practical reliable bayesian recognition of 2d and 3d objects using implicit polynomials and algebraic invariants we treat the use of more complex higher degree polynomial curves and surfaces of degree higher than 2 which have many desirable properties for object recognition and position estimation and attack the instability problem arising in their use with partial and noisy data the scenario discussed in this paper is one where we have a set of objects that are modeled as implicit polynomial functions or a set of representations of classes of objects with each object in a class modeled as an implicit polynomial function stored in the database then given partial data from one of the objects we want to recognize the object or the object class or collect more data in order to get better parameter estimates for more reliable recognition two problems arising in this scenario are discussed 1 the problem of recognizing these polynomials by comparing them in terms of their coefficients and 2 the problem of where to collect data so as to improve the parameter estimates as quickly as possible we use an asymptotic bayesian approximation for solving the two problems the intrinsic dimensionality of polynomials and the use of the mahalanobis distance are discussed

topologically faithful fitting of simple closed curves implicit representations of curves have certain advantages over explicit representation one of them being the ability to determine with ease whether a point is inside or outside the curve inside outside functions however save for some special cases it is not known how to construct implicit representations which are guaranteed to preserve the curve s topology as a result points may be erroneously classified with respect to the curve the paper offers to overcome this problem by using a representation which is guaranteed to yield the correct topology of a simple closed curve by using homeomorphic mappings of the plane to itself if such a map carries the curve onto the unit circle then a point is inside the curve if and only if its image is inside the unit circle

the richer representation the better registration in this paper the registration problem is formulated as a point to model distance minimization unlike most of the existing works which are based on minimizing a point wise correspondence term this formulation avoids the correspondence search that is time consuming in the first stage the target set is described through an implicit function by employing a linear least squares fitting this function can be either an implicit polynomial or an implicit b spline from a coarse to fine representation in the second stage we show how the obtained implicit representation is used as an interface to convert point to point registration into point to implicit problem furthermore we show that this registration distance is smooth and can be minimized through the levengberg marquardt algorithm all the formulations presented for both stages are compact and easy to implement in addition we show that our registration method can be handled using any implicit representation though some are coarse and others provide finer representations hence a tradeoff between speed and accuracy can be set by employing the right implicit function experimental results and comparisons in 2d and 3d show the robustness and the speed of convergence of the proposed approach

local and global controllability for nonlinear systems a technique to study local and global controllability properties for a wide class of nonlinear systems is presented in addition to an extensive study of systems on r2 we propose as an application of our method a new criterion for global controllability of systems with polynomial drift term defined on rn in the case of linear systems the criterion reduces to the classical kalman condition a study of local controllability at the equilibrium point of the drift term of systems defined on r2 enables us not only to rederive a local controllability result derived by hermes 4 5 but also to extend this result when no assumptions are made on the boundedness of the controls

on the radius of convergence of interconnected analytic nonlinear input output systems a complete analysis is presented of the radii of convergence of the parallel product cascade and feedback interconnections of analytic nonlinear input output systems represented as fliess operators such operators are described by convergent functional series which are indexed by words over a noncommutative alphabet their generating series are therefore specified in terms of noncommutative formal power series given growth conditions for the coefficients of the generating series for the subsystems the radius of convergence of each interconnected system is computed assuming the subsystems are either all locally convergent or all globally convergent in the process of deriving the radius of convergence for the feedback connection it is shown definitively that local convergence is preserved under feedback this had been an open problem in the literature until recently

faa di bruno hopf algebra of the output feedback group for multivariable fliess operators abstract given two nonlinear input output systems written in terms of chen fliess functional expansions i e fliess operators it is known that the feedback interconnected system is always well defined and in the same class an explicit formula for the generating series of a single input single output closed loop system was provided by the first two authors in earlier work via hopf algebra methods this paper is a sequel it has four main innovations first the full multivariable extension of the theory is presented next a major simplification of the basic setup is introduced using a new type of grading that has recently appeared in the literature this grading also facilitates a fully recursive algorithm to compute the antipode of the hopf algebra of the output feedback group and thus the corresponding feedback product can be computed much more efficiently the final innovation is an improved convergence analysis of the antipode operation namely the radius of convergence of the antipode is computed

an adaptive and stable method for fitting implicit polynomial curves and surfaces representing 2d and 3d data sets with implicit polynomials ips has been attractive because of its applicability to various computer vision issues therefore many ip fitting methods have already been proposed however the existing fitting methods can be and need to be improved with respect to computational cost for deciding on the appropriate degree of the ip representation and to fitting accuracy while still maintaining the stability of the fit we propose a stable method for accurate fitting that automatically determines the moderate degree required our method increases the degree of ip until a satisfactory fitting result is obtained the incrementability of qr decomposition with gram schmidt orthogonalization gives our method computational efficiency furthermore since the decomposition detects the instability element precisely our method can selectively apply ridge regression based constraints to that element only as a result our method achieves computational stability while maintaining fitting accuracy experimental results demonstrate the effectiveness of our method compared with prior methods

bivariate survival models induced by frailties abstract when two observed survival times depend via a proportional hazards model on the same unobserved variable called a frailty this common dependence induces an association between the observed times this article considers the class of bivariate survival distributions that can arise in this way extends it to allow negative association and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter a cross ratio function easily estimated even from censored data is the key to both the characterization results and inferential procedures and diagnostic plots that are introduced and illustrated by real examples the models considered are the natural counterpart for survival data of the latent variable models that have long been used in factor analysis for continuous data or in latent structure analysis for binary data the main distinguishing feature of survival data is the possibility of censoring which makes the standard methods difficu

nilpotent bases for distributions and control systems abstract let v m be the lie algebra infinite dimensional of real analytic vector fields on the n dimensional manifold m necessary conditions that a real analytic k dimensional distibution on m have a local basis which generates a nilpotent subalgebra of v m are derived two methods for sufficient conditions are given the first depending on the existence of a solution to a system of partial differential equations the second using darboux s theorem to give a computable test for an n 1 dimensional distribution a nonlinear control system in which the control variables appear linearly can be transformed into an orbit equivalent system whose describing vector fields generate a nilpotent algebra if the distribution generated by the original describing vector fields admits a nilpotent basis when this is the case local analysis of the control system is greatly simplified

brief analysis of exclusively kinetic two link underactuated mechanical systems analysis of exclusively kinetic two link underactuated mechanical systems is undertaken in this paper it is first shown that such systems are not full state feedback linearizable around any equilibrium point also the equilibrium points for which the system is small time locally controllable stlc is at most a one dimensional submanifold a concept less restrictive than stlc termed the small time local output controllability stloc is introduced the satisfaction of which guarantees that a chosen configuration output can be controlled at its desired value it is shown that the class of systems considered is stloc if the inertial coupling between the input and output is nonzero also in such a case the system is nonminimum phase an example section illustrates all the results presented

local controllability of non linear systems an example abstract an example of a locally controllable nonlinear system on r3 is given the system is of the type x f ug with f g analytic vector fields and u bounded the fields f and g are such that the dimension of the vector space spanned at x0 by the lie brackets which contain g an odd number of times is 2

direct least square fitting of hyperellipsoids this paper presents two new computationally efficient direct methods for fitting n dimensional ellipsoids to noisy data they conduct the fitting by minimizing the algebraic distance in subject to suitable quadratic constraints the hyperellipsoid specific hes method is an elaboration of existing ellipse and 3d ellipsoid specific fitting methods it is shown that hes is ellipsoid specific in n dimensional space a limitation of hes is that it may provide biased fitting results with data originating from an ellipsoid with a large ratio between the longest and shortest main axis the sum of discriminants sod method does not have such a limitation the constraint used by sod rejects a subset of non ellipsoidal quadrics which enables a high tendency to produce ellipsoidal solutions moreover a regularization technique is presented to force the solutions towards ellipsoids with sod the regularization technique is compatible also with several existing 2d and 3d fitting methods the new methods are compared through extensive numerical experiments with n dimensional variants of three commonly used direct fitting approaches for quadratic surfaces the results of the experiments imply that in addition to the superior capability to create ellipsoidal solutions the estimation accuracy of the new methods is better or equal to that of the reference approaches

linear regression analysis for highly stratified failure time data abstract in this article we consider cases where data consist of many small and independent groups of correlated failure time observations for each failure time which may be censored some important covariates are also recorded our goal is to examine the covariate effects on the individual failure time observations we assume that the logarithm of each failure time is linearly related to its covariates we then take a population averaged model approach to obtain inference procedures for the regression parameters without specifying the joint distribution of the observations within the group the new proposals do not need complicated and unstable nonparametric estimates for the hazard function of the error term their properties are extensively examined for practical sample sizes comparisons among various procedures are also performed all the methods studied in this article are illustrated with examples

fitting curves and surfaces with constrained implicit polynomials a problem which often arises while fitting implicit polynomials to 2d and 3d data sets is the following although the data set is simple the fit exhibits undesired phenomena such as loops holes extraneous components etc previous work tackled these problems by optimizing heuristic cost functions which penalize some of these topological problems in the fit the paper suggests a different approach to design parameterized families of polynomials whose zero sets are guaranteed to satisfy certain topological properties namely we construct families of polynomials with star shaped zero sets as well as polynomials whose zero sets are guaranteed not to intersect an ellipse circumscribing the data or to be entirely contained in such an ellipse this is more rigorous than using heuristics which may fail and result in pathological zero sets the ability to parameterize these families depends heavily on the ability to parameterize positive polynomials to achieve this we use some powerful results from real algebraic geometry

algebraic differential equations and rational control systems an equivalence is shown between realizability of input output i o operators by rational control systems and high order algebraic differential equations for i o pairs this generalizes to nonlinear systems the equivalence between autoregressive representations and finite dimensional linear realizability

lie brackets and local controllability a sufficient condition for scalar input systems we develop a general formalism based on exponential lie series which can be used to study control variations we apply the formalism to prove a result conjectured by h hermes that gives a sufficient condition for small time local controllability for single input systems

a class of multivanate failure time distributions summary a class of continuous multivariate lifetime distributions is proposed the dependence between individuals in a group is modelled by a group specific quantity which can be interpreted as an unobserved covariate common to the individuals in the group and assumed to follow a positive stable distribution it is possible to include covariates in the model and discuss whether the dependence is still present after specific covariates are taken into account if the conditional hazards are proportional then the hazards in the marginal distributions are also proportional but with different constants of proportionality also the hazard for the minimum in a group is proportional to the marginal hazards if the conditional distributions given the group quantity are weibull then the marginal distributions are also weibull this class can be used to test the hypothesis of independence of litter mates in the proportional hazards model

controllability of a class of underactuated mechanical systems with symmetry in this paper we develop results based on geometric mechanics to study the controllability of a class of controlled under actuated left invariant mechanical systems on lie groups we exploit the invariance of the controlled nonlinear dynamics to the group action symmetry to derive a set of reduced dynamics for the system we first present sufficient conditions for the controllability of the reduced dynamics we prove conditions boundedness of coadjoint orbits and existence of a radially unbounded lyapunov function under which the drift vector field of the reduced system is weakly positively poisson stable wpps the wpps nature of the drift vector field along with the lie algebra rank condition is used to show controllability of the reduced system we then extend these results to the unreduced dynamics considering separately the cases when the symmetry group is compact and noncompact in the noncompact case under further assumptions of equilibrium controllability sufficient conditions for controllability of the unreduced dynamics are derived jetpuck hovercraft and underwater vehicles are used as mechanical systems to motivate our work and illustrate our theoretical results

a combinatorial hopf algebra for nonlinear output feedback control systems abstract in this work a combinatorial description is provided of a faa di bruno type hopf algebra which naturally appears in the context of fliess operators in nonlinear feedback control theory it is a connected graded commutative and non cocommutative hopf algebra defined on rooted circle trees a cancellation free forest formula for its antipode is given

a quantitative condition for the well posedness of interconnected dynamical systems a sufficient condition for the well posedness of interconnected dynamical systems is reported the condition is stated in terms of the uniform instantaneous gains of subsystems and interconnections and includes vidyasagar s condition 8 as a special case the result is useful for testing the validity of the dynamical model of a large scale system which is obtained by combining the models of subsystems

stable fitting of 2d curves and 3d surfaces by implicit polynomials this work deals with fitting 2d and 3d implicit polynomials ips to 2d curves and 3d surfaces respectively the zero set of the polynomial is determined by the ip coefficients and describes the data the polynomial fitting algorithms proposed in this paper aim at reducing the sensitivity of the polynomial to coefficient errors errors in coefficient values may be the result of numerical calculations when solving the fitting problem or due to coefficient quantization it is demonstrated that the effect of reducing this sensitivity also improves the fitting tightness and stability of the proposed two algorithms in fitting noisy data as compared to existing algorithms like the well known 3l and gradient one algorithms the development of the proposed algorithms is based on an analysis of the sensitivity of the zero set to small coefficient changes and on minimizing a bound on the maximal error for one algorithm and minimizing the error variance for the second simulation results show that the proposed algorithms provide a significant reduction in fitting errors particularly when fitting noisy data of complex shapes with high order polynomials as compared to the performance obtained by the above mentioned existing algorithms

configuration controllability of mechanical systems underactuated by one control we investigate local configuration controllability for mechanical control systems within the affine connection formalism we rely on previous results on controllability and series expansions for the evolution of mechanical systems starting from rest extending the work by lewis for the single input case we are able to characterize local configuration controllability for systems with n degrees of freedom and n 1 input forces

weak small controls and approximations associated with controllable affine control systems abstract in this paper is shown that solutions associated with an extended affine control system can be obtained as a limit process using solutions for a parameterized affine control system and weak small controls

controllability of linear systems on generalized heisenberg groups this paper is devoted to the study of global controllability of linear systems on higher dimensional heisenberg groups hn necessary conditions and sufficient ones are provided they are compared to the known necessary and sufficient conditions on h1 stated in dath and jouan 2016 controllability of linear systems on low dimensional nilpotent and solvable lie groups journal of dynamical and control systems 22 2 207 225 the notion of decoupled systems is introduced in order to get examples and counter examples and more precise controllability criteria are stated for them

a simple estimator for a shared frailty regression model summary we propose a simple estimation procedure for a proportional hazards frailty regression model for clustered survival data in which the dependence is generated by a positive stable distribution inferences for the frailty parameter can be obtained by using output from cox regression analyses the computational burden is substantially less than that of the other approaches to estimation the large sample behaviour of the estimator is studied and simulations show that the approximations are appropriate for use with realistic sample sizes the methods are motivated by studies of familial associations in the natural history of diseases their practical utility is illustrated with sib pair data from beaver dam wisconsin

permutation tests for comparing marginal survival functions with clustered failure time data we propose a class of two sample non parametric permutation tests to compare the marginal survival distributions of two groups when the failure times are correlated within cluster with clusters nested within each group the permutation distribution effectively takes into account the correlation between failure times within a cluster the method is able to handle data with clusters of either fixed or variable sizes moreover this class of test statistics is sensitive to various alternatives the size and power of the proposed tests are assessed by a series of simulation studies the method is illustrated by application to data from the hypertension detection and follow up program trial

non causal fliess operators and their shuffle algebra fliess operators as a class of non linear operators have been well studied in several respects they have a well developed realization theory and convenient representations in terms of directed infinite products of exponential lie series their interconnection as subsystems has been studied as has their relationship to rational systems they find applications in such diverse areas as discretization methods for controls systems optimal control neural network analysis and the numerical solution of stochastic differential equations one issue concerning fliess operators however that has received little attention is their possible generalization to the non causal case examples of such operators appear implicitly in the literature addressing hilbert adjoints of causal non linear operators and system inversion for the purpose of output tracking but a general systematic treatment of the subject has not appeared in this paper a non causal extension of a fliess operator is developed with the primary focus being on local convergence continuity the associated shuffle algebra and computing adjoint operators

local stabilization and controllability of a class of non triangular nonlinear systems this paper considers the problems of local asymptotic stabilization using continuous static state feedback lcfs and small time local controllability stlc of single input nonlinear systems a specific class of nontriangular systems called the essentially triangular form is introduced for this class of systems sufficient conditions for lcfs and necessary and sufficient conditions for stlc are obtained in particular it is shown that stlc implies lcfs a motivating physical example of the etf system is presented

implicit polynomial representation through a fast fitting error estimation this paper presents a simple distance estimation for implicit polynomial fitting it is computed as the height of a simplex built between the point and the surface i e a triangle in 2 d or a tetrahedron in 3 d which is used as a coarse but reliable estimation of the orthogonal distance the proposed distance can be described as a function of the coefficients of the implicit polynomial moreover it is differentiable and has a smooth behavior hence it can be used in any gradient based optimization in this paper its use in a levenberg marquardt framework is shown which is particularly devoted for nonlinear least squares problems the proposed estimation is a generalization of the gradient based distance estimation which is widely used in the literature experimental results both in 2 d and 3 d data sets are provided comparisons with state of the art techniques are presented showing the advantages of the proposed approach

configuration controllability of simple mechanical control systems in this paper we present a definition of configuration controllability for mechanical systems whose lagrangian is kinetic energy with respect to a riemannian metric minus potential energy a computable test for this new version of controllability is derived this condition involves an object that we call the symmetric product of particular interest is a definition of equilibrium controllability for which we are able to derive computable sufficient conditions examples illustrate the theory

generating series for interconnected analytic nonlinear systems given two analytic nonlinear input output systems represented as fliess operators four system interconnections are considered in a unified setting the parallel connection product connection cascade connection and feedback connection in each case the corresponding generating series is produced and conditions for the convergence of the corresponding fliess operator are given in the process an existing notion of a composition product for formal power series has its set of known properties significantly expanded in addition the notion of a feedback product for formal power series is shown to be well defined in a broad context and its basic properties are characterized

a faa di bruno hopf algebra for a group of fliess operators with applications to feedback a faa di bruno type hopf algebra is developed for a group of integral operators known as fliess operators where operator composition is the group product such operators are normally written in terms of generating series over a noncommutative alphabet using a general series expansion for the antipode an explicit formula for the generating series of the compositional inverse operator is derived the result is applied to analytic nonlinear feedback systems to produce an explicit formula for the feedback product that is the generating series for the fliess operator representation of the closed loop system written in terms of the generating series of the fliess operator component systems this formula is employed to provide a proof that local convergence is preserved under feedback

combining stratified and unstratified log rank tests in paired survival data the log rank test is the most widely used nonparametric method for testing treatment differences in survival between two treatment groups due to its efficiency under the proportional hazards model most previous work on the log rank test has assumed that the samples from the two treatment groups are independent this assumption is not always true in multi center clinical trials survival times of patients in the same medical center may be correlated due to factors specific to each center for such data we can construct both stratified and unstratified log rank tests these two tests turn out to have very different powers for correlated samples an appropriate linear combination of these two tests may give a more powerful test than either of the individual test under a bivariate frailty model we obtain closed form asymptotic local alternative distributions and the correlation coefficient between these two tests based on these results we construct an optimal linear combination of the two test statistics to maximize the local power simulation studies with hougaard s model confirm our construction we also study the robustness of the combined test by simulations

on recognizing and positioning curved 3 d objects from image contours an approach for explicitly relating the shape of image contours to models of curved three dimensional objects is presented this relationship is used for object recognition and positioning object models consist of collections of parametric surface patches and their intersection curves this includes nearly all representations used in computer aided geometric design and computer vision the image contours considered are the projections of surface discontinuities and occluding contours elimination theory provides a method for constructing the implicit equation of these contours for an object observed under orthographic or perspective projection this equation is parameterized by the object s position and orientation with respect to the observer determining these parameters is reduced to a fitting problem between the theoretical contour and the observed data points the proposed approach readily extends to parameterized models it has been implemented for a simple world composed of various surfaces of revolution and tested on several real images

scene understanding by reasoning stability and safety this paper presents a new perspective for 3d scene understanding by reasoning object stability and safety using intuitive mechanics our approach utilizes a simple observation that by human design objects in static scenes should be stable in the gravity field and be safe with respect to various physical disturbances such as human activities this assumption is applicable to all scene categories and poses useful constraints for the plausible interpretations parses in scene understanding given a 3d point cloud captured for a static scene by depth cameras our method consists of three steps i recovering solid 3d volumetric primitives from voxels ii reasoning stability by grouping the unstable primitives to physically stable objects by optimizing the stability and the scene prior and iii reasoning safety by evaluating the physical risks for objects under physical disturbances such as human activity wind or earthquakes we adopt a novel intuitive physics model and represent the energy landscape of each primitive and object in the scene by a disconnectivity graph dg we construct a contact graph with nodes being 3d volumetric primitives and edges representing the supporting relations then we adopt a swendson wang cuts algorithm to partition the contact graph into groups each of which is a stable object in order to detect unsafe objects in a static scene our method further infers hidden and situated causes disturbances in the scene and then introduces intuitive physical mechanics to predict possible effects e g falls as consequences of the disturbances in experiments we demonstrate that the algorithm achieves a substantially better performance for i object segmentation ii 3d volumetric recovery and iii scene understanding with respect to other state of the art methods we also compare the safety prediction from the intuitive mechanics model with human judgement

a unified approach to generating series for mixed cascades of analytic nonlinear input output systems the primary goal is to describe in a unified fashion the generating series for the cascade connection of any two analytic nonlinear input output systems in particular it will be shown that a single general definition of a composition product can be formulated in terms of formal power series to describe any possible cascade connection of analytic integral operators fliess operators and analytic functions provided that the composite system is well defined and resides in one of these two classes in each case the radius of convergence of the interconnection is computed

local controllability of nonlinear systems abstract the local controllability of control systems with an arbitrary number of controls is considered first on an open set and then at a given point necessary conditions are derived concerning the lie algebra t generated by the input vector fields and applied to gradient systems the main results are a geometric sufficient condition for local controllability at a point and an equivalent condition based on the computation of lie brackets assuming t to be n 1 dimensional

the medial scaffold of 3d unorganized point clouds we introduce the notion of the medial scaffold a hierarchical organization of the medial axis of a 3d shape in the form of a graph constructed from special medial curves connecting special medial points a key advantage of the scaffold is that it captures the qualitative aspects of shape in a hierarchical and tightly condensed representation we propose an efficient and exact method for computing the medial scaffold based on a notion of propagation along the scaffold itself starting from initial sources of the flow and constructing the scaffold during the propagation we examine this method specifically in the context of an unorganized cloud of points in 3d e g as obtained from laser range finders which typically involve hundreds of thousands of points but the ideas are generalizable to data arising from geometrically described surface patches the computational bottleneck in the propagation based scheme is in finding the initial sources of the flow we thus present several ideas to avoid the unnecessary consideration of pairs of points which cannot possibly form a medial point source such as the visibility of a point from another given a third point and the interaction of clusters of points an application of using the medial scaffold for the representation of point samplings of real life objects is also illustrated

on the relation between local controllability and stabilizability for a class of nonlinear systems the problem of local stabilizability of locally controllable nonlinear systems is considered it is well known that contrary to the linear case local controllability does not necessarily imply stabilizability a class of nonlinear systems for which local controllability implies local asymptotic stabilizability using continuous static state feedback is described as for this class of systems the well known hermes controllability condition is necessary and sufficient for local controllability

local controllability along a reference trajectory abstract local controllability along a reference trajectory of analytic and smooth affine single input control systems without any a priori bounds on the control is considered and a geometric proof of a version of the hermes conjecture is given

fast multidimensional ellipsoid specific fitting by alternating direction method of multipliers many problems in computer vision can be formulated as multidimensional ellipsoid specific fitting which is to minimize the residual error such that the underlying quadratic surface is a multidimensional ellipsoid in this paper we present a fast and robust algorithm for solving ellipsoid specific fitting directly our method is based on the alternating direction method of multipliers which does not introduce extra positive semi definiteness constraints the computation complexity is thus significantly lower than those of semi definite programming sdp based methods more specifically to fit n data points into a p dimensional ellipsoid our complexity is o p 6 np 4 o p 3 where the former o results from preprocessing data once while that of the state of the art sdp method is o p 6 np 4 n frac 3 2 p 2 for each iteration the storage complexity of our algorithm is about frac 1 2 np 2 which is at most 1 4 of those of sdp methods extensive experiments testify to the great speed and accuracy advantages of our method over the state of the art approaches the implementation of our method is also much simpler than sdp based methods

implicit b spline surface reconstruction this paper presents a fast and flexible curve and surface reconstruction technique based on implicit b spline this representation does not require any parameterization and it is locally supported this fact has been exploited in this paper to propose a reconstruction technique through solving a sparse system of equations this method is further accelerated to reduce the dimension to the active control lattice moreover the surface smoothness and user interaction are allowed for controlling the surface finally a novel weighting technique has been introduced in order to blend small patches and smooth them in the overlapping regions the whole framework is very fast and efficient and can handle large cloud of points with very low computational cost the experimental results show the flexibility and accuracy of the proposed algorithm to describe objects with complex topologies comparisons with other fitting methods highlight the superiority of the proposed approach in the presence of noise and missing data

constructing simple stable descriptions for image partitioning a new formulation of the image partitioning problem is presented construct a complete and stable description of an image in terms of a specified descriptive language that is simplest in the sense of being shortest we show that a descriptive language limited to a low order polynomial description of the intensity variation within each region and a chain code like description of the region boundaries yields intuitively satisfying partitions for a wide class of images the advantage of this formulation is that it can be extended to deal with subsequent steps of the image understanding problem or to deal with other attributes such as texture in a natural way by augmenting the descriptive language experiments performed on a variety of both real and synthetic images demonstrate the superior performance of this approach over partitioning techniques based on clustering vectors of local image attributes and standard edge detection techniques

local uncontrollability for affine control systems with jumps abstractthis paper investigates affine control systems with jumps for which the ideal if g1 gm generated by the drift vector field f in the lie algebra l f g1 gm can be imbedded as a kernel of a linear first order partial differential equation it will lead us to uncontrollable affine control systems with jumps for which the corresponding reachable sets are included in explicitly described differentiable manifolds

recognition of 3d objects based on implicit polynomials closed form expressions for a new set of 3d rotation invariants that are linear quadratic and angular combinations of implicit polynomial ip coefficients are developed based on these invariants we propose a 3d object recognition method that outperforms recognition based on ip fitting after pose estimation and the mpeg 7 ssd technique

local controllability for families of diffeomorphisms abstract we study groups and semigroups which are generated by analytic families of diffeomorphisms the central notion is that of local controllability of a family of diffeomorphisms at a given point of the state manifold which generalizes the familiar notion of local controllability of control systems with continuous as well as discrete time lie theory methods are used we systematically exploit the so called fast switching variations and properties of the jet spaces of curves on the state manifold

optimization in differentiable manifolds in order to determine the method of construction of prehistoric wall paintings in this paper a general methodology is introduced for the determination of potential prototype curves used for the drawing of prehistoric wall paintings the approach includes 1 preprocessing of the wall paintings contours to properly partition them according to their curvature 2 choice of prototype curves families 3 analysis and optimization in 4 manifold for a first estimation of the form of these prototypes 4 clustering of the contour parts and the prototypes to determine a minimal number of potential guides and 5 further optimization in 4 manifold applied to each cluster separately in order to determine the exact functional form of the potential guides together with the corresponding drawn contour parts the methodology introduced simultaneously deals with two problems 1 the arbitrariness in data points orientation and 2 the determination of one proper form for a prototype curve that optimally fits the corresponding contour data arbitrariness in orientation has been dealt with a novel curvature based error while the proper forms of curve prototypes have been exhaustively determined by embedding curvature deformations of the prototypes into 4 manifolds application of this methodology to celebrated wall paintings excavated at tyrins greece and the greek island of thera manifests that it is highly probable that these wall paintings were drawn by means of geometric guides that correspond to linear spirals and hyperbolae these geometric forms fit the drawings lines with an exceptionally low average error less than 0 39 mm hence the approach suggests the existence of accurate realizations of complicated geometric entities more than 1 000 years before their axiomatic formulation in the classical ages

reconstructing surfaces by volumetric regularization using radial basis functions we present a new method of surface reconstruction that generates smooth and seamless models from sparse noisy nonuniform and low resolution range data data acquisition techniques from computer vision such as stereo range images and space carving produce 3d point sets that are imprecise and nonuniform when compared to laser or optical range scanners traditional reconstruction algorithms designed for dense and precise data do not produce smooth reconstructions when applied to vision based data sets our method constructs a 3d implicit surface formulated as a sum of weighted radial basis functions we achieve three primary advantages over existing algorithms 1 the implicit functions we construct estimate the surface well in regions where there is little data 2 the reconstructed surface is insensitive to noise in data acquisition because we can allow the surface to approximate rather than exactly interpolate the data and 3 the reconstructed surface is locally detailed yet globally smooth because we use radial basis functions that achieve multiple orders of smoothness

improving the stability of algebraic curves for applications an algebraic curve is defined as the zero set of a polynomial in two variables algebraic curves are practical for modeling shapes much more complicated than conics or superquadrics the main drawback in representing shapes by algebraic curves has been the lack of repeatability in fitting algebraic curves to data usually arguments against using algebraic curves involve references to mathematicians wilkinson and runge the first goal of this article is to understand the stability issue of algebraic curve fitting then a fitting method based on ridge regression and restricting the representation to well behaved subsets of polynomials is proposed and its properties are investigated the fitting algorithm is of sufficient stability for very fast position invariant shape recognition position estimation and shape tracking based on invariants and new representations among appropriate applications are shape based indexing into image databases

discrete time approximations of fliess operators a convenient way to represent a nonlinear input output system in control theory is via a chen fliess functional expansion or fliess operator the general goal of this paper is to describe how to approximate fliess operators with iterated sums and to provide accurate error estimates for two different scenarios one where the series coefficients are growing at a local convergence rate and the other where they are growing at a global convergence rate in each case it is shown that the error estimates are asymptotically achievable for certain worst case inputs the paper then focuses on the special case where the operators are rational i e they have rational generating series and thus are realizable in terms of bilinear ordinary differential state equations in particular it is shown that a discretization of the state equation via a kind of euler approximation coincides exactly with the discrete time fliess operator approximator of the continuous time rational operator

the 3l algorithm for fitting implicit polynomial curves and surfaces to data we introduce a completely new approach to fitting implicit polynomial geometric shape models to data and to studying these polynomials the power of these models is in their ability to represent nonstar complex shapes in two 2d and three dimensional 3d data to permit fast repeatable fitting to unorganized data which may not be uniformly sampled and which may contain gaps to permit position invariant shape recognition based on new complete sets of euclidean and affine invariants and to permit fast stable single computation pose estimation the algorithm represents a significant advancement of implicit polynomial technology for four important reasons first it is orders of magnitude taster than existing fitting methods for implicit polynomial 2d curves and 3d surfaces and the algorithms for 2d and 3d are essentially the same second it has significantly better repeatability numerical stability and robustness than current methods in dealing with noisy deformed or missing data third it can easily fit polynomials of high such as 14th or 16th degree fourth additional linear constraints can be easily incorporated into the fitting process and general linear vector space concepts apply

bilinear system interconnections and generating series of weighted petri nets this paper has three objectives the first objective is to provide a simpler proof concerning a sufficient condition due to ferfera under which bilinearity is preserved for cascade interconnections the next objective is to provide a specific counterexample to show that this condition does not apply to the feedback connection the final objective is to show that the well known correspondence between rational series and formal power series recognized by weighted finite state automata can be generalized to produce a correspondence between the generating series of cascaded and feedback connected bilinear systems and a class of weighted petri nets

low order controllability and kinematic reductions for affine connection control systems controllability and kinematic modeling notions are investigated for a class of mechanical control systems first low order controllability results are given for the class of mechanical control systems second a precise connection is made between those mechanical systems which are dynamic i e have forces as inputs and those which are kinematic i e have velocities as inputs interestingly and surprisingly these two subjects are characterized and linked by a certain intrinsic vector valued quadratic form that can be associated to an affine connection control system

nonparametric models and methods for designs with dependent censored data part i we consider a nonparametric np approach to the analysis of repeated measures designs with censored data using the np model of akritas and arnold 1994 journal of the american statistical association 89 336 343 for marginal distributions we present test procedures for the np hypotheses of no main effects no interaction and no simple effects this extends the existing np methodology for such designs wei and lachin 1984 journal of the american statistical association 79 653 661 the procedures do not require any modeling assumptions and should be useful in cases where the assumptions of proportional hazards or location shift fail to be satisfied the large sample distribution of the test statistics is based on an i i d representation for kaplan meier integrals the testing procedures apply also to ordinal data and to data with ties useful small sample approximations are presented and their performance is examined in a simulation study finally the methodology is illustrated with two real life examples one with censored and one with missing data it is indicated that one of the data sets does not conform to any set of assumptions underlying the available methods and also that the present method provides a useful additional analysis even when data sets conform to modeling assumptions

estimation of planar curves surfaces and nonplanar space curves defined by implicit equations with applications to edge and range image segmentation the author addresses the problem of parametric representation and estimation of complex planar curves in 2 d surfaces in 3 d and nonplanar space curves in 3 d curves and surfaces can be defined either parametrically or implicitly with the latter representation used here a planar curve is the set of zeros of a smooth function of two variables x y a surface is the set of zeros of a smooth function of three variables x y z and a space curve is the intersection of two surfaces which are the set of zeros of two linearly independent smooth functions of three variables x y z for example the surface of a complex object in 3 d can be represented as a subset of a single implicit surface with similar results for planar and space curves it is shown how this unified representation can be used for object recognition object position estimation and segmentation of objects into meaningful subobjects that is the detection of interest regions that are more complex than high curvature regions and hence more useful as features for object recognition

fliess operators on lp spaces convergence and continuity fliess operators as input output mappings are particularly useful in a number of fundamental problems concerning nonlinear realization theory in the classical analysis of these operators certain growth conditions on the coe3cients in their series representations insure uniform and absolute convergence provided every input is uniformly bounded by some 4xed upperbound in some emerging applications however it is more natural to consider other classes of inputs in this paper lp function spaces are considered in particular it is shown that the classic growth conditions also provide su3cient conditions for convergence and continuity when the admissible inputs are from a ball in lp t0 t 0 t where t is bounded and p 1 in addition stronger global growth conditions are given that apply even for the case where t is unbounded when the coe3cients of a fliess operator have a state space representation it is shown that the state space model will always locally realize the correspondinginput output map on lp t0 t 0 t for su3ciently small t 0 if certain well posedness conditions are satis4ed then the state space model will globally realized the input output mapping for unbounded t when the coe3cients satisfy the global growth condition c 2002 elsevier science b v all rights reserved

a comparison of several tests for censored paired data this paper reviews several tests for censored paired data and uses monte carlo methods to evaluate their sizes and powers each of the tests maintains its size the akritas test and the paired prentice wilcoxon test are somewhat more powerful than the gehan statistic or the generalized signed rank test for most of the distributions studied if the survival times follow an exponential distribution then the gehan and the generalized signed rank tests are more powerful against a location shift alternative

median spheres theory algorithms applications a generalized hypersphere is either a hyperplane or a hypersphere which consists of all points equidistant from a center geometrically a weighted median hypersphere minimizes a weighted average of the distances from it to finitely many data points as proved here for each finite data set there exists at least one weighted median generalized hypersphere moreover denote the sums of the weights of the data points inside by w outside by w and on the hypersphere by w 0 the present results show that each weighted median hypersphere is a weighted pseudo halving hypersphere in the sense that w w w 0 and passes through at least two distinct data points combinatorically a hypersphere is blocked if and only if it passes through data points in general position in the sense that no other hypersphere passes through the same data points a hypersphere is a halving hypersphere if and only if it is blocked contains exactly k data points inside confines exactly l data points outside and k l 1 in the plane the present results also show that if a median circle is not a halving circle then moving its center along a median between two data points on it until it passes through the next data point yields a halving circle relative to the center if the direction cosines of the external and internal data points have the same mean and variance then the median circle must be blocked and stays so under sufficiently small perturbations of the data moreover for every set of four points at least one unweighted median circle is blocked these results lend credence to a variant of a method used by archaeologists and explain some findings from operations research

left inversion of analytic nonlinear siso systems via formal power series methods given a single input single output siso system f and a function y in the range of f the left inversion problem is to determine an input u such that y f u the goal of this paper is to provide an exact and explicit analytical solution to this problem in the case where f is an analytic mapping in the sense that it has a convergent chen fliess functional expansion and y is a real analytic function in particular it will be shown that given a certain condition on the generating series c of f a corresponding unique analytic u can always be determined via operations on formal power series the condition on c turns out to be equivalent to having a well defined relative degree when f has an input affine analytic state space realization with finite dimension but the method is applicable even when f does not have such a realization the technique is demonstrated on four examples including a continuous stirred chemical reactor

a fast algorithm for multidimensional ellipsoid specific fitting by minimizing a new defined vector norm of residuals using semidefinite programming a quadratic surface in n dimensional space is defined as the locus of zeros of a quadratic polynomial the quadratic polynomial may be compactly written in notation by an n 1 vector and a real symmetric matrix of order n 1 where the vector represents homogenous coordinates of an n d point and the symmetric matrix is constructed from the quadratic coefficients if an n d quadratic surface is an n d ellipsoid the leading n times n principal submatrix of the symmetric matrix would be positive or opposite definite as we know to impose a matrix being positive or opposite definite perhaps the best choice may be to employ semidefinite programming sdp from such straightforward and intuitive knowledge in the literature until 2002 calafiore first proposed a feasible method for multidimensional ellipsoid specific fitting using sdp which minimizes the 2 norm of the algebraic residual vector however the runtime of the method is significantly long and memory is often out when the number of fitted points is greater than several thousand in this paper we propose a fast and easily implemented algorithm for multidimensional ellipsoid specific fitting by minimizing a new defined vector norm of the algebraic residual vector using sdp which drastically decreases the size of the sdp problem while preserving accuracy the proposed fast method can handle several million fitted points without any difficulty

describing complicated objects by implicit polynomials this paper introduces and focuses on two problems first is the representation power of closed implicit polynomials of modest degree for curves in 2 d images and surfaces in 3 d range data super quadrics are a small subset of object boundaries that are well fitted by these polynomials the second problem is the stable computationally efficient fitting of noisy data by closed implicit polynomial curves and surfaces the attractive features of these polynomials for vision is discussed

local equilibrium controllability of multibody systems controlled via shape change we study local equilibrium controllability of shape controlled multibody systems the multibody systems are defined on a trivial principal fiber bundle by a lagrangian that characterizes the base body motion and shape dynamics a potential dependent on an advected parameter e g uniform gravitational potential is considered this potential breaks base body symmetries but a symmetry subgroup is assumed to exist symmetric product formulas are derived and important properties are obtained for symmetric products of horizontal shape control vector fields and a potential vector field that is dependent on an advected parameter based on these properties sufficient conditions for local equilibrium controllability and local fiber equilibrium controllability are developed these results are applied to two classes of shape controlled multibody systems in a uniform gravitational field multibody attitude systems and neutrally buoyant multibody underwater vehicles

the complexity of deciding controllability abstract it is shown that the problem of deciding whether a control system is small time locally controllable or not is np hard this is an extension of a recent paper by sontag to single input systems and to bounded controls