convergence properties of the softassign quadratic assignment algorithm the softassign quadratic assignment algorithm is a discrete time continuous state synchronous updating optimizing neural network while its effectiveness has been shown in the traveling salesman problem graph matching and graph partitioning in thousands of simulations its convergence properties have not been studied here we construct discrete time lyapunov functions for the cases of exact and approximate doubly stochastic constraint satisfaction which show convergence to a fixed point the combination of good convergence properties and experimental success makes the softassign algorithm an excellent choice for neural quadratic assignment optimization

optimal tracking control of nonlinear dynamical systems this paper presents a simple methodology for obtaining the entire set of continuous controllers that cause a nonlinear dynamical system to exactly track a given trajectory the trajectory is provid

asymptotic perturbed feedback linearisation of underactuated euler s dynamics a unifying methodology is introduced for smooth asymptotic stabilisation of underactuated rigid body dynamics under one and two degrees of actuation the methodology is based on the concept of generalised inversion and it aims to realise a perturbation from the unrealisable feedback linearising transformation a desired linear dynamics in a norm measure of the angular velocity components about the unactuated axes is evaluated along solution trajectories of euler s underactuated dynamical equations resulting in a linear relation in the control variables this relation is used to assess asymptotic stabilisability of underactuated rigid bodies with arbitrary values of inertia parameters and generalised inversion of the relation produces a control law that consists of particular and auxiliary parts the generalised inverse in the particular part is scaled by a dynamic factor such that it uniformly converges to the moore penrose inverse and the null control vector in the auxiliary part is chosen for asympto

a non iterative probabilistic method for contextual correspondence matching abstract in this paper we develop a framework for non iterative structural matching using contextual information it is based on bayesian reasoning and involves the explicit modelling of the binary relations between the objects the difference between this and previously developed theories of the kind lies in the assumption that the binary relations used are derivable from the unary measurements that refer to individual objects this leads to a non iterative formula for probabilistic reasoning which is amenable to real time implementation and produces good results the theory is demonstrated using two applications one on stereo matching of linear features and the other on automatic map registration the breaking points of the theory are also identified experimentally and the situations under which the proposed algorithm is applicable are discussed

nonlinear feedback control of highly manoeuvrable aircraft abstract this paper describes the application of nonlinear quadratic regulator nlqr theory to the design of control laws for a typical high performance aircraft the nlqr controller design is performed using truncated solutions of the hamil ton jacobi bellman equation of optimal control theory the performance of the nlqr controller is compared with the performance of a conventional p i gain scheduled controller designed by applying standard frequency response techniques to the equations of motion of the aircraft linearized at various angles of attack both techniques result in control laws which are very similar in structure to one another and which yield similar performance the results of applying both control laws to a high g vertical turn are illustrated by nonlinear simulation

kronecker product graph matching abstract in this paper the interpolator based kronecker product graph matching ibkpgm algorithm for performing attributed graph matching is presented the ibkpgm algorithm is based on the kronecker product graph matching kpgm formulation this new formulation incorporates a general approach to a wide class of graph matching problems based on attributed graphs allowing the structure of the graphs to be based on multiple sets of attributes salient features of the ibkpgm algorithm are that no assumption is made about the adjacency structure of the graphs to be matched and that the explicit calculation of compatibility values between all vertices of the reference and input graphs as well as between all edges of the reference and input graphs are avoided

nonlinear generalised dynamic inversion for aircraft manoeuvring control the nonlinear control problem of aircraft trajectory tracking is tackled in the framework of multiple linear time varying constrained control using the newly developed paradigm of generalised dynamic inversion the time differential forms of the multiple constraints encapsulate the control objectives and are inverted to obtain the reference trajectory realising control law the inversion process utilises the moore penrose generalised inverse and the associated nullspace projection and it predictably involves the problematic generalised inversion singularity thus a singularity avoidance scheme based on a new type of dynamically scaled generalised inverses is introduced that guarantees both asymptotically stable tracking and singularity avoidance the steady state closed loop system allows for two inherently noninterfering control actions working towards a unified goal to exploit the aircraft s control authority over the entire state space one control action is performed by the particular part of the c

relaxation matching techniques a comparison many different relaxation schemes have been proposed for image analysis tasks we have developed a general matching procedure for comparing semantic network descriptions of images and we have implemented a variety of relaxation techniques an automatic segmentation and description system is used to produce the image representations so that the matching procedures must cope with variations in feature values missing objects and possible multiple matches this environment is used to test different relaxation matching schemes under a variety of conditions the best performance of those we compared in terms of the number of iterations and the number of errors is for the gradient based optimization approach of faugeras and price the related optimization approach of hummel and zucker performed almost as well with differences primarily in difficult matches i e where much of the evidence is against the match for instance poor segmentations the product combination rule proposed by peleg was extremely fast indeed too fast to work when global context is needed the classical rosenfeld hummel and zucker method is included for historical comparisons and performed only adequately producing fewer correct matches and taking more iterations

symbolic graph matching with the em algorithm abstract this paper describes how relational graph matching can be effected using the expectation and maximisation algorithm according to this viewpoint matching is realised as a two step iterative em like process firstly updated symbolic matches are located so as to minimise the divergence between the model and data graphs secondly with the updated matches to hand probabilities describing the affinity between nodes in the model and data graphs may be computed the probability distributions underpinning this study are computed using a simple model of uniform matching errors as a result the expected likelihood function is defined over a family of exponential distributions of hamming distance we evaluate our matching method and offer comparison with both mean field annealing and quadratic assignment

a surface based approach to 3 d object recognition using a mean field annealing neural network abstract three dimensional 3 d object recognition identifies objects in an input image using a modelbase we present a 3 d object recognition system in which a symbolic description of the object is generated from the input range data in terms of the visible surface patches the segmented surface representation of an object is regarded as a graph in which nodes contain the information about the individual surface patches whereas links represent the relationships between them such as connectivity object recognition is achieved by matching the object graph of a scene with the model graph of a modelbase in the proposed approach a mean field annealing mfa neural network nn is employed as a constraint satisfaction network in which an energy function robust to occlusion is proposed for effective matching the energy level is at its minimum when the optimal match is achieved simulation results with synthetic and real range images having various occlusion rates are presented to show the effectiveness of the proposed algorithm

matching invariant to translations rotations and scale changes abstract an optimization approach to invariant matching is proposed in this approach an object or a pattern is invariantly represented by an object centred description called an attributed relational structure ars embedding invariant properties and relations between the primitives of the pattern such as line segments and points noise effect is taken into account such that a scene can consist of noisy sub parts of a model the matching is then to find the optimal mapping between the arss of the scene and the model a gain functional is formulated to measure the goodness of fit and is to be maximized by using the relaxation labelling method experiments are shown to illustrate the matching algorithm and to demonstrate that the approach is truly invariant to arbitrary translations rotations and scale changes under noise

an eigendecomposition approach to weighted graph matching problems an approximate solution to the weighted graph matching problem is discussed for both undirected and directed graphs the weighted graph matching problem is that of finding the optimum matching between two weighted graphs which are graphs with weights at each arc the proposed method uses an analytic instead of a combinatorial or iterative approach to the optimum matching problem using the eigendecompositions of the adjacency matrices in the case of the undirected graph matching problem or hermitian matrices derived from the adjacency matrices in the case of the directed graph matching problem a matching close to the optimum can be found efficiently when the graphs are sufficiently close to each other simulation results are given to evaluate the performance of the proposed method

optimal encoding of graph homomorphism energy using fuzzy information aggregation operators abstract the attributed relational graph matching arg strategy is a well known approach to object pattern recognition in the past for the parallel solution of arg matching problem an overall objective function was constructed using linearly weighted information aggregation function and one set of parameter values was chosen for all models by trial and error for the parameters in the function in this paper the compatibility between every pair of model and scene attributes is interpreted as a fuzzy value and subsequently the nonlinear fuzzy information aggregation operators are used to fuse the information captured in the chosen attributes to learn the parameters in the fuzzy information aggregation operators the learning from samples strategy is used the learning of weight parameters is formulated as an optimisation problem and solved using the gradient projection algorithm based learning procedure the learning procedure implicitly evaluates ambiguity robustness and discriminatory power of the relational attributes chosen for graph matching and assigns weights appropriately to the chosen attributes the learning procedure also enables us to compute a distinct set of optimal parameters for every model to reflect the characteristics of the model so that the homomorphic arg matching problem can be optimally encoded in the energy function for the model experimental results are presented to illustrate effectiveness and necessity of the parameter estimation and learning procedures

on the foundations of relaxation labeling processes a large class of problems can be formulated in terms of the assignment of labels to objects frequently processes are needed which reduce ambiguity and noise and select the best label among several possible choices relaxation labeling processes are just such a class of algorithms they are based on the parallel use of local constraints between labels this paper develops a theory to characterize the goal of relaxation labeling the theory is founded on a definition of con sistency in labelings extending the notion of constraint satisfaction in certain restricted circumstances an explicit functional exists that can be maximized to guide the search for consistent labelings this functional is used to derive a new relaxation labeling operator when the restrictions are not satisfied the theory relies on variational cal culus it is shown that the problem of finding consistent labelings is equivalent to solving a variational inequality a procedure nearly identical to the relaxation operator derived under restricted circum stances serves in the more general setting further a local convergence result is established for this operator the standard relaxation labeling formulas are shown to approximate our new operator which leads us to conjecture that successful applications of the standard methods are explainable by the theory developed here observations about con vergence and generalizations to higher order compatibility relations are described

nonlinear system identification based on a fock space framework a method is presented for the identification of a nonlinear dynamical system whose input output map is assumed to be a volterra series mapping inputs u belonging to l 2 i to outputs y in the sobolev space h n 2 i where i is a compact interval of the real line and n is a nonnegative integer the input output relation is denoted by y t v u t triangleq v t u t in i it is assumed also that a set of test input output pairs u j in l 2 i y j in h n 2 i j 1 cdots m are provided our system identification procedure is based on the construction of a reproducing kernel hilbert space namely a symmetric fock space f rho for the nonlinear functional v t the corresponding nonlinear operator v then belongs to a bochner space b n 2 we obtain the best estimate hat v of v based on the input output data in the form of a generalized inverse in b n 2 both the noncausal and causal versions of hat v are derived the concept of varepsilon causality which i

intermittent phase synchronization of coupled spatiotemporal chaotic systems phase synchronization is studied with a discrete system formed by two coupled map lattices in which phases are measured in two dimensional vectors simulation results show that by imposing external coupling between the two lattices phase synchronization can be found in all two dimensional phase planes between them when the system is approaching the phase synchronizing state unstable phase synchronization is observed this is referred to as intermittent phase synchronization that appears when the trajectories on two interacting phase planes have opposite directions of rotation but with only a small phase difference the intermittent phase synchronization could also be observed in coupled autonomous systems with diffusive attractors although their phase concepts are inconsistent our results show that the intermittent phase synchronization of both discrete and autonomous systems relates to the diffusion or the complexity of the attractors

exact nonlinear control of large angle rotational maneuvers the rigid body attitude control problem with external torques is transformed into an equivalent linear form implementable by three double integrators the linearizing transformations themselves are formulated in vector algebra requiring no integrators for implementation it is thereby shown that optimal command generation for fast slewing maneuvers can be carried out exactly in the transformed system together with regulator design without gain scheduling for correction of unmodeled disturbances in particular a general rest to rest maneuver is computed in closed form and coupled with a previously obtained exact detumbling maneuver so that arbitrary initial conditions can be accommodated an illustrative simulation is appended

optimization in model matching and perceptual organization we introduce an optimization approach for solving problems in computer vision that involve multiple levels of abstraction our objective functions include compositional and specialization hierarchies we cast vision problems as inexact graph matching problems formulate graph matching in terms of constrained optimization and use analog neural networks to perform the optimization the method is applicable to perceptual grouping and model matching preliminary experimental results are shown

a new algorithm for subgraph optimal isomorphism abstract in this paper a new algorithm for subgraph isomorphism is proposed the main idea of the new algorithm is to decompose the graphs to be matched into smaller subgraphs the matching process is then done at the level of the decomposed subgraphs based on the concept of error correcting transformations the cost of matching two graphs is defined as the minimum of a weighted bipartite graph constructed from the decomposed subgraphs the average computational complexity of the proposed algorithm is found to be o n 4 the results of the application of the new algorithm show that the new technique is quite efficient and in many respects superior to similar existing techniques in the literature besides it overcomes most of the problems encountered in using tree search algorithms the new algorithm is also suitable for parallel processing implementation

an improved algorithm for relational distance graph matching one of the problems in computer vision is to give a computer a representation of a scene and recognize the objects in the scene and their spatial relationships this involves low level vision image processing mid level vision feature extraction and measurement and high level vision interpretation one important part of high level vision is relational matching the process of matching two relational descriptions of objects often for the purpose of object identification this paper presents an improvement of the original method by shapiro and haralick for solving the relational distance graph matching problem for unlabeled graphs on a parallel computer

constrained nets for graph matching and other quadratic assignment problems some time ago durbin and willshaw proposed an interesting parallel algorithm the elastic net for approximately solving some geometric optimization problems such as the traveling salesman problem recently it has been shown that their algorithm is related to neural networks of hopfield and tank and that they both can be understood as the semiclassical approximation to statistical mechanics of related physical models the main point of the elastic net algorithm is seen to be in the way one deals with the constraints when evaluating the effective cost function free energy in the thermodynamic analogy and not in its geometric foundation emphasized originally by durbin and willshaw as a consequence the elastic net algorithm is a special case of the more general physically based computations and can be generalized to a large class of nongeometric problems in this paper we further elaborate on this observation and generalize the elastic net to the quadratic assignment problem we work out in detail its special case the graph matching problem because it is an important problem with many applications in computational vision and neural modeling simulation results on random graphs and on structured hand designed graphs of moderate size 20 100 nodes are discussed

graph matching using a direct classification of node attendance abstract an algorithm has been developed that finds isomorphisms between both graphs and subgraphs the development is introduced in the object recognition problem domain the method isolates matching subgraphs finds a node to node mapping and reorders nodes thus permitting a direct comparison to be made between the resultant graphs the algorithm is of polynomial order it yields approximate results maintaining a performance level for subgraph isomorphisms at or above 95 under a wide variety of conditions and with varying levels of noise the performance on the full size comparisons associated with graph isomorphisms has been found to be 100 100 also under a variety of conditions performance metrics methods of testing and results are presented