diffusion snakes introducing statistical shape knowledge into the mumford shah functional we present a modification of the mumford shah functional and its cartoon limit which facilitates the incorporation of a statistical prior on the shape of the segmenting contour by minimizing a single energy functional we obtain a segmentation process which maximizes both the grey value homogeneity in the separated regions and the similarity of the contour with respect to a set of training shapes we propose a closed form parameter free solution for incorporating invariance with respect to similarity transformations in the variational framework we show segmentation results on artificial and real world images with and without prior shape information in the cases of noise occlusion or strongly cluttered background the shape prior significantly improves segmentation finally we compare our results to those obtained by a level set implementation of geodesic active contours

a multiphase dynamic labeling model for variational recognition driven image segmentation we propose a variational framework for the integration of multiple competing shape priors into level set based segmentation schemes by optimizing an appropriate cost functional with respect to both a level set function and a vector valued labeling function we jointly generate a segmentation by the level set function and a recognition driven partition of the image domain by the labeling function which indicates where to enforce certain shape priors our framework fundamentally extends previous work on shape priors in level set segmentation by directly addressing the central question of where to apply which prior it allows for the seamless integration of numerous shape priors such that while segmenting both multiple known and unknown objects the level set process may selectively use specific shape knowledge for simultaneously enhancing segmentation and recognizing shape

on the unification of line processes outlier rejection and robust statistics with applications in early vision the modeling of spatial discontinuities for problems such as surface recovery segmentation image reconstruction and optical flow has been intensely studied in computer vision while line process models of discontinuities have received a great deal of attention there has been recent interest in the use of robust statistical techniques to account for discontinuities this paper unifies the two approaches to achieve this we generalize the notion of a line process to that of an analog outlier process and show how a problem formulated in terms of outlier processes can be viewed in terms of robust statistics we also characterize a class of robust statistical problems for which an equivalent outlier process formulation exists and give a straightforward method for converting a robust estimation problem into an outlier process formulation we show how prior assumptions about the spatial structure of outliers can be expressed as constraints on the recovered analog outlier processes and how traditional continuation methods can be extended to the explicit outlier process formulation these results indicate that the outlier process approach provides a general framework which subsumes the traditional line process approaches as well as a wide class of robust estimation problems examples in surface reconstruction image segmentation and optical flow are presented to illustrate the use of outlier processes and to show how the relationship between outlier processes and robust statistics can be exploited an appendix provides a catalog of common robust error norms and their equivalent outlier process formulations

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

on measuring the distance between histograms abstract a distance measure between two histograms has applications in feature selection image indexing and retrieval pattern classification and clustering etc we propose a distance between sets of measurement values as a measure of dissimilarity of two histograms the proposed measure has the advantage over the traditional distance measures regarding the overlap between two distributions it takes the similarity of the non overlapping parts into account as well as that of overlapping parts we consider three versions of the univariate histogram corresponding to whether the type of measurement is nominal ordinal and modulo and their computational time complexities are b b and o b2 for each type of measurements respectively where b is the number of levels in histograms

geodesic active regions and level set methods for supervised texture segmentation this paper presents a novel variational framework to deal with frame partition problems in computer vision this framework exploits boundary and region based segmentation modules under a curve based optimization objective function the task of supervised texture segmentation is considered to demonstrate the potentials of the proposed framework the textured feature space is generated by filtering the given textured images using isotropic and anisotropic filters and analyzing their responses as multi component conditional probability density functions the texture segmentation is obtained by unifying region and boundary based information as an improved geodesic active contour model the defined objective function is minimized using a gradient descent method where a level set approach is used to implement the obtained pde according to this pde the curve propagation towards the final solution is guided by boundary and region based segmentation forces and is constrained by a regularity force the level set implementation is performed using a fast front propagation algorithm where topological changes are naturally handled the performance of our method is demonstrated on a variety of synthetic and real textured frames

a review of statistical approaches to level set segmentation integrating color texture motion and shape since their introduction as a means of front propagation and their first application to edge based segmentation in the early 90 s level set methods have become increasingly popular as a general framework for image segmentation in this paper we present a survey of a specific class of region based level set segmentation methods and clarify how they can all be derived from a common statistical framework region based segmentation schemes aim at partitioning the image domain by progressively fitting statistical models to the intensity color texture or motion in each of a set of regions in contrast to edge based schemes such as the classical snakes region based methods tend to be less sensitive to noise for typical images the respective cost functionals tend to have less local minima which makes them particularly well suited for local optimization methods such as the level set method we detail a general statistical formulation for level set segmentation subsequently we clarify how the integration of various low level criteria leads to a set of cost functionals we point out relations between the different segmentation schemes in experimental results we demonstrate how the level set function is driven to partition the image plane into domains of coherent color texture dynamic texture or motion moreover the bayesian formulation allows to introduce prior shape knowledge into the level set method we briefly review a number of advances in this domain

fuzzy g congruences on a groupoid abstract the definition of a fuzzy reflexive relation on a set s is generalized by demanding that x y z z 0 for all x y z s fuzzy equivalence relations on a given set and fuzzy congruences on a given groupoid are studied under this generalized setting

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

robust optical flow integration we analyze the problem of how to correctly construct dense point trajectories from optical flow fields first we show that simple euler integration is unavoidably inaccurate no matter how good is the optical flow estimator then an inverse integration scheme is analyzed which is more robust to bias and input noise and shows better stability properties our contribution is threefold 1 a theoretical analysis that demonstrates why and in what sense inverse integration is more accurate 2 a rich experimental validation both on synthetic and real image data and 3 an algorithm for approximate online inverse integration this new technique is precious whether one is trying to propagate information densely available on a reference frame to the other frames in the sequence or conversely to assign information densely over each frame by pulling it from the reference

finding community structure in networks using the eigenvectors of matrices we consider the problem of detecting communities or modules in networks groups of vertices with a higher than average density of edges connecting them previous work indicates that a robust approach to this problem is the maximization of the benefit function known as modularity over possible divisions of a network here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix which plays a role in community detection similar to that played by the graph laplacian in graph partitioning calculations this result leads us to a number of possible algorithms for detecting community structure as well as several other results including a spectral measure of bipartite structure in networks and a centrality measure that identifies vertices that occupy central positions within the communities to which they belong the algorithms and measures proposed are illustrated with applications to a variety of real world complex networks

oriented structure of the occlusion distortion is it reliable in the energy spectrum of an occlusion sequence the distortion term has the same orientation as the velocity of the occluding signal other works claimed that this oriented structure can be used to distinguish the occluding velocity from the occluded one we argue that the orientation structure of the distortion cannot always work as a reliable feature due to the rapidly decreasing energy contribution this already weak orientation structure is further blurred by a superposition of distinct distortion components we also indicate that the superposition principle of shizawa and mase 1991 for multiple motion estimation needs to be adjusted

a geometric model for active contours in image processing we propose a new model for active contours based on a geometric partial differential equation our model is intrinsec stable satisfies the maximum principle and permits a rigorous mathematical analysis it enables us to extract smooth shapes we cannot retrieve angles and it can be adapted to find several contours simultaneously moreover as a consequence of the stability we can design robust algorithms which can be engineed with no parameters in applications numerical experiments are presented

dynamical statistical shape priors for level set based tracking in recent years researchers have proposed introducing statistical shape knowledge into level set based segmentation methods in order to cope with insufficient low level information while these priors were shown to drastically improve the segmentation of familiar objects so far the focus has been on statistical shape priors which are static in time yet in the context of tracking deformable objects it is clear that certain silhouettes such as those of a walking person may become more or less likely over time in this paper we tackle the challenge of learning dynamical statistical models for implicitly represented shapes we show how these can be integrated as dynamical shape priors in a bayesian framework for level set based image sequence segmentation we assess the effect of such shape priors with memory on the tracking of familiar deformable objects in the presence of noise and occlusion we show comparisons between dynamical and static shape priors between models of pure deformation and joint models of deformation and transformation and we quantitatively evaluate the segmentation accuracy as a function of the noise level and of the camera frame rate our experiments demonstrate that level set based segmentation and tracking can be strongly improved by exploiting the temporal correlations among consecutive silhouettes which characterize deforming shapes

active contours for tracking distributions a new approach to tracking using active contours is presented the class of objects to be tracked is assumed to be characterized by a probability distribution over some variable such as intensity color or texture the goal of the algorithm is to find the region within the current image such that the sample distribution of the interior of the region most closely matches the model distribution two separate criteria for matching distributions are examined and the curve evolution equations are derived in each case the flows are shown to perform well in experiments

a generic framework for tracking using particle filter with dynamic shape prior tracking deforming objects involves estimating the global motion of the object and its local deformations as functions of time tracking algorithms using kalman filters or particle filters pfs have been proposed for tracking such objects but these have limitations due to the lack of dynamic shape information in this paper we propose a novel method based on employing a locally linear embedding in order to incorporate dynamic shape information into the particle filtering framework for tracking highly deformable objects in the presence of noise and clutter the pf also models image statistics such as mean and variance of the given data which can be useful in obtaining proper separation of object and background

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

a low dimensional fluid motion estimator in this paper we propose a new motion estimator for image sequences depicting fluid flows the proposed estimator is based on the helmholtz decomposition of vector fields this decomposition consists in representing the velocity field as a sum of a divergence free component and a vorticity free component the objective is to provide a low dimensional parametric representation of optical flows by depicting them as deformations generated by a reduced number of vortex and source particles both components are approximated using a discretization of the vorticity and divergence maps through regularized dirac measures the resulting so called irrotational and solenoidal fields consist of linear combinations of basis functions obtained through a convolution product of the green kernel gradient and the vorticity map or the divergence map respectively the coefficient values and the basis function parameters are obtained by minimization of a functional relying on an integrated version of mass conservation principle of fluid mechanics results are provided on synthetic examples and real world sequences

behavior classification by eigendecomposition of periodic motions we show how periodic motions can be represented by a small number of eigenshapes that capture the whole dynamic mechanism of the motion spectral decomposition of a silhouette of a moving object serves as a basis for behavior classification by principle component analysis the boundary contour of the walking dog for example is first computed efficiently and accurately after normalization the implicit representation of a sequence of silhouette contours given by their corresponding binary images is used for generating eigenshapes for the given motion singular value decomposition produces these eigenshapes that are then used to analyze the sequence we show examples of object as well as behavior classification based on the eigendecomposition of the binary silhouette sequence

a stochastic filtering technique for fluid flow velocity fields tracking in this paper we present a method for the temporal tracking of fluid flow velocity fields the technique we propose is formalized within a sequential bayesian filtering framework the filtering model combines an ito diffusion process coming from a stochastic formulation of the vorticity velocity form of the navier stokes equation and discrete measurements extracted from the image sequence in order to handle a state space of reasonable dimension the motion field is represented as a combination of adapted basis functions derived from a discretization of the vorticity map of the fluid flow velocity field the resulting nonlinear filtering problem is solved with the particle filter algorithm in continuous time an adaptive dimensional reduction method is applied to the filtering technique relying on dynamical systems theory the efficiency of the tracking method is demonstrated on synthetic and real world sequences

curve evolution implementation of the mumford shah functional for image segmentation denoising interpolation and magnification we first address the problem of simultaneous image segmentation and smoothing by approaching the mumford shah 1989 paradigm from a curve evolution perspective in particular we let a set of deformable contours define the boundaries between regions in an image where we model the data via piecewise smooth functions and employ a gradient flow to evolve these contours each gradient step involves solving an optimal estimation problem for the data within each region connecting curve evolution and the mumford shah functional with the theory of boundary value stochastic processes the resulting active contour model offers a tractable implementation of the original mumford shah model i e without resorting to elliptic approximations which have traditionally been favored for greater ease in implementation to simultaneously segment and smoothly reconstruct the data within a given image in a coupled manner various implementations of this algorithm are introduced to increase its speed of convergence we also outline a hierarchical implementation of this algorithm to handle important image features such as triple points and other multiple junctions next by generalizing the data fidelity term of the original mumford shah functional to incorporate a spatially varying penalty we extend our method to problems in which data quality varies across the image and to images in which sets of pixel measurements are missing this more general model leads us to a novel pde based approach for simultaneous image magnification segmentation and smoothing thereby extending the traditional applications of the mumford shah functional which only considers simultaneous segmentation and smoothing

fuzzy equivalence relations abstract in this note we define and discuss properties of fuzzy equivalence relations on a set in particular we show that there exists a correspondence between fuzzy equivalence relations and certain classes of fuzzy subsets we also study the cuts of fuzzy equivalence relations finally certain lattice theoretic properties of fuzzy equivalence relations are discussed

stochastic uncertainty models for the luminance consistency assumption in this paper a stochastic formulation of the brightness consistency used in many computer vision problems involving dynamic scenes for instance motion estimation or point tracking is proposed usually this model which assumes that the luminance of a point is constant along its trajectory is expressed in a differential form through the total derivative of the luminance function this differential equation linearly links the point velocity to the spatial and temporal gradients of the luminance function however when dealing with images the available information only holds at discrete time and on a discrete grid in this paper we formalize the image luminance as a continuous function transported by a flow known only up to some uncertainties related to such a discretization process relying on stochastic calculus we define a formulation of the luminance function preservation in which these uncertainties are taken into account from such a framework it can be shown that the usual deterministic optical flow constraint equation corresponds to our stochastic evolution under some strong constraints these constraints can be relaxed by imposing a weaker temporal assumption on the luminance function and also in introducing anisotropic intensity based uncertainties we also show that these uncertainties can be computed at each point of the image grid from the image data and hence provide meaningful information on the reliability of the motion estimates to demonstrate the benefit of such a stochastic formulation of the brightness consistency assumption we have considered a local least squares motion estimator relying on this new constraint this new motion estimator significantly improves the quality of the results

a combinatorial solution for model based image segmentation and real time tracking we propose a combinatorial solution to determine the optimal elastic matching of a deformable template to an image the central idea is to cast the optimal matching of each template point to a corresponding image pixel as a problem of finding a minimum cost cyclic path in the three dimensional product space spanned by the template and the input image we introduce a cost functional associated with each cycle which consists of three terms a data fidelity term favoring strong intensity gradients a shape consistency term favoring similarity of tangent angles of corresponding points and an elastic penalty for stretching or shrinking the functional is normalized with respect to the total length to avoid a bias toward shorter curves optimization is performed by lawler s minimum ratio cycle algorithm parallelized on state of the art graphics cards the algorithm provides the optimal segmentation and point correspondence between template and segmented curve in computation times that are essentially linear in the number of pixels to the best of our knowledge this is the only existing globally optimal algorithm for real time tracking of deformable shapes

linear dimensionality reduction by maximizing the chernoff distance in the transformed space linear dimensionality reduction ldr techniques are quite important in pattern recognition due to their linear time complexity and simplicity in this paper we present a novel ldr technique which though linear aims to maximize the chernoff distance in the transformed space thus augmenting the class separability in such a space we present the corresponding criterion which is maximized via a gradient based algorithm and provide convergence and initialization proofs we have performed a comprehensive performance analysis of our method combined with two well known classifiers linear and quadratic on synthetic and real life data and compared it with other ldr techniques the results on synthetic and standard real life data sets show that the proposed criterion outperforms the latter when combined with both linear and quadratic classifiers

a region merging prior for variational level set image segmentation in current level set image segmentation methods the number of regions is assumed to known beforehand as a result it remains constant during the optimization of the objective functional how to allow it to vary is an important question which has been generally avoided this study investigates a region merging prior related to regions area to allow the number of regions to vary automatically during curve evolution thereby optimizing the objective functional implicitly with respect to the number of regions we give a statistical interpretation to the coefficient of this prior to balance its effect systematically against the other functional terms we demonstrate the validity and efficiency of the method by testing on real images of intensity color and motion

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

using prior shapes in geometric active contours in a variational framework in this paper we report an active contour algorithm that is capable of using prior shapes the energy functional of the contour is modified so that the energy depends on the image gradient as well as the prior shape the model provides the segmentation and the transformation that maps the segmented contour to the prior shape the active contour is able to find boundaries that are similar in shape to the prior even when the entire boundary is not visible in the image i e when the boundary has gaps a level set formulation of the active contour is presented the existence of the solution to the energy minimization is also established we also report experimental results of the use of this contour on 2d synthetic images ultrasound images and fmri images classical active contours cannot be used in many of these images

an analysis of physics based optical flow a variational solution of the physics based optical flow equation is studied for extraction of high resolution velocity fields from flow visualization images the solution to preserve discontinuities in a fluid velocity field is mathematically justified the uniqueness of the solution and the convergence of a successive approximation sequence are proven a numerical algorithm is developed and examined through numerical experiments

parameterized strain estimation for vascular ultrasound elastography with sparse representation ultrasound vascular strain imaging has shown its potential to interrogate the motion of the vessel wall induced by the cardiac pulsation for predicting plaque instability in this study a sparse model strain estimator smse is proposed to reconstruct a dense strain field at a high resolution with no spatial derivatives and a high computation efficiency this sparse model utilizes the highly compacted property of discrete cosine transform dct coefficients thereby allowing to parameterize displacement and strain fields with truncated dct coefficients the derivation of affine strain components axial and lateral strains and shears was reformulated into solving truncated dct coefficients and then reconstructed with them moreover an analytical solution was derived to reduce estimation time with simulations the smse reduced estimation errors by up to 50 compared with the state of the art window based lagrangian speckle model estimator lsme the smse was also proven to be more robust than the lsme against global and local noise for in vitro and in vivo tests residual strains assessing cumulated errors with the smse were 2 to 3 times lower than with the lsme regarding computation efficiency the processing time of the smse was reduced by 4 to 25 times compared with the lsme according to simulations in vitro and in vivo results finally phantom studies demonstrated the enhanced spatial resolution of the proposed smse algorithm against lsme

a theoretical framework for convex regularizers in pde based computation of image motion many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy typically these energy functionals consist of two terms a data term which requires e g that a brightness constancy assumption holds and a regularizer that encourages global or piecewise smoothness of the flow field in this paper we present a systematic classification of rotation invariant convex regularizers by exploring their connection to diffusion filters for multichannel images this taxonomy provides a unifying framework for data driven and flow driven isotropic and anisotropic as well as spatial and spatio temporal regularizers while some of these techniques are classic methods from the literature others are derived here for the first time we prove that all these methods are well posed they posses a unique solution that depends in a continuous way on the initial data an interesting structural relation between isotropic and anisotropic flow driven regularizers is identified and a design criterion is proposed for constructing anisotropic flow driven regularizers in a simple and direct way from isotropic ones its use is illustrated by several examples

variability analysis of complex networks measures based on stochastic distances abstract complex networks can model the structure and dynamics of different types of systems it has been shown that they are characterized by a set of measures in this work we evaluate the variability of complex network measures face to perturbations and for this purpose we impose controlled perturbations and quantify their effect we analyze theoretical models random small world and scale free and real networks a collaboration network and a metabolic networks along with the shortest path length vertex degree local cluster coefficient and betweenness centrality measures in such an analysis we propose the use of three stochastic quantifiers the kullback leibler divergence and the jensen shannon and hellinger distances the sensitivity of these measures was analyzed with respect to the following perturbations edge addition edge removal edge rewiring and node removal all of them applied at different intensities the results reveal that the evaluated measures are influenced by these perturbations additionally hypotheses tests were performed to verify the behavior of the degree distribution to identify the intensity of the perturbations that leads to break this property

reliable estimation of dense optical flow fields with large displacements in this paper we show that a classic optical flow technique by nagel and enkelmann 1986 ieee trans pattern anal mach intell vol 8 pp 565 593 can be regarded as an early anisotropic diffusion method with a diffusion tensor we introduce three improvements into the model formulation that i avoid inconsistencies caused by centering the brightness term and the smoothness term in different images ii use a linear scale space focusing strategy from coarse to fine scales for avoiding convergence to physically irrelevant local minima and iii create an energy functional that is invariant under linear brightness changes applying a gradient descent method to the resulting energy functional leads to a system of diffusion reaction equations we prove that this system has a unique solution under realistic assumptions on the initial data and we present an efficient linear implicit numerical scheme in detail our method creates flow fields with 100 density over the entire image domain it is robust under a large range of parameter variations and it can recover displacement fields that are far beyond the typical one pixel limits which are characteristic for many differential methods for determining optical flow we show that it performs better than the optical flow methods with 100 density that are evaluated by barron et al 1994 int j comput vision vol 12 pp 43 47 our software is available from the internet

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

entropy optimization of scale free networks robustness to random failures abstract many networks are characterized by highly heterogeneous distributions of links which are called scale free networks and the degree distributions follow p k ck we study the robustness of scale free networks to random failures from the character of their heterogeneity entropy of the degree distribution can be an average measure of a network s heterogeneity optimization of scale free networks robustness to random failures with average connectivity constant is equivalent to maximizing the entropy of the degree distribution by examining the relationship of the entropy of the degree distribution scaling exponent and the minimal connectivity we get the optimal design of scale free networks to random failures we conclude that the entropy of the degree distribution is an effective measure of network s resilience to random failures

dense estimation of fluid flows in this paper we address the problem of estimating and analyzing the motion of fluids in image sequences due to the great deal of spatial and temporal distortions that intensity patterns exhibit in images of fluids the standard techniques from computer vision originally designed for quasi rigid motions with stable salient features are not well adapted in this context we thus investigate a dedicated minimization based motion estimator the cost function to be minimized includes a novel data term relying on an integrated version of the continuity equation of fluid mechanics which is compatible with large displacements this term is associated with an original second order div curl regularization which prevents the washing out of the salient vorticity and divergence structures the performance of the resulting fluid flow estimator is demonstrated on meteorological satellite images in addition we show how the sequences of dense motion fields we estimate can be reliably used to reconstruct trajectories and to extract the regions of high vorticity and divergence

robust point matching via vector field consensus in this paper we propose an efficient algorithm called vector field consensus for establishing robust point correspondences between two sets of points our algorithm starts by creating a set of putative correspondences which can contain a very large number of false correspondences or outliers in addition to a limited number of true correspondences inliers next we solve for correspondence by interpolating a vector field between the two point sets which involves estimating a consensus of inlier points whose matching follows a nonparametric geometrical constraint we formulate this a maximum a posteriori map estimation of a bayesian model with hidden latent variables indicating whether matches in the putative set are outliers or inliers we impose nonparametric geometrical constraints on the correspondence as a prior distribution using tikhonov regularizers in a reproducing kernel hilbert space map estimation is performed by the em algorithm which by also estimating the variance of the prior model initialized to a large value is able to obtain good estimates very quickly e g avoiding many of the local minima inherent in this formulation we illustrate this method on data sets in 2d and 3d and demonstrate that it is robust to a very large number of outliers even up to 90 we also show that in the special case where there is an underlying parametric geometrical model e g the epipolar line constraint that we obtain better results than standard alternatives like ransac if a large number of outliers are present this suggests a two stage strategy where we use our nonparametric model to reduce the size of the putative set and then apply a parametric variant of our approach to estimate the geometric parameters our algorithm is computationally efficient and we provide code for others to use it in addition our approach is general and can be applied to other problems such as learning with a badly corrupted training data set

dense estimation and object based segmentation of the optical flow with robust techniques we address the issue of recovering and segmenting the apparent velocity field in sequences of images as for motion estimation we minimize an objective function involving two robust terms the first one cautiously captures the optical flow constraint while the second a priori term incorporates a discontinuity preserving smoothness constraint to cope with the nonconvex minimization problem thus defined we design an efficient deterministic multigrid procedure it converges fast toward estimates of good quality while revealing the large discontinuity structures of flow fields we then propose an extension of the model by attaching to it a flexible object based segmentation device based on deformable closed curves different families of curve equipped with different kinds of prior can be easily supported experimental results on synthetic and natural sequences are presented including an analysis of sensitivity to parameter tuning

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

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

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

constrained restoration and the recovery of discontinuities the linear image restoration problem is to recover an original brightness distribution x sup 0 given the blurred and noisy observations y kx sup 0 b where k and b represent the point spread function and measurement error respectively this problem is typical of ill conditioned inverse problems that frequently arise in low level computer vision a conventional method to stabilize the problem is to introduce a priori constraints on x sup 0 and design a cost functional h x over images x which is a weighted average of the prior constraints regularization term and posterior constraints data term the reconstruction is then the image x which minimizes h a prominent weakness in this approach especially with quadratic type stabilizers is the difficulty in recovering discontinuities the authors therefore examine prior smoothness constraints of a different form which permit the recovery of discontinuities without introducing auxiliary variables for marking the location of jumps and suspending the constraints in their vicinity in this sense discontinuities are addressed implicitly rather than explicitly

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

generalized correlation for shape alignment ordered set valued functions are introduced in this study to represent arbitrary shapes in a simple manner the arithmetic of ordered set valued functions is meaningless hence a novel concept namely generalized correlation is proposed to handle shape alignment problems generalized correlation is an extension of correlation from single valued functions to ordered set valued functions it is especially designed for shape alignment but not for a general mathematical definition moreover efficient algorithms are proposed to compute generalized correlation in 2d and 3d cases experiments indicate that the proposed alignment methods converge rapidly and globally furthermore generalized correlation is used handle registration problems to demonstrate its potential in computer vision tasks

tracking using motion estimation with physically motivated inter region constraints we propose a method for tracking structures e g ventricles and myocardium in cardiac images e g magnetic resonance by propagating forward in time a previous estimate of the structures using a new physically motivated motion estimation scheme our method estimates motion by regularizing only within structures so that differing motions among different structures are not mixed it simultaneously satisfies the physical constraints at the interface between a fluid and a medium that the normal component of the fluid s motion must match the normal component of the medium s motion and the no slip condition which states that the tangential velocity approaches zero near the interface we show that these conditions lead to partial differential equations with robin boundary conditions at the interface which couple the motion between structures we show that propagating a segmentation across frames using our motion estimation scheme leads to more accurate segmentation than traditional motion estimation that does not use physical constraints our method is suited to interactive segmentation prominently used in commercial applications for cardiac analysis where segmentation propagation is used to predict a segmentation in the next frame we show that our method leads to more accurate predictions than a popular and recent interactive method used in cardiac segmentation

observation model based on scale interactions for optical flow estimation in this paper an original observation model for multiresolution optical flow estimation is introduced multiresolution frameworks often based on coarse to fine warping strategies are widely used by state of the art optical flow methods they allow the recovery of large motions by successive estimations of the flow field at several resolution levels although such approaches perform very efficiently and usually lead to faster minimizations they generally consider independent problems at each resolution levels and do not exploit the existing interactions between scales especially the influences of fine scales on larger ones in this paper we tackle this issue by proposing a flexible framework inspired from fluid mechanics able to partly counter these limitations for each resolution level our process filters the equations of interest and decomposes the key variables into resolved i e at a given resolution and unresolved i e at finer resolutions components this enables to derive a new data term that takes into account at coarse resolutions the influence of their unresolved parts from this new term we propose two different estimation strategies depending on whether we explicitly know the type of relations between the different scales as for physical processes or not in order to test the efficiency of this new observation model we have embedded it in a simple multiresolution lucas kanade estimator comparing the usual optical flow constraint equation with this new term in the same motion estimation procedure it clearly appears that the proposed term leads to more consistent estimates and prevents from errors propagation apparition during the estimation in all situations synthetic real physical images or not our new term is able to greatly improve the results compared with usual conservation constraints

region competition unifying snakes region growing and bayes mdl for multiband image segmentation we present a novel statistical and variational approach to image segmentation based on a new algorithm named region competition this algorithm is derived by minimizing a generalized bayes minimum description length mdl criterion using the variational principle the algorithm is guaranteed to converge to a local minimum and combines aspects of snakes balloons and region growing the classic snakes balloons and region growing algorithms can be directly derived from our approach we provide theoretical analysis of region competition including accuracy of boundary location criteria for initial conditions and the relationship to edge detection using filters it is straightforward to generalize the algorithm to multiband segmentation and we demonstrate it on gray level images color images and texture images the novel color model allows us to eliminate intensity gradients and shadows thereby obtaining segmentation based on the albedos of objects it also helps detect highlight regions

view invariant action recognition based on artificial neural networks in this paper a novel view invariant action recognition method based on neural network representation and recognition is proposed the novel representation of action videos is based on learning spatially related human body posture prototypes using self organizing maps fuzzy distances from human body posture prototypes are used to produce a time invariant action representation multilayer perceptrons are used for action classification the algorithm is trained using data from a multi camera setup an arbitrary number of cameras can be used in order to recognize actions using a bayesian framework the proposed method can also be applied to videos depicting interactions between humans without any modification the use of information captured from different viewing angles leads to high classification performance the proposed method is the first one that has been tested in challenging experimental setups a fact that denotes its effectiveness to deal with most of the open issues in action recognition

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

video extrapolation method based on time varying energy optimization and cip video extrapolation prediction methods are often used to synthesize new videos from images for fluid like images and dynamic textures as well as moving rigid objects most state of the art video extrapolation methods use non physics based models that learn orthogonal bases from a number of images but at high computation cost unfortunately data truncation can cause image degradation i e blur artifact and insufficient motion changes to extrapolate videos that more strictly follow physical rules this paper proposes a physics based method that needs only a few images and is truncation free we utilize physics based equations with image intensity and velocity optical flow navier stokes continuity and advection equations these allow us to use partial difference equations to deal with the local image feature changes image degradation during extrapolation is minimized by updating model parameters where a novel time varying energy balancer model that uses energy based image features i e texture velocity and edge moreover the advection equation is discretized by high order constrained interpolation profile for lower quantization error than can be achieved by the previous finite difference method in long term videos experiments show that the proposed energy based video extrapolation method outperforms the state of the art video extrapolation methods in terms of image quality and computation cost

robust level set image segmentation via a local correntropy based k means clustering it is still a challenging task to segment real world images since they are often distorted by unknown noise and intensity inhomogeneity to address these problems we propose a novel segmentation algorithm via a local correntropy based k means lck clustering due to the correntropy criterion the clustering algorithm can decrease the weights of the samples that are away from their clusters as a result lck based clustering algorithm can be robust to the outliers the proposed lck clustering algorithm is incorporated into the region based level set segmentation framework the iteratively re weighted algorithm is used to solve the lck based level set segmentation method extensive experiments on synthetic and real images are provided to evaluate our method showing significant improvements on both noise sensitivity and segmentation accuracy as compared with the state of the art approaches

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

reliable and efficient computation of optical flow in this paper we present two very efficient and accurate algorithms for computing optical flow the first is a modified gradient based regularization method and the other is an ssd based regularization method for the gradient based method to amend the errors in the discrete image flow equation caused by numerical differentiation as well as temporal and spatial aliasing in the brightness function we propose to selectively combine the image flow constraint and a contour based flow constraint into the data constraint by using a reliability measure each data constraint is appropriately normalized to obtain an approximate minimum distance of the data point to the linear flow equation constraint instead of the conventional linear flow constraint these modifications lead to robust and accurate optical flow estimation we propose an incomplete cholesky preconditioned conjugate gradient algorithm to solve the resulting large and sparse linear system efficiently our ssd based regularization method uses a normalized ssd measure based on a similar reasoning as in the gradient based scheme as the data constraint in a regularization framework the nonlinear conjugate gradient algorithm in conjunction with an incomplete cholesky preconditioning is developed to solve the resulting nonlinear minimization problem experimental results on synthetic and real image sequences for these two algorithms are given to demonstrate their performance in comparison with competing methods reported in literature

physically consistent and efficient variational denoising of image fluid flow estimates imaging plays an important role in experimental fluid dynamics it is equally important both for scientific research and a range of industrial applications it is known however that estimated velocity fields of fluids often suffer from various types of corruptions like missing data for instance that make their physical interpretation questionable we present an algorithm that accepts a wide variety of corrupted 2 d vector fields as input data and allows to recover missing data fragments and to remove noise in a physically plausible way our approach essentially exploits the physical properties of incompressible fluid flows and does not rely upon any particular model of noise as a result the developed algorithm performs well and robust for different types of noise and estimation errors the computational algorithm is sufficiently simple to scale up to large 3 d problems

fuzzy invariant subgroups and fuzzy ideals abstract the purpose of this paper is to introduce some basic concepts of fuzzy algebra as fuzzy invariant subgroups fuzzy ideals and to prove some fundamental properties in particular it will give a characteristic of a field by a fuzzy ideal

multi class pairwise linear dimensionality reduction using heteroscedastic schemes linear dimensionality reduction ldr techniques have been increasingly important in pattern recognition pr due to the fact that they permit a relatively simple mapping of the problem onto a lower dimensional subspace leading to simple and computationally efficient classification strategies although the field has been well developed for the two class problem the corresponding issues encountered when dealing with multiple classes are far from trivial in this paper we argue that as opposed to the traditional ldr multi class schemes if we are dealing with multiple classes it is not expedient to treat it as a multi class problem per se rather we shall show that it is better to treat it as an ensemble of chernoff based two class reductions onto different subspaces whence the overall solution is achieved by resorting to either voting weighting or to a decision tree strategy the experimental results obtained on benchmark datasets demonstrate that the proposed methods are not only efficient but that they also yield accuracies comparable to that obtained by the optimal bayes classifier

motion estimation for dynamic texture videos based on locally and globally varying models motion estimation i e optical flow of fluid like and dynamic texture dt images videos is an important challenge particularly for understanding outdoor scene changes created by objects and or natural phenomena most optical flow models use smoothness based constraints using terms such as fluidity from the fluid dynamics framework with constraints typically being incompressibility and low reynolds numbers re such constraints are assumed to impede the clear capture of locally abrupt image intensity and motion changes i e discontinuities and or high re over time this paper exploits novel physics based optical flow models constraints for both smooth and discontinuous changes using a wave generation theory that imposes no constraint on re or compressibility of an image sequence iterated two step optimization between local and global optimization is also used first an objective function with varying multiple sine cosine bases with new local image properties i e orientation and frequency and with a novel transformed dispersion relationship equation are used second the statistical property of image features is used to globally optimize model parameters experiments on synthetic and real dt image sequences with smooth and discontinuous motions demonstrate that the proposed locally and globally varying models outperform the previous optical flow models

optimizing controllability of complex networks by minimum structural perturbations to drive a large complex networked dynamical system toward some desired state using as few external signals as possible is a fundamental issue in the emerging field of controlling complex networks optimal control is referred to the situation where such a network can be fully controlled using only one driving signal we propose a general approach to optimizing the controllability of complex networks by judiciously perturbing the network structure the principle of our perturbation method is validated theoretically and demonstrated numerically for homogeneous and heterogeneous random networks and for different types of real networks as well the applicability of our method is discussed in terms of the relative costs of establishing links and imposing external controllers besides the practical usage of our approach its implementation elucidates interestingly the intricate relationship between certain structural properties of the network and its controllability

tracking monotonically advancing boundaries in image sequences using graph cuts and recursive kernel shape priors we introduce a probabilistic computer vision technique to track monotonically advancing boundaries of objects within image sequences our method incorporates a novel technique for including statistical prior shape information into graph cut based segmentation with the aid of a majorization minimization algorithm extension of segmentation from single images to image sequences then follows naturally using sequential bayesian estimation our methodology is applied to two unrelated sets of real biomedical imaging data and a set of synthetic images our results are shown to be superior to manual segmentation

graph cuts and efficient n d image segmentation combinatorial graph cut algorithms have been successfully applied to a wide range of problems in vision and graphics this paper focusses on possibly the simplest application of graph cuts segmentation of objects in image data despite its simplicity this application epitomizes the best features of combinatorial graph cuts methods in vision global optima practical efficiency numerical robustness ability to fuse a wide range of visual cues and constraints unrestricted topological properties of segments and applicability to n d problems graph cuts based approaches to object extraction have also been shown to have interesting connections with earlier segmentation methods such as snakes geodesic active contours and level sets the segmentation energies optimized by graph cuts combine boundary regularization with region based properties in the same fashion as mumford shah style functionals we present motivation and detailed technical description of the basic combinatorial optimization framework for image segmentation via s t graph cuts after the general concept of using binary graph cut algorithms for object segmentation was first proposed and tested in boykov and jolly 2001 this idea was widely studied in computer vision and graphics communities we provide links to a large number of known extensions based on iterative parameter re estimation and learning multi scale or hierarchical approaches narrow bands and other techniques for demanding photo video and medical applications

computing optical flow with physical models of brightness variation although most optical flow techniques presume brightness constancy it is well known that this constraint is often violated producing poor estimates of image motion this paper describes a generalized formulation of optical flow estimation based on models of brightness variations that are caused by time dependent physical processes these include changing surface orientation with respect to a directional illuminant motion of the illuminant and physical models of heat transport in infrared images with these models we simultaneously estimate the 2d image motion and the relevant physical parameters of the brightness change model the estimation problem is formulated using total least squares with confidence bounds on the parameters experiments in four domains with both synthetic and natural inputs show how this formulation produces superior estimates of the 2d image motion

bayesian estimation of turbulent motion based on physical laws describing the multiscale structure of turbulent flows this paper proposes a regularizer for fluid motion estimation from an image sequence regularization is achieved by imposing some scale invariance property between histograms of motion increments computed at different scales by reformulating this problem from a bayesian perspective an algorithm is proposed to jointly estimate motion regularization hyperparameters and to select the most likely physical prior among a set of models hyperparameter and model inference are conducted by posterior maximization obtained by marginalizing out non gaussian motion variables the bayesian estimator is assessed on several image sequences depicting synthetic and real turbulent fluid flows results obtained with the proposed approach exceed the state of the art results in fluid flow estimation

discriminative metric preservation for tracking low resolution targets tracking low resolution lr targets is a practical yet quite challenging problem in real video analysis applications lack of discriminative details in the visual appearance of the lr target leads to the matching ambiguity which confronts most existing tracking methods although artificially enhancing the video resolution by superresolution sr techniques before analyzing might be an option the high demand of computational cost can hardly meet the requirements of the tracking scenario this paper presents a novel solution to track lr targets without explicitly performing sr this new approach is based on discriminative metric preservation that preserves the data affinity structure in the high resolution hr feature space for effective and efficient matching of lr images in addition we substantialize this new approach in a solid case study of differential tracking under metric preservation and derive a closed form solution to motion estimation for lr video in addition this paper extends the basic linear metric preservation method to a more powerful nonlinear kernel metric preservation method such a solution to lr target tracking is discriminative robust and efficient extensive experiments validate the entrustments and effectiveness of the proposed approach and demonstrate the improved performance of the proposed method in tracking lr targets

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

simultaneous higher order optical flow estimation and decomposition we study the estimation and decomposition of optical flows from highly nonrigid motions to this end recent methods from image decomposition into structural and textural parts are combined with variational optical flow estimation the approaches we suggest amount to minimizing discrete convex functionals using second order cone programming higher order regularization is necessary in order to accurately recover important flow structure like vortices and to incorporate key physical properties such as vanishing divergence for proper discretization we apply the finite mimetic difference method which preserves the identities fulfilled by the continuous differential operators numerical examples demonstrate the feasibility of the complex approaches

scaling and percolation in the small world network model in this paper we study the small world network model of watts and strogatz which mimics some aspects of the structure of networks of social interactions we argue that there is one nontrivial length scale in the model analogous to the correlation length in other systems which is well defined in the limit of infinite system size and which diverges continuously as the randomness in the network tends to zero giving a normal critical point in this limit this length scale governs the crossover from large to small world behavior in the model as well as the number of vertices in a neighborhood of given radius on the network we derive the value of the single critical exponent controlling behavior in the critical region and the finite size scaling form for the average vertex vertex distance on the network and using series expansion and pad e approximants find an approximate analytic form for the scaling function we calculate the effective dimension of small world graphs and show that this dimension varies as a function of the length scale on which it is measured in a manner reminiscent of multifractals we also study the problem of site percolation on small world networks as a simple model of disease propagation and derive an approximate expression for the percolation probability at which a giant component of connected vertices first forms in epidemiological terms the point at which an epidemic occurs the typical cluster radius satisfies the expected finite size scaling form with a cluster size exponent close to that for a random graph all our analytic results are confirmed by extensive numerical simulations of the model

bayesian inference of models and hyperparameters for robust optical flow estimation selecting optimal models and hyperparameters is crucial for accurate optical flow estimation this paper provides a solution to the problem in a generic bayesian framework the method is based on a conditional model linking the image intensity function the unknown velocity field hyperparameters and the prior and likelihood motion models inference is performed on each of the three levels of this so defined hierarchical model by maximization of marginalized a posteriori probability distribution functions in particular the first level is used to achieve motion estimation in a classical a posteriori scheme by marginalizing out the motion variable the second level enables to infer regularization coefficients and hyperparameters of non gaussian m estimators commonly used in robust statistics the last level of the hierarchy is used for selection of the likelihood and prior motion models conditioned to the image data the method is evaluated on image sequences of fluid flows and from the middlebury database experiments prove that applying the proposed inference strategy yields better results than manually tuning smoothing parameters or discontinuity preserving cost functions of the state of the art methods

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

fuzzy congruences and fuzzy normal subgroups abstract a complete description of the congruences on a group in terms of its normal subgroups can be seen in papers by a rosenfeld and w j howie in this paper we shall introduce the concept of fuzzy congruences on a groupoid and a group and characterize fuzzy congruences on a group in terms of fuzzy normal subgroups

optical flow and advection on 2 riemannian manifolds a common framework dynamic pattern analysis and motion extraction can be efficiently addressed using optical flow techniques this paper presents a generalization of these questions to nonflat surfaces where optical flow is tackled through the problem of evolution processes on non euclidean domains the classical equations of optical flow in the euclidean case are transposed to the theoretical framework of differential geometry we adopt this formulation for the regularized optical flow problem prove its mathematical well posedness and combine it with the advection equation the optical flow and advection problems are dual a motion field may be retrieved from some scalar evolution using optical flow conversely a scalar field may be deduced from a velocity field using advection these principles are illustrated with qualitative and quantitative evaluations from numerical simulations bridging both approaches the proof of concept is further demonstrated with preliminary results from time resolved functional brain imaging data where organized propagations of cortical activation patterns are evidenced using our approach

kernel density estimation and intrinsic alignment for shape priors in level set segmentation in this paper we make two contributions to the field of level set based image segmentation firstly we propose shape dissimilarity measures on the space of level set functions which are analytically invariant under the action of certain transformation groups the invariance is obtained by an intrinsic registration of the evolving level set function in contrast to existing approaches to invariance in the level set framework this closed form solution removes the need to iteratively optimize explicit pose parameters the resulting shape gradient is more accurate in that it takes into account the effect of boundary variation on the object s pose secondly based on these invariant shape dissimilarity measures we propose a statistical shape prior which allows to accurately encode multiple fairly distinct training shapes this prior constitutes an extension of kernel density estimators to the level set domain in contrast to the commonly employed gaussian distribution such nonparametric density estimators are suited to model aribtrary distributions we demonstrate the advantages of this multi modal shape prior applied to the segmentation and tracking of a partially occluded walking person in a video sequence and on the segmentation of the left ventricle in cardiac ultrasound images we give quantitative results on segmentation accuracy and on the dependency of segmentation results on the number of training shapes