fractal properties of robust strange nonchaotic attractors in maps of two or more dimensions we consider the existence of robust strange nonchaotic attractors in a simple class of quasiperiodically forced systems rigorous results are presented demonstrating that the resulting attractors are strange in the sense that their box counting dimension d 0 is larger than their information dimension d 1 by 1 i e d 0 d 1 1 we also show how this property is manifested in numerical experiments

fuzzy geometry an updated overview abstract this paper briefly reviews work on the fuzzy topology and geometry of image subsets including adjacency separation and connectedness distance and relative position area perimeter and diameter convexity medial axes and thinning as well as some applications of these concepts in image processing and analysis

skeletonization based on error reduction the accuracy of a non pixel based skeletonization method is largely dependent on the contour information chosen as input when using a constrained delaunay triangulation to construct an object s skeleton a number of contour pixels must be chosen as a basis for triangulation this paper presents a new method of selecting these contour pixels a new method for measuring skeletonization error is proposed which quantifies the deviation of a skeleton segment from the true medial axis of a stroke in an image the goal of the proposed algorithm is to reduce this error to an acceptable level whilst retaining the superior efficiencies of previous non pixel based techniques experimental results show that the proposed method is adept at following the medial axis of an image and is capable of producing a skeleton that is confirmed by a human s perception of the image it is also computationally efficient and robust against noise

singularities in vibro impact dynamics abstract the non differentiable nature of vibro impact dynamics can lead to breakdown of the global stable manifold theorem applicable to smooth dynamical systems in one dimensional periodically excited system the breakdown leads to the shredding of the stable manifolds and this process is analyzed in detail bodily translation of filaments of stable manifolds can lead to homoclinic intersections and this topic is discussed in the context of a new bifurcation due to re entrance shredding leads to a strong similarity between the geometries of the singular subspaces and the geometries of homoclinic tangles and strange attracting sets

codimension 2 hopf bifurcation of a two degree of freedom vibro impact system abstract codimension 2 hopf bifurcation problem of a two degree of freedom system vibrating against a rigid surface is investigated in this paper the four dimensional poincare map of the vibro impact system is reduced to a two dimensional normal form by virtue of a center manifold reduction and a normal form technique then the theory of hopf bifurcation of maps in r 2 is applied to conclude the existence of codimension 2 hopf bifurcation of the vibro impact system the quasi periodic response of the system by theoretical analysis is well supported by numerical simulations it is shown that there exists codimension 2 hopf bifurcation in multi degree of freedom vibro impact systems the codimension 2 tori doubling phenomenon and the routes of quasi periodic impacts to chaos are reported briefly

fast recursive algorithms for two dimensional thresholding two dimensional 2d thresholding behaves well in segmenting images of low siginal to noise ratio but the computation complexity of the conventional 2d entropic algorithm is bounded by o l4 in this paper firstly a fast recursive 2d entropic thresholding algorithm is proposed by rewriting the formula for calculation of entropy in recurrence form a lengthy calculation is saved analysis shows that the computation complexity of 2d entropic thresholding is reduced to o l2 the fast recursive algorithm is also used successfully in 2d otsu thresholding method experimental results show that the processing time of each image is reduced from more than 2 h to less than 10 s the required memory space is also greatly reduced

robustness of shape descriptors to incomplete contour representations with inspiration from psychophysical researches of the human visual system we propose a novel aspect and a method for performance evaluation of contour based shape recognition algorithms regarding their robustness to incompleteness of contours we use complete contour representations of objects as a reference training set incomplete contour representations of the same objects are used as a test set the performance of an algorithm is reported using the recognition rate as a function of the percentage of contour retained we call this evaluation procedure the icr test we consider three types of contour incompleteness viz segment wise contour deletion occlusion and random pixel depletion as an illustration the robustness of two shape recognition algorithms to contour incompleteness is evaluated these algorithms use a shape context and a distance multiset as local shape descriptors qualitatively both algorithms mimic human visual perception in the sense that recognition performance monotonously increases with the degree of completeness and that they perform best in the case of random depletion and worst in the case of occluded contours the distance multiset method performs better than the shape context method in this test framework

a periodically forced piecewise linear oscillator a single degree of freedom non linear oscillator is considered the non linearity is in the restoring force and is piecewise linear with a single change in slope such oscillators provide models for mechanical systems in which components make intermittent contact a limiting case in which one slope approaches infinity an impact oscillator is also considered harmonic subharmonic and chaotic motions are found to exist and the bifurcations leading to them are analyzed

fractalization route to strange nonchaotic dynamics in the fractalization route for the formation of strange nonchaotic attractors sna s in quasiperiodically driven nonlinear dynamical systems a smooth torus gradually becomes a fractal as the forcing amplitude is increased while the lyapunov exponent remains nonpositive using techniques introduced by kim et al to identify unstable sets in sna s we study torus fractalization in a sequence of approximations wherein the quasiperiodic drive is replaced by periodic forcing of increasing period this allows us to identify an unstable set embedded in the attractor in the periodically forced system we show that there is a cascade of attractor merging crises and argue that the quasiperiodic analogue of such crises causes fractalization of tori to create sna s

random walks on graphs for salient object detection in images we formulate the problem of salient object detection in images as an automatic labeling problem on the vertices of a weighted graph the seed labeled nodes are first detected using markov random walks performed on two different graphs that represent the image while the global properties of the image are computed from the random walk on a complete graph the local properties are computed from a sparse k regular graph the most salient node is selected as the one which is globally most isolated but falls on a locally compact object a few background nodes and salient nodes are further identified based upon the random walk based hitting time to the most salient node the salient nodes and the background nodes will constitute the labeled nodes a new graph representation of the image that represents the saliency between nodes more accurately the pop out graph model is computed further based upon the knowledge of the labeled salient and background nodes a semisupervised learning technique is used to determine the labels of the unlabeled nodes by optimizing a smoothness objective label function on the newly created pop out graph model along with some weighted soft constraints on the labeled nodes

a novel multiresolution spatiotemporal saliency detection model and its applications in image and video compression salient areas in natural scenes are generally regarded as areas which the human eye will typically focus on and finding these areas is the key step in object detection in computer vision many models have been proposed to simulate the behavior of eyes such as saliencytoolbox stb neuromorphic vision toolkit nvt and others but they demand high computational cost and computing useful results mostly relies on their choice of parameters although some region based approaches were proposed to reduce the computational complexity of feature maps these approaches still were not able to work in real time recently a simple and fast approach called spectral residual sr was proposed which uses the sr of the amplitude spectrum to calculate the image s saliency map however in our previous work we pointed out that it is the phase spectrum not the amplitude spectrum of an image s fourier transform that is key to calculating the location of salient areas and proposed the phase spectrum of fourier transform pft model in this paper we present a quaternion representation of an image which is composed of intensity color and motion features based on the principle of pft a novel multiresolution spatiotemporal saliency detection model called phase spectrum of quaternion fourier transform pqft is proposed in this paper to calculate the spatiotemporal saliency map of an image by its quaternion representation distinct from other models the added motion dimension allows the phase spectrum to represent spatiotemporal saliency in order to perform attention selection not only for images but also for videos in addition the pqft model can compute the saliency map of an image under various resolutions from coarse to fine therefore the hierarchical selectivity hs framework based on the pqft model is introduced here to construct the tree structure representation of an image with the help of hs a model called multiresolution wavelet domain foveation mwdf is proposed in this paper to improve coding efficiency in image and video compression extensive tests of videos natural images and psychological patterns show that the proposed pqft model is more effective in saliency detection and can predict eye fixations better than other state of the art models in previous literature moreover our model requires low computational cost and therefore can work in real time additional experiments on image and video compression show that the hs mwdf model can achieve higher compression rate than the traditional model

dynamical behavior of vibro impact machinery near a point of codimension two bifurcation a dual component system with vibro impact is considered local codimension two bifurcation of maps involving a real eigenvalue and a complex conjugate pair escaping the unit circle simultaneously is analyzed by using the center manifold and normal form method for maps the period n single impact motion and poincare map of the vibro impact system are derived analytically stability and local bifurcation of single impact periodic motion are analyzed by using the poincare map a center manifold theorem technique is applied to reduce the poincare map to a three dimensional one and the normal form map associated with the codimension two bifurcation is obtained local behavior of the dual component system with vibro impact near the point of codimension two bifurcation is analyzed it is found that near the point of codimension two bifurcation there exists not only hopf bifurcation of period one single impact motion but also hopf bifurcation of period two double impact motion period doubling bifurcation of period one single impact motion commonly exists near the point of codimension two bifurcation however no period doubling cascade emerges due to change of the type of period two fixed points and occurrence of hopf bifurcation associated with period two fixed points the period two fixed points are symmetrical about the corresponding period one point the results from simulation show that the attracting invariant circles associated with period two points are symmetrical about the corresponding period one point near the value of hopf bifurcation of period two points two actual examples the impact forming machinery and inertial shaker are chosen to analyze further the phenomena of codimension two bifurcation of maps and local bifurcation analysis and numerical simulation are carried out to unfold dynamical behavior of these vibro impact systems near the points of codimension two bifurcations

image approximation from gray scale medial axes several types of gray weighted medial axes have been defined this paper shows that one of them the min max medial axis can be used to reconstruct good approximations to the original image based on a relatively small amount of information

pattern spectrum and multiscale shape representation the results of a study on multiscale shape description smoothing and representation are reported multiscale nonlinear smoothing filters are first developed using morphological opening and closings g matheron 1975 used openings and closings to obtain probabilistic size distributions of euclidean space sets continuous binary images these distributions are used to develop a concept of pattern spectrum a shape size descriptor a pattern spectrum is introduced for continuous graytone images and arbitrary multilevel signals as well as for discrete images by developing a discrete size family of patterns large jumps in the pattern spectrum at a certain scale indicate the existence of major protruding or intruding substructures of the signal at the scale an entropy like shape size complexity measure is also developed based on the pattern spectrum for shape representation a reduced morphological skeleton transform is introduced for discrete binary and graytone images this transform is a sequence of skeleton components sparse images which represent the original shape at various scales it is shown that the partially reconstructed images from the inverse transform on subsequences of skeleton components are the openings of the image at a scale determined by the number of eliminated components in addition two way correspondences are established among the degree of shape smoothing via multiscale openings or closings the pattern spectrum zero values and the elimination or nonexistence of skeleton components at certain scales

a min max medial axis transformation blum s medial axis transformation mat of the set s of 1 s in a binary picture can be defined by an iterative shrinking and reexpanding process which detects corners on the contours of constant distance from s and thereby yields a skeleton of s for unsegmented gray level pictures one can use an analogous definition in which local min and max operations play the roles of shrinking and expanding to compute a mmmat value at each point of the picture the set of points having high values defines a good skeleton for the set of high gray level points in the given picture

periodic motions and global bifurcations of a two degree of freedom system with plastic vibro impact a two degree of freedom d o f impact system with proportional damping is considered the maximum displacement of one of the masses is limited to a threshold value by a rigid wall which gives rise to a non linearity in the system a limiting case of a dynamical problem arising in the mechanical systems with amplitude constraints is investigated for the perfectly plastic vibro impact case dynamics of a two degree of freedom vibratory system contacting a single stop is represented by a three dimensional map existence and stability of period n single impact motions are analyzed by analytical and numerical methods it is shown that the vibro impact system may exhibit two different types of periodic motions due to the piecewise property of the map transitions of two types of period n single impact motions are demonstrated the singularities of the poincare map caused by grazing boundary motion of the impact oscillator are considered due to the piecewise discontinuities and singularities of the map the vibro impact system is shown to undergo period doubling bifurcations followed by complex sequence of transitions in which the period doubling cascades do not occur and extremely long periodic and chaotic motions are generated directly with the motions with grazing boundary occurring finally the influence of system parameters on periodic impacts and global bifurcations is discussed

general approach to the localization of unstable periodic orbits in chaotic dynamical systems we present a method to detect the unstable periodic orbits of a multidimensional chaotic dynamical system our approach allows us to locate in an efficient way the unstable cycles of in principle arbitrary length with a high accuracy based on a universal set of linear transformations the originally unstable periodic orbits are transformed into stable ones and can consequently be detected and analyzed easily this method is applicable to dynamical systems of any dimension and requires no preknowledges with respect to the solutions of the original chaotic system as an example of application of our method we investigate the ikeda attractor in some detail

gray level image thresholding based on fisher linear projection of two dimensional histogram abstract thresholding is an important form of image segmentation and is a first step in the processing of images for many applications the selection of suitable thresholds is ideally an automatic process requiring the use of some criterion on which the selection is based most such criteria are only based on the one dimensional id gray level histogram of image in an effort to use more information available in the image the present approaches use the criteria based on the two dimensional 2d histogram of the image however these methods which simply extend the 1d histogram based algorithms to the 2d histogram give rise to the exhaustive search for the threshold values in this paper an optimal projection of the 2d histogram is derived by applying fisher linear discriminant the optimal projection turns out to be the local average histogram analysis and experimental results show that thresholding an image based on the local average histogram one can obtain segmentation better than that of those simply using criteria based on 2d histogram while the spent computation time is as much as that costed by the ones using criteria based on 1d histogram

the birth of strange nonchaotic attractors abstract a mechanism is described for the development of strange nonchaotic attractors from two frequency quasiperiodic attractors in quasiperiodically driven maps this mechanism is intimately tied to the phenomenon of torus doubling the transition to strange nonchaotic behavior occurs when a period doubled torus collides with its unstable parent torus as the collision is approached the period doubled torus becomes extremely wrinkled ultimately becoming fractal at the collision the lyapunov exponent remains negative through the collision these collisions are shown to be a new type of attractor merging crisis the new feature is the possibility of nonchaotic attractors taking part in the crisis this mechanism is illustrated via numerical and analytical studies of a quasiperiodically driven logistic map

threshold superposition in morphological image analysis systems it is shown that four composite morphological systems namely morphological edge detection peak valley extraction skeletonization and shape size distributions obey a weak linear superposition called threshold linear superposition the output image signal or measurement from each system is shown to be the sum of outputs due to input binary images that result from thresholding the input gray level image at all levels these results are generalized to a vector space formulation e g to any finite linear combination of simple morphological systems thus many such systems processing gray level images are reduced to corresponding binary image processing systems which are easier to analyze and implement

singular continuous spectra in dissipative dynamics we demonstrate the occurrence of regimes with singular continuous fractal fourier spectra in autonomous dissipative dynamical systems the particular example is an ordinary differential equation system at the accumulation points of bifurcation sequences associated with the creation of complicated homoclinic orbits two different mechanisms responsible for the appearance of such spectra are proposed in the first case when the geometry of the attractor is symbolically represented by the thue morse sequence both the continuous time process and its discrete poincar e map have singular power spectra the other mechanism is due to the logarithmic divergence of the first return times near the saddle point here the poincar e map possesses the discrete spectrum while the continuous time process displays the singular one a method is presented for computing the multifractal characteristics of the singular continuous spectra with the help of the usual fourier analysis technique

renormalization of correlations and spectra of a strange non chaotic attractor we study a simple nonlinear mapping with a strange nonchaotic attractor characterized by a singular continuous power spectrum we show that the symbolic dynamics is exactly described by a language generated from a suitable inflation rule we derive renormalization transformations for both the power spectrum and the autocorrelation function thus obtaining a quantitative description of the scaling properties the multifractal nature of the spectrum is also discussed

hopf bifurcation of a two degree of freedom vibro impact system abstract the bifurcation problem of a two degree of freedom system vibrating against a rigid surface is studied in this paper it is shown that there exist hopf bifurcations in the vibro impact systems with two or more degrees of freedom under suitable system parameters in the paper a centre manifold theorem technique is applied to reduce the poincare map of the vibro impact system to a two dimensional one and then the theory of hopf bifurcation of maps in r 2 is applied to conclude the existence of hopf bifurcation of the vibro impact system the theoretical solutions are verified by numerical computations the quasi periodic response of the system represented by invariant circles in the projected poincare sections is obtained by numerical simulations and routes of quasi periodic impacts to chaos are stated briefly

stagnation point von karman coefficient on the basis of various direct numerical simulations dns of turbulent channel flows the following picture is proposed i at a distance y from either wall the taylor microscale lambda is proportional to the average distance l s between stagnation points of the fluctuating velocity field i e lambda y b 1 l s y with b 1 constant for delta nu y or approximately equal to delta where the wall unit delta nu is defined as the ratio of kinematic viscosity nu to skin friction velocity u tau and delta is the channel s half width ii the number density n s of stagnation points varies with height according to n s c s delta nu 3 y 1 where y identical with y delta nu and c s is constant in the range delta nu y or approximately equal to delta iii in that same range the kinetic energy dissipation rate per unit mass equals 2 3 e u tau 3 kappa s y where e is the total kinetic energy per unit mass normalized by u tau 2 and kappa s b 1 2 c s is the stagnation point von karman coefficient iv in the limit of exceedingly large reynolds numbers re tau identical with delta delta nu large enough for the reynolds stress uv to equal u tau 2 in the range delta nu y delta and assuming that production of turbulent kinetic energy balances dissipation locally in that range and limit the mean velocity u normalized by u tau obeys d dy u approximately equal to 2 3 e kappa s y in that same range v it follows that the von karman coefficient kappa is a meaningful and well defined coefficient and the log law holds in turbulent channel pipe flows only if e is independent of y and re tau in that range in which case kappa approximately kappa s vi in support of d dy u approximately equal to 2 3 e kappa s y dns data of turbulent channel flows which include the highest currently available values of re tau are best fitted by e approximately equal to 2 3 b 4 y 2 15 and d dy u approximately equal to b 4 kappa s y 1 2 15 with b4 independent of y in delta nu y delta if the significant departure from uv approximately equal to u tau 2 at these re tau values is taken into account

the use of variance and entropic thresholding methods for image segmentation in this paper we investigate methods for the automatic thresholding of x ray images of food packets in order to determine their suitability for the detection of contaminants or foreign objects that may be present within single and dual threshold schemes based on variance and entropic measures of the image histogram are applied a modified entropic measure is proposed which decides whether a single or dual threshold is appropriate dependent on the histogram data the performance of each of the methods is evaluated and compared using images containing real and computer generated foreign object samples

slic superpixels compared to state of the art superpixel methods computer vision applications have come to rely increasingly on superpixels in recent years but it is not always clear what constitutes a good superpixel algorithm in an effort to understand the benefits and drawbacks of existing methods we empirically compare five state of the art superpixel algorithms for their ability to adhere to image boundaries speed memory efficiency and their impact on segmentation performance we then introduce a new superpixel algorithm simple linear iterative clustering slic which adapts a k means clustering approach to efficiently generate superpixels despite its simplicity slic adheres to boundaries as well as or better than previous methods at the same time it is faster and more memory efficient improves segmentation performance and is straightforward to extend to supervoxel generation

fuzzy medial axis transformation fmat practical feasibility abstract the fuzzy medial axis transformation fmat of a fuzzy set f is a set of fuzzy disks whose sup is f unfortunately specifying the fmat sometimes requires more storage space than specifying f itself the present paper describes some techniques to improve the compact representation of fmat thereby making it practically feasible and useful the algorithms involve reduction of redundancy in fmat its approximation and reduction of the searching spaces for its computation the computational aspects for the convenience of writing an efficient program have also been described a concept of sponsoring capability of a pixel is described in order to view the principle of removing redundancy in fmat and to generate its approximation two kinds of approximations are made namely distributed approximation and optimum fuzzy compactness the aforesaid features have been demonstrated on a gray image

min max operators in texture analysis a signature is generated for a given picture by operating on it with different masks the operations are gray level generalizations of shrink and expand for binary pictures using serra s morphological methods 10 the signature is a set of numbers each corresponding to an application of an operator at a certain scale and direction and can be used to analyze the discriminate textures it is shown that this family of signatures includes as special cases several currently used texture descriptors

a novel image thresholding method based on parzen window estimate image segmentation is one of the most important and fundamental tasks in image processing and techniques based on image thresholding are typically simple and computationally efficient however the image segmentation results depend heavily on the chosen image thresholding methods in this paper histogram is integrated with the parzen window technique to estimate the spatial probability distribution of gray level image values and a novel criterion function is designed by optimizing the criterion function an optimal global threshold is obtained the experimental results for synthetic real world and images demonstrate the success of the proposed image thresholding method as compared with the otsu method the met method and the entropy based method

a ridge following algorithm for finding the skeleton of a fuzzy image abstract a typical method for finding the skeleton of a grayscale image is to threshold the image then thin the result with one of several binary thinning algorithms this process loses information in the intensity dimension by reducing all intensities to either one of two values the loss of intensity information causes the skeleton of non uniform grayscale images to be centrally located within the thresholded image but may not lie along the maximum intensity ridge line in this paper we propose a method that avoids thresholding instead we transform the grayscale image into a fuzzy set and use the degree of membership in the underlying object to find the skeleton along the maximum intensity ridge line topographical labeling methods find a ridge line by topographically labeling pixels the ride line is the union of peak ridge and saddle point pixels these methods require preprocessing or postprocessing to find connected single pixel skeletons we show the results of our algorithm on images varying in uniformity from a gaussian smoothed binary rectangle to a scanned image of a grayscale object we compare results with the threshold and thin and topographical labeling methods

efficient detection of periodic orbits in chaotic systems by stabilizing transformations an algorithm for detecting periodic orbits in chaotic systems r l davidchack and y c lai phys rev e 3 60 1999 pp 6172 6175 which combines the set of stabilizing transformations proposed by schmelcher and diakonos phys rev lett 78 1997 pp 4733 4736 with a modified semi implicit euler iterative scheme and seeding with periodic orbits of neighboring periods has been shown to be highly efficient when applied to low dimensional systems the difficulty in applying the algorithm to higher dimensional systems is mainly due to the fact that the number of the stabilizing transformations grows extremely fast with increasing system dimension here we analyze the properties of stabilizing transformations and propose an alternative approach for constructing a smaller set of transformations the performance of the new approach is illustrated on the four dimensional kicked double rotor map and the six dimensional system of three coupled henon maps

the multiresolution gradient vector field skeleton many algorithms suppress skeleton associated with boundary perturbation by preventing their formation or by costly branch pruning this work proposes a novel concept of structural and textural skeletons the former is associated with the general shape structure and the latter with boundary perturbations these skeletons remain disconnected to facilitate gross shape matching without the need for branch pruning they are extracted from a multiresolution gradient vector field that is efficiently generated within a pyramidal framework experimental results show that these skeletons are scale and rotation invariant they are less affected by boundary noise compared to skeletons extracted by popular iterative and non iterative techniques

a thresholding method based on two dimensional renyi s entropy in this paper we present a new thresholding technique based on two dimensional renyi s entropy the two dimensional renyi s entropy was obtained from the two dimensional histogram which was determined by using the gray value of the pixels and the local average gray value of the pixels this new method extends a method due to sahoo et al pattern recognition 30 1997 71 and includes a previously proposed global thresholding method due to abutaleb pattern recognition 47 1989 22 further our method extends a global thresholding method due to chang et al ieee trans image process 4 1995 370 to the two dimensional setting the effectiveness of the proposed method is demonstrated by using examples from the real world and synthetic images

thinning approach for noisy digital patterns abstract many problems difficult to solve by traditional computer algorithms can be explored by the principles of human visual perception from the hint of human visual symmetry a thinning approach for noisy digital patterns is presented in this paper it includes three main algorithms algorithm 1 is designed to find the effective circular range for each pixel containing the maximum effective information algorithm 2 is designed to compute the symmetry score of the pixel distribution in the circular range and convert the symmetry information into a gray scale image algorithm 3 provides a modified gray scale thinning algorithm for thinning the gray scale image to obtain a connected thin line experiments show that the thinning results obtained by the proposed method are properly acceptable whensnr 2 2 db and the connectedness of the thin line can be preserved

correlations and spectra of strange non chaotic attractors we consider correlations and spectra of strange nonchaotic attractors in quasiperiodically driven nonlinear systems it is demonstrated that a self similar autocorrelation function and a singular continuous spectrum may be observed in such systems the properties of correlations and spectra depend very subtly on the rotation number of the quasiperiodic force and on the parameters of the system for some parameter values the usual discrete spectrum is restored

thresholding of digital images using two dimensional entropies abstract thresholding is an important form of image segmentation and is a first step in the processing of images for many applications the selection of suitable thresholds is ideally an automatic process requiring the use of some criterion on which to base the selection one such criterion is the maximization of the information theoretic entropy of the resulting background and object probability distributions most processes using this concept have made use of the one dimensional 1d grey level histogram of the image in an effort to use more of the information available in the image the present approach evaluates two dimensional 2d entropies based on the 2d grey level local average grey level histogram or scatterplot the 2d threshold vector that maximizes both background and object class entropies is selected

interruption of torus doubling bifurcation and genesis of strange nonchaotic attractors in a quasiperiodically forced map mechanisms and their characterizations a simple quasiperiodically forced one dimensional cubic map is shown to exhibit very many types of routes to chaos via strange nonchaotic attractors snas in a two parameter a ensuremath f space the routes include transitions to chaos via snas from both a one frequency torus and a period doubled torus in the former case we identify the fractalization and type i intermittency routes in the latter case we point out that at least four distinct routes for the truncation of the torus doubling bifurcation and the creation of snas occur in this model in particular the formation of snas through heagy hammel fractalization and type iii intermittent mechanisms is described in addition it has been found that in this system there are some regions in the parameter space where a dynamics involving a sudden expansion of the attractor which tames the growth of period doubling bifurcation takes place creating the sna the snas created through different mechanisms are characterized by the behavior of the lyapunov exponents and their variance by the estimation of the phase sensitivity exponent and through the distribution of finite time lyapunov exponents

double neimark sacker bifurcation and torus bifurcation of a class of vibratory systems with symmetrical rigid stops abstract a multidegree of freedom system having symmetrically placed rigid stops and subjected to periodic excitation is considered the system consists of linear components but the maximum displacement of one of the masses is limited to a threshold value by the symmetrical rigid stops repeated impacts usually occur in the vibratory system due to the rigid amplitude constraints such models play an important role in the studies of mechanical systems with clearances or gaps double neimark sacker bifurcation of the system is analyzed by using the center manifold and normal form method of maps the period one double impact symmetrical motion and homologous disturbed map of the system are derived analytically a center manifold theorem technique is applied to reduce the poincare map to a four dimensional one and the normal form map associated with double neimark sacker bifurcation is obtained the bifurcation sets for the normal form map are illustrated in detail local behavior of the vibratory systems with symmetrical rigid stops near the points of double neimark sacker bifurcations is reported by the presentation of results for a three degree of freedom vibratory system with symmetrical stops the existence and stability of period one double impact symmetrical motion are analyzed explicitly also local bifurcations at the points of change in stability are analyzed thus giving some information on dynamical behavior near the points of double neimark sacker bifurcations near the value of double neimark sacker bifurcation there exist period one double impact symmetrical motion and quasi periodic impact motions the quasi periodic impact motions are represented by the closed circle and tire like attractor in projected poincare sections with change of system parameters the quasi periodic impact motions usually lead to chaos via tire like torus doubling

visual saliency based on scale space analysis in the frequency domain we address the issue of visual saliency from three perspectives first we consider saliency detection as a frequency domain analysis problem second we achieve this by employing the concept of nonsaliency third we simultaneously consider the detection of salient regions of different size the paper proposes a new bottom up paradigm for detecting visual saliency characterized by a scale space analysis of the amplitude spectrum of natural images we show that the convolution of the image amplitude spectrum with a low pass gaussian kernel of an appropriate scale is equivalent to an image saliency detector the saliency map is obtained by reconstructing the 2d signal using the original phase and the amplitude spectrum filtered at a scale selected by minimizing saliency map entropy a hypercomplex fourier transform performs the analysis in the frequency domain using available databases we demonstrate experimentally that the proposed model can predict human fixation data we also introduce a new image database and use it to show that the saliency detector can highlight both small and large salient regions as well as inhibit repeated distractors in cluttered images in addition we show that it is able to predict salient regions on which people focus their attention

invariant graphs for forced systems abstract many applications of nonlinear dynamics involve forced systems we consider the case where for a fixed input the driven system is contracting this is for instance the situation in certain classes of filters and in the study of synchronization when such contraction is uniform it is well known that there exists a globally attracting invariant set which is the graph of a function from the driving state space to the driven state space if the contraction is sufficiently strong then is smooth we describe the theoretical framework for such results and discuss a number of applications to the filtering of time series to synchronization and to quasiperiodically forced systems we go on to give recent generalizations to the case of non uniform contraction that is contraction measured by lyapunov exponent like quantities we conclude with a number of new results for quasiperiodic forcing a corollary of these is that a strange non chaotic attractor for such a system cannot be the graph of a continuous function nor roughly speaking can it have as open attracting neighbourhood in other words its closure must contain some repelling orbits

a fast two dimensional entropic thresholding algorithm abstract two dimensional 2d entropic thresholding is one of the important thresholding techniques for image segmentation the selection of the global threshold vector is usually through a maximin optimization procedure a fast two phase 2d entropic thresholding algorithm is proposed in order to reduce the computation time first 9l 2 3 candidate threshold vectors are estimated from a quantized image of the original the global threshold vector is then obtained by checking candidates only the optimal computation complexity is o l 2 3 by quantizing the gray level into l 2 3 levels experimental results show that the processing time of each image is reduced from more than 2 h to about 2 min the required memory space is also greatly reduced

non periodic motion caused by grazing incidence in an impact oscillator the motion of a single degree of freedom periodically forced oscillator subjected to a rigid amplitude constraint is considered using analytical methods the singularities caused by grazing impact are studied it is shown that as a stable periodic orbit comes to grazing impact under the control of a single parameter a special type of bifurcation occurs the motion after the bifurcation may be non periodic and a criterion for this based on orientation and eigenvalues is given

fast adaptive pnn based thresholding algorithms abstract thresholding is a fundamental operation in image processing based on the pairwise nearest neighbor technique and the variance criterion this theme presents two fast adaptive thresholding algorithms the proposed first algorithm takes o m k m time where k denotes the number of thresholds specified by the user m denotes the size of the compact image histogram and the parameter has the constraint 1 m on a set of different real images experimental results reveal that the proposed first algorithm is faster than the previous three algorithms considerably while having a good feature preserving capability the previous three mentioned algorithms need o m k time given a specific peak signal to noise ratio psnr we further present the second thresholding algorithm to determine the number of thresholds as few as possible in order to obtain a thresholded image satisfying the given psnr the proposed second algorithm takes o m k m n time where n and denote the image size and the fewest number of thresholds required respectively some experiments are carried out to demonstrate the thresholded images that are encouraging since the time complexities required in our proposed two thresholding algorithms are polynomial they could meet the real time demand in image preprocessing

a novel graph based optimization framework for salient object detection in traditional graph based optimization framework for salient object detection an image is over segmented into superpixels and mapped to one single graph the saliency value of each superpixel is then computed based on the similarity between connected nodes and the saliency related queries when applying the traditional graph based optimization framework to the salient object detection problem in natural scene images we observe at least two limitations only one graph is employed to describe the information contained in an image and no cognitive property about visual saliency is explicitly modeled in the optimization framework in this work we propose a novel graph based optimization framework for salient object detection firstly we employ multiple graphs in our optimization framework a natural scene image is usually complex employing multiple graphs from different image properties can better describe the complex information contained in the image secondly we model one popular cognitive property about visual saliency visual rarity in our graph based optimization framework making this framework more suitable for saliency detection problem specifically we add a regularization term to constrain the saliency value of each superpixel according to visual rarity in our optimization framework our experimental results on four benchmark databases with comparisons to fifteen representative methods demonstrate that our graph based optimization framework is effective and computationally efficient highlightsa novel graph based optimization framework for salient object detection is proposed in the paper multiple graphs are employed in our optimization framework to better describe a natural scene image visual rarity is modeled as a regularization term in our framework to better detect saliency experimental results on four datasets with fifteen methods prove the effectiveness of our method

torus doubling bifurcations and strange nonchaotic attractors in a vibro impact system whether strange nonchaotic attractors snas can occur typically in dynamical systems other than quasiperiodically driven systems has been an open problem here we show that the snas can be induced by the interruption of torus doubling bifurcation in a periodically driven vibro impact system it is found that the creation of snas occurs due to the collision of doubled torus with some unstable periodic orbits based on the poincare map technique two types of codimension 3 bifurcations are represented and typical torus doubling bifurcations can occur in the neighborhood of these bifurcation points we use the singular continuous fourier spectrum and its scaling to verify the strangeness nondifferentiability of the attractors the implicitly transcendental map is used to calculate the largest lyapunov exponent by qr based algorithm which ensures that the underlying dynamics with nonpositive lyapunov exponents is nonchaotic the associated mechanism is described for the creation of snas through detecting unstable periodic orbits from poincare map series

a mathematical morphology approach to euclidean distance transformation a distance transformation technique for a binary digital image using a gray scale mathematical morphology approach is presented applying well developed decomposition properties of mathematical morphology one can significantly reduce the tremendous cost of global operations to that of small neighborhood operations suitable for parallel pipelined computers first the distance transformation using mathematical morphology is developed then several approximations of the euclidean distance are discussed the decomposition of the euclidean distance structuring element is presented the decomposition technique employs a set of 3 by 3 gray scale morphological erosions with suitable weighted structuring elements and combines the outputs using the minimum operator real valued distance transformations are considered during the processes and the result is approximated to the closest integer in the final output image

automatic and robust computation of 3d medial models incorporating object variability this paper presents a novel processing scheme for the automatic and robust computation of a medial shape model which represents an object population with shape variability the sensitivity of medial descriptions to object variations and small boundary perturbations are fundamental problems of any skeletonization technique these problems are approached with the computation of a model with common medial branching topology and grid sampling this model is then used for a medial shape description of individual objects via a constrained model fit the process starts from parametric 3d boundary representations with existing point to point homology between objects the voronoi skeleton of each sampled object boundary is partitioned into non branching medial sheets and simplified by a novel pruning algorithm using a volumetric contribution criterion using the surface homology medial sheets are combined to form a common medial branching topology finally the medial sheets are sampled and represented as meshes of medial primitives results on populations of up to 184 biological objects clearly demonstrate that the common medial branching topology can be described by a small number of medial sheets and that even a coarse sampling leads to a close approximation of individual objects

a skeletonization algorithm by maxima tracking on euclidean distance transform abstract a simple and efficient algorithm using the maxima tracking approach on euclidean distance transform to detect skeleton points is presented the advantages of the skeleton obtained are 1 connectivity preservation 2 single pixel in width and 3 its locations as close as to the most symmetrical axes besides the condition of the least slope change of skeleton is used to ensure the fairness of the digital medial axes with the least effort the algorithm can be modified to eliminate non significant short skeletal branches originating from the object contour while the critical shape informative medial axes are preserved

mechanism for the intermittent route to strange nonchaotic attractors intermittent strange nonchaotic attractors snas appear typically in quasiperiodically forced period doubling systems as a representative model we consider the quasiperiodically forced logistic map and investigate the mechanism for the intermittent route to snas using rational approximations to the quasiperiodic forcing it is found that a smooth torus transforms into an intermittent sna via a phase dependent saddle node bifurcation when it collides with a new type of ring shaped unstable set

euclidean skeletons of digital image and volume data in linear time by the integer medial axis transform a general algorithm for computing euclidean skeletons of 2d and 3d data sets in linear time is presented these skeletons are defined in terms of a new concept called the integer medial axis ima transform we prove a number of fundamental properties of the ima skeleton and compare these with properties of the cmd centers of maximal disks skeleton several pruning methods for ima skeletons are introduced constant linear and square root pruning and their properties studied the algorithm for computing the ima skeleton is based upon the feature transform using a modification of a linear time algorithm for euclidean distance transforms the skeletonization algorithm has a time complexity which is linear in the number of input points and can be easily parallelized we present experimental results for several data sets looking at skeleton quality memory usage and computation time both for 2d images and 3d volumes

a multi scale morphologic edge detector in this paper we present a morphologic edge detection methods using multi scale approach for detecting edges of various fineness under noisy condition it is shown that the proposed edge detector has the desirable properties that a good edge detector should have comparative study reveals its superiority over other morphologic edge detectors