a maximum likelihood surface estimator for dense range data describes how to estimate 3d surface models from dense sets of noisy range data taken from different points of view i e multiple range maps the proposed method uses a sensor model to develop an expression for the likelihood of a 3d surface conditional on a set of noisy range measurements optimizing this likelihood with respect to the model parameters provides an unbiased and efficient estimator the proposed numerical algorithms make this estimation computationally practical for a wide variety of circumstances the results from this method compare favorably with state of the art approaches that rely on the closest point or perpendicular distance metric a convenient heuristic that produces biased solutions and fails completely when surfaces are not sufficiently smooth as in the case of complex scenes or noisy range measurements empirical results on both simulated and real ladar data demonstrate the effectiveness of the proposed method for several different types of problems furthermore the proposed method offers a general framework that can accommodate extensions to include surface priors more sophisticated noise models and other sensing modalities such as sonar or synthetic aperture radar

controllability and observability for affine nonlinear hamiltonian systems it is shown that an affine nonlinear hamiltonian system is controllable if and only if it is observable in the sense that strong accessibility implies local weak observability and vice versa furthermore it is shown that a nonminimal hamiltonian system can be reduced to a locally weakly observable and strongly accessible system in such a way that the reduced system is again hamiltonian

shape spectrum based view grouping and matching of 3d free form objects we address the problem of constructing view aspects of 3d free form objects for efficient matching during recognition we introduce a novel view representation based on shape spectrum features and propose a general and powerful technique for organizing multiple views of objects of complex shape and geometry into compact and homogeneous clusters our view grouping technique obviates the need for surface segmentation and edge detection experiments on 6 400 synthetically generated views of 20 free form objects and 100 real range images of 10 sculpted objects demonstrate the good performance of our shape spectrum based model view selection technique

a method for registration of 3 d shapes the authors describe a general purpose representation independent method for the accurate and computationally efficient registration of 3 d shapes including free form curves and surfaces the method handles the full six degrees of freedom and is based on the iterative closest point icp algorithm which requires only a procedure to find the closest point on a geometric entity to a given point the icp algorithm always converges monotonically to the nearest local minimum of a mean square distance metric and the rate of convergence is rapid during the first few iterations therefore given an adequate set of initial rotations and translations for a particular class of objects with a certain level of shape complexity one can globally minimize the mean square distance metric over all six degrees of freedom by testing each initial registration one important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model prior to shape inspection experimental results show the capabilities of the registration algorithm on point sets curves and surfaces

symmetric centrosymmetric matrix vector multiplication abstract we present a method for the multiplication of an arbitrary vector by a symmetric centrosymmetric matrix requiring 5 4 n 2 o n floating point operations rather than the 2n 2 operations needed in the case of an arbitrary matrix combining this method with trench s algorithm for toeplitz matrix inversion yields a method for solving toeplitz systems with the same complexity as levinson s algorithm

registering multiview range data to create 3d computer objects concerns the problem of range image registration for the purpose of building surface models of 3d objects the registration task involves finding the translation and rotation parameters which properly align overlapping views of the object so as to reconstruct from these partial surfaces an integrated surface representation of the object the registration task is expressed as an optimization problem we define a function which measures the quality of the alignment between the partial surfaces contained in two range images as produced by a set of motion parameters this function computes a sum of euclidean distances from control points on one surfaces to corresponding points on the other the strength of this approach is in the method used to determine point correspondences it reverses the rangefinder calibration process resulting in equations which can be used to directly compute the location of a point in a range image corresponding to an arbitrary point in 3d space a stochastic optimization technique very fast simulated reannealing vfsr is used to minimize the cost function dual view registration experiments yielded excellent results in very reasonable time a multiview registration experiment took a long time a complete surface model was then constructed from the integration of multiple partial views the effectiveness with which registration of range images can be accomplished makes this method attractive for many practical applications where surface models of 3d objects must be constructed

computing the square roots of matrices with central symmetry for computing square roots of a nonsingular matrix a which are functions of a two well known fast and stable algorithms which are based on the schur decomposition of a were proposed by bjork and hammarling a bjork s hammarling a schur method for the square root of a matrix linear alg appl 52 53 1983 127 140 for square roots of general complex matrices and by higham n j higham computing real square roots of a real matrix linear alg appl 88 89 1987 405 430 for real square roots of real matrices in this paper we further consider the computation of the square roots of matrices with central symmetry we first investigate the structure of the square roots of these matrices and then develop several algorithms for computing the square roots we show that our algorithms ensure significant savings in computational costs as compared to the use of standard algorithms for arbitrary matrices

observability and controllability for smooth nonlinear systems the definition of a smooth nonlinear system as proposed recently by willems is elaborated as a natural generalization of the more common definitions of a smooth nonlinear input output system mini

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

the iterative methods for centrosymmetric matrices in this paper we give some new centrosymmetric splittings of a centrosymmetric matrix a and obtain corresponding iterative methods for a linear system ax b these iterative schemes are particularly based on the centrosymmetric property of a and aimed at reduction of the cost of computation and storage

r s conjugate solution to a pair of linear matrix equations abstract let r and s be m m and n n nontrivial real symmetric involutions an m n complex matrix a is termed r s conjugate if a ras where a denotes the conjugate of a in this paper necessary and sufficient conditions are established for the existence of the r s conjugate solution to the system of matrix equations ax c and xb d the expression is also presented for such solution to this system in addition the explicit expression of this solution to the corresponding optimal approximation problem is obtained furthermore the least squares r s conjugate solution with least norm to this system mentioned above is considered the representation of such solution is also derived finally an algorithm and numerical examples are given

symmetries conservation laws and time reversibility for hamiltonian systems with external forces a system theoretic framework is given for the description of hamiltonian systems with external forces and partial observations of the state it is shown how symmetries and conservation laws can be defined within this framework a generalization of noether s theorem is obtained finally a precise definition of time reversibility is given and its consequences are explored

iterative point matching for registration of free form curves and surfaces a heuristic method has been developed for registering two sets of 3 d curves obtained by using an edge based stereo system or two dense 3 d maps obtained by using a correlation based stereo system geometric matching in general is a difficult unsolved problem in computer vision fortunately in many practical applications some a priori knowledge exists which considerably simplifies the problem in visual navigation for example the motion between successive positions is usually approximately known from this initial estimate our algorithm computes observer motion with very good precision which is required for environment modeling e g building a digital elevation map objects are represented by a set of 3 d points which are considered as the samples of a surface no constraint is imposed on the form of the objects the proposed algorithm is based on iteratively matching points in one set to the closest points in the other a statistical method based on the distance distribution is used to deal with outliers occlusion appearance and disappearance which allows us to do subset subset matching a least squares technique is used to estimate 3 d motion from the point correspondences which reduces the average distance between points in the two sets both synthetic and real data have been used to test the algorithm and the results show that it is efficient and robust and yields an accurate motion estimate

reduction of hamiltonian systems with symmetry abstract this paper presents an alternative phase space reduction process for hamiltonian systems with symmetry using a lie algebra of infinitesimal symmetries instead of a lie group of symmetries this approach avoids the use of the various conditions on the action of the group or of the isotropy subgroup necessary for the usual construction of a reduced phase space quotient with a globally defined symplectic manifold structure the existence of such a reduced phase space is proved without recourse to the existence of an equivariant moment map instead it is assumed that the orbits of the action associated to the lie algebra can be described as the level sets of some analytic map an assumption that holds in many of the known examples the relation between the two reduction processes is discussed in particular some cases where the marsden weinstein process leads to a quotient space which is not a smooth manifold are shown to be amenable to the method now proposed the natural control theoretic interpretation of the techniques used is also discussed

computing matrix vector products with centrosymmetric and centrohermitian matrices an algorithm proposed recently by melman reduces the costs of computing the product ax with a symmetric centrosymmetric matrix a as compared to the case of an arbitrary a we show that the same result can be achieved by a simpler algorithm which requires only that a be centrosymmetric however if a is hermitian or symmetric this can be exploited to some extent also we show that similar gains are possible when a is a skew centrosymmetric or a centrohermitian matrix

symmetries and conservation laws for hamiltonian systems with inputs and outputs a generalization of noether s theorem the definition of symmetries and conservation laws for autonomous i e without external cases hamiltonian systems are generalized to hamiltonian systems with inputs and outputs it is shown that a symmetry implies the existence of a conservation law and vice versa thereby generalizing noether s theorem for autonomous hamiltonian systems

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

on the hss iteration methods for positive definite toeplitz linear systems we study the hss iteration method for large sparse non hermitian positive definite toeplitz linear systems which first appears in bai golub and ng s paper published in 2003 z z bai g h golub m k ng hermitian and skew hermitian splitting methods for non hermitian positive definite linear systems siam j matrix anal appl 24 2003 603 626 and hss stands for the hermitian and skew hermitian splitting of the coefficient matrix a in this note we use the hss iteration method based on a special case of the hss splitting where the symmetric part h 12 a a t is a centrosymmetric matrix and the skew symmetric part s 12 a a t is a skew centrosymmetric matrix for a given toeplitz matrix hence fast methods are available for computing the two half steps involved in the hss and ihss iteration methods some numerical results illustrate their effectiveness

stabilization of hamiltonian systems 1 hamiltonian systems in this paper we will be concerned with the stabilization by feedback of hamiltonian systems in order to facilitate our discussions especially when applying lyapunov s second method we will restrict ourselves to a particular although natural subclass of hamiltonian systems given in the following way l let q be an n dimensional smooth manifold denoting the configuration space and let t q be the cotangent bundle denoting the phase space or srufe space furthermore there is a smooth m dimensional output manifold y m n and a smooth output map c q y smooth will mean c or ck with k sufficiently big although we shall restrict ourselves in the second part of section 2 to analytic data for simplicity we take c to be submersive so rank dc q m we assume that the system on t q has an internal energy which is the sum of a kinetic energy k and a porentiul energy v this means that there exists a riemannian metric on q in local coordinates q q j for q given by

a hermitian toeplitz matrix is unitarily similar to a real toeplitz plus hankel matrix two unitary matrices are presented that transform a hermitian toeplitz matrix into a real toeplitz plus hankel matrix and vice versa additional properties and consequences of these unitary transformations are also presented for a certain class of n dimensional toeplitz plus hankel systems of equations an efficient method of solution is presented an example is given to illustrate the similarity transforms toeplitz plus hankel systems arise in a wide variety of applications such as linear filtering theory discrete inverse scattering and discretization of certain integral equations arising in mathematical physics

a note on computing matrix vector products with generalized centrosymmetric centrohermitian matrices to reduce the costs of computing matrix vector product ax related to a centrosymmetric matrix a as compared to the case of an arbitrary matrix a two algorithms were proposed recently one was designed by melman a melman symmetric centrosymmetric matrix vector multiplication linear algebra appl 320 2000 193 198 for symmetric centrosymmetric matrices another was presented by fassbender and ikramov h fassbender k d ikramov computing matrix vector products with centrosymmetric and centrohermitian matrices linear algebra appl 364 2003 235 241 for general centrosymmetric matrices in this note we further discuss this topic of computing ax where a is a generalized centrosymmetric matrix we firstly investigate the reducibility of a generalized centrosymmetric matrix and then provide an algorithm which can be viewed as a generalization of one h fassbender k d ikramov computing matrix vector products with centrosymmetric and centrohermitian matrices linear algebra appl 364 2003 235 241 we show that our algorithm is suitable for computing many matrix vector products with the same matrix furthermore we show that similar results can be obtained for certain subclasses of generalized centrosymmetric matrices as compared to the case of a centrosymmetric matrix and analogue gains are available for generalized skew centrosymmetric or generalized centrohermitian matrices

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