a linear time combinatorial algorithm to find the orthogonal hull of an object on the digital plane a combinatorial algorithm to compute the orthogonal hull of a digital object imposed on a background grid is presented in this paper the resolution and complexity of the orthogonal hull can be controlled by varying the grid size which may be used for a multiresolution analysis of a given object existing algorithms on finding the convex hull are based on divide and conquer strategy sweepline approach etc whereas the proposed algorithm is combinatorial in nature whose time complexity is linear on the object perimeter instead of the object area for a larger grid size the perimeter of an object decreases in length in terms of grid units and hence the runtime of the algorithm reduces significantly the algorithm uses only comparison and addition in the integer domain thereby making it amenable to usage in real world applications where speed is a prime factor experimental results including the cpu time demonstrate the elegance and efficacy of the proposed algorithm

inverse halftoning and kernel estimation for error diffusion two different approaches in the inverse halftoning of error diffused images are considered the first approach uses linear filtering and statistical smoothing that reconstructs a gray scale image from a given error diffused image the second approach can be viewed as a projection operation where one assumes the error diffusion kernel is known and finds a gray scale image that will be halftoned into the same binary image two projection algorithms viz minimum mean square error mmse projection and maximum a posteriori probability map projection that differ on the way an inverse quantization step is performed are developed among the filtering and the two projection algorithms map projection provides the best performance for inverse halftoning using techniques from adaptive signal processing we suggest a method for estimating the error diffusion kernel from the given halftone this means that the projection algorithms can be applied in the inverse halftoning of any error diffused image without requiring any a priori information on the error diffusion kernel it is shown that the kernel estimation algorithm combined with map projection provide the same performance in inverse halftoning compared to the case where the error diffusion kernel is known

state feedback control of high order stochastic nonlinear systems with siiss inverse dynamics this technical note considers a class of high order stochastic nonlinear systems with stochastic integral input to state stability siiss inverse dynamics and drift and diffusion terms depending upon the stochastic inverse dynamics and all the states a new design and analysis approach to the problem of state feedback global regulation is developed to guarantee that all the signals of the closed loop system are bounded almost surely and the states can be regulated to zero almost surely

behaviour of third order terms in quadratic approximations of lr statistics in multivariate generalized linear models on presente des bornes d erreurs globales pour des modeles logit et log lineaire et des modeles dependant de la loi gamma

further results on global adaptive stabilisation for a class of uncertain stochastic nonlinear systems this paper considers the global adaptive stabilisation for a class of uncertain stochastic nonlinear systems comparing with the existing relevant literature the systems under investigation allow more serious unknowns uncertainties more importantly by remarkably reducing the dimension of dynamic compensator for system unknowns from n to 2 and considerably diminishing the overparametrisation in the existing literature this paper proposes an improved design scheme for adaptive state feedback controllers it is turned out that with the designed controller in loop all the closed loop system states are globally bounded and the original system states converge to the origin both in the sense of probability one a simulation example is also given to demonstrate the effectiveness of the theoretical results

exact tracking control of nonlinear systems with time delays and dead zone input this paper is concerned with the control design problem for a class of nonlinear systems with the state time varying time delays and nonsymmetric dead zone the problem addressed is to design adaptive controllers that guarantee the exact tracking of a given reference signal two continuous robust adaptive control schemes are proposed a positive nonlinear control gain function which is not required to satisfy an inequality but is expressed explicitly is carefully constructed and is used in the control law and adaptive law an illustrative example is provided to demonstrate the validity of the proposed design method

restoration of error diffused images using projection onto convex sets a novel inverse halftoning method is proposed to restore a continuous tone image from a given half tone image a set theoretic formulation is used where three sets are defined using the prior information about the problem a new space domain projection is introduced assuming the halftoning is performed using error diffusion and the error diffusion filter kernel is known the space domain frequency domain and space scale domain projections are used alternately to obtain a feasible solution for the inverse halftoning problem which does not have a unique solution

a combined homogeneous domination and sign function approach to output feedback stabilization of stochastic high order nonlinear systems for a class of stochastic high order nonlinear systems by introducing the combined homogeneous domination and sign function design approach this technical note solves the problem of output feedback control under the weaker high order and nonlinear growth conditions

finite time stabilization of stochastic nonlinear systems in strict feedback form in this paper we investigate the problem of almost surely finite time stabilization of a class of stochastic nonlinear systems based on the recently proposed almost surely finite time stability theorem in yin khoo man and yu 2011 we prove that almost surely global finite time stability of stochastic nonlinear systems in strict feedback form can be guaranteed by a continuous control law a systematic design algorithm is developed for the construction of the controller simulation results are given to illustrate the theoretical analysis

completeness of arbitrarily sampled discrete time wavelet transforms an arbitrarily sampled discrete time wavelet transform is said to be complete if it is uniquely invertible i e if the underlying signal can be uniquely recovered from the available samples of the wavelet transform we develop easy to compute necessary and sufficient conditions and necessary but not sufficient conditions for the completeness of an arbitrarily sampled dyadic discrete time wavelet transform of a periodic signal in particular we provide necessary and sufficient conditions for completeness of the sampled wavelet transform when the lowpass filter associated with the dyadic wavelet filter bank has no unit circle zeros other than those at z 1 we present necessary but not sufficient conditions for completeness when the lowpass filter associated with the dyadic wavelet filter bank has arbitrary unit circle zeros we also provide necessary and sufficient conditions for completeness of a set of samples of both the lowpass approximation to the signal and its wavelet transform all the conditions we derive use only information about the location of the retained samples and the analyzing wavelet filter bank they can easily be checked without explicitly computing of the rank of a matrix finally we present a simple signal reconstruction procedure that can be used once we have determined the arbitrarily sampled discrete time wavelet transform is complete

stochastic nonlinear stabilization i a backstepping design while the current robust nonlinear control toolbox includes a number of methods for systems affine in deterministic bounded disturbances the problem when the disturbance is unbounded stochastic noise has hardly been considered we present a control design which achieves global asymptotic lyapunov stability in probability for a class of strict feedback nonlinear continuous time systems driven by white noise in a companion paper we develop inverse optimal control laws for general stochastic systems affine in the noise input and for strict feedback systems a reader of this paper needs no prior familiarity with techniques of stochastic control

output feedback regulation of stochastic nonlinear systems with stochastic iiss inverse dynamics this paper develops a unifying framework for output feedback regulation of stochastic nonlinear systems with more general stochastic inverse dynamics the contributions of this work are characterized by the following novel features 1 motivated by the concept of integral input to state stability iiss in deterministic systems and stochastic input to state stability siss using lyapunov function in stochastic systems a concept of stochastic integral input to state stability siiss using lyapunov function is first introduced two important properties of siiss are obtained i siiss is strictly weaker than siss using lyapunov function ii siiss is stronger than the minimum phase property however only under the minimum phase assumption there is no dynamic output feedback control law for global stabilization in probability 2 almost sure boundedness a reasonable and stronger concept than boundedness in probability is introduced the purpose of introducing the concept is to prove the boundedness and convergence of some signals in the closed loop control system 3 some important mathematical tools which play an essential role in the boundedness and convergence analysis of the closed loop system are established 4 a unifying framework is proposed to design a dynamic output feedback control law which drives the states to the origin almost surely while maintaining all the closed loop signals bounded almost surely

a novel classification method of halftone image via statistics matrices existing classification methods tend not to work well on various error diffusion patterns thus a novel classification method for halftone image via statistics matrices is proposed the statistics matrix descriptor of halftone image is constructed according to the characteristic of error diffusion filters on this basis an extraction algorithm is developed based on halftone image patches the feature modeling is formulated as an optimization problem and then a gradient descent method is used to seek optimum class feature matrices by minimizing the total square error a maximum likelihood method is proposed according to priori knowledge of training samples in experiments the performance evaluation method is provided and comparisons of performance between our method and seven similar methods are made then the influence of parameters performance under various attacks computational time complexity and the limitations are discussed from our experimental study it is observed that our method has lower classification error rate when compared with other similar methods in addition it is robust against usual attacks

global finite time stabilization via time varying feedback for uncertain nonlinear systems this paper focuses on the global finite time stabilization via time varying state feedback for a class of uncertain time varying nonlinear systems the problem is rather difficult to solve mainly due to the presence of more serious unknowns and time variations and higher nonlinearities in the systems under investigation particularly those in the control coefficients of the systems to solve the problem by skillfully combining time varying methods and finite time control theory in the existing literature a novel time varying nonadaptive design scheme is successfully proposed to finite time stabilizing controllers the remarkable feature of the design scheme is the selection of time varying design functions which can capture the unknowns and time variations in the systems as time increases it is shown that if the design parameters and design functions in the designed controller are suitably chosen then all the signals i e the system states and control input of the closed loop system are globally

brief paper finite time stability and instability of stochastic nonlinear systems this paper presents a new definition of finite time stability for stochastic nonlinear systems this definition involves stability in probability and finite time attractiveness in probability an important lyapunov theorem on finite time stability for stochastic nonlinear systems is established a theorem extending the stochastic lyapunov theorem is also proved moreover an example and a lemma are presented to illustrate the scope of extension a useful inequality extended from bihari s inequality is derived which plays an important role in showing the lyapunov theorem finally a lyapunov theorem on finite time instability is proved which states that almost surely globally asymptotical stability is not equivalent to finite time stability for some stochastic systems two simulation examples are given to illustrate the theoretical analysis

adaptive fuzzy output feedback tracking backstepping control of strict feedback nonlinear systems with unknown dead zones in this paper an adaptive fuzzy backstepping control approach is considered for a class of nonlinear strict feedback systems with unknown functions unknown dead zones and immeasurable states fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a fuzzy filters state observer is designed to estimate the immeasurable states by using the adaptive backstepping recursive design technique and constructing the dead zone inverse a new adaptive fuzzy backstepping output feedback control approach is developed it is mathematically proved that all the signals of the resulting closed loop adaptive control system are semiglobally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin by appropriate choice of design parameters the proposed approach cannot only solve the problem of the dead zones but also cancel the restrictive assumption in the previous literature that the states are all available for measurement two simulation examples are provided to show the effectiveness of the proposed approach

global state feedback stabilisation of nonlinear systems with high order and low order nonlinearities this paper studies the state feedback control problem for a class of nonlinear systems with high order and low order nonlinearities the introduction of the sign function together with the method of adding a power integrator and lyapunov stability theorem makes the closed loop system globally asymptotically stable exploiting the idea of how to deal with growth nonlinearities with both high order and low order being relaxed to some intervals is the focus of this work

global finite time stabilisation by output feedback for a class of uncertain nonlinear systems this article considers the problem of global finite time stabilisation by output feedback for a class of nonlinear systems comprised of a chain of power integrators perturbed by an uncertain vector field to solve the problem we first construct a homogeneous observer and controller in a recursive way for the nominal system without the perturbing nonlinearities then using the homogeneous domination approach we scale the homogeneous observer and controller with an appropriate choice of gain to render the uncertain nonlinear system globally finite time stable due to the use of a reduced order observer the proposed output feedback controller is applicable to those systems with unknown gains associated with the power integrators

signal recovery from wavelet transform maxima the paper presents an iterative algorithm for signal recovery from discrete time wavelet transform maxima the signal recovery algorithm is developed by using the method of projections onto convex sets convergence of the algorithm is assured

practical output feedback risk sensitive control for stochastic nonlinear systems with stable zero dynamics this paper addresses the design problem of practical or satisfaction output feedback controls for stochastic strict feedback nonlinear systems in observer canonical form with stable zero dynamics under long term average tracking risk sensitive cost criteria the cost function adopted here is of the quadratic integral type usually encountered in practice rather than the quartic integral one used to avoid difficulty in control design and performance analysis of the closed loop system a sequence of coordinate diffeomorphisms is introduced to separate the zero dynamics from the entire system so that the transformed system has an appropriate form suitable for integrator backstepping design for any given risk sensitivity parameter and desired cost value by using the integrator backstepping methodology an output feedback control is constructively designed such that a the closed loop system is bounded in probability and b the long term average risk sensitive cost is upper bounded by the desired value in addition this paper does not require the uniform boundedness of the gain functions of the system noise furthermore an example is given to show the effectiveness of the theory

observer based adaptive fuzzy tracking control of mimo stochastic nonlinear systems with unknown control directions and unknown dead zones in this paper an adaptive fuzzy backstepping output feedback tracking control approach is proposed for a class of multi input and multi output mimo stochastic nonlinear systems the mimo stochastic nonlinear systems under study are assumed to possess unstructured uncertainties unknown dead zones and unknown control directions by using a linear state transformation the unknown control coefficients and the unknown slopes characteristic of the dead zones are lumped together and the original system is transformed to a new system on which the control design becomes feasible fuzzy logic systems are used to approximate the unstructured uncertainties and a fuzzy state observer is designed to estimate the unmeasured states by introducing a special nussbaum gain function into the backstepping control design a stable adaptive fuzzy output feedback tracking control scheme is developed the main features of the proposed adaptive control approach are that it can guarantee the stability of the closed loop system and the tracking errors converge to a small neighborhood of zero moreover it can solve the problems of unknown control direction unknown dead zone and unmeasured states simultaneously two simulation examples are provided to show the effectiveness of the proposed approach

brief paper small gain control method for stochastic nonlinear systems with stochastic iiss inverse dynamics this paper investigates the small gain type conditions on stochastic iiss siiss systems and makes full use of these conditions in the design and analysis of the controller the contributions are as follows 1 a new proof of the stochastic lasalle theorem is provided 2 the small gain type conditions on siiss are developed and their relationship is discussed 3 based on the stochastic lasalle theorem and siiss small gain type conditions the adaptive controllers are designed to guarantee that all of the closed loop signals are bounded almost surely and the stochastic closed loop systems are globally asymptotically stable in probability

finite time stabilisation of a class of stochastic nonlinear systems with dead zone input this paper addresses the problem of finite time stabilisation by state feedback for a class of stochastic nonlinear systems in strict feedback form remarkably the system under consideration posse

halftone image classification using lms algorithm and naive bayes former research on inverse halftoning most focus on developing a general purpose method for all types of halftone patterns such as error diffusion ordered dithering etc while fail to consider the natural discrepancies among various halftoning methods to achieve optimal image quality for each halftoning method the classification of halftone images is highly demanded this study employed the least mean square filter for improving the robustness of the extracted features and employed the naive bayes classifier to verify all the extracted features for classification nine of the most well known halftoning methods were involved for testing the experimental results demonstrated that the classification performance can achieve a 100 accuracy rate and the number of distinguishable halftoning methods is more than that of a former method established by chang and yu

global finite time stabilisation for a class of stochastic nonlinear systems by output feedback in this paper the problem of global finite time stabilisation by output feedback is considered for a class of stochastic nonlinear systems first based on homogeneous systems theory and the adding a power integrator technique a homogeneous reduced order observer and control law are constructed in a recursive manner for the nominal system then the homogeneous domination approach is used to deal with the nonlinearities in drift and diffusion terms it is shown that the proposed output feedback control law can guarantee that the closed loop system is global finite time stable in probability finally simulation examples are carried out to demonstrate the effectiveness of the proposed control scheme

image restoration by the method of convex projections part 1ߞtheory a projection operator onto a closed convex set in hilbert space is one of the few examples of a nonlinear map that can be defined in simple abstract terms moreover it minimizes distance and is nonexpansive and therefore shares two of the more important properties of ordinary linear orthogonal projections onto closed linear manifolds in this paper we exploit the properties of these operators to develop several iterative algorithms for image restoration from partial data which permit any number of nonlinear constraints of a certain type to be subsumed automatically their common conceptual basis is as follows every known property of an original image f is envisaged as restricting it to lie in a well defined closed convex set thus m such properties place f in the intersection e0 ei of the corresponding closed convex sets e1 e2 em given only the projection operators pi onto the individual ei s i 1 m we restore f by recursive means clearly in this approach the realization of the pi s in a hilbert space setting is one of the major synthesis problems section i describes the geometrical significance of the three main theorems in considerable detail and most of the underlying ideas are illustrated with the aid of simple diagrams section ii presents rules for the numerical implementation of 11 specific projection operators which are found to occur frequently in many signal processing applications and the appendix contains proofs of all the major results

inverse halftoning via map estimation there has been a tremendous amount of research in the area of image halftoning where the goal has been to find the most visually accurate representation given a limited palette of gray levels often just two black and white this paper focuses on the inverse problem that of finding efficient techniques for reconstructing high quality continuous tone images from their halftoned versions the proposed algorithms are based on a maximum a posteriori map estimation criteria using a markov random field mrf model for the prior image distribution image estimates obtained with the proposed model accurately reconstruct both the smooth regions of the image and the discontinuities along image edges algorithms are developed and example gray level reconstructions are presented generated from both dithered and error diffused halftone originals application of the technique to the problems of rescreening and the processing of halftone images are shown

halftone to continuous tone conversion of error diffusion coded images considers the problem of reconstructing a continuous tone contone image from its halftoned version where the halftoning process is done by error diffusion the authors present an iterative nonlinear decoding algorithm for halftone to contone conversion and show simulation results that compare the performance of the algorithm to that of conventional linear low pass filtering they find that the new technique results in subjectively superior reconstruction as there is a natural relationship between error diffusion and spl sigma spl delta modulation the reconstruction algorithm can also be applied to the decoding problem for spl sigma spl delta modulators

stabilization of stochastic nonlinear systems driven by noise of unknown covariance this paper poses and solves a new problem of stochastic nonlinear disturbance attenuation where the task is to make the system solution bounded by a monotone function of the supremum of the covariance of the noise this is a natural stochastic counterpart of the problem of input to state stabilization in the sense of sontag 1989 our development starts with a set of new global stochastic lyapunov theorems for an exemplary class of stochastic strict feedback systems with vanishing nonlinearities where the equilibrium is preserved in the presence of noise we develop an adaptive stabilization scheme based on tuning functions that requires no a priori knowledge of a bound on the covariance next we introduce a control lyapunov function formula for stochastic disturbance attenuation finally we address optimality and solve a differential game problem with the control and the noise covariance as opposing players for strict feedback systems the resulting isaacs equation has a closed form solution

image restoration by the method of convex projections part 2 applications and numerical results the image restoration theory discussed in a previous paper by youla and webb 1 is applied to a simulated image and the results compared with the well known method known as the gerchberg papoulis algorithm the results show that the method of image restoration by projection onto convex sets by providing a convenient technique for utilizing a priori information performs significantly better than the gerchberg papoulis method

output feedback stabilization of stochastic high order nonlinear systems under weaker conditions under the weaker conditions on the power order and the nonlinear functions this paper investigates the output feedback stabilization problem for a class of stochastic high order nonlinear systems based on the backstepping design method and homogeneous domination technique the closed loop system can be proved to be globally asymptotically stable in probability

backstepping controller design for nonlinear stochastic systems under a risk sensitive cost criterion this paper develops a methodology for recursive construction of optimal and near optimal controllers for strict feedback stochastic nonlinear systems under a risk sensitive cost function criterion the design procedure follows the integrator backstepping methodology and the controllers obtained guarantee any desired achievable level of long term average cost for a given risk sensitivity parameter theta furthermore they lead to closed loop system trajectories that are bounded in probability and in some cases asymptotically stable in the large these results also generalize to nonlinear systems with strongly stabilizable zero dynamics a numerical example included in the paper illustrates the analytical results

nonsmooth stabilization of a class of nonlinear cascaded systems a global nonsmooth stabilization scheme is presented for a class of nonlinear cascaded systems with uncontrollable linearization a stepwise constructive control methodology is proposed for the driving subsystem by using the adding a power integrator technique under suitable conditions and based on homogeneous properties it is proved that the stabilization of the driving subsystem implies the stabilization of the overall cascaded system due to the versatility of the adding a power integrator technique and homogeneous properties the proposed controller not only can be used to stabilize the cascaded system asymptotically but also is able to lead to an interesting result of finite time stabilization under appropriate conditions

finite time stabilization of high order stochastic nonlinear systems in strict feedback form this paper deals with the problem of finite time stabilization for a class of high order stochastic nonlinear systems in strict feedback form by using ito s formula mathematical induction and backstepping design method a novel state feedback controller is constructed to guarantee that the closed loop high order nonlinear system has a unique solution and the solution of the closed loop high order nonlinear system is finite time stable a systematic design algorithm is developed for the construction of the backstepping controller finally the effectiveness of the state feedback controller is illustrated by two examples

further results on adaptive state feedback stabilization for stochastic high order nonlinear systems this paper aims to relax the results in xie and tian 2009 from the following two aspects completely removing the power order restriction and largely relaxing the growth conditions of nonlinear functions by using the backstepping design method and homogeneous domination technique this paper investigates the problem of adaptive state feedback stabilization for a class of stochastic high order nonlinear systems with nonlinear parameterization the closed loop system can be proved to be globally stable in probability and the states can be regulated to the origin almost surely the efficiency of the adaptive state feedback controller is demonstrated by a simulation example