized using a gradient descent method a new approach named hermes is proposed which exploits aspects from the well known front propagation algorithms and compares favorably to them very promising experimental results are provided using real video sequences

dynamic active contours for visual tracking visual tracking using active contours is usually set in a static framework the active contour tracks the object of interest in a given frame of an image sequence a subsequent prediction step ensures good initial placement for the next frame this approach is unnatural the curve evolution gets decoupled from the actual dynamics of the objects to be tracked true dynamical approaches exist all being marker particle based and thus prone to the shortcomings of such particle based implementations in particular topological changes are not handled naturally in this framework the now classical level set approach is tailored for evolutions of manifolds of codimension one however dynamic curve evolution is at least a codimension two problem we propose an efficient level set based approach for dynamic curve evolution which addresses the artificial separation of segmentation and prediction while retaining all the desirable properties of the level set formulation it is based on a new energy minimization functional which for the first time puts dynamics into the geodesic active contour framework

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

image zooming method using edge directed moving least squares interpolation based on exponential polynomials this paper presents a nonlinear image interpolation algorithm the suggested method is based on the moving least squares mls projection technique but introduces a fundamental modification the algebraic polynomial based mls methods provide very satisfactory results however the associated approximation space is shift and scale invariant so that it cannot be adjusted according to the characteristic of a given data as a result when upsampling images it has a limitation in producing sharp edges such that edges are often blurred in the magnified images to recover sharper edges we need to reduce smoothing parameter or adapt a new parameter sharpening the edges motivated by this observations we propose a novel mls method governed by a set of exponential polynomials with tension parameters such that they can be tuned to the characteristic of given data moreover for a better match to the local structures around the edges the suggested algorithm uses weights which consider the edge orientation numerical results are presented and compared visually and by using some quantitative fidelity measures psnr epsnr ssim and fsim to the bicubic spline interpolation and other recently developed nonlinear methods the results demonstrate the new algorithm s ability to magnify an image while preserving edge features

fast pixelwise adaptive visual tracking of non rigid objects in this paper we present a new algorithm for real time single object tracking in videos in unconstrained environments the algorithm comprises two different components that are trained in one shot at the first video frame a detector that makes use of the generalized hough transform with color and gradient descriptors and a probabilistic segmentation method based on global models for foreground and background color distributions both components work at pixel level and are used for tracking in a combined way adapting each other in a co training manner moreover we propose an adaptive shape model as well as a new probabilistic method for updating the scale of the tracker through effective model adaptation and segmentation the algorithm is able to track objects that undergo rigid and non rigid deformations and considerable shape and appearance variations the proposed tracking method has been thoroughly evaluated on challenging benchmarks and outperforms the state of the art tracking methods designed for the same task finally a very efficient implementation of the proposed models allows for extremely fast tracking

the tau method and a new preconditioner in relations to the order of linear ordinary differential equations using a modified form of the chebyshev or legendre and gegenbauer polynomials some particular integral operators are introduced these are used to give a factorization of the operators arising from the application of the chebyshev or legendre tau method the new tau method presented in this article is then compared with the standard tau method and preconditioned method of cabos the new tau method shows a superior performance an analysis of error and a bound for condition number is given numerical examples applying iterative solvers show dramatic reduction in condition number and improved convergence for the tau method with the new preconditioner

region tracking via level set pdes without motion computation we propose an approach to region tracking that is derived from a bayesian formulation the novelty of the approach is twofold first no motion field or motion parameters need to be computed this removes a major burden since accurate motion computation has been and remains a challenging problem and the quality of region tracking algorithms based on motion critically depends on the computed motion fields and parameters the second novelty of this approach is that very little a priori information about the region being tracked is used in the algorithm in particular unlike numerous tracking algorithms no assumption is made on the strength of the intensity edges of the boundary of the region being tracked nor is its shape assumed to be of a certain parametric form the problem of region tracking is formulated as a bayesian estimation problem and the resulting tracking algorithm is expressed as a level set partial differential equation we present further extensions to this partial differential equation allowing the possibility of including additional information in the tracking process such as priors on the region s intensity boundaries and we present the details of the numerical implementation very promising experimental results are provided

developing a local least squares support vector machines based neuro fuzzy model for nonlinear and chaotic time series prediction local modeling approaches owing to their ability to model different operating regimes of nonlinear systems and processes by independent local models seem appealing for modeling identification and prediction applications in this paper we propose a local neuro fuzzy lnf approach based on the least squares support vector machines lssvms the proposed lnf approach employs lssvms which are powerful in modeling and predicting time series as local models and uses hierarchical binary tree hbt learning algorithm for fast and efficient estimation of its parameters the hbt algorithm heuristically partitions the input space into smaller subdomains by axis orthogonal splits in each partitioning the validity functions automatically form a unity partition and therefore normalization side effects e g reactivation are prevented integration of lssvms into the lnf network as local models along with the hbt learning algorithm yield a high performance approach for modeling and prediction of complex nonlinear time series the proposed approach is applied to modeling and predictions of different nonlinear and chaotic real world and hand designed systems and time series analysis of the prediction results and comparisons with recent and old studies demonstrate the promising performance of the proposed lnf approach with the hbt learning algorithm for modeling and prediction of nonlinear and chaotic systems and time series

a tutorial on particle filters for online nonlinear non gaussian bayesian tracking increasingly for many application areas it is becoming important to include elements of nonlinearity and non gaussianity in order to model accurately the underlying dynamics of a physical system moreover it is typically crucial to process data on line as it arrives both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics in this paper we review both optimal and suboptimal bayesian algorithms for nonlinear non gaussian tracking problems with a focus on particle filters particle filters are sequential monte carlo methods based on point mass or particle representations of probability densities which can be applied to any state space model and which generalize the traditional kalman filtering methods several variants of the particle filter such as sir asir and rpf are introduced within a generic framework of the sequential importance sampling sis algorithm these are discussed and compared with the standard ekf through an illustrative example

an edge guided image interpolation algorithm via directional filtering and data fusion preserving edge structures is a challenge to image interpolation algorithms that reconstruct a high resolution image from a low resolution counterpart we propose a new edge guided nonlinear interpolation technique through directional filtering and data fusion for a pixel to be interpolated two observation sets are defined in two orthogonal directions and each set produces an estimate of the pixel value these directional estimates modeled as different noisy measurements of the missing pixel are fused by the linear minimum mean square error estimation lmmse technique into a more robust estimate using the statistics of the two observation sets we also present a simplified version of the lmmse based interpolation algorithm to reduce computational cost without sacrificing much the interpolation performance experiments show that the new interpolation techniques can preserve edge sharpness and reduce ringing artifacts

deform pf mt particle filter with mode tracker for tracking nonaffine contour deformations we propose algorithms for tracking the boundary contour of a deforming object from an image sequence when the nonaffine local deformation over consecutive frames is large and there is overlapping clutter occlusions low contrast or outlier imagery when the object is arbitrarily deforming each or at least most contour points can move independently contour deformation then forms an infinite in practice very large dimensional space direct application of particle filters pf for large dimensional problems is impractically expensive however in most real problems at any given time most of the contour deformation occurs in a small number of dimensions effective basis space while the residual deformation in the rest of the state space residual space is small this property enables us to apply the particle filtering with mode tracking pf mt idea that was proposed for such large dimensional problems in recent work since most contour deformation is low spatial frequency we propose to use the space of deformation at a subsampled set of locations as the effective basis space the resulting algorithm is called deform pf mt it requires significant modifications compared to the original pf mt because the space of contours is a non euclidean infinite dimensional space

shape tracking with occlusions via coarse to fine region based sobolev descent we present a method to track the shape of an object from video the method uses a joint shape and appearance model of the object which is propagated to match shape and radiance in subsequent frames determining object shape self occlusions and dis occlusions of the object from camera and object motion pose difficulties to joint shape and appearance models in tracking they are unable to adapt to new shape and appearance information leading to inaccurate shape detection in this work we model self occlusions and dis occlusions in a joint shape and appearance tracking framework self occlusions and the warp to propagate the model are coupled thus we formulate a joint optimization problem we derive a coarse to fine optimization method advantageous in tracking that initially perturbs the model by coarse perturbations before transitioning to finer scale perturbations seamlessly this coarse to fine behavior is automatically induced by gradient descent on a novel infinite dimensional riemannian manifold that we introduce the manifold consists of planar parameterized regions and the metric that we introduce is a novel sobolev metric experiments on video exhibiting occlusions dis occlusions complex radiance and background show that occlusion dis occlusion modeling leads to superior shape accuracy

geometric observers for dynamically evolving curves this paper proposes a deterministic observer design for visual tracking based on nonparametric implicit level set curve descriptions the observer is continuous discrete with continuous time system dynamics and discrete time measurements its state space consists of an estimated curve position augmented by additional states e g velocities associated with every point on the estimated curve multiple simulation models are proposed for state prediction measurements are performed through standard static segmentation algorithms and optical flow computations special emphasis is given to the geometric formulation of the overall dynamical system the discrete time measurements lead to the problem of geometric curve interpolation and the discrete time filtering of quantities propagated along with the estimated curve interpolation and filtering are intimately linked to the correspondence problem between curves correspondences are established by a laplace equation approach the proposed scheme is implemented completely implicitly by eulerian numerical solutions of transport equations and thus naturally allows for topological changes and subpixel accuracy on the computational grid

video tracking based on sequential particle filtering on graphs in this paper we develop a novel solution for particle filtering on general graphs we provide an exact solution for particle filtering on directed cycle free graphs the proposed approach relies on a partial order relation in an antichain decomposition that forms a high order markov chain over the partitioned graph we subsequently derive a closed form sequential updating scheme for conditional density propagation using particle filtering on directed cycle free graphs we also provide an approximate solution for particle filtering on general graphs by splitting graphs with cycles into multiple directed cycle free subgraphs we then use the sequential updating scheme by alternating among the directed cycle free subgraphs to obtain an estimate of the density propagation we rely on the proposed method for particle filtering on general graphs for two video tracking applications 1 object tracking using high order markov chains and 2 distributed multiple object tracking based on multi object graphical interaction models experimental results demonstrate the improved performance of the proposed approach to particle filtering on graphs compared with existing methods for video tracking