tangent bundle elastica and computer vision visual curve completion an early visual process that completes the occluded parts between observed boundary fragments a k a inducers is a major problem in perceptual organization and a critical step toward higher level visual tasks in both biological and machine vision most computational contributions to solving this problem suggest desired perceptual properties that the completed contour should satisfy in the image plane and then seek the mathematical curves that provide them alternatively few studies including by the authors have suggested to frame the problem not in the image plane but rather in the unit tangent bundler 2 s 1 the space that abstracts the primary visual cortex where curve completion allegedly occurs combining both schools here we propose and develop a biologically plausible theory of elastica in the tangent bundle that provides not only perceptually superior completion results but also a rigorous computational prediction that inducer curvatures greatly affects the shape of the completed curve as indeed indicated by human perception

controlling chaos and deterministic directed transport in inertia ratchets using backstepping control we address the problem of controlling chaotic motion and deterministic directed transport in inertia ratchets we employ a recursive backstepping nonlinear control technique to control intermittent chaos and then track a desired trajectory by means of the same technique for the parameter regime where two non identical attractors coexist in phase space we propose a new backstepping control scheme that is capable of controlling the directed transport exhibited by these attractors numerical simulations show that the controllers are singularity free and the closed loop systems are globally stable

global detection of salient convex boundaries as an important geometric property of many structures or structural components convexity plays an important role in computer vision and image understanding in this paper we describe a general approach that can force various edge grouping algorithms to detect only convex structures from a set of boundary fragments the basic idea is to remove some fragments and fragment connections so that on the remaining ones a prototype edge grouping algorithm that detects closed boundaries without the convexity constraint can only produce convex closed boundaries we show that this approach takes polynomial time and preserves the grouping optimality by not excluding any valid convex boundary from the search space choosing the recently developed ratio contour algorithm as the prototype grouping algorithm we develop a new convex grouping algorithm which can detect convex salient boundaries with good continuity and proximity in a globally optimal fashion to facilitate the application of this convex grouping algorithm we develop a new fragment connection method based on four point bezier curves we demonstrate the performance of this convex grouping algorithm by conducting experiments on both synthetic and real images in addition we provide a comparison with some prior edge grouping algorithms finally we show that the proposed convex grouping algorithm can be further extended to detect convex open boundaries derive region based image hierarchies and incorporate some simple human computer interactions

completion energies and scale the detection of smooth curves in images and their completion over gaps are two important problems in perceptual grouping we examine the notion of completion energy of curve elements showing and exploiting its intrinsic dependence on length and width scales we introduce a fast method for computing the most likely completion between two elements by developing novel analytic approximations and a fast numerical procedure for computing the curve of least energy we then use our newly developed energies to find the most likely completions in images through a generalized summation of induction fields this is done through multiscale procedures i e separate processing at different scales with some interscale interactions such procedures allow the summation of all induction fields to be done in a total of only o n log n operations where n is the number of pixels in the image more important such procedures yield a more realistic dependence of the induction field on the length and width scales the field of a long element is very different from the sum of the fields of its composing short segments

stochastic completion fields a neural model of illusory contour shape and salience we describe an algorithm and representation level theory of illusory contour shape and salience unlike previous theories our model is derived from a single assumption that the prior probability distribution of boundary completion shape can be modeled by a random walk in a lattice whose points are positions and orientations in the image plane i e the space that one can reasonably assume is represented by neurons of the mammalian visual cortex our model does not employ numerical relaxation or other explicit minimization but instead relies on the fact that the probability that a particle following a random walk will pass through a given position and orientation on a path joining two boundary fragments can be computed directly as the product of two vector field convolutions we show that for the random walk we define the maximum likelihood paths are curves of least energy that is on average random walks follow paths commonly assumed to model the shape of illusory contours a computer model is demonstrated on numerous illusory contour stimuli from the literature

trace inference curvature consistency and curve detection an approach is described for curve inference that is based on curvature information the inference procedure is divided into two stages a trace inference stage which is the subject of the present work and a curve synthesis stage it is shown that recovery of the trace of a curve requires estimating local models for the curve at the same time and that tangent and curvature information are sufficient these make it possible to specify powerful constraints between estimated tangents to a curve in terms of a neighborhood relationship called cocircularity and between curvature estimates in terms of a curvature consistency relation because all curve information is quantized special care must be taken to obtain accurate estimates of trace points tangents and curvatures this issue is addressed specifically to the introduction of a smoothness constraint and a maximum curvature constraint the procedure is applied to two types of images artificial images designed to evaluate curvature and noise sensitivity and natural images

two theorems of generalized unsynchronization for coupled chaotic systems generalized chaos synchronization has been widely studied and many control methods have been presented but up to now no criterion has been given for generalized unsynchronization the generalized unsynchronization means that the state variables of two coupled chaotic systems cannot approach generalized synchronization in this paper we propose two theorems which give the criteria of generalized unsynchronization for two different chaotic dynamic systems with whatever large strength of linear coupling two simulated examples are also given

characterizing the distribution of completion shapes with corners using a mixture of random processes abstract we derive an analytic expression for the distribution of contours x t generated by fluctuations in x t x t t due to random impulses of two limiting types the first type are frequent but weak while the second are infrequent but strong the result has applications in computational theories of figural completion and illusory contours because it can be used to model the prior probability distribution of short smooth completion shapes punctuated by occasional discontinuities in orientation i e corners this work extends our previous work on characterizing the distribution of completion shapes which dealt only with the case of frequently acting weak impulses

the design and use of steerable filters the authors present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters allowing one to adaptively steer a filter to any orientation and to determine analytically the filter output as a function of orientation steerable filters may be designed in quadrature pairs to allow adaptive control over phase as well as orientation the authors show how to design and steer the filters and present examples of their use in the analysis of orientation and phase angularly adaptive filtering edge detection and shape from shading one can also build a self similar steerable pyramid representation the same concepts can be generalized to the design of 3 d steerable filters

learning probabilistic models for contour completion in natural images using a large set of human segmented natural images we study the statistics of region boundaries we observe several power law distributions which likely arise from both multi scale structure within individual objects and from arbitrary viewing distance accordingly we develop a scale invariant representation of images from the bottom up using a piecewise linear approximation of contours and constrained delaunay triangulation to complete gaps we model curvilinear grouping on top of this graphical geometric structure using a conditional random field to capture the statistics of continuity and different junction types quantitative evaluations on several large datasets show that our contour grouping algorithm consistently dominates and significantly improves on local edge detection

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

perceptual grouping by selection of a logically minimal model this paper presents a logic based approach to grouping and perceptual organization called minimal model theory and presents efficient methods for computing interpretations in this framework grouping interpretations are first defined as logical structures built out of atomic qualitative scene descriptors regularities that are derived from considerations of non accidentalness these interpretations can then be partially ordered by their degree of regularity or constraint measured numerically by their logical depth the genericity constraint the principle that interpretations should minimize coincidences in the observed configuration dictates that the preferred interpretation will be the minimum in this partial order i e the interpretation with maximum depth this maximum depth interpretation also called the minimal model or minimal interpretation is in a sense the simplest algebraically minimal interpretation available of the image configuration as a side effect the most salient or most structured part of the scene can be identified as the maximum depth subtree of the minimal model an efficient o n2 method for computing the minimal interpretation is presented along with examples computational experiments show that the algorithm performs well under a wide range of parameter settings

a comparison of measures for detecting natural shapes in cluttered backgrounds we propose a new measure of perceptual saliency and quantitatively compare its ability to detect natural shapes in cluttered backgrounds to five previously proposed measures as defined in the new measure the saliency of an edge is the fraction of closed random walks which contain that edge the transition probability matrix defining the random walk between edges is based on a distribution of natural shapes modeled by a stochastic motion each of the saliency measures in our comparison is a function of a set of affinity values assigned to pairs of edges although the authors of each measure define the affinity between a pair of edges somewhat differently all incorporate the gestalt principles of good continuation and proximity in some form in order to make the comparison meaningful we use a single definition of affinity and focus instead on the performance of the different functions for combining affinity values the primary performance criterion is accuracy we compute false positive rates in classifying edges as signal or noise for a large set of test figures in almost every case the new measure significantly outperforms previous measures

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

robust synchronization of chaotic systems the question of robustness of synchronization with respect to small arbitrary perturbations of the underlying dynamical systems is addressed we present examples of chaos synchronization demonstrating that normal hyperbolicity is a necessary and sufficient condition for the synchronization manifold to be smooth and persistent under small perturbations the same examples however show that in real applications normal hyperbolicity is not sufficient to give quantitative bounds for deformations of the synchronization manifold i e even in the case of normal hyperbolicity two almost identical systems may cause large synchronization errors

a bayesian multiple hypothesis approach to edge grouping and contour segmentation a contour segmentation algorithm is presented that takes an edge map and extracts continuous curves of arbitrary smoothness correctly handling curve intersections and capable of extrapolating over significant measurement gaps the algorithm incorporates noise models of the edge detection process and limited scene statistics it is based on an explicit contour model and employs a statistical distance measure to quantify the likelihood of each segmentation hypothesis a bayesian multiple hypothesis tree organizes possible segementations making it possible to postpone grouping decisions until a sufficient amount of information is available we have demonstrated its performance on real and synthetic images

steerable wedge filters for local orientation analysis steerable filters have been used to analyze local orientation patterns in imagery such filters are typically based on directional derivatives whose symmetry produces orientation responses that are periodic with period spl pi independent of image structure we present a more general set of steerable filters that alleviate this problem

transmitting information by controlling nonlinear oscillators the transmission of information relying on the perturbation of nonlinear oscillators vector fields can be approached in a unified manner this can be accomplished by making use of the information transmission via control principle which is stated and proved in the present work in short this principle establishes that any controller used to identically synchronize pairs of nonlinear oscillators including chaotic ones as a special case can be actually employed as demodulator decoder in the process of information recovery other theoretical results related to the practical realization of the itvc principle are presented and experimental data is provided showing a good agreement with the proposed theory

cortical spatiotemporal dimensionality reduction for visual grouping the visual systems of many mammals including humans are able to integrate the geometric information of visual stimuli and perform cognitive tasks at the first stages of the cortical processing this is thought to be the result of a combination of mechanisms which include feature extraction at the single cell level and geometric processing by means of cell connectivity we present a geometric model of such connectivities in the space of detected features associated with spatiotemporal visual stimuli and show how they can be used to obtain low level object segmentation the main idea is to define a spectral clustering procedure with anisotropic affinities over data sets consisting of embeddings of the visual stimuli into higher dimensional spaces neural plausibility of the proposed arguments will be discussed

the design of quasi sliding mode control for a permanent magnet synchronous motor with unmatched uncertainties in this study the concept of a quasi sliding mode control qsmc is introduced for the robust control of a permanent magnet synchronous motor pmsm system subjected to unmatched uncertainties and even with input nonlinearity on the basis of the new concept of qsmc continuous control is obtained to avoid the chattering phenomenon as expected the system state can be stabilized and driven into a predictable neighborhood of zero also this approach only uses a single controller to achieve chaos control which reduces the cost and complexity of implementation the results of numerical simulations demonstrate the validity of the proposed qsmc design method

detecting generalized synchrony an improved approach we examine some of the difficulties involved in detecting generalized synchrony gs in systems that exhibit noninvertibility and or wrinkling these latter features severely hinder identification of gs by conventional techniques it is shown that it is possible to greatly improve detection by reducing the pseudofalse neighbors effects here we propose the ensuremath delta p neighbor method to overcome the noninvertibility effect and the ensuremath delta p q method to detect gs in systems with wrinkled structures

stochastic differential equations and geometric flows in previous years curve evolution applied to a single contour or to the level sets of an image via partial differential equations has emerged as an important tool in image processing and computer vision curve evolution techniques have been utilized in problems such as image smoothing segmentation and shape analysis we give a local stochastic interpretation of the basic curve smoothing equation the so called geometric heat equation and show that this evolution amounts to a tangential diffusion movement of the particles along the contour moreover assuming that a priori information about the shapes of objects in an image is known we present modifications of the geometric heat equation designed to preserve certain features in these shapes while removing noise we also show how these new flows may be applied to smooth noisy curves without destroying their larger scale features in contrast to the original geometric heat flow which tends to circularize any closed curve

potentials valleys and dynamic global coverings we present a new approach to effect the transition between local and global representations it is based on the notion of a covering or a collection of objects whose union is equivalent to the full one the mathematics of computing global coverings are developed in the context of curve detection where an intermediate representation the tangent field provides a reliable local description of curve structure this local information is put together globally in the form of a potential distribution the elements of the covering are then short curves each of which evolves in parallel to seek the valleys of the potential distribution the initial curve positions are also derived from the tangent field and their evolution is governed by variational principles when stationary configurations are achieved the global dynamic covering is defined by the union of the local dynamic curves

controlling chaotic and hyperchaotic systems via a simple adaptive feedback controller this paper investigates the problem of chaos control and proposes a simple adaptive feedback control method for it under a reasonable assumption in comparison with previous methods the present control technique is simple both in the form of the controller and in its application a numerical example using the genesio chaotic system verifies the effectiveness and correctness of the proposed approach

adaptive backstepping synchronization between chaotic systems with unknown lipschitz constant abstract the error between two nonlinear terms is a key point of many synchronization problems however the lipschitz constant of the nonlinear term is not always easy to calculate for the stability analysis of the controlled error system thus the nonlinear systems with unknown parameters and unknown lipschitz constant is considered in this paper their scalar synchronous controller is proposed based on the thought of backstepping design without the need to evaluate the invariant set and calculate the lipschitz constant an assistant adaptive estimator is designed for the lipschitz constant what s more as a problem solving skill two different estimators are used on the same unknown parameter finally the synchronization control for both chaotic autonomous van der pol duffing advp systems and chaotic genesio systems with unknown parameters are given as examples to verify the control effect

globally optimal regions and boundaries as minimum ratio weight cycles we describe a new form of energy functional for the modeling and identification of regions in images the energy is defined on the space of boundaries in the image domain and can incorporate very general combinations of modeling information both from the boundary intensity gradients etc and from the interior of the region texture homogeneity etc we describe two polynomial time digraph algorithms for finding the global minima of this energy one of the algorithms is completely general minimizing the functional for any choice of modeling information it runs in a few seconds on a 256 spl times 256 image the other algorithm applies to a subclass of functionals but has the advantage of being extremely parallelizable neither algorithm requires initialization

inferring global perceptual contours from local features we address the problem of contour inference from partial data as obtained from state of the art edge detectors we argue that in order to obtain more pereeptually salient contours it is necessary to impose generic constraints such as continuity and co curvilinearity the implementation is in the form of a convolution with a mask which encodes both the orientation and the strength of the possible continuations we first show how the mask called the extension field is derived then how the contributions from different sites are collected to produce a saliency map we show that the scheme can handle a variety of input data from dot patterns to oriented edgels in a unified manner and demonstrate results on a variety of input stimuli we also present a similar approach to the problem of inferring contours formed by end points in both cases the scheme is non linear non iterative and unified in the sense that all types of input tokens are handled in the same manner

harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems abstract the paper considers the problem of determining the conditions under which a nonlinear dynamical system can give rise to a chaotic behaviour on the basis of the harmonic balance principle which is widely used in the frequency analysis of nonlinear control systems two practical methods are presented for predicting the existence and the location of chaotic motions this is formulated as a function of the system parameters when the system structure is fixed by rather general input output or state equation models several examples of application are presented to show the rather straightforward computations involved in the proposed methods the kind of results which can be obtained and due to the heuristic approach to the problem their corresponding approximation

a probabilistic spectral framework for grouping and segmentation this paper presents an iterative spectral framework for pairwise clustering and perceptual grouping our model is expressed in terms of two sets of parameters firstly there are cluster memberships which represent the affinity of objects to clusters secondly there is a matrix of link weights for pairs of tokens we adopt a model in which these two sets of variables are governed by a bernoulli model we show how the likelihood function resulting from this model may be maximised with respect to both the elements of link weight matrix and the cluster membership variables we establish the link between the maximisation of the log likelihood function and the eigenvectors of the link weight matrix this leads us to an algorithm in which we iteratively update the link weight matrix by repeatedly refining its modal structure each iteration of the algorithm is a three step process first we compute a link weight matrix for each cluster by taking the outer product of the vectors of current cluster membership indicators for that cluster second we extract the leading eigenvector from each modal link weight matrix third we compute a revised link weight matrix by taking the sum of the outer products of the leading eigenvectors of the modal link weight matrices

general geometric good continuation from taylor to laplace via level sets good continuation is the gestalt observation that parts often group in particular ways to form coherent wholes perceptual integration of edges for example involves orientation good continuation a property which has been exploited computationally very extensively but more general local global relationships such as for shading or color have been elusive while taylor s theorem suggests certain modeling and smoothness criteria the consideration of level set geometry indicates a different approach using such first principles we derive for the first time a generalization of good continuation to all those visual structures that can be abstracted as scalar functions over the image plane based on second order differential constraints that reflect good continuation our analysis leads to a unique class of harmonic models and a cooperative algorithm for structure inference among the different applications of good continuation here we apply these results to the denoising of shading and intensity distributions and demonstrate how our approach eliminates spurious measurements while preserving both singularities and regular structure a property that facilitates higher level processes which depend so critically on both of these classes of visual structures

sledge sequential labeling of image edges for boundary detection our goal is to detect boundaries of objects or surfaces occurring in an arbitrary image we present a new approach that discovers boundaries by sequential labeling of a given set of image edges a visited edge is labeled as on or off a boundary based on the edge s photometric and geometric properties and evidence of its perceptual grouping with already identified boundaries we use both local gestalt cues e g proximity and good continuation and the global helmholtz principle of non accidental grouping a new formulation of the helmholtz principle is specified as the entropy of a layout of image edges for boundary discovery we formulate a new policy iteration algorithm called sledge training of sledge is iterative in each training image sledge labels a sequence of edges which induces loss with respect to the ground truth these sequences are then used as training examples for learning sledge in the next iteration such that the total loss is minimized for extracting image edges that are input to sledge we use our new low level detector it finds salient pixel sequences that separate distinct textures within the image on the benchmark berkeley segmentation datasets 300 and 500 our approach proves robust and effective we outperform the state of the art both in recall and precision for different input sets of image edges

a tangent bundle theory for visual curve completion visual curve completion is a fundamental perceptual mechanism that completes the missing parts e g due to occlusion between observed contour fragments previous research into the shape of completed curves has generally followed an axiomatic approach where desired perceptual geometrical properties are first defined as axioms followed by mathematical investigation into curves that satisfy them however determining psychophysically such desired properties is difficult and researchers still debate what they should be in the first place instead here we exploit the observation that curve completion is an early visual process to formalize the problem in the unit tangent bundle r2 s1 which abstracts the primary visual cortex v1 and facilitates exploration of basic principles from which perceptual properties are later derived rather than imposed exploring here the elementary principle of least action in v1 we show how the problem becomes one of finding minimum length admissible curves in r2 s1 we formalize the problem in variational terms we analyze it theoretically and we formulate practical algorithms for the reconstruction of these completed curves we then explore their induced visual properties vis a vis popular perceptual axioms and show how our theory predicts many perceptual properties reported in the corresponding perceptual literature finally we demonstrate a variety of curve completions and report comparisons to psychophysical data and other completion models

3d stochastic completion fields for mapping connectivity in diffusion mri the 2d stochastic completion field algorithm introduced by williams and jacobs 1 2 uses a directional random walk to model the prior probability of completion curves in the plane this construct has had a powerful impact in computer vision where it has been used to compute the shapes of likely completion curves between edge fragments in visual imagery motivated by these developments we extend the algorithm to 3d using a spherical harmonics basis to achieve a rotation invariant computational solution to the fokker planck equation describing the evolution of the probability density function underlying the model this provides a principled way to compute 3d completion patterns and to derive connectivity measures for orientation data in 3d as arises in 3d tracking motion capture and medical imaging we demonstrate the utility of the approach for the particular case of diffusion magnetic resonance imaging where we derive connectivity maps for synthetic data on a physical phantom and on an in vivo high angular resolution diffusion image of a human brain

salient closed boundary extraction with ratio contour we present ratio contour a novel graph based method for extracting salient closed boundaries from noisy images this method operates on a set of boundary fragments that are produced by edge detection boundary extraction identifies a subset of these fragments and connects them sequentially to form a closed boundary with the largest saliency we encode the gestalt laws of proximity and continuity in a novel boundary saliency measure based on the relative gap length and average curvature when connecting fragments to form a closed boundary this new measure attempts to remove a possible bias toward short boundaries we present a polynomial time algorithm for finding the most salient closed boundary we also present supplementary preprocessing steps that facilitate the application of ratio contour to real images we compare ratio contour to two closely related methods for extracting closed boundaries elder and zucker s method based on the shortest path algorithm and williams and thornber s method based on spectral analysis and a strongly connected components algorithm this comparison involves both theoretic analysis and experimental evaluation on both synthesized data and real images

left invariant diffusions on the space of positions and orientations and their application to crossing preserving smoothing of hardi images hardi high angular resolution diffusion imaging is a recent magnetic resonance imaging mri technique for imaging water diffusion processes in fibrous tissues such as brain white matter and muscles in this article we study left invariant diffusion on the group of 3d rigid body movements i e 3d euclidean motion group se 3 and its application to crossing preserving smoothing of hardi images the linear left invariant convection diffusions are forward kolmogorov equations of brownian motions on the space of positions and orientations in 3d embedded in se 3 and can be solved by 3 s 2 convolution with the corresponding green s functions we provide analytic approximation formulas and explicit sharp gaussian estimates for these green s functions in our design and analysis for appropriate nonlinear convection diffusions on hardi data we explain the underlying differential geometry on se 3 we write our left invariant diffusions in covariant derivatives on se 3 using the cartan connection this cartan connection has constant curvature and constant torsion and so have the exponential curves which are the auto parallels along which our left invariant diffusion takes place we provide experiments of our crossing preserving euclidean invariant diffusions on artificial hardi data containing crossing fibers

the perceptual organization of texture flow a contextual inference approach locally parallel dense patterns sometimes called texture flows define a perceptually coherent structure of particular significance to perceptual organization we argue that with applications ranging from image segmentation and edge classification to shading analysis and shape interpretation texture flows deserve attention equal to edge segment grouping and curve completion this paper develops the notion of texture flow from a geometrical point of view to argue that local measurements of such structures must incorporate two curvatures we show how basic theoretical considerations lead to a unique model for the local behavior of the flow and to a notion of texture flow good continuation this in turn translates to a specification of consistency constraints between nearby flow measurements which we use for the computation of globally piecewise coherent structure through the contextual framework of relaxation labeling we demonstrate the results on synthetic and natural images

segmentation of multiple salient closed contours from real images using a saliency measure based on the global property of contour closure we have developed a segmentation method which identifies smooth closed contours bounding objects of unknown shape in real images the saliency measure incorporates the gestalt principles of proximity and good continuity that previous methods have also exploited unlike previous methods we incorporate contour closure by finding the eigenvector with the largest positive real eigenvalue of a transition matrix for a markov process where edges from the image serve as states element i j of the transition matrix is the conditional probability that a contour which contains edge j will also contain edge i we show how the saliency measure defined for individual edges can be used to derive a saliency relation defined for pairs of edges and further show that strongly connected components of the graph representing the saliency relation correspond to smooth closed contours in the image finally we report for the first time results on large real images for which segmentation takes an average of about 10 seconds per object on a general purpose workstation

on generalized synchronization of different order chaotic systems a submanifold approach regulation theory is used to address the synchronization phenomena of chaotic systems our results are based on the solution of the francis isidori byrnes equations to derive the synchronization submanifold thus conditions for complete or partial synchronization are depicted this analysis is not restrictive with respect to the master and the slave systems dimensions therefore it can be applied to strictly different systems with the same order or even different order systems finally workbench examples are presented to illustrate the results