synchronization in general complex dynamical networks with coupling delays abstract complex networks have attracted increasing attention from various fields of science and engineering today due to the finite speeds of transmission and spreading as well as traffic congestions a signal or influence travelling through a complex network often is associated with time delays and this is very common in biological and physical networks in this paper we introduce complex dynamical network models with coupling delays for both continuous and discrete time cases and then investigate their synchronization phenomena and criteria based on these new complex network models we derive synchronization conditions for both delay independent and delay dependent asymptotical stabilities in terms of linear matrix inequalities lmi we finally use a network with a fixed delay and a specific coupling scheme as an example to illustrate the theoretical results

structural optimization a new dual method using mixed variables a new and powerful mathematical programming method is described which is capable of solving a broad class of structural optimization problems the method employs mixed direct reciprocal design variables in order to get conservative first order approximations to the objective function and to the constraints by this approach the primary optimization problem is replaced with a sequence of explicit subproblems each subproblem being convex and separable it can be efficiently solved by using a dual formulation an attractive feature of the new method lies in its inherent tendency to generate a sequence of steadily improving feasible designs examples of application to real life aerospace structures are offered to demonstrate the power and generality of the approach presented

visible surface reconstruction via local minimax approximation abstract visible surface reconstruction is an important early stage in the processing and analysis of 3 d imagery as it provides a compact and manipulable representation of the 3 d structure of perceived objects in a scene in this paper we describe an algorithm for reconstructing visible surfaces from scattered surface depth orientation data using approximation methods the basic unit of the proposed algorithm is a minimax approximation routine which operates over regions of local surface support the minimax approach is attractive for several reasons and the computational cost is not high using fast algorithms a window based scheme is used to achieve a smooth surface reconstruction while maintaining discontinuities arising from object occlusions or sudden changes in surface orientation the discontinuities are detected as part of the algorithm results of the technique as applied to several test objects are provided

new approach to synchronization analysis of linearly coupled ordinary differential systems in this paper a general framework is presented for analyzing the synchronization stability of linearly coupled ordinary differential equations lcodes the uncoupled dynamical behavior at each node is general and can be chaotic or otherwise the coupling configuration is also general with the coupling matrix not assumed to be symmetric or irreducible on the basis of geometrical analysis of the synchronization manifold a new approach is proposed for investigating the stability of the synchronization manifold of coupled oscillators in this way criteria are obtained for both local and global synchronization these criteria indicate that the left and right eigenvectors corresponding to eigenvalue zero of the coupling matrix play key roles in the stability analysis of the synchronization manifold furthermore the roles of the uncoupled dynamical behavior on each node and the coupling configuration in the synchronization process are also studied

surface reconstruction and representation of 3 d scenes abstract this paper describes a method of reconstructing and representing the surface of objects in a 3 d scene from a set of parallel planar slices or cross sections the 3 d scene may consist of several occluding objects each slice may consist of a number of distinct 2 d regions defining the 2 d structure at that particular cross section the method described does not require that the scene description be a completely segmented one i e separate object structures need not be distinguished from each other the method can be used where only incomplete description due to missing data are available the generation of surface description consists of three steps first the contours of 2 d regions are traced and an attempt to segment the 3 d scene is made by associating contours on different slices second a triangulation process is performed over pairs of associated contours to generate the local bounding surface structure finally a surface hierarchy is established by coalescing adjacent triangular patches of same orientation into polygonal facets these facets are then integrated to form the object and scene description the surface structure thus obtained is a collection of polygonal facets which bound the outer surface of the objects

explicit constraint approximation forms in structural optimization part 1 analyses and projections abstract an analytical study of several alternative forms of constraint approximation relevant to problems in structural design is presented limitations of the existing forms of the constraint approximations are stated and methods are outlined to improve them a new generalized form of constraint approximation is proposed for optimal design problems with and without design variable linking a power form of constraint approximation is derived for bending types of finite elements having nonlinear size stiffness relationships a detailed analysis to determine the relative effectiveness of the various forms is included a rating guideline is proposed to quantify the characteristics of chosen approximations or family of approximations on grounds of accuracy and of conservatism of remaining feasible

recognizing cylindrical objects by single camera views a new approach to recognition of cylindrical objects by single camera views using camera calibration surface backprojection and model matching techniques is proposed cylindrical objects to be recognized can be of different radii and heights both the silhouette shapes and the surface patterns of objects are utilized in the recognition scheme a new camera calibration technique is first employed to compute the camera parameters analytically using a single camera view of the object a surface backprojection technique is then adopted to reconstruct the pattern on the surface patch of the input object the reconstructed surface pattern is finally matched with that of each object model using a partial shape matching technique to find the best matching surface patch pattern of the models from which the input object is classified accordingly experimental results showing the feasibility of the proposed approach are also included

incremental model building of polyhedral objects using structured light abstract a vision method using active sensing to construct the complete geometric model of a polyhedral object is presented the model is constructed incrementally from multiple views each view produces a partial object model three different methods are described for integrating all the partial models into a final complete model theorems regarding the sufficient number of views required and how these views can be set up during the reconstruction process are also given from theoretical analysis and experimental results our method is shown to produce an accurate object geometric model not just an approximate model furthermore it does not rely on a precise object to image space transformation moreover the method is fast and robust since the basic geometric entity it derives is a face instead of a point

synchronization analysis of linearly coupled systems described by differential equations with a coupling delay when a transmission delay occurs in the interconnection of linearly coupled systems described by ordinary differential equations lcodes both synchronization and the final synchronized state will vary in this paper mathematical analysis is presented on the synchronization phenomena of lcodes with a single coupling delay criteria are derived for both local and global synchronization it is known that in addition to the dynamical behaviors of the underlying uncoupled system and the coupling configuration the coupling strength and the coupling delay also play key roles on the stability of synchronization both theoretical and numerical analysis indicate that under some conditions if the coupling strength is large enough the coupled system can be completely synchronized for any coupling delay on the other hand in some cases the coupled system can be synchronized if the coupling delay is small enough

non convex dual forms based on exponential intervening variables with application to weight minimization we study the weight minimization problem in a dual setting we propose new dual formulations for non linear multipoint approximations with diagonal approximate hessian matrices which derive from separable series expansions in terms of exponential intervening variables these generally nonconvex approximations are formulated in terms of intervening variables with negative exponents and are therefore applicable to the solution of the weight minimization problem in a sequential approximate optimization sao framework problems in structural optimization are traditionally solved using sao algorithms like the method of moving asymptotes which require the approximate subproblems to be strictly convex hence during solution the nonconvex problems are approximated using convex functions and this process may in general be inefficient we argue based on falk s definition of the dual that it is possible to base the dual formulation on nonconvex approximations to this end we reintroduce a nonconvex approach to the weight minimization problem originally due to fleury and we explore certain convex and nonconvex forms for subproblems derived from the exponential approximations by the application of various methods of mixed variables we show in each case that the dual is well defined for the form concerned which may consequently be of use to the future code developers

connection graph stability method for synchronized coupled chaotic systems this paper elucidates the relation between network dynamics and graph theory a new general method to determine global stability of total synchronization in networks with different topologies is proposed this method combines the lyapunov function approach with graph theoretical reasoning in this context the main step is to establish a bound on the total length of all paths passing through an edge on the network connection graph in particular the method is applied to the study of synchronization in rings of 2k nearest neighbor coupled oscillators a rigorous bound is given for the minimum coupling strength sufficient for global synchronization of all oscillators this bound is explicitly linked with the average path length of the coupling graph contrary to the master stability function approach developed by pecora and carroll the connection graph stability method leads to global stability of synchronization and it permits not only constant but also time dependent interaction coefficients in a companion paper blinking model and synchronization in small world networks with a time varying coupling see this issue this method is extended to the blinking model of small world networks where in addition to the fixed 2 k nearest neighbor interactions all the remaining links are rapidly switched on and off independently of each other

an intriguing hybrid synchronization phenomenon of two coupled complex networks this paper investigates the hybrid synchronization problem of two coupled complex networks employing the linear feedback and the adaptive feedback control methods which are simple efficient and easy to implement in practical applications we obtain some useful criteria of the hybrid synchronization of two coupled networks based on the lyapunov stability theory and lasalle s invariance principle it shows that under suitable conditions two coupled complex networks can realize an intriguing hybrid synchronization the outer anti synchronization between the driving network and the response network and the inner complete synchronization in the driving network and the response network respectively numerical simulations demonstrate the effectiveness of the proposed hybrid synchronization scheme

curvature based fuzzy surface classification in this paper a fuzzy surface classification paradigm which is an extension to the conventional techniques based on the sign of the mean h and gaussian k curvatures respectively is presented with the conventional methods two of the major problems that limit object descriptions are 1 their inability to describe surfaces in a natural way and 2 computation of curvatures being highly sensitive to noise as well as limited by resolution problem 1 is addressed by treating the transitional regions between distinct surface types as smoothly varying fuzzy surface types problem 2 gets partially resolved while fuzzifying the signs of the surface curvatures for surface description the new segmentation technique is demonstrated in a model based object recognition system and its performance is compared with a system based on conventional surface classification

a special full state hybrid projective synchronization in symmetrical chaotic systems a special full state hybrid projective synchronization type is proposed in this paper the anti synchronization and complete synchronization can be achieved simultaneously in this new synchronization phenomenon we point out how to realize this synchronization in chaotic systems anti synchronization in symmetrical coordinate subspace and complete synchronization in its normal coordinate subspace two illustrative examples multi scroll chaotic system by the partial lyapunov stability theory and a four dimensional chaotic system by the invariance principle of differential equation are presented to exhibit this new synchronization

computation of surface orientation and structure of objects using grid coding in this correspondence algorithms are introduced to infer surface orientation and structure of visible object surfaces using grid coding we adopt the active lighting technique to spatially encode the scene for analysis the observed objects which can have surfaces of arbitrary shape are assumed to rest on a plane base plane in a scene which is encoded with light cast through a grid plane two orthogonal grid patterns are used where each pattern is obtained with a set of equally spaced stripes marked on a glass pane the scene is observed through a camera and the object surface orientation is determined using the projected patterns on the object surface if the surfaces under consideration obey certain smoothness constraints a dense orientation map can be obtained through proper interpolation the surface structure can then be recovered given this dense orientation map both planar and curved surfaces can be handled in a uniform manner the algorithms we propose yield reasonably accurate results and are relatively tolerant to noise especially when compared to shape from shading techniques in contrast to other grid coding techniques reported which match the grid junctions for depth reconstruction under the stereopsis principle our techniques use the direction of the projected stripes to infer local surface orientation and do not require any correspondence relationship between either the grid lines or the grid junctions to be specified the algorithm has the ability to register images and can therefore be embedded in a system which integrates knowledge from multiple views

on concave constraint functions and duality in predominantly black and white topology optimization abstract we study the classical discrete solid void or black and white topology optimization problem in which minimum compliance is sought subject to constraints on the available material resource we assume that this problem is solved using methods that relax the discreteness requirements during intermediate steps and that the associated programming problems are solved using sequential approximate optimization sao algorithms based on duality more specifically we assume that the advantages of the well known falk dual are exploited such algorithms represent the state of the art in large scale topology optimization when multiple constraints are present an important example being the method of moving asymptotes mma we depart by noting that the aforementioned sao algorithms are invariably formulated using strictly convex subproblems we then numerically illustrate that strictly concave constraint functions like those present in volumetric penalization as recently proposed by bruns and co workers may increase the difficulty of the topology optimization problem when strictly convex approximations are used in the sao algorithm in turn volumetric penalization methods are of notable importance since they seem to hold much promise for generating predominantly solid void or discrete designs we then argue that the nonconvex problems we study may in some instances efficiently be solved using dual sao methods based on nonconvex strictly concave approximations which exhibit monotonicity with respect to the design variables indeed for the topology problem resulting from simp like volumetric penalization we show explicitly that convex approximations are not necessary even though the volumetric penalization constraint is strictly concave the maximum of the resulting dual subproblem still corresponds to the optimum of the original primal approximate subproblem

generalized synchronization of chaos in directionally coupled chaotic systems synchronization of chaotic systems is frequently taken to mean actual equality of the variables of the coupled systems as they evolve in time we explore a generalization of this condition which equates dynamical variables from one subsystem with a function of the variables of another subsystem this means that synchronization implies a collapse of the overall evolution onto a subspace of the system attractor in full space we explore this idea in systems where a response system bold y ital t is driven with the output of a driving system bold x ital t but there is no feedback to the driver we lose generality but gain tractability with this restriction to investigate the existence of the synchronization condition bold y ital t phi bold x ital t we introduce the idea of mutual false nearest neighbors to determine when closeness in response space implies closeness in driving space the synchronization condition also implies that the response dynamics is determined by the drive alone and we provide tests for this as well examples are drawn from computer simulations on various known cases of synchronization and on data from nonlinear electrical circuits determining the presence of generalized synchronization will be quite important when one has only scalarmore observations from the drive and from the response systems since the use of time delay or other embedding methods will produce imperfect coordinates in which strict equality of the synchronized variables is unlikely to transpire less

anti synchronization of two different chaotic systems abstract in this paper the anti synchronization of two different chaotic systems is investigated on the basis of a nonlinear control scheme and lyapunov theory sufficient conditions for the stability of the error dynamics are derived where the controllers are designed by using the sum of the relevant variables in chaotic systems numerical simulations are performed for the genesio rossler system to demonstrate the effectiveness of the proposed control strategy

synchronization of singular complex dynamical networks with time varying delays abstract this paper considers delay dependent synchronizations of singular complex dynamical networks with time varying delays a modified lyapunov krasovskii functional is used to derive a sufficient condition for synchronization in terms of lmis linear matrix inequalities which can be easily solved by various convex optimization algorithms numerical examples show the effectiveness of the proposed method

recovering three dimensional shape from a single image of curved objects an algorithm to recover three dimensional shape i e surface orientation and relative depth from a single segmented image is presented it is assumed that the scene is composed of opaque regular solid objects bounded by piecewise smooth surfaces with no markings or textures it is also assumed that the reflectance map r n is known for the canonical case of lambertian surfaces illuminated by a point light source this implies knowing the light source direction a variational formulation of line drawing and shading constraints in a common framework is developed the global constraints are partitioned into constraint sets corresponding to the faces edges and vertices in the scene for a face the constraints are given by horn s image irradiance equation a variational formulation of the constraints at an edge both from the known direction of the image curve corresponding to the edge and shading is developed at a vertex the constraints are modeled by a system of nonlinear equations an algorithm is presented to solve this system of constraints

experiments in computing optical flow with the gradient based multiconstraint method abstract in this paper we present results on experiments in computing optical flow with the multiconstraint approach this approach relies on the gradient equation which relates spatial and temporal changes in the image to optical flow and the use of various image functions the experiments reported here are performed on camera acquired pictures and use feature operators to derive image functions from the original luminance function results indicate that this approach is promising

least squares fitting of two 3 d point sets two point sets pi and p i i 1 2 n are related by p i rpi t ni where r is a rotation matrix t a translation vector and ni a noise vector given pi and p i we present an algorithm for finding the least squares solution of r and t which is based on the singular value decomposition svd of a 3 3 matrix this new algorithm is compared to two earlier algorithms with respect to computer time requirements

on the equivalence of optimality criterion and sequential approximate optimization methods in the classical topology layout problem we study the classical topology optimization problem in which minimum compliance is sought subject to linear constraints using a dual statement we propose two separable and strictly convex subproblems for use in sequential approximate optimization sao algorithms respectively the subproblems use reciprocal and exponential intermediate variables in approximating the non linear compliance objective function any number of linear constraints or linearly approximated constraints are provided for the relationships between the primal variables and the dual variables are found in analytical form for the special case when only a single linear constraint on volume is present we note that application of the ever popular optimality criterion oc method to the topology optimization problem combined with arbitrary values for the heuristic numerical damping factor proposed by bendsoe results in an updating scheme for the design variables that is identical to the application of a rudimentary dual sao algorithm in which the subproblems are based on exponential intermediate variables what is more we show that the popular choice for the damping factor 0 5 is identical to the use of sao with reciprocal intervening variables finally computational experiments reveal that subproblems based on exponential intervening variables result in improved efficiency and accuracy when compared to sao subproblems based on reciprocal intermediate variables and hence the heuristic topology oc method hitherto used this is attributed to the fact that a different exponent is computed for each design variable in the two point exponential approximation we have used using gradient information at the previously visited point copyright 2007 john wiley sons ltd

computational geometric methods in volumetric intersection for 3d reconstruction abstract generation and analysis of 3d models is an important task that enables automatic inspection placement and manipulation of physical objects by robotic systems this work presents a new approach to the generation of 3d models of arbitrarily shaped physical objects the models are generated from intensity images obtained from known view positions the objects are modelled by contours on successive parallel planes the model becomes more refined as more images are used the contour model supports the ability to generate the surface of an object by means of tessellation we have developed a model that supports efficient intersection not only to perform reconstruction but also to support inclusion testing and collision detection we have implemented this algorithm using images of real objects the algorithm s time complexity is linear with the number of views used and with the number of objects reconstructed the resolution of the algorithm in reconstructing the contours is limited only by machine precision constraints this is because the intersection points of the contours are determined analytically by solving sets of simultaneous equations which describe the line segments that compose the contours

topology optimization of non linear elastic structures and compliant mechanisms abstract a linear elastic response is assumed in most structural topology optimization problems while this assumption is valid for a wide variety of problems it is not valid for structures undergoing large displacements the elastic structural analysis used here accommodates geometric and material non linearities the material density field is filtered to enforce a length scale on the field variation and is penalized to remove less effective intermediate densities the filtering scheme is embedded in the structural analysis to resolve the non existent solution to the solid void topology problem in this way we know precisely what optimization problem is being solved the structural topology optimization formulation is also used to design compliant mechanisms

error analysis in stereo determination of 3 d point positions the relationship between the geometry of a stereo camera setup and the accuracy in obtaining three dimensional position information is of great practical importance in many imaging applications assuming a point in a scene has been correctly identified in each image its three dimensional position can be recovered via a simple geometrical method known as triangulation the probability that position estimates from triangulation are within some specified error tolerance is derived an ideal pinhole camera model is used and the error is modeled as known spatial image plane quantization a point s measured position maps to a small volume in 3 d determined by the finite resolution of the stereo setup with the assumption that the point s actual position is uniformly distributed inside this volume closed form expressions for the probability distribution of error in position along each coordinate direction horizontal vertical and range are derived following this the probability that range error dominates over errors in the point s horizontal or vertical position is determined it is hoped that the results presented will have an impact upon both sensor design and error modeling of position measuring systems for computer vision and related applications

identification of space curves from two dimensional perspective views this paper describes a new method to be used for matching three dimensional objects with curved surfaces to two dimensional perspective views the method requires for each three dimensional object a stored model consisting of a closed space curve representing some characteristic connected curved edges of the object the input is a two dimensional perspective projection of one of the stored models represented by an ordered sequence of points the input is converted to a spline representation which is sampled at equal intervals to derive a curvature function the fourier transform of the curvature function is used to represent the shape the actual matching is reduced to a minimization problem which is handled by the levenberg marquardt algorithm 3

matching three dimensional objects using silhouettes a method for matching three dimensional objects against a library of models from an observed sequence of silhouettes is presented in this correspondence based upon the observed silhouettes the three dimensional structure of the object is constructed and refined the principal moments and three primary silhouettes are computed for the constructed three dimensional objects to represent the aggregate and detailed structure parameters the adaptive matching technique requires that sufficient silhouettes be added to modify the structure of the unknown object until consistent and steady matching results are obtained the library for matching is based on three primary silhouettes of the model objects experiments conducted show a fast convergence to a consistent result may be achieved provided that a reasonable choice of silhouettes is made

the visual hull concept for silhouette based image understanding many algorithms for both identifying and reconstructing a 3 d object are based on the 2 d silhouettes of the object in general identifying a nonconvex object using a silhouette based approach implies neglecting some features of its surface as identification clues the same features cannot be reconstructed by volume intersection techniques using multiple silhouettes of the object this paper addresses the problem of finding which parts of a nonconvex object are relevant for silhouette based image understanding for this purpose the geometric concept of visual hull of a 3 d object is introduced this is the closest approximation of object s that can be obtained with the volume intersection approach it is the maximal object silhouette equivalent to s i e which can be substituted for s without affecting any silhouette only the parts of the surface of s that also lie on the surface of the visual hull can be reconstructed or identified using silhouette based algorithms the visual hull depends not only on the object but also on the region allowed to the viewpoint two main viewing regions result in the external and internal visual hull in the former case the viewing region is related to the convex hull of s in the latter it is bounded by s the internal visual hull also admits an interpretation not related to silhouettes algorithms for computing visual hulls are presented and their complexity analyzed in general the visual hull of a 3 d planar face object turns out to be bounded by planar and curved patches

geometric reasoning for constructing 3d scene descriptions from images abstract there are many applications for a vision system which derives a three dimensional model of a scene from one or more images and stores the model for easy retrieval and matching the derivation of a 3d model of a scene involves transformations between four levels of representation images 2d features 3d structures and 3d geometric models geometric reasoning is used to perform these transformations as well as for the eventual model matching since the image formation process is many to one the problem of deriving 3d features from 2d features is ill constrained additional constraints may be derived from knowledge of the domain from which the images were taken the 3d mosaic system has successfully used domain specific knowledge to drive the geometric reasoning necessary to acquire 3d models for complex real world urban scenes to generalize this approach a framework for the representation and use of domain knowledge for geometric reasoning for vision is proposed

the method of moving asymptotes a new method for structural optimization a new method for non linear programming in general and structural optimization in particular is presented in each step of the iterative process a strictly convex approximating subproblem is generated and solved the generation of these subproblems is controlled by so called moving asymptotes which may both stabilize and speed up the convergence of the general process

polyhedron recognition using three view analysis abstract using three view analysis this paper proposes a new approach for single polyhedron recognition both the 3d surface data and 2d image projection patterns are used to find the exact corresponding model of an unknown input object the recognition process first applies a hypothesis generation verification process to match the 3d partial object of the unknown input which is reconstructed by applying the three view matching strategy chiou et al proc ics 88 pp 1516 1521 1988 and the polyhedron reconstruction process hung et al pattern recognition 22 231 246 1989 against the data based models for selecting the possible corresponding models candidates it then backprojects each candidate onto the three image planes and matches the outer boundaries of the three backprojections by a simple method for judging the exact corresponding model measurement error is also analyzed theoretically to give a bound of the threshold value so that it can be automatically chosen in each decision making process the approach is implemented on a pc level vision system experimental results show that the system is feasible and reliable even in a noisy environment