reach controllability of single input affine systems on a simplex we study the reach control problem rcp for a single input affine system with a simplicial state space we extend previous results by exploring arbitrary triangulations of the state space particularly allowing the set of possible equilibria to intersect the interior of simplices in the studied setting it is shown that closed loop equilibria nevertheless only arise on the boundary of simplices this allows to define a notion of reach controllability which quantifies the effect of the control input on boundary equilibria using reach controllability we obtain necessary and sufficient conditions for solvability of rcp by affine feedback

necessary and sufficient conditions for reachability on a simplex in this paper we solve the general problem of designing a feedback controller to reach a set of facets of an n dimensional simplex in finite time for a system evolving with linear affine dynamics necessary and sufficient conditions are presented in the form of bilinear inequalities on the vertices of the simplex by exploiting the structure of the problem the bilinear inequalities are converted to a series of linear programming problems

a region and gradient based active contour model and its application in boundary tracking on anal canal ultrasound images a novel gaussian mixture model gmm based region and gradient active contour model is proposed for general object boundary tracking and the purpose of boundary tracking for anal muscle layers motion information is extracted from adjacent slice and is used to guide the first step of boundary tracking procedure the idea is that gmm is introduced into the statistical feature computation for object region and background region thereby providing an accurate model for regional pixel intensity description expectation maximization algorithm and k means algorithm are used for parameter solutions of gmm based on the available region information gradient information and the self constraints of the contour a unifying active contour model is proposed the proposed active contour models and tracking algorithm were tested on synthetic images and simulated ultrasound images to evaluate some generic features of the model for boundary tracking furthermore it was applied to perform boundary tracking of anal muscle layers the tracking results were evaluated by three experts the results showed that the proposed method has a good performance for boundary tracking on anal wall ultrasound image

tracking deformable objects in the plane using an active contour model the problems of segmenting a noisy intensity image and tracking a nonrigid object in the plane are discussed in evaluating these problems a technique based on an active contour model commonly called a snake is examined the technique is applied to cell locomotion and tracking studies the snake permits both the segmentation and tracking problems to be simultaneously solved in constrained cases a detailed analysis of the snake model emphasizing its limitations and shortcomings is presented and improvements to the original description of the model are proposed problems of convergence of the optimization scheme are considered in particular an improved terminating criterion for the optimization scheme that is based on topographic features of the graph of the intensity image is proposed hierarchical filtering methods as well as a continuation method based on a discrete sale space representation are discussed results for both segmentation and tracking are presented possible failures of the method are discussed

reach control on simplices by continuous state feedback this paper studies a theoretical problem of whether continuous state feedback and affine feedback are equivalent from the point of view of making an affine system defined on a simplex reach a prespecified facet in finite time we show that the two classes of feedbacks are equivalent as a byproduct new necessary and sufficient conditions for solvability based more directly on the problem data are obtained

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

ltl receding horizon control for finite deterministic systems this paper considers receding horizon control of finite deterministic systems which must satisfy a high level rich specification expressed as a linear temporal logic formula under the assumption that time varying rewards are associated with states of the system and these rewards can be observed in real time the control objective is to maximize the collected reward while satisfying the high level task specification in order to properly react to the changing rewards a controller synthesis framework inspired by model predictive control is proposed where the rewards are locally optimized at each time step over a finite horizon and the optimal control computed for the current time step is applied by enforcing appropriate constraints the infinite trajectory produced by the controller is guaranteed to satisfy the desired temporal logic formula simulation results demonstrate the effectiveness of the approach

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

using dynamic programming for solving variational problems in vision dynamic programming is discussed as an approach to solving variational problems in vision dynamic programming ensures global optimality of the solution is numerically stable and allows for hard constraints to be enforced on the behavior of the solution within a natural and straightforward structure as a specific example of the approach s efficacy applying dynamic programming to the energy minimizing active contours is described the optimization problem is set up as a discrete multistage decision process and is solved by a time delayed discrete dynamic programming algorithm a parallel procedure for decreasing computational costs is discussed

spatiotemporal motion boundary detection and motion boundary velocity estimation for tracking moving objects with a moving camera a level sets pdes approach with concurrent camera motion compensation the purpose of this study is to investigate a method of tracking moving objects with a moving camera this method estimates simultaneously the motion induced by camera movement the problem is formulated as a bayesian motion based partitioning problem in the spatiotemporal domain of the image sequence an energy functional is derived from the bayesian formulation the euler lagrange descent equations determine simultaneously an estimate of the image motion field induced by camera motion and an estimate of the spatiotemporal motion boundary surface the euler lagrange equation corresponding to the surface is expressed as a level set partial differential equation for topology independence and numerically stable implementation the method can be initialized simply and can track multiple objects with nonsimultaneous motions velocities on motion boundaries can be estimated from geometrical properties of the motion boundary several examples of experimental verification are given using synthetic and real image sequences

on the oscillatory behavior of solutions of second order differential equations a generalized nonlinear second order differential equation is considered oscillation and nonoscillation criteria are given

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

oscillation theorems for certain nonlinear differential equations of second order abstract we present new oscillation criteria for the second order nonlinear differential equations these criteria involve the use of averaging functions our theorems are stated in general form they complement and extend related results known in the literature also the relevance of our results is to show that some of manojlovic s results contain the superfluous condition

linear systems with state and control constraints the theory and application of maximal output admissible sets the initial state of an unforced linear system is output admissible with respect to a constraint set y if the resulting output function satisfies the pointwise in time condition y t in y t or 0 the set of all possible such initial conditions is the maximal output admissible set o sub infinity the properties of o sub infinity and its characterization are investigated in the discrete time case it is generally possible to represent o sub infinity or a close approximation of it by a finite number of functional inequalities practical algorithms for generating the functions are described in the continuous time case simple representations of the maximal output admissible set are not available however it is shown that the discrete time results may be used to obtain approximate representations

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

embedding gestalt laws in markov random fields the goal of this paper is to study a mathematical framework of 2d object shape modeling and learning for middle level vision problems such as image segmentation and perceptual organization for this purpose we pursue generic shape models which characterize the most common features of 2d object shapes in this paper shape models are learned from observed natural shapes based on a minimax entropy learning theory the learned shape models are gibbs distributions defined on markov random fields mrfs the neighborhood structures of these mrfs correspond to gestalt laws colinearity cocircularity proximity parallelism and symmetry thus both contour based and region based features are accounted for stochastic markov chain monte carlo mcmc algorithms are proposed for learning and model verification furthermore this paper provides a quantitative measure for the so called nonaccidental statistics and thus justifies some empirical observations of gestalt psychology by information theory our experiments also demonstrate that global shape properties can arise from interactions of local features

signal matching through scale space given a collection of similar signals that have been deformed with respect to each other the general signal matching problem is to recover the deformation we formulate the problem as the minimization of an energy measure that combines a smoothness term and a similarity term the minimization reduces to a dynamic system governed by a set of coupled first order differential equations the dynamic system finds an optimal solution at a coarse scale and then tracks it continuously to a fine scale among the major themes in recent work on visual signal matching have been the notions of matching as constrained optimization of variational surface reconstruction and of coarse to fine matching our solution captures these in a precise succinct and unified form results are presented for one dimensional signals a motion sequence and a stereo pair

affine and projective active contour models we investigate the evolution of active contours in terms of progressive modification of an initial contour following the chosen lie group of object to image transformations because of non fronto parallel viewing of an object or due to relative motion between the camera and the object the resultant image may undergo affine or projective object to image transformations in a recent paper we have shown that in the case of object tracking frame to frame deformations of an initial curve obtained through euler lagrange descent equations of a curve functional can be used to enact a desired lie group of plane transformations a r mansouri d p mukherjee s t acton constraining active contour evolution via lie groups of transformation ieee trans image process 13 2004 853 863 in this work we propose an energy functional that encodes the lie group transformation parameters which in turn guide shape distortion due to oblique viewing additional constraints such as transformation smoothness are imposed on the active contour by modifying the energy functional the functional is minimized using numerical schemes similar to the conjugate gradient technique and the convergence properties are discussed the success of the technique for affine and projective scenes is demonstrated with both synthetic and real image examples and compared with the related approaches

texture decomposition by harmonics extraction from higher order statistics in this paper a method of harmonics extraction from higher order statistics hos is developed for texture decomposition we show that the diagonal slice of the fourth order cumulants is proportional to the autocorrelation of a related noiseless sinusoidal signal with identical frequencies we propose to use this fourth order cumulants slice to estimate a power spectrum from which the harmonic frequencies can be easily extracted hence a texture can be decomposed into deterministic components and indeterministic components as in a unified texture model through a wold like decomposition procedure the simulation and experimental results demonstrated that this method is effective for texture decomposition and it performs better than traditional lower order statistics based decomposition methods

constraining active contour evolution via lie groups of transformation we present a novel approach to constraining the evolution of active contours used in image analysis the proposed approach constrains the final curve obtained at convergence of curve evolution to be related to the initial curve from which evolution begins through an element of a desired lie group of plane transformations constraining curve evolution in such a way is important in numerous tracking applications where the contour being tracked in a certain frame is known to be related to the contour in the previous frame through a geometric transformation such as translation rotation or affine transformation for example it is also of importance in segmentation applications where the region to be segmented is known up to a geometric transformation our approach is based on suitably modifying the euler lagrange descent equations by using the correspondence between lie groups of plane actions and their lie algebras of infinitesimal generators and thereby ensures that curve evolution takes place on an orbit of the chosen transformation group while remaining a descent equation of the original functional the main advantage of our approach is that it does not necessitate any knowledge of nor any modification to the original curve functional and is extremely straightforward to implement our approach therefore stands in sharp contrast to other approaches where the curve functional is modified by the addition of geometric penalty terms we illustrate our algorithm on numerous real and synthetic examples

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

regularization of inverse visual problems involving discontinuities inverse problems such as the reconstruction problems that arise in early vision tend to be mathematically ill posed through regularization they may be reformulated as well posed variational principles whose solutions are computable standard regularization theory employs quadratic stabilizing functionals that impose global smoothness constraints on possible solutions discontinuities present serious difficulties to standard regularization however since their reconstruction requires a precise spatial control over the smoothing properties of stabilizers this paper proposes a general class of controlled continuity stabilizers which provide the necessary control over smoothness these nonquadratic stabilizing functionals comprise multiple generalized spline kernels combined with noncontinuous continuity control functions in the context of computational vision they may be thought of as controlled continuity constraints these generic constraints are applicable to visual reconstruction problems that involve both continuous regions and discontinuities for which global smoothness constraints fail

a real time algorithm for the approximation of level set based curve evolution in this paper we present a complete and practical algorithm for the approximation of level set based curve evolution suitable for real time implementation in particular we propose a two cycle algorithm to approximate level set based curve evolution without the need of solving partial differential equations pdes our algorithm is applicable to a broad class of evolution speeds that can be viewed as composed of a data dependent term and a curve smoothness regularization term we achieve curve evolution corresponding to such evolution speeds by separating the evolution process into two different cycles one cycle for the data dependent term and a second cycle for the smoothness regularization the smoothing term is derived from a gaussian filtering process in both cycles the evolution is realized through a simple element switching mechanism between two linked lists that implicitly represents the curve using an integer valued level set function by careful construction all the key evolution steps require only integer operations a consequence is that we obtain significant computation speedups compared to exact pde based approaches while obtaining excellent agreement with these methods for problems of practical engineering interest in particular the resulting algorithm is fast enough for use in real time video processing applications which we demonstrate through several image segmentation and video tracking experiments

oscillation criteria for second order functional differential equations in this paper oscillation criteria for general second order functional differential equations are given integral criterion for oscillation using recent nth primitive method introduced by cheh chih yeh is considered

symmetry seeking models and 3d object reconstruction we propose models of 3d shape which may be viewed as deformable bodies composed of simulated elastic material in contrast to traditional purely geometric models of shape deformable models are active their shapes change in response to externally applied forces we develop a deformable model for 3d shape which has a preference for axial symmetry symmetry is represented even though the model does not belong to a parametric shape family such as generalized cylinders rather a symmetry seeking property is designed into internal forces that constrain the deformations of the model we develop a framework for 3d object reconstruction based on symmetry seeking models instances of these models are formed from monocular image data through the action of external forces derived from the data the forces proposed in this paper deform the model in space so that the shape of its projection into the image plane is consistent with the 2d silhouette of an object of interest the effectiveness of our approach is demonstrated using natural images

reach control on simplices by piecewise affine feedback we study the reach control problem for affine systems on simplices and the focus is on cases when the problem is not solvable by continuous state feedback we examine from a geometric viewpoint the structural properties of the system which make continuous state feedback fail this structure is encoded by so called reach control indices which are defined and developed in the paper based on these indices we propose a subdivision algorithm and associated piecewise affine feedback the method is shown to solve the reach control problem in all remaining cases assuming it is solvable by open loop controls

on oscillation of second order neutral type delay differential equations oscillation criteria are obtained by using the so called h method for the second order neutral type delay differential equations of the form r t j x t z t q t f x s t 0 t t 0 where z t x t p t x t t r p q t s c t 0 r and f email protected c r r the results of the paper contains several results obtained previously as special cases furthermore we are also able to fix an error in a recent paper related to the oscillation of second order nonneutral delay differential equations

multiple motion segmentation with level sets segmentation of motion in an image sequence is one of the most challenging problems in image processing while at the same time one that finds numerous applications to date a wealth of approaches to motion segmentation have been proposed many of them suffer from the local nature of the models used global models such as those based on markov random fields perform in general better in this paper we propose a new approach to motion segmentation that is based on a global model the novelty of the approach is twofold first inspired by recent work of other researchers we formulate the problem as that of region competition but we solve it using the level set methodology the key features of a level set representation as compared to active contours often used in this context are its ability to handle variations in the topology of the segmentation and its numerical stability the second novelty of the paper is the formulation in which unlike in many other motion segmentation algorithms we do not use intensity boundaries as an accessory the segmentation is purely based on motion this permits accurate estimation of motion boundaries of an object even when its intensity boundaries are hardly visible since occasionally intensity boundaries may prove beneficial we extend the formulation to account for the coincidence of motion and intensity boundaries in addition we generalize the approach to multiple motions we discuss possible discretizations of the evolution pde equations and we give details of an initialization scheme so that the results could be duplicated we show numerous experimental results for various formulations on natural images with either synthetic or natural motion

a topological obstruction in a control problem abstract one of the important discoveries in control theory is a topological obstruction to continuous feedback stabilization for general nonlinear control systems in this note we describe another topological obstruction arising from a very different control problem called the reach control problem motivated by a classical topological obstruction for extending continuous maps on spheres we introduce the problem of extending continuous maps on simplices it is shown that the same condition as in the sphere case gives rise to the obstruction

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

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

geometrically induced force interaction for three dimensional deformable models in this paper we propose a novel 3 d deformable model that is based upon a geometrically induced external force field which can be conveniently generalized to arbitrary dimensions this external force field is based upon hypothesized interactions between the relative geometries of the deformable model and the object boundary characterized by image gradient the evolution of the deformable model is solved using the level set method so that topological changes are handled automatically the relative geometrical configurations between the deformable model and the object boundaries contribute to a dynamic vector force field that changes accordingly as the deformable model evolves the geometrically induced dynamic interaction force has been shown to greatly improve the deformable model performance in acquiring complex geometries and highly concave boundaries and it gives the deformable model a high invariancy in initialization configurations the voxel interactions across the whole image domain provide a global view of the object boundary representation giving the external force a long attraction range the bidirectionality of the external force field allows the new deformable model to deal with arbitrary cross boundary initializations and facilitates the handling of weak edges and broken boundaries in addition we show that by enhancing the geometrical interaction field with a nonlocal edge preserving algorithm the new deformable model can effectively overcome image noise we provide a comparative study on the segmentation of various geometries with different topologies from both synthetic and real images and show that the proposed method achieves significant improvements against existing image gradient techniques

linearized control systems and applications to smooth stabilization for a control system dot x f x u the author proves that for generic feedback laws u such that f x u x does not vanish the linearized control systems around the trajectories of dot x f x u x have the same strong accessibility algebra as f applications are given to the smooth stabilization problem

tracking pylorus in ultrasonic image sequences with edge based optical flow tracking pylorus in ultrasonic image sequences is an important step in the analysis of duodenogastric reflux dgr we propose a joint prediction and segmentation method jps which combines optical flow with active contour to track pylorus the goal of the proposed method is to improve the pyloric tracking accuracy by taking account of not only the connection information among edge points but also the spatio temporal information among consecutive frames the proposed method is compared with other four tracking methods by using both synthetic and real ultrasonic image sequences several numerical indexes hausdorff distance hd average distance ad mean edge distance med and edge curvature ec have been calculated to evaluate the performance of each method jps achieves the minimum distance metrics hd ad and med and a smaller ec the experimental results indicate that jps gives a better tracking performance than others by the best agreement with the gold curves while keeping the smoothness of the result

on the controllability of switching linear systems this note presents a necessary and sufficient condition for small time controllability of a linear switching system that is a collection of linear time invariant control systems where a trajectory is any concatenation of trajectories of the individual systems this result extends the controllability condition recently obtained for unconstrained linear switching systems to the case of control which is constrained in a cone

improving performance of distribution tracking through background mismatch this paper proposes a new density matching method based on background mismatching for tracking of nonrigid moving objects the new tracking method extends the idea behind the original density matching tracker which tracks an object by finding a contour in which the photometric density sampled from the enclosed region most closely matches a model density this method can be quite sensitive to the initial curve placements and model density the new method eliminates these sensitivities by adding a second term to the optimization the mismatch between the model density and the density sampled from the background by maximizing this term the tracking algorithm becomes significantly more robust in practice furthermore we show the enhanced ability of the algorithm to deal with target objects which possess smooth or diffuse boundaries the tracker is in the form of a partial differential equation and is implemented using the level set framework experiments on synthesized images and real video sequences show our proposed methods are effective and robust the results are compared with several existing methods

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

admissible sets and feedback control for discrete time linear dynamical systems with bounded controls and states for linear discrete time dynamical systems necessary and sufficient conditions are given for a control sequence belonging to a polyhedral constraint set to stabilize the system under the condition that the state is restricted to a polyhedral state constraint set a variable structure linear state feedback controller given in terms of the controls at the vertices of the polyhedral state constraint set is presented

level set methods an overview and some recent results the level set method was devised by s osher and j a sethian 1988 j comput phys 79 12 49 as a simple and versatile method for computing and analyzing the motion of an interface in two or three dimensions bounds a possibly multiply connected region the goal is to compute and analyze the subsequent motion of under a velocity field v this velocity can depend on position time the geometry of the interface and the external physics the interface is captured for later time as the zero level set of a smooth at least lipschitz continuous function x t i e t x x t 0 is positive inside negative outside and is zero on t topological merging and breaking are well defined and easily performed in this review article we discuss recent variants and extensions including the motion of curves in three dimensions the dynamic surface extension method fast methods for steady state problems diffusion generated motion and the variational level set approach we also give a user s guide to the level set dictionary and technology and couple the method to a wide variety of problems involving external physics such as compressible and incompressible possibly reacting flow stefan problems kinetic crystal growth epitaxial growth of thin films vortex dominated flows and extensions to multiphase motion we conclude with a discussion of applications to computer vision and image processing

time varying affine feedback for reach control on simplices abstract we study the reach control problem for affine systems on simplices and the focus is on cases when it is known that the problem is not solvable by continuous state feedback in previous work we used the reach control indices to construct a discontinuous piecewise affine control that solves the problem here we investigate the extent to which time varying feedbacks can be used a simple time varying affine feedback is proposed and shown to solve the problem

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

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

constrained approximate controllability in the paper constrained approximate controllability for linear dynamical systems described by abstract differential equations with unbounded control operator is considered using methods of spectral analysis for linear self adjoint operators and general constrained controllability results given by son 1990 necessary and sufficient conditions of the constrained approximate controllability for the piecewise polynomial controls with values in a given cone are formulated and proved moreover as illustrative examples constrained approximate boundary controllability of one dimensional distributed parameter dynamical systems described by partial differential equations of parabolic type with dirichlet and neumann boundary conditions are investigated the constrained controllability conditions obtained in the paper represent an extension of the unconstrained controllability results given by glothin 1974 and klamka 1991

finding trajectories of feature points in a monocular image sequence identifying the same physical point in more than one image the correspondence problem is vital in motion analysis most research for establishing correspondence uses only two frames of a sequence to solve this problem by using a sequence of frames it is possible to exploit the fact that due to inertia the motion of an object cannot change instantaneously by using smoothness of motion it is possible to solve the correspondence problem for arbitrary motion of several nonrigid objects in a scene we formulate the correspondence problem as an optimization problem and propose an iterative algorithm to find trajectories of points in a monocular image sequence a modified form of this algorithm is useful in case of occlusion also we demonstrate the efficacy of this approach considering synthetic laboratory and real scenes

bittracker a bitmap tracker for visual tracking under very general conditions this paper addresses the problem of visual tracking under very general conditions a possibly non rigid target whose appearance may drastically change over time general camera motion a 3d scene and no a priori information except initialization this is in contrast to the vast majority of trackers which rely on some limited model in which for example the target s appearance is known a priori or restricted the scene is planar or a pan tilt zoom camera is used their goal is to achieve speed and robustness but their limited context may cause them to fail in the more general case the proposed tracker works by approximating in each frame a pdf probability distribution function of the target s bitmap and then estimating the maximum a posteriori bitmap the pdf is marginalized over all possible motions per pixel thus avoiding the stage in which optical flow is determined this is an advantage over other general context trackers that do not use the motion cue at all or rely on the error prone calculation of optical flow using a gibbs distribution with respect to the first order neighborhood system yields a bitmap pdf whose maximization may be transformed into that of a quadratic pseudo boolean function the maximum of which is approximated via a reduction to a maximum flow problem many experiments were conducted to demonstrate that the tracker is able to track under the aforementioned general context

oscillation and nonoscillation criteria for second order nonlinear differential equations i abstract a second order nonlinear differential equation is considered oscillation and nonoscillation criteria are given

an obstruction to solvability of the reach control problem using affine feedback this paper studies the reach control problem rcp using affine feedback on simplices the contributions of this paper are threefold first we identify a new obstruction to solvability of the rcp using affine feedback and provide necessary and sufficient conditions for occurrence of such an obstruction second for two input systems these conditions are formulated in terms of scalar linear inequalities third computationally efficient necessary conditions are proposed for checking the obstruction for multi input systems as feasibility programs in terms of linear inequalities in contrast to the previous work in the literature no assumption is imposed on the set of possible equilibria so the results are applicable to the general rcp

reachability and control synthesis for piecewise affine hybrid systems on simplices in this paper we consider the synthesis of control laws for piecewise affine hybrid systems on simplices the construction is based on the solution to the control to facet problem at the continuous level and on dynamic programming at the discrete level the construction is given as an explicit algorithm using only linear algebra and reach set computations for automata no numerical integration is required the method is conservative in that it may fail to find a control law where one exists but one cannot hope for a sharp algorithm for control synthesis since reachability for piecewise affine hybrid systems is undecidable

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

detection and segmentation of generic shapes based on affine modeling of energy in eigenspace this paper presents a novel approach for detection and segmentation of man made generic shapes in cluttered images the set of shapes to be detected are members of affine transformed versions of basic geometric shapes such as rectangles circles etc the shape set is represented by its vectorial edge map transformed over a wide range of affine parameters we use vectorial boundary instead of regular boundary to improve the robustness to noise background clutter and partial occlusion our approach consists of a detection stage and a verification stage in the detection stage we first derive the energy from the principal eigenvectors of the set next an a posteriori probability map of energy distribution is computed from the projection of the edge map representation in a vectorial eigen space local peaks of the posterior probability map are located and indicate candidate detections we use energy probability based detection since we find that the underlying distribution is not gaussian and resembles a hypertoroid in the verification stage each candidate is verified using a fast search algorithm based on a novel representation in angle space and the corresponding pose information of the detected shape is obtained the angular representation used in the verification stage yields better results than a euclidean distance representation experiments are performed in various interfering distortions and robust detection and segmentation are achieved

a variational approach for the segmentation of the left ventricle in cardiac image analysis in this paper we propose a level set method to segment mr cardiac images our approach is based on a coupled propagation of two cardiac contours and integrates visual information with anatomical constraints the visual information is expressed through a gradient vector flow based boundary component and a region term that aims at best separating the cardiac contours regions according to their global intensity properties in order to deal with misleading visual support an anatomical constraint is considered that couples the propagation of the cardiac contours according to their relative distance the resulting motion equations are implemented using a level set approach and a fast and stable numerical approximation scheme the additive operator splitting encouraging experimental results are provided using real data