automatic ventricular cavity boundary detection from sequential ultrasound images using simulated annealing an automatic algorithm has been developed for high speed detection of cavity boundaries in sequential 2 d echocardiograms using an optimization algorithm called simulated annealing sa the algorithm has three stages 1 a predetermined window of size n m is decimated to size n m after low pass filtering 2 an iterative radial gradient algorithm is employed to determine the center of gravity cg of the cavity 3 64 radii which originate from the cg defined in stage 2 are bounded by the high probability region each bounded radius is defined as a link in a 1 d 64 member cyclic markov random field this algorithm is unique in that it compounds spatial and temporal information along with a physical model in its decision rule whereas most other algorithms base their decisions on spatial data alone this is the first implementation of a relaxation algorithm for edge detection in echocardiograms results attained using this algorithm on real data have been highly encouraging

globally solvable systems of complex vector fields we consider a class of involutive systems of n smooth vector fields on the n 1 dimensional torus we obtain a complete characterization for the global solvability of this class in terms of liouville forms and of the connectedness of all sublevel and superlevel sets of the primitive of a certain 1 form in the minimal covering space

dynamic 3d models with local and global deformations deformable superquadrics the authors present a physically based approach to fitting complex three dimensional shapes using a novel class of dynamic models that can deform both locally and globally they formulate the deformable superquadrics which incorporate the global shape parameters of a conventional superellipsoid with the local degrees of freedom of a spline the model s six global deformational degrees of freedom capture gross shape features from visual data and provide salient part descriptors for efficient indexing into a database of stored models the local deformation parameters reconstruct the details of complex shapes that the global abstraction misses the equations of motion which govern the behavior of deformable superquadrics make them responsive to externally applied forces the authors fit models to visual data by transforming the data into forces and simulating the equations of motion through time to adjust the translational rotational and deformational degrees of freedom of the models model fitting experiments involving 2d monocular image data and 3d range data are presented

solution of a non convex optimization arising in pi pid control design as shown by astrom et al automatica 34 5 1998 585 the problem of designing a stabilizing pi controller based on minimizing integral of error associated with step load disturbance while subjecting to constraints on maximum sensitivity and or complementary sensitivity amounts to that of finding the maximum allowable integral gain the latter problem is a non convex optimization problem whose true solution cannot be obtained with a guarantee by a gradient based search algorithm in this paper we present a novel and effective approach to solve such a non convex optimization problem our approach is based on regarding an equality constraint set on controller gain parameters as a two dimensional value set in the complex plane and using the notion of principal points to characterize its boundary with this treatment we are able to derive analytical expressions for describing the boundary of an equality constraint set in the controller gain plane these expressions allow one to trace the boundaries of equality constraint sets using an existing path following algorithm hence by constructing the boundary of the feasible domain in the controller gain space the maximum allowable integral gain can be obtained in addition to having the ability to obtain global optimal solution our approach can handle sensitivity and complementary sensitivity constraints simultaneously without using an iterative procedure

the computation of visible surface representations a computational theory of visible surface representations is developed the visible surface reconstruction process that computes these quantitative representations unifies formal solutions to the key problems of 1 integrating multiscale constraints on surface depth and orientation from multiple visual sources 2 interpolating dense piecewise smooth surfaces from these constraints 3 detecting surface depth and orientation discontinuities to apply boundary conditions on interpolation and 4 structuring large scale distributed surface representations to achieve computational efficiency visible surface reconstruction is an inverse problem a well posed variational formulation results from the use of a controlled continuity surface model discontinuity detection amounts to the identification of this generic model s distributed parameters from the data finite element shape primitives yield a local discretization of the variational principle the result is an efficient algorithm for visible surface reconstruction

closed form solutions for physically based shape modeling and recognition the authors present a closed form physically based solution for recovering a three dimensional 3 d solid model from collections of 3 d surface measurements given a sufficient number of independent measurements the solution is overconstrained and unique except for rotational symmetries the proposed approach is based on the finite element method fem and parametric solid modeling using implicit functions this approach provides both the convenience of parametric modeling and the expressiveness of the physically based mesh formulation and in addition can provide great accuracy at physical simulation a physically based object recognition method that allows simple closed form comparisons of recovered 3 d solid models is presented the performance of these methods is evaluated using both synthetic range data with various signal to noise ratios and using laser rangefinder data

constraints on deformable models recovering 3d shape and nongrid motion abstract inferring the 3d structures of nonrigidly moving objects from images is a difficult yet basic problem in computational vision our approach makes use of dynamic elastically deformable object models that offer the geometric flexibility to satisfy a diversity of real world visual constraints we specialize these models to include intrinsic forces inducing a preference for axisymmetry image based constraints are applied as extrinsic forces that mold the symmetry seeking model into shapes consistent with image data we describe an extrinsic force that applies constraints derived from profiles of monocularly viewed objects we generalize this constraint force to incorporate profile information from multiple views and use it to exploit binocular image data for time varying images the force becomes dynamic and the model is able to infer not only depth but nonrigid motion as well we demonstrate the recovery of 3d shape and nonrigid motion from natural imagery

global properties of a class of overdetermined systems abstract we consider an overdetermined system of complex vector fields on the three dimensional torus which is naturally associated to a real analytic closed 1 form on the two dimensional torus by means of a detailed study of the geometry of level sets of a primitive of the pull back of the 1 form via the universal covering we prove that a necessary condition for the system to be globally solvable in the non exact case is that each connected component of the critical set has a point at which the local primitives of the 1 form are open maps when this condition is violated we also construct global solutions to the inhomogenous equations having analytic singularities

comutations underlying the measuremnt of visual motion abstract the organization of movement in a changing image provides a valuable source of information for analyzing the environment in terms of objects their motion in space and their three dimensional structure a description of this movement is not provided to our visual system directly however it must be inferred from the pattern of changing intensity that reaches the eye this paper examines the problem of motion measurement which we formulate as the computation of an instantaneous two dimensional velocity field initial motion measurements occur at the location of significant intensity changes as suggested by marr and ullman 1 these measurements provide only one component of velocity and must be integrated to compute the two dimensional velocity field a fundamental problem for this integration is that motion is not determined uniquely from the changing image an additional constraint of smoothness of the velocity field is formulated based on the physical assumption that surfaces are generally smooth allowing the computation of a unique solution a theoretical analysis of the conditions under which this computation yields the correct velocity field suggests that the solution is physically plausible empirical studies show the results to be consistent with human motion perception

design of fuzzy pid controllers using modified triangular membership functions a design method for fuzzy proportional integral derivative pid controllers is investigated in this study based on conventional triangular membership functions used in fuzzy inference systems the modified triangular membership functions are proposed to improve a system s performance according to knowledge based reasonings the parameters of the considered controllers are tuned by means of genetic algorithms gas using a fitness function associated with the system s performance indices the merits of the proposed controllers are illustrated by considering a model of the induction motor control system and a higher order numerical model

brief probabilistic solutions to some np hard matrix problems during recent years it has been shown that a number of problems in matrix theory are np hard including robust nonsingularity robust stability robust positive semidefiniteness robust bounded norm state feedback stabilization with structural and norm constraints etc in this paper we use standard bounds on empirical probabilities as well as recent results from statistical learning theory on the vc dimension of families of sets defined by a finite number of polynomial inequalities to show that for each of the above problems as well as for still more general and more difficult problems there exists a polynomial time randomized algorithm that can provide a yes or no answer to arbitrarily small levels of accuracy and confidence

global solvability of real analytic involutive systems on compact manifolds part 2 the focus of this work is the smooth global solvability of a linear partial differential operator mathbb l associated to a real analytic closed non exact 1 form b defined on a real analytic closed n manifold that may be naturally regarded as the first operator of the complex induced by a locally integrable structure of tube type and co rank one we define an appropriate covering projection widetilde m rightarrow m such that the pullback of b has a primitive widetilde b and prove that the operator is globally solvable if and only if the superlevel and sublevel sets of widetilde b are connected as a byproduct we obtain a new geometric characterization for the global hypoellipticity of the operator when m is orientable we prove a connection between the global solvability of mathbb l and that of mathbb l n 1 which is the last non trivial operator of the complex in particular we prove that mathbb l is globally solvable if and only if mathbb l n 1 is globally solvable in the smooth category we are able to provide analogous geometric characterizations of the global solvability and the global hypoellipticity when b is a morse 1 form i e when the structure is of mizohata type

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

regularization of inverse visual problems involving discontinuities inverse problems such as the reconstruction problems that arise in early vision tend to be mathematically ill posed through regularization they may be reformulated as well posed variational principles whose solutions are computable standard regularization theory employs quadratic stabilizing functionals that impose global smoothness constraints on possible solutions discontinuities present serious difficulties to standard regularization however since their reconstruction requires a precise spatial control over the smoothing properties of stabilizers this paper proposes a general class of controlled continuity stabilizers which provide the necessary control over smoothness these nonquadratic stabilizing functionals comprise multiple generalized spline kernels combined with noncontinuous continuity control functions in the context of computational vision they may be thought of as controlled continuity constraints these generic constraints are applicable to visual reconstruction problems that involve both continuous regions and discontinuities for which global smoothness constraints fail

on three dimensional surface reconstruction methods a survey is presented of some of the surface reconstruction methods that can be found in the literature the focus is on a small recent and important subset of the published reconstruction techniques the techniques are classified based on the surface representation used implicit versus explicit functions a study is made of the important aspects of the surface reconstruction techniques one aspect is the viewpoint invariance of the methods this is an important property if object recognition is the ultimate objective the robustness of the various methods is examined it is determined whether the parameter estimates are biased and the sensitivity to obscuration is addressed the latter two aspects are particularly important for fitting functions in the implicit form a detailed description is given of a parametric reconstruction method for three dimensional object surfaces that involves numeric grid generation techniques and variational principle formulations this technique is invariant to rigid motion in dimensional space

symmetry seeking models and 3d object reconstruction we propose models of 3d shape which may be viewed as deformable bodies composed of simulated elastic material in contrast to traditional purely geometric models of shape deformable models are active their shapes change in response to externally applied forces we develop a deformable model for 3d shape which has a preference for axial symmetry symmetry is represented even though the model does not belong to a parametric shape family such as generalized cylinders rather a symmetry seeking property is designed into internal forces that constrain the deformations of the model we develop a framework for 3d object reconstruction based on symmetry seeking models instances of these models are formed from monocular image data through the action of external forces derived from the data the forces proposed in this paper deform the model in space so that the shape of its projection into the image plane is consistent with the 2d silhouette of an object of interest the effectiveness of our approach is demonstrated using natural images

integrated surface model optimization for freehand three dimensional echocardiography the major obstacle of three dimensional 3 d echocardiography is that the ultrasound image quality is too low to reliably detect features locally almost all available surface finding algorithms depend on decent quality boundaries to get satisfactory surface models we formulate the surface model optimization problem in a bayesian framework such that the inference made about a surface model is based on the integration of both the low level image evidence and the high level prior shape knowledge through a pixel class prediction mechanism we model the probability of pixel classes instead of making explicit decisions about them therefore we avoid the unreliable edge detection or image segmentation problem and the pixel correspondence problem an optimal surface model best explains the observed images such that the posterior probability of the surface model for the observed images is maximized the pixel feature vector as the image evidence includes several parameters such as the smoothed grayscale value and the minimal second directional derivative statistically we describe the feature vector by the pixel appearance probability model obtained by a nonparametric optimal quantization technique qualitatively we display the imaging plane intersections of the optimized surface models together with those of the ground truth surfaces reconstructed from manual delineations quantitatively we measure the projection distance error between the optimized and the ground truth surfaces in our experiment we use 20 studies to obtain the probability models offline the prior shape knowledge is represented by a catalog of 86 left ventricle surface models in another set of 25 test studies the average epicardial and endocardial surface projection distance errors are 3 2 spl plusmn 0 85 mm and 2 6 spl plusmn 0 78 mm respectively

prescribing analytic singularities for solutions of a class of vector fields on the torus we consider the operator l t a t ib t x acting on distributions on the two torus t 2 where and b are real valued real analytic functions defined on the unit circle t 1 we prove among other things that when b changes sign given any subset s of the set of the local extrema of the local primitives of b there exists a singular solution of l such that the t projection of its analytic singular support is furthermore for any t l and any closed subset f of t 1 x there exists u d t 2 such that lu c t 2 and sing supp a u x f we also provide a microlocal result concerning the truce of u at t

fast convolution with laplacian of gaussian masks we present a technique for computing the convolution of an image with log laplacian of gaussian masks it is well known that a log of variance a can be decomposed as a gaussian mask and a log of variance 1 we take advantage of the specific spectral characteristics of these filters in our computation the log is a bandpass filter we can therefore fold the spectrum of the image after low pass filtering without loss of information which is equivalent to reducing the resolution we present a complete evaluation of the parameters involved together with a complexity analysis that leads to the paradoxical result that the computation time decreases when increases we illustrate the method on two images

global gevrey hypoellipticity on the torus for a class of systems of complex vector fields abstract let l j t j a j i b j t j x j 1 n be a system of vector fields defined on the torus t t n t x 1 where the coefficients a j and b j are real valued functions belonging to the gevrey class g s t 1 s 1 the global s hypoellipticity of this system is characterized in terms of diophantine approximations and the nirenberg treves condition p

stability analysis and design of fuzzy control systems abstract the stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed first we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams we derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks in order to preserve some properties in a connection of fuzzy blocks continuous piecewise polynomial membership functions are defined secondly a sufficient condition which guarantees the stability of fuzzy systems is obtained in terms of lyapunov s direct method we give an important fact based on this condition thirdly we propose a new design technique of a fuzzy controller the fuzzy block diagrams and the stability analysis are applied to the design problems of a model based fuzzy controller

bayesian recognition of local 3 d shape by approximating image intensity functions with quadric polynomials the recognition in image data of viewed patches of spheres cylinders and planes in the 3 d world is discussed as a first step to complex object recognition or complex object location and orientation estimation accordingly an image is partitioned into small square windows each of which is a view of a piece of a sphere or of a cylinder or of a plane windows are processed in parallel for recognition of content new concepts and techniques include approximations of the image within a window by 2 d quadric polynomials where each approximation is constrained by one of the hypotheses that the 3 d surface shape seen is either planar cylindrical or spherical a recognizer based upon these approximations to determine whether the object patch viewed is a piece of a sphere or a piece of a cylinder or a piece of a plane lowpass filtering of the image by the approximation the shape recognition is computationally simple and for large windows is approximately bayesian minimum probability of error recognition these classifications are useful for many purposes one such purpose is to enable a following processor to use an appropriate estimator to estimate shape and orientation and location parameters for the 3 d surface seen within a window

an investigation of smoothness constraints for the estimation of displacement vector fields from image sequences a mapping between one frame from an image sequence and the preceding or following frame can be represented as a displacement vector field in most situations the mere gray value variations do not provide sufficient information in order to estimate such a displacement vector field supplementary constraints are necessary for example the postulate that a displacement vector field varies smoothly as a function of the image position taken as a general requirement this creates difficulties at gray value transitions which correspond to occluding contours nagel therefore introduced the oriented smoothness requirement which restricts variations of the displacement vector field only in directions with small or no variation of gray values this contribution reports results of an investigation about how such an oriented smoothness constraint may be formulated and evaluated

epicardial boundary detection using fuzzy reasoning a fully automated system for detecting the endocardial and epicardial boundaries in a two dimensional echocardiography by using fuzzy reasoning techniques is proposed the image is first enhanced by applying the laplacian of gaussian edge detector second the center of the left ventricle is determined automatically by analyzing the original image next a search process radiated from the estimated center is performed to locate the endocardial boundary by using the zero crossing points after this step the estimation of the range of radius of a possible epicardial boundary is carried out by comparing the high level knowledge of intensity changes along all directions with the actual image intensity changes the high level knowledge of global intensity change in the image is acquired from experts in advance and is represented in the form of fuzzy linguistic descriptions and relations knowledge of local intensity change can therefore be deduced from the knowledge of global intensity change through fuzzy reasoning

robust synthesis of a pid controller by uncertain multimodel approach this paper presents an effective method to design a pid or pi controller for nonlinear systems where desirable robustness and performance properties must be maintained across a large range of operating conditions for this purpose an uncertain multimodel of the original nonlinear system is used the uncertainties affecting the system are treated as stochastic matrices based on this multimodel representation a robust pid controller can be designed in order to obtain acceptable performance for all operating conditions numerical examples show the practical applicability of the proposed method

on optimally combining pieces of information with application to estimating 3 d complex object position from range data new asymptotic methods are introduced that permit computationally simple bayesian recognition and parameter estimation for many large data sets described by a combination of algebraic geometric and probabilistic models the techniques introduced permit controlled decomposition of a large problem into small problems for separate parallel processing where maximum likelihood estimation or bayesian estimation or recognition can be realized locally these results can be combined to arrive at globally optimum estimation or recognition the approach is applied to the maximum likelihood estimation of 3 d complex object position to this end the surface of an object is modeled as a collection of patches of primitive quadrics i e planar cylindrical and spherical patches possibly augmented by boundary segments the primitive surface patch models are specified by geometric parameters reflecting location orientation and dimension information the object position estimation is based on sets of range data points each set associated with an object primitive probability density functions are introduced that model the generation of range measurement points this entails the formulation of a noise mechanism in three space accounting for inaccuracies in the 3 d measurements and possibly for inaccuracies in the 3 d modeling we develop the necessary techniques for optimal local parameter estimation and primitive boundary or surface type recognition for each small patch of data and then optimal combining of these inaccurate locally derived parameter estimates in order to arrive at roughly globally optimum object position estimation

on the global solvability for overdetermined systems we consider a class of systems of two smooth vector fields on the 3 torus associated to a closed 1 form the global solvability of such systems is completely determined by the connectedness of the sublevel and superlevel sets of a primitive of this 1 form in the minimal covering the main point of this talk is addressing the case when the 1 form is non exact and its periods are rationally dependent this is a work in collaboration with a bergamasco a kirilov and w nunes

numerical shape from shading and occluding boundaries an iterative method for computing shape from shading using occluding boundary information is proposed some applications of this method are shown we employ the stereographic plane to express the orientations of surface patches rather than the more commonly used gradient space use of the stereographic plane makes it possible to incorporate occluding boundary information but forces us to employ a smoothness constraint different from the one previously proposed the new constraint follows directly from a particular definition of surface smoothness we solve the set of equations arising from the smoothness constraints and the image irradiance equation iteratively using occluding boundary information to supply boundary conditions good initial values are found at certain points to help reduce the number of iterations required to reach a reasonable solution numerical experiments show that the method is effective and robust finally we analyze scanning electron microscope sem pictures using this method other applications are also proposed

global solvability of real analytic involutive systems on compact manifolds the focus of this work is the smooth global solvability of a linear partial differential operator mathbb l associated to a real analytic closed non exact 1 form b defined on a real analytic closed n manifold that may be naturally regarded as the first operator of the complex induced by a locally integrable structure of tube type and co rank one we define an appropriate covering projection widetilde m rightarrow m such that the pullback of b has a primitive widetilde b and prove that the operator is globally solvable if and only if the superlevel and sublevel sets of widetilde b are connected as a byproduct we obtain a new geometric characterization for the global hypoellipticity of the operator when m is orientable we prove a connection between the global solvability of mathbb l and that of mathbb l n 1 which is the last non trivial operator of the complex in particular we prove that mathbb l is globally solvable if and only if mathbb l n 1 is globally solvable in the smooth category we are able to provide analogous geometric characterizations of the global solvability and the global hypoellipticity when b is a morse 1 form i e when the structure is of mizohata type

recovery of parametric models from range images the case for superquadrics with global deformations a method for recovery of compact volumetric models for shape representation of single part objects in computer vision is introduced the models are superquadrics with parametric deformations bending tapering and cavity deformation the input for the model recovery is three dimensional range points model recovery is formulated as a least squares minimization of a cost function for all range points belonging to a single part during an iterative gradient descent minimization process all model parameters are adjusted simultaneously recovery position orientation size and shape of the model such that most of the given range points lie close to the model s surface a specific solution among several acceptable solutions where are all minima in the parameter space can be reached by constraining the search to a part of the parameter space the many shallow local minima in the parameter space are avoided as a solution by using a stochastic technique during minimization results using real range data show that the recovered models are stable and that the recovery procedure is fast

global solvability for a class of overdetermined systems abstract in this work we consider systems of two smooth vector fields on the three dimensional torus associated to a closed 1 form we prove that for such systems the global solvability in the space of smooth functions is characterized by the property of all the sublevel and superlevel sets of a certain primitive of the 1 form being connected

recovery of the 3 d shape of the left ventricle from echocardiographic images a computational method is reported which allows the fully automated recovery of the three dimensional shape of the cardiac left ventricle from a reduced set of apical echo views two typically ill posed problems have been faced 1 the detection of the left ventricle contours in each view and 2 the integration of the detected contour points which form a sparse and partially inconsistent data set into a single surface representation the authors solution to these problems is based on a careful integration of standard computer vision algorithms with neural networks boundary detection comprises three steps edge detection edge grouping and edge classification the first and second steps which are typical early vision tasks not involving specific domain knowledge have been performed through fast well established algorithms of computer vision the higher level task of left ventricle edge discrimination which involves the exploitation of specific knowledge about the left ventricle silhouette has been performed by feedforward neural networks following the most recent results in the field of computer vision the first step in solving the problem of recovering the ventricle surface has been the adoption of a physically inspired model of it basically the authors have modeled the left ventricle surface as a closed thin elastic surface and the data as a set of radial springs acting on it the recovery process is equivalent to the settling of the surface plus springs system into a stable configuration of minimum potential energy the finite element discretization of this model leads directly to an analog neural network implementation the efficiency of such an implementation has been remarkably enhanced through a learning algorithm which embeds specific knowledge about the shape of the left ventricle in the network experiments using clinical echographic sequences are described four apical views each with a different rotation of the probe have been acquired during a heartbeat from a set of seven normal subjects these images have been utilized to set the various processing modules and test their capabilities

remarks about global analytic hypoellipticity we present a characterization of the operators l 8 ot a t ib t x which are globally analytic hypoelliptic on the torus we give information about the global analytic hypoellipticity of certain overdetermined systems and of sums of squares

on the global solvability of involutive systems abstract we consider a class of involutive systems in t n 1 associated with a closed 1 form defined on the torus t n we prove that under a geometric condition the global solvability of this class is equivalent to a diophantine condition involving liouville forms and the connectedness of all sublevel and superlevel sets of a global primitive associated with the system

fuzzy controllers as gain scheduling approximators abstract nonlinear systems can be linearized according to lyapunov s linearization method and then approximated by takagi sugeno ts fuzzy models the paper shows that the corresponding control strategy with ts controllers is closely related to traditional gain scheduling generally speaking gain scheduling deals with the connection of different linear controllers acting as a global nonlinear control law ts control defines a linear controller for each linearized region as well as smooth control transitions between those regions in this connection slowly varying operating conditions are assumed for the design of the linear controllers the lqr design method has been used which guarantees optimal control of a linearized system with respect to an integral criterion however since ts control is an approximation method solutions are bound to be suboptimal and stability is hence a concern the method is compared with a continuous change of control parameters based on the continuous on line lqr design for each point in state space additional control rule weights have been introduced to promote optimization the above method is illustrated by a simple one link manipulator arm