systems over a principal ideal domain a polynomial model approach the polynomial model approach to linear dynamical systems over a field was developed principally by p a fuhrmann starting in 1976 j franklin inst 305 1976 pp 521 540 in this paper an analogous approach is proposed for systems over a principal ideal domain when the concept of extended linear i o map is introduced fractional representations of transfer function matrices arise naturally in this theoretical framework a correspondence between fractional representations of the transfer function matrix of a given i o map and its reachable or observable realizations is established the mcmillan degree of a linear i o map is proved to be equal to the degree of the determinant of the matrix appearing as denominator in a coprime fractional representation of the associated transfer function matrix

an mrf model based approach to simultaneous recovery of depth and restoration from defocused images in this paper we propose a map markov random field mrf based scheme for recovering the depth and the focused image of a scene from two defocused images the space variant blur parameter and the focused image of the scene are both modeled as mrfs and their map estimates are obtained using simulated annealing the scheme is amenable to the incorporation of smoothness constraints on the spatial variations of the blur parameter as well as the scene intensity it also allows for inclusion of line fields to preserve discontinuities the performance of the proposed scheme is tested on synthetic as well as real data and the estimates of the depth are found to be better than that of the existing window based depth from defocus technique the quality of the space variant restored image of the scene is quite good even under severe space varying blurring conditions

technical communique disturbance attenuation by dynamic output feedback for input delay systems this paper addresses the optimal disturbance attenuation problem by output feedback for multivariable linear systems with delayed inputs the attenuation is optimal in the sense that the controller minimizes the maximal amplitude of the plant output in response to such a disturbance the controller is a general feedback involving an observer a state predictor and a predicted state feedback the optimal disturbance attenuation problem is formulated in terms of an equivalent system without delay the optimal bound of the disturbance attenuation is then characterized and it is shown that the optimal controller tends to have high gains a necessary and sufficient condition to guarantee the existence of an optimal solution is provided using the geometric approach

the fractional representation approach to synthesis problems an algebraic analysis viewpoint part i weakly doubly coprime factorizations in this paper we show how to reformulate the fractional representation approach to analysis and synthesis problems within an algebraic analysis framework in terms of modules we give necessary and sufficient conditions so that a system admits weakly left right doubly coprime factorizations moreover we explicitly characterize the integral domains a such that every plant defined by means of a transfer matrix whose entries belong to the quotient field of a admits weakly doubly coprime factorizations finally we show that this algebraic analysis approach allows us to recover on the one hand the approach developed in m c smith ieee trans automat control 34 1989 pp 1005 1007 and on the other hand the ones developed in k mori and k abe siam j control optim 39 2001 pp 1952 1973 v r sule siam j control optim 32 1994 pp 1675 1695 and 36 1998 pp 2194 2195 m vidyasagar h schneider and b a francis ieee trans automat control 27 1982 pp 880 894 m vidyasagar control system synthesis a factorization approach mit press cambridge ma 1985

reciprocal focus profile a focus profile having a steeper peak is more resistant to image noise in the autofocus af process of a digital camera however a focus profile of such shape normally has a flatter out of focus region on either side of the profile resulting in a slow af process due to the lack of clue about where the lens should move when the lens is in such regions to address the problem we provide a statistical analysis of the focus profile and show that a strictly monotonic transformation of the focus profile preserves the accuracy of the af on the basis of this analysis we propose a new focus profile representation that transforms the focus profile to the reciprocal domain in which the reciprocal focus profile is modeled by a polynomial function this transformation makes the af mathematically tractable and boosts the search speed experimental results are shown to demonstrate the advantage of the proposed representation

block decoupling for linear systems over rings abstract this paper studies the block decoupling problem for injective linear systems defined over unique factorization domains and necessary and sufficient conditions for its solvability are obtained using the algebraic properties of transfer matrices further it is shown that if the problem is solvable the decoupling can be achieved by a biproper compensator and such a compensator can be realized by a regular static state feedback finally an example is given to illustrate the results

shape from focus the shape from focus method presented here uses different focus levels to obtain a sequence of object images the sum modified laplacian sml operator is developed to provide local measures of the quality of image focus the operator is applied to the image sequence to determine a set of focus measures at each image point a depth estimation algorithm interpolates a small number of focus measure values to obtain accurate depth estimates a fully automated shape from focus system has been implemented using an optical microscope and tested on a variety of industrial samples experimental results are presented that demonstrate the accuracy and robustness of the proposed method these results suggest shape from focus to be an effective approach for a variety of challenging visual inspection tasks

decoupling of multivariable control systems over unique factorization domains necessary and sufficient conditions are established for the existence of a state variable feedback decoupling of an m input m output time invariant linear control system over a unique factorization domain an explicit computation is provided for the feedback and the feedforward gain matrix also necessary and sufficient conditions for the existence of a stability preserving state feedback decoupling are given the results are illustrated by some examples

input output feedback linearization of time delay systems in this note the input output linearization problem iolp for a class of single input single output nonlinear systems with multiple delays in the input the output and the state is studied the problem is solved by means of various static or dynamic compensators including state and output feedback the mathematical setting is based on some noncommutative algebraic tools and the introduction of a nonlinear version of the so called roesser models for this class of systems these are claimed to be the cornerstones for studying nonlinear time delay systems necessary and sufficient conditions are given for the existence of a static or pure shift output feedback which solves the iolp sufficient conditions for the existence of a dynamic state feedback solution are included as well

decoupling of square linear systems with delays the aim of this paper is to exhibit matricial necessary and sufficient conditions for the decoupling problem of linear systems with commensurate delays under static nonpredictive and stable state feedbacks a matrix approach is used which is similar to the falb wolovich one for systems without delay the conditions obtained here are quite simple easily computable and less restrictive than the previous ones moreover we give the only possible design of the physically realizable control law that satisfies the problem

integrability for nonlinear time delay systems in this note the notion of integrability is defined for 1 forms defined in the time delay context while in the delay free case a set of 1 forms defines a vector space it is shown that 1 forms computed for time delay systems have to be viewed as elements of a module over a certain non commutative polynomial ring two notions of integrability are defined strong and weak integrability which coincide in the delay free case necessary and sufficient conditions are given to check if a set of 1 forms is strongly or weakly integrable to show the importance of the topic integrability of 1 forms is used to characterize the accessibility property for nonlinear time delay systems the possibility of transforming a system into a certain normal form is also considered

prolongation structures of nonlinear equations and infinite dimensional algebras prolongation structures of the sine gordon equation the ernst equation and the chiral model are systematically discussed it is shown that the prolongation structures generate the kac moody algebra for the sine gordon equation and another type of infinite dimensional algebra for the ernst equation this algebra includes the kac moody algebra and the virasoro algebra as its subalgebra

a transfer matrix approach to feedback invariants of linear systems application to decoupling abstract the transfer matrix approach allows one to exhibit fairly easily fundamental invariants of multivariable systems under the action of transformation groups these transformation groups include the classical state feedback state and input changes of coordinates then the solvability of numerous classical control problems e g decouplability disturbance rejection model following can be expressed directly in terms of these invariants in this expository paper we present in a unified way three lists of feedback invariants related to the infinite behavior of linear systems these invariants turn out to be crucial in studying feedback decoupling problems the main tools for this study are factorization of transfer matrices over the p i d of proper rational functions when dealing with stability we factor transfer matrices over the p i d of proper rational stable functions we illustrate the use of these invariants by studying some decoupling problems

regular paper model matching for linear systems with delays and 2d systems model matching problem for linear systems with delays is considered via a transfer matrix approach we deal with a general class of neutral delay differential systems which is equivalent to 2d systems from a realizability point of view the solution of the problem is based on the decomposition of the ring of the causal rational functions which is not a principal ideal domain as the intersection of two suitable principal ideal domains

the robust regulation problem with robust stability a subspace valued function approach among the most common purposes are the tracking of reference signals and the rejection of disturbance signals in the face of uncertainties the related design problem is called the robust regulation problem here we investigate the tradeoff between the robust regulation constraint and the requirement of robust stability with respect to perturbations in the normalized coprime factors of the plant we use an approach in terms of subspace valued functions associated to plant and controller in this way necessary and sufficient conditions for robust regulation with robust stability can be related to a simple geometric property

shape from focus using multilayer feedforward neural networks the conventional shape from focus sff methods have inaccuracies because of piecewise constant approximation of the focused image surface fis we propose a scheme for sff based on representation of three dimensional 3 d fis in terms of neural network weights the neural networks are trained to learn the shape of the fis that maximizes the focus measure

internal model control in the shift and delta domains we construct multivariable internal model controllers in the shift and delta domains to do so we develop a linear algebraic approach to the multivariable command following and disturbance rejection problem that facilitates a unified treatment of the differential shift and delta domains

multifocus image fusion by combining with mixed order structure tensors and multiscale neighborhood a new fusion scheme based on multiscale neighborhood technique is proposed for multifocus image fusion a new focus measure by combining the structure tensors of mixed order differential is developed an effective focused region detection method is presented based on multiscale neighborhood technique an averaging fusion scheme is presented based on the fusion decision maps of different scale for uncertain regions our method outperforms the traditional methods in various experiments in this study we propose a new method for multifocus image fusion by combining with the structure tensors of mixed order differentials and the multiscale neighborhood in this method the structure tensor of an integral differential is utilized to detect the high frequency regions and the structure tensor of the fractional differential is used to detect the low frequency regions to improve the performance of the fusion method we propose a new focus measure based on the multiscale neighborhood technique to generate the initial fusion decision maps by exploiting the advantages of different scales next based on the multiscale neighborhood technique a post processing method is used to update the initial fusion decision maps during the fusion process the pixels located in the focused inner regions are selected to produce the fused image in order to avoid discontinuities in the transition zone between the focused and defocused regions we propose a new averaging scheme based on the fusion decision maps at different scales our experimental results demonstrate that the proposed method outperformed the conventional multifocus image fusion methods in terms of both their subjective and objective quality

a moment preserving approach for depth from defocus abstract for range sensing using depth from defocus methods the distance d of a point object from the lens can be evaluated by the concise depth formula d p q d b where p and q are constants for a given camera setting and db is the diameter of the blur circle for the point object on the image detector plane the amount of defocus db is traditionally estimated from the spatial parameter of a gaussian point spread function using a complex iterative solution in this paper we use a straightforward and computationally fast method to estimate the amount of defocus from a single camera the observed gray level image is initially converted into a gradient image using the sobel edge operator for the edge point of interest the proportion of the blurred edge region pe in a small neighborhood window is then calculated using the moment preserving technique the value of pe increases as the amount of defocus increases and therefore is used as the description of degradation of the point spread function in addition to the use of the geometric depth formula for depth estimation artificial neural networks are also proposed in this study to compensate for the estimation errors from the depth formula experiments have shown promising results that the rms depth errors are within 5 for the depth formula and within 2 for the neural networks

feedback representation of precompensators application to decoupling linear multi input multi output plants in this paper we examine the problem of internally stabilizing and simultaneously diagonally decoupling a linear multivariable system by two parameter compensation based on our earlier results boussaid and guerin 1996 we prove that any given plant p of full row rank can be decoupled with stability by the considered configuration computation of the decoupling compensators follows by easy constructions the decoupling problem with a minimum number of unstable zeros in the decoupled system is also formulated and solved in the generic case

a geometric approach to the general autonomous regulator problem in the time delay framework abstract the aim of this paper is to show the applicability of geometric techniques to a regulation problem for linear time delay systems given a plant whose dynamics equations include delays and an exosystem that generates a reference signal the problem we consider consists in finding a feedback regulator which guarantees asymptotic stability of the regulation loop and asymptotic command following of the reference signal for any initial condition of the overall system in the presence of disturbances by associating to the time delay plant a corresponding abstract system with coefficients in a ring it is possible to place our investigation in a finite dimensional algebraic context where intuition and results obtained in the classical case that is without delays may be exploited in particular using tools and methods of the geometric approach to systems with coefficients in a ring sufficient conditions for the solvability of the considered problem are found and a constructive procedure which works under specific hypotheses is given

brief analysis of nonlinear time delay systems using modules over non commutative rings the theory of non commutative rings is introduced to provide a basis for the study of nonlinear control systems with time delays the left ore ring of non commutative polynomials defined over the field of meromorphic function is suggested as the framework for such a study this approach is then generalized to a broader class of nonlinear systems with delays that are called generalized roesser systems finally the theory is applied to analyze nonlinear time delay systems a weak observability is defined and characterized generalizing the well known linear result properties of closed submodules are then developed to obtain a result on the accessibility of such systems

improvements in shape from focus for holographic reconstructions with regard to focus operators neighborhood size and height value interpolation this paper presents a shape from focus method which is improved with regard to the mathematical operator used for contrast measurement the selection of the neighborhood size surface refinement through interpolation and surface postprocessing three dimensional models of living human faces are presented with such a high resolution that single hairs are visible

the block decoupling problem for systems over a ring the decoupling problem by static state feedback for a system with coefficients in a ring is investigated using a geometric approach the notion of a precontrollability submodule which captures the geometric aspects of the notion of controllability subset of the state space in the present context is introduced and it is used for stating solvability conditions for the decoupling problem for a system with coefficients in a noetherian ring this result extends and improves previous results concerning systems with coefficients in a principal ideal domain and it can in particular be used for dealing with decoupling problem involving delay differential systems

pseudopotentials lax equations and backlund transformations for nonlinear evolution equations it is shown how to generate both lax equations and backlund transformations for nonlinear evolution equations using the concept of pseudopotentials associated with the properties of the riccati equation several examples are given modified korteweg de vries harry dym kaup kupershmidt and sawada kotera equations

robust sliding mode control of nonlinear systems with delay a design via polytopic formulation this paper outlines the possibility to control nonlinear uncertain systems with single possibly time varying state delay these systems are submitted to additive perturbations possibly nonvanishing the control is of sliding mode type and the sliding surface is designed so to maximize the calculable set of delays which do not destabilize the system the way to deal with the nonlinear parts of the model relies on a polytopic formulation the conditions for the existence of the sliding regime are studied by using both a lyapunov krasovskii functionnal and a lyapunov razumikhin function the optmization precedure for the choice of the sliding surface is expressed in terms of lmis an example illustrates the proposed method

a novel algorithm for estimation of depth map using image focus for 3d shape recovery in the presence of noise three dimensional shape recovery from one or multiple observations is a challenging problem of computer vision in this paper we present a new focus measure for the estimation of a depth map using image focus this depth map can subsequently be used in techniques and algorithms leading to the recovery of a three dimensional structure of the object a requirement of a number of high level vision applications the proposed focus measure has shown robustness in the presence of noise as compared to the earlier focus measures this new focus measure is based on an optical transfer function implemented in the fourier domain the results of the proposed focus measure have shown drastic improvements in estimation of a depth map with respect to the earlier focus measures in the presence of various types of noise including gaussian shot and speckle noises the results of a range of focus measures are compared using root mean square error and correlation metric measures

on feedback invariance properties for systems over a principal ideal domain simple necessary and sufficient conditions for the solvability of many control problems for linear systems over a field are based on the equivalence between the a b invariance property and the a bf invariance or feedback invariance property for systems over a ring this equivalence is no longer true and many results of the geometric control theory cannot be extended we present new algorithmically checkable characterizations of the a bf invariance property for systems defined over a principal ideal domain and a new solvability condition for the disturbance rejection problem

non parametric blur map regression for depth of field extension real camera systems have a limited depth of field dof which may cause an image to be degraded due to visible misfocus or too shallow dof in this paper we present a blind deblurring pipeline able to restore such images by slightly extending their dof and recovering sharpness in regions slightly out of focus to address this severely ill posed problem our algorithm relies first on the estimation of the spatially varying defocus blur drawing on local frequency image features a machine learning approach based on the recently introduced regression tree fields is used to train a model able to regress a coherent defocus blur map of the image labeling each pixel by the scale of a defocus point spread function a non blind spatially varying deblurring algorithm is then used to properly extend the dof of the image the good performance of our algorithm is assessed both quantitatively using realistic ground truth data obtained with a novel approach based on a plenoptic camera and qualitatively with real images

multiresolution 3 d range segmentation using focus cues this paper describes a novel system for computing a three dimensional 3 d range segmentation of an arbitrary visible scene using focus information the process of range segmentation is divided into three steps an initial range classification a surface merging process and a 3 d multiresolution range segmentation first range classification is performed to obtain quantized range estimates the range classification is performed by analyzing focus cues within a bayesian estimation framework a combined energy functional measures the degree of focus and the gibbs distribution of the class field the range classification provides an initial range segmentation second a statistical merging process is performed to merge the initial surface segments this gives a range segmentation at a coarse resolution third 3 d multiresolution range segmentation 3 d mrs is performed to refine the range segmentation into finer resolutions the proposed range segmentation method does not require initial depth estimates it allows the analysis of scenes containing multiple objects and it provides a rich description of the 3 d structure of a scene

removal of partial occlusion from single images this paper examines large partial occlusions in an image which occur near depth discontinuities when the foreground object is severely out of focus we model these partial occlusions using matting with the alpha value determined by the convolution of the blur kernel with a pinhole projection of the occluder the main contribution is a method for removing the image contribution of the foreground occluder in regions of partial occlusion which improves the visibility of the background scene the method consists of three steps first the region of complete occlusion is estimated using a curve evolution method second the alpha value at each pixel in the partly occluded region is estimated third the intensity contribution of the foreground occluder is removed in regions of partial occlusion experiments demonstrate the method s ability to remove the effects of partial occlusion in single images with minimal user input

variational depth from focus reconstruction this paper deals with the problem of reconstructing a depth map from a sequence of differently focused images also known as depth from focus dff or shape from focus we propose to state the dff problem as a variational problem including a smooth but nonconvex data fidelity term and a convex nonsmooth regularization which makes the method robust to noise and leads to more realistic depth maps in addition we propose to solve the nonconvex minimization problem with a linearized alternating directions method of multipliers allowing to minimize the energy very efficiently a numerical comparison to classical methods on simulated as well as on real data is presented

dynamics of director fields an asymptotic equation for weakly nonlinear hyperbolic waves governed by variational principles is derived and analyzed the equation is used to study a nonlinear instability in the director field of a nematic liquid crystal it is shown that smooth solutions of the asymptotic equation break down in finite time also constructed are weak solutions of the equation that are continuous despite the fact that their spatial derivative blows up

tunable halfband pair wavelet filter banks and application to multifocus image fusion traditional maximally flat wavelet filters are highly regular but suffer from poor frequency selectivity because of their wide transition band in this paper an efficient method is proposed for the design of biorthogonal perfect reconstruction wavelet filter banks known as halfband pair filter banks hpfb to be used in several applications in image processing and pattern recognition the formulation is based on representation of a general halfband polynomial in the variable x we first derive filter coefficients in the polynomial domain in the variable x in terms of the coefficients of the corresponding function in z domain using convex optimization techniques and due to the simple structure of a parametric polynomial in general we can impose some free parameters to provide a tuning opportunity to optimize and control the wavelet filter characteristics perfect reconstruction and desired number of vanishing moments nvm are incorporated into the design procedure the method is systematic renders a reasonable optimization problem and it offers wavelet filters ranging from the maximally flat to the sharpest transition band therefore it can provide a useful design tool with a fine tuning option which is required in many applications such as watermarking detection segmentation fusion denoising and feature extraction the application of the wavelet pairs which have sharper transition band and better frequency selectivity is shown in multifocus imaging to obtain a fully focused image from a set of registered input images at varying foci by employing the distance transform and exponentially decaying function on the subbands in the wavelet domain various images are tested and experimental results compare favorably to the results in the literature

shape from focus using fast discrete curvelet transform a new method for focus measure computation is proposed to reconstruct 3d shape using image sequence acquired under varying focus plane adaptive histogram equalization is applied to enhance varying contrast across different image regions for better detection of sharp intensity variations fast discrete curvelet transform fdct is employed for enhanced representation of singularities along curves in an input image followed by noise removal using bivariate shrinkage scheme based on locally estimated variance the fdct coefficients with high activity are exploited to detect high frequency variations of pixel intensities in a sequence of images finally focus measure is computed utilizing neighborhood support of these coefficients to reconstruct the shape and a well focused image of the scene being probed

optimal depth estimation by combining focus measures using genetic programming three dimensional 3d shape reconstruction is a fundamental problem in machine vision applications shape from focus sff is one of the passive optical methods for 3d shape recovery that uses degree of focus as a cue to estimate 3d shape in this approach usually a single focus measure operator is applied to measure the focus quality of each pixel in the image sequence however the applicability of a single focus measure is limited to estimate accurately the depth map for diverse type of real objects to address this problem we develop optimal composite depth ocd function through genetic programming gp for accurate depth estimation the ocd function is constructed by optimally combining the primary information extracted using one or more focus measures the genetically developed composite function is then used to compute the optimal depth map of objects the performance of the developed nonlinear function is investigated using both the synthetic and the real world image sequences experimental results demonstrate that the proposed estimator is more useful in computing accurate depth maps as compared to the existing sff methods moreover it is found that the heterogeneous function is more effective than homogeneous function

a novel iterative shape from focus algorithm based on combinatorial optimization shape from focus sff is a technique to estimate the depth and 3d shape of an object from a sequence of images obtained at different focus settings in this paper the sff is presented as a combinatorial optimization problem the proposed algorithm tries to find the combination of pixel frames which produces maximum focus measure computed over pixels lying on those frames to reduce the high computational complexity a local search method is proposed after the estimate of the initial depth map solution of an object the neighborhood is defined and an intermediate image volume is generated from the neighborhood the updated depth map solution is found from the intermediate image volume this update process of the depth map solution continues until the amount of improvement is negligible the results of the proposed sff algorithm have shown significant improvements in both the accuracy of the depth map estimation and the computational complexity with respect to the existing sff methods

rational filters for passive depth from defocus a fundamental problem in depth from defocus is the measurement of relative defocus between images the performance of previously proposed focus operators are inevitably sensitive to the frequency spectra of local scene textures as a result focus operators such as the laplacian of gaussian result in poor depth estimates an alternative is to use large filter banks that densely sample the frequency space though this approach can result in better depth accuracy it sacrifices the computational efficiency that depth from defocus offers over stereo and structure from motion we propose a class of broadband operators that when used together provide invariance to scene texture and produce accurate and dense depth maps since the operators are broadband a small number of them are sufficient for depth estimation of scenes with complex textural properties in addition a depth confidence measure is derived that can be computed from the outputs of the operators this confidence measure permits further refinement of computed depth maps experiments are conducted on both synthetic and real scenes to evaluate the performance of the proposed operators the depth detection gain error is less than 1 irrespective of texture frequency depth accuracy is found to be 0 5 1 2 of the distance of the object from the imaging optics

cascade control of systems over integral domains necessary and sufficient conditions for the existence of cascade compensators and dynamic equivalence of linear systems over integral domains arc derived the considerations lead to constructive procedures for dynamic compensation

a state space technique for the evaluation of diagonalizing compensators this note develops a technique for designing diagonalizing compensators based on state space descriptions the relationship with stable decoupling invariants is also explored

fifth order evolution equations describing pseudospherical surfaces we consider differential equations which describe pseudospherical surfaces with associated 1 forms i fi1dx fi2dt 1 i 3 we characterize all such equations of type ut uxxxxx g u ux uxxxx whose associated 1 forms satisfy fp1 pf11 p p p r 2 p 3 in addition to a generic technical assumption we also classify all of these equations which are independent of any of the real parameters p p obtaining as particular cases the fifth order korteweg de vries the sawada kotera and the kaup kupershmidt equations we determine huge classes of equations describing pseudospherical surfaces and their respective linear problems in which particular cases are obtained by merely specifying certain functions which depend on u and its derivatives with respect to x

exact solutions for some nonlinear evolution equations which describe pseudo spherical surfaces for some nonlinear evolution equations which describe pseudo spherical surfaces two new exact solution classes are generated from known solutions either the seed solution is constant or a traveling wave exact traveling wave and solitary wave solutions for burgers equation and also for a fifth order evolution equation containing the fifth order korteweg de vries equation and also the sawada kotera equation are obtained by using an improved sine cosine method and the wu s elimination method we also apply backlund transformations to these solutions and generate new soliton solution classes

analysis of focus measure operators for shape from focus shape from focus sff has widely been studied in computer vision as a passive depth recovery and 3d reconstruction method one of the main stages in sff is the computation of the focus level for every pixel of an image by means of a focus measure operator in this work a methodology to compare the performance of different focus measure operators for shape from focus is presented and applied the selected operators have been chosen from an extensive review of the state of the art the performance of the different operators has been assessed through experiments carried out under different conditions such as image noise level contrast saturation and window size such performance is discussed in terms of the working principles of the analyzed operators

duality between invariant spaces for max plus linear discrete event systems we extend the notions of conditioned and controlled invariant spaces to linear dynamical systems over the max plus or tropical semiring we establish a duality theorem relating both notions which we use to construct dynamic observers these are useful in situations in which some of the system coefficients may vary within certain intervals the results are illustrated by an application to a manufacturing system

max plus a b invariant spaces and control of timed discrete event systems the concept of a b invariant subspace or controlled invariant of a linear dynamical system is extended to linear systems over the max plus semiring although this extension presents several difficulties which are similar to those encountered in the same kind of extension to linear dynamical systems over rings it appears capable of providing solutions to many control problems like in the cases of linear systems over fields or rings sufficient conditions are given for computing the maximal a b invariant subspace contained in a given space and the existence of linear state feedbacks is discussed an application to the study of transportation networks which evolve according to a timetable is considered

on differential equations describing pseudo spherical surfaces abstract we give a complete classification of the evolution equations u t f u u x k u x k which describe pseudo spherical surfaces without any a priori assumptions on the presence of a spectral parameter we also prove a local existence theorem to the effect that given two differential equations describing pseudo spherical surfaces not necessarily evolutionary there exists under a technical assumption a smooth mapping transforming any suitably generic solution of one equation into a solution of the other

correspondence theorems for hierarchies of equations of pseudo spherical type hierarchies of evolution equations of pseudo spherical type are introduced thereby generalizing the notion of a single equation describing pseudo spherical surfaces due to s s chern and k tenenblat and providing a connection between differential geometry and the study of hierarchies of equations which are the integrability condition of sl 2 r valued linear problems as an application it is shown that there exist local correspondences between any two suitably generic solutions of arbitrary hierarchies of equations of pseudo spherical type

generation of all in focus images by noise robust selective fusion of limited depth of field images the limited depth of field of some cameras prevents them from capturing perfectly focused images when the imaged scene covers a large distance range in order to compensate for this problem image fusion has been exploited for combining images captured with different camera settings thus yielding a higher quality all in focus image since most current approaches for image fusion rely on maximizing the spatial frequency of the composed image the fusion process is sensitive to noise in this paper a new algorithm for computing the all in focus image from a sequence of images captured with a low depth of field camera is presented the proposed approach adaptively fuses the different frames of the focus sequence in order to reduce noise while preserving image features the algorithm consists of three stages 1 focus measure 2 selectivity measure 3 and image fusion an extensive set of experimental tests has been carried out in order to compare the proposed algorithm with state of the art all in focus methods using both synthetic and real sequences the obtained results show the advantages of the proposed scheme even for high levels of noise

wiener hopf design of optimal decoupled multivariable feedback control system an important consideration in the design of many control systems is decoupling each command input controlling only one output the 2dof two degree of freedom or 3dof three degree of freedom structure is ideally suited to this task since only one of the degrees of freedom is affected by the decoupling requirement the decoupling constraint on this degree of freedom however can lead to some deterioration in achievable system performance a design procedure which minimizes this performance deterioration is established the parameterization of the class of all decoupled systems is given for which the cost functional representing system performance remains finite

computation of maximal pre controllability submodules over a noetherian ring for dynamical systems with coefficient in a ring it is not always possible to compute by a finite procedure the maximal a b invariant submodule contained in the kernel of the output map c namely v kerc this difficulty prevents one from checking necessary and sufficient geometric conditions for the solvability of noninteracting control problems in this paper we will prove that for dynamical systems with coefficients in a noetherian ring it is always possible to compute by a finite procedure the maximal pre controllability submodule contained in the kernel of the output map c namely r kerc this result is useful in dealing with the block decoupling problem or the disturbance rejection problem

a focus fusion framework with anisotropic depth map smoothing focus fusion is the task of combining a set of images focused at different depths into a single image that is entirely in focus the crucial point of all focus fusion methods is the decision about the in focus areas to this end we present a general framework for focus fusion that introduces a modern regularisation strategy on these per pixel decisions we assume that neighbouring pixels in the fused image belong to similar depth layers following this assumption we smooth the depth map with a sophisticated anisotropic diffusion process combined with a robust data fidelity term the experiments with synthetic and real world data demonstrate that our new model yields a better quality than several existing focus fusion methods moreover our methodology is general and can be applied to improve many fusion approaches highlightswe show that depth map regularisation is an important tool for focus fusion we incorporate modern concepts such as a coupled anisotropic diffusion term we substantially improve the runtime with a fast gpu implementation we evaluate different in focus measures we compare the overall performance to several methods from the literature

output regulation by error dynamic feedback in hybrid systems with periodic state jumps abstract this work deals with output regulation in multivariable hybrid systems featuring a continuous time linear dynamics periodically affected by instantaneous changes of the state more precisely given a hybrid linear plant and a hybrid linear exogenous system with periodic state jumps the problem consists in finding a hybrid feedback regulator with the same characteristics achieving global asymptotic stability of the closed loop dynamics and asymptotic tracking of the reference generated by the exogenous system for all the initial states starting from a general necessary and sufficient condition for the existence of a solution the discussion leads to a more specific sufficient condition which outlines the computational framework for a straightforward synthesis of the compensator the internal model principle is shown to hold in a more general formulation than the original one adapted to the hybrid systems considered a numerical example is worked out with the aim of illustrating how to implement the devised technique the geometric approach is the key methodology in attaining these results

development of autofocusing algorithm based on fuzzy transforms in this paper we propose a new passive auto focusing algorithm to acquire images with enhanced quality through a digital camera the focus measure operations play a key role in a passive auto focusing method the proposed focus measure operation is based on a localized version of image variance method the localization of the image variance focus measure operation can be implemented with the use of fuzzy partition and fuzzy transform in order to validate our approach experimental comparative studies are conducted on test images with the use of different focus measure operators the selected operators have been chosen from an extensive review of the state of the art approaches a comparative analysis demonstrates that the proposed algorithm is superior to the conventional methods

feedback realization of nonsingular precompensators for linear systems with delays the problem of realization of dynamic precompensators for linear systems with delays by static or dynamic state feedback and static output feedback is considered necessary and sufficient conditions for the solutions are given

noninteracting control of 2 d systems necessary and sufficient conditions for the existence of a decoupling bicausal precompensator for multivariable 2 d systems are derived in state space and frequency domains in general the decoupling problem for 2 d systems can be solved by feedback compensators if suitable injectivity assumptions are introduced on the input state matrices the structure of dynamic compensators is derived for this case and the 2 d decoupling problem with stability is solved

nonlinear approach for enhancement of image focus volume in shape from focus mostly shape from focus algorithms use local averaging using a fixed rectangle window to enhance the initial focus volume in this linear filtering the window size affects the accuracy of the depth map a small window is unable to suppress the noise properly whereas a large window oversmoothes the object shape moreover the use of any window size smoothes focus values uniformly consequently an erroneous depth map is obtained in this paper we suggest the use of iterative 3 d anisotropic nonlinear diffusion filtering andf to enhance the image focus volume in contrast to linear filtering andf utilizes the local structure of the focus values to suppress the noise while preserving edges the proposed scheme is tested using image sequences of synthetic and real objects and results have demonstrated its effectiveness

disturbance decoupling with closed loop modes stability in switched linear systems this work deals with the problem of rendering the output of a switched linear system insensitive to a disturbance input with the requirement that the dynamics of the closed loop system be exponentially stable for all switching signals with a sufficiently large dwell time a necessary and sufficient condition for the problem to have a solution is shown a complete computational procedure to check the solvability condition and to synthesize the compensation scheme is provided a worked out example is presented with the aim of showing the effectiveness of the devised method

controllability of driftless nonlinear time delay systems the controllability of a class of nonlinear driftless time delay systems is fully characterized for the first time this result is obtained within a newly introduced geometric approach moreover all those possible autonomous or non controllable elements which can depend on the delayed variables are also characterized when the system is not controllable and in consequence a canonical form of those systems is derived

transformations of solutions for equations and hierarchies of pseudo spherical type it is known that if an equation describes non trivial one parameter families of pseudo spherical surfaces its conservation laws generalized nonlocal symmetries and backlund transformations can be studied by geometrical means 4 10 in this letter it is pointed out that there exist correspondences or generalized backlund transformations between arbitrary solutions satisfying some genericity conditions of any two single equations describing pseudo spherical surfaces then the notion of a hierarchy of equations of pseudo spherical type is introduced and a theorem stating that there also exist correspondences between arbitrary solutions of any two such hierarchies is presented a full account of these results appears elsewhere 12 13

the disturbance decoupling problem for systems over a ring up to now the use of geometric methods in the study of disturbance decoupling problems ddps for systems over a ring has provided only necessary conditions for the existence of solutions in this paper we study such problems considering separately the case in which only static feedback solutions are allowed and the one in which dynamic feedback solutions are admitted in the first case we give a complete geometric characterization of the solvability conditions of such problems for injective systems with coefficients in a commutative ring practical procedures for testing the solvability conditions and for constructing solutions if any exist are given in the case of systems with coefficients in a principal ideal domain pid in the second case we give a complete geometric characterization of the solvability conditions for systems with coefficients in a pid

c a invariance of modules over principal ideal domains for discrete time linear systems over a principal ideal domain three types of c a invariance can be distinguished connections between these notions are investigated for pure submodules necessary and sufficient conditions for dynamic c a injection invariance are given sufficient conditions are obtained in the general case

dynamic feedback a b invariant submodules for linear systems over commutative noetherian domains abstract in this paper some basic characterizations of a b invariant submodules for linear systems over commutative noetherian domains are studied first a notion of dynamic feedback a b invariant submodules for such systems is introduced and then it is shown that this notion is equivalent to a b invariance

real time focus range sensor structures of dynamic scenes can only be recovered using a real time range sensor depth from defocus offers an effective solution to fast and dense range estimation however accurate depth estimation requires theoretical and practical solutions to a variety of problems including recovery of textureless surfaces precise blur estimation and magnification variations caused by defocusing both textured and textureless surfaces are recovered using an illumination pattern that is projected via the same optical path used to acquire images the illumination pattern is optimized to maximize accuracy and spatial resolution in computed depth the relative blurring in two images is computed using a narrow band linear operator that is designed by considering all the optical sensing and computational elements of the depth from defocus system defocus invariant magnification is achieved by the use of an additional aperture in the imaging optics a prototype focus range sensor has been developed that has a workspace of 1 cubic foot and produces up to 512 spl times 480 depth estimates at 30 hz with an average rms error of 0 2 several experimental results are included to demonstrate the performance of the sensor

reconstructing arbitrarily focused images from two differently focused images using linear filters we present a novel filtering method for reconstructing an all in focus image or an arbitrarily focused image from two images that are focused differently the method can arbitrarily manipulate the degree of blur of the objects using linear filters without segmentation the filters are uniquely determined from a linear imaging model in the fourier domain an effective and accurate blur estimation method is developed the simulation results show that the accuracy and computational time of the proposed method are improved compared with the previous iterative method and that the effects of blur estimation error on the quality of the reconstructed image are very small the method performs well for real images acquired without visible artifacts

robust control of delay systems a sliding mode control design via lmi this paper considers the sliding mode control of uncertain systems with single or multiple constant or time varying state delays submitted to additive perturbations the sliding surface is designed so to maximize the calculable set of admissible delays the conditions for the existence of the sliding regime are studied by using lyapunov krasovskii functionals and lyapunov razumikhin functions lmis are used for the optimization procedure two examples illustrate the proposed method

the disturbance decoupling problem with stability for switching dynamical systems abstract the disturbance decoupling problem with stability is dealt with by means of the geometric approach for switching systems the existence of feedbacks which decouple the disturbance and at the same time assure stability is difficult to characterize since the action of the feedback couples with that of the switching law under suitable conditions it is shown that the above requirement can be dealt with in separate ways and this allows us to state a checkable necessary condition and on that basis also a sufficient condition for solvability of the problem

shape from focus by tensor voting in this correspondence we address the task of recovering shape from focus sff as a perceptual organization problem in 3 d using tensor voting depth hypotheses from different focus operators are validated based on their likelihood to be part of a coherent 3 d surface thereby exploiting scene geometry and focus information to generate reliable depth estimates the proposed method is fast and yields significantly better results compared with existing sff methods

improving shape from focus using defocus cue the shape from focus sff method uses a sequence of frames to estimate the structure of a 3 d object its accuracy depends on the step size by which the translational table is moved while capturing the images existing sff algorithms use an ad hoc interpolation strategy to account for the error due to the finite step size we propose an improved sff method that uses relative defocus blur derived from actual image data to arrive at the final estimates of the structure of the object a space variant image restoration scheme is also proposed to obtain a focused image of the 3 d object the reconstructed 3 d structure as well as the quality of the restored image are superior for the proposed method in comparison to traditional sff

sampling for shape from focus in optical microscopy shape from focus sff which relies on image focus as a cue within sequenced images represents a passive technique in recovering object shapes in scenes although numerous methods have been recently proposed less attention has been paid to particular factors affecting them in regard to sff one such critical factor impacting system application is the total number of images a large data set requires a huge amount of computation power whereas decreasing the number of images causes shape reconstruction to be crude and erroneous the total number of images is inversely proportional to interframe distance or sampling step size in this paper interframe distance or sampling step size criteria for sff systems have been formulated in particular light ray focusing is approximated by the use of a gaussian beam followed by the formulation of a sampling expression using nyquist sampling consequently a fitting function for focus curves is also obtained experiments are performed on simulated and real objects to validate the proposed schemes

decoupling without prediction of linear systems with delays a structural approach we exhibit using a new structural approach specific for linear systems with delays a necessary and sufficient condition for static row by row decoupling without prediction moreover the decoupling problem is analyzed through two different concepts the total one without any time assumption and the partial one in a temporal mean which can be considered if the total one has no solution

the disturbance decoupling problem for time delay nonlinear systems in this paper the disturbance decoupling problem ddp for a class of siso nonlinear systems with multiple delays in the input and the state is studied a pioneering mathematical approach is introduced for this class of systems and is claimed to be the cornerstone of the problem necessary and sufficient conditions are given for the existence of a bicausal feedback that solves the ddp sufficient conditions for the existence of a solution within other classes of compensators are included as well

decoupling linear multiinput multioutput plants by dynamic output feedback an algebraic theory this paper presents an algebraic theory for the design of a decoupling compensator for linear time invariant multiinput multioutput systems the design method uses a two input one output compensator which gives a convenient parametrization of all diagonal input output i o maps and all disturbance to output d o maps achievable by a stabilizing compensator for a given plant it is shown that this method has two degrees of freedom any achievable diagonal i o map and any achievable d o map can be realized simultaneously by a choice of an appropriate compensator the difference between all achievable diagonal and nondiagonal i o maps and the cost of decoupling is discussed for some particular algebraic settings

depth from defocus a spatial domain approach a new method named stm is described for determining distance of objects and rapid autofocusing of camera systems stm uses image defocus information and is based on a new spatial domain convolution deconvolution transform the method requires only two images taken with different camera parameters such as lens position focal length and aperture diameter both images can be arbitrarily blurred and neither of them needs to be a focused image therefore stm is very fast in comparison with depth from focus methods which search for the lens position or focal length of best focus the method involves simple local operations and can be easily implemented in parallel to obtain the depth map of a scene stm has been implemented on an actual camera system named sparcs experiments on the performance of stm and their results on real world planar objects are presented the results indicate that the accuracy of stm compares well with depth from focus methods and is useful in practical applications the utility of the method is demonstrated for rapid autofocusing of electronic cameras

new insights on the analysis of nonlinear time delay systems application to the triangular equivalence in this paper we present recent advances towards an algebraic framework for the analysis and control of nonlinear systems with delays we show the usefulness of these results by applying them to obtain a constructive characterization of the equivalence of a given system to the so called triangular form

accessibility of nonlinear time delay systems a full characterization of accessibility is provided for nonlinear time delay systems it generalizes the rank condition which is known for weak controllability of linear time delay systems as well as the celebrated geometric approach for delay free nonlinear systems and the characterization of their accessibility besides fundamental results are derived on integrability and basis completion which are of major importance for a number of general control problems for nonlinear time delay systems they are shown to impact preconceived ideas about canonical forms for nonlinear time delay systems