an energy decaying scheme for nonlinear dynamics of shells a novel integration scheme for nonlinear dynamics of geometrically exact shells is developed based on the inextensible director assumption the new algorithm is designed so as to imply the strict decay of the system total mechanical energy at each time step and consequently unconditional stability is achieved in the nonlinear regime furthermore the scheme features tunable high frequency numerical damping and it is therefore stiffly accurate the method is tested for a finite element spatial formulation of shells based on mixed interpolations of strain tensorial components and on a two parameter representation of director rotations the robustness of the scheme is illustrated with the help of numerical examples

an efficient algorithm for decomposing a polygon into star shaped polygons abstract in this paper we show how a theorem in plane geometry can be converted into a o n log n algorithm for decomposing a polygon into star shaped subsets the computational efficiency of this new decomposition contrasts with the heavy computational burden of existing methods

a morphological signature transform for shape description abstract a novel shape description method based on the multiresolution morphological image processing by non convex multiple structuring elements is presented a binary image which contains the object shape to be described is represented by means of a multiresolution pyramid a set of primary structuring elements along with their rotated versions is used the method is based on the successive morphological erosions of the input image at different resolutions by primary and rotated structuring elements the areas of successively eroded images are computed for each structuring element at each pyramid level the obtained set of numbers is arranged into vectors ordered and used as a shape descriptor results are included to show that the method is robust against noise and invariant to both rotation and scale change

morphological decomposition of 2 d binary shapes into conditionally maximal convex polygons mathematical morphology is an approach to image analysis based on the geometric concept of shape and size naturally it provides a very effective tool for shape analysis in this paper we present a morphological shape segmentation algorithm that decomposes a 2 d two dimensional binary shape into a collection of restricted convex polygons we use simple morphological operations to extract shape information from different skeleton subsets to form a group of conditionally maximal convex polygonal shape components then a set of more meaningful and natural convex polygonal components are constructed from these maximal components the resulting algorithm is very simple and the decomposition is always unique the components produced have well defined mathematical characterizations and they seem to be in good agreement with the nature structures of the given shapes the shape segments produced can be used to construct structural shape description and for other shape analysis purposes

inspection of 2 d objects using pattern matching method abstract a pattern matching scheme is developed for the inspection of objects in industrial environment the inspection includes dimensional verification and shape matching which compares a 2 dimensional image of an object to a pattern image the method proves to be computationally efficient and accurate for real time application

segmenting dot patterns by voronoi diagram concavity this correspondence defines a signed distance called internal concavity on paths of the voronoi diagram of a dot pattern an algorithm using internal concavity to segment dot patterns is described the segmentation algorithm produces subsets of the dirichlet tessellation delaunay triangulation of the dot pattern

velocity based approach in non linear dynamics of three dimensional beams with enforced kinematic compatibility abstract in the paper we present a new finite element formulation for the dynamic analysis of geometrically exact three dimensional beams we limit our studies to implicit time integration schemes and possible approaches for increasing their robustness and numerical stability in contrast to standard displacement rotation based approach we present here a spatial and temporal discretization based on velocities and angular velocities to describe the rotational degrees of freedom quaternions are used the time integration scheme and the governing equations of the three dimensional beam are modified accordingly in the numerical implementation the galerkin type discretization is employed to obtain the finite element formulation of the problem the result of our studies is simple but accurate efficient and robust numerical model

integrating finite rotations abstract we study the integration of problems of evolution in the rotation group instead of attacking the problem in the nonlinear differential manifold so 3 pure rotational dynamics as is usually done we derive equations for the complete problem of motion translational and rotational dynamics on an extended manifold we develop a generalization of runge kutta methods that by design ensures that the solution will remain on the manifold for any choice of the tableau this is obtained through configuration updates performed via the exponential map we show how certain terms can be approximated while retaining the order of accuracy of the scheme and how the method conserves the total momentum of the system within this framework we develop two nonlinearly unconditionally stable time integration schemes that are associated with discrete laws of conservation dissipation of the total energy the dissipating algorithm generalizes to the nonlinear case the high frequency damping characteristics provided by some well known conventional methods we present numerical results to support our analysis and we develop a complete application of this methodology to the nonlinear dynamics of three dimensional rods undergoing large displacements and finite rotations under the assumption of small strains

some np hard polygon decomposition problems the inherent computational complexity of polygon decomposition problems is of theoretical interest to researchers in the field of computational geometry and of practical interest to those working in syntactic pattern recognition three polygon decomposition problems are shown to be np hard and thus unlikely to admit efficient algorithms the problems are to find minimum decompositions of a polygonal region into perhaps overlapping convex star shaped or spiral subsets we permit the polygonal region to contain holes the proofs are by transformation from boolean three satisfiability a known np complete problem several open problems are discussed

integration of elastic multibody systems by invariant conserving dissipating algorithms ii numerical schemes and applications abstract this work presents a novel methodology for the dynamic analysis of general non linear multibody systems composed of rigid and deformable bodies the latter under the small strain assumption in part i we developed the 6 d compact representation and parameterization of motion for constrained bodies part ii is devoted to the design of a class of modified runge kutta rk methods dedicated to non linear dynamics these are capable of integrating on the configuration manifold and of preserving linear and angular momenta within this class of methods two second order algorithms are designed under the requirement of attaining non linear unconditional stability the energy preserving ep and energy decaying ed methods these schemes are associated with an algorithmic law of conservation and dissipation respectively of the total mechanical energy of the system together with the vanishing of the algorithmic work done by ideal time independent constraints their performances are assessed with the aid of some representative numerical applications which confirm the non conventional properties predicted in the analysis

linear time euclidean distance transform algorithms two linear time and hence asymptotically optimal algorithms for computing the euclidean distance transform of a two dimensional binary image are presented the algorithms are based on the construction and regular sampling of the voronoi diagram whose sites consist of the unit feature pixels in the image the first algorithm which is of primarily theoretical interest constructs the complete voronoi diagram the second more practical algorithm constructs the voronoi diagram where it intersects the horizontal lines passing through the image pixel centers extensions to higher dimensional images and to other distance functions are also discussed

numerical integration of non linear elastic multi body systems this paper is concerned with the modelling of nonlinear elastic multi body systems discretized using the finite element method the formulation uses cartesian co ordinates to represent the position of each elastic body with respect to a single inertial frame the kinematic constraints among the various bodies of the system are enforced via the lagrange multiplier technique the resulting equations of motion are stiff non linear differential algebraic equations the integration of these equations presents a real challenge as most available techniques are either numerically unstable or present undesirable high frequency oscillations of a purely numerical origin an approach is proposed in which the equations of motion are discretized so that they imply conservation of the total energy for the elastic components of the system whereas the forces of constraint are discretized so that the work they perform vanishes exactly the combination of these two features of the discretization guarantees the stability of the numerical integration process for non linear elastic multi body systems examples of the procedure are presented

on a convex hull algorithm for polygons and its application to triangulation problems abstract a frequently used algorithm for finding the convex hull of a simple polygon in linear running time has been recently shown to fail in some cases due to its simplicity the algorithm is nevertheless attractive in this paper it is shown that the algorithm does in fact work for a family of simple polygons known as weakly externally visible polygons some application areas where such polygons occur are briefly discussed in addition it is shown that with a trivial modification the algorithm can be used to internally and externally triangulate certain classes of polygons in 0 n time

finding contour based abstractions of planar patterns abstract an algorithm is described to detect a number of points on the contour of a planar shape which constitute the vertices of a schematic polygonal representation of the shape itself a set of points initially extracted from the chain coded representation of the contour is iteratively examined while removing some points and inserting new ones the number of selected points decreases in size from iteration to iteration and the selection process converges towards an expected perceptually significant set of points the polygon obtained by linking successive points approximates the contour in an intuitive way it is not constrained within a given tolerance and is likely to locally change from a coarse to a more faithful approximating shape in correspondence with contour regions increasing in details

counting objects which behave like irreducible brauer characters of finite groups let n 0 g where g is a finite group so that g acts on irr n the set of irreducible ordinary complex characters of n suppose 8 e irr n is g invariant and write irr g 10 to denote the set of those x e irr g such that x involves and hence is a multiple of 8 how large is irr g io the answer to this question is well known and not very hard to prove analogously to the fact that lirr g i is equal to the number of conjugacy classes of g it turns out that iirr gjb l is equal to the number of certain good classes in the group g n there are two equivalent descriptions of which classes of g n these are one characterization depends on a certain complex twisted group algebra of g n and in this formulation the result which counts irr g 1 t9 is due to i schur s the other formulation of this result due to p x gallagher z defines goodness internally to g it depends on the character theory of g and its subgroups specifically gallagher defines an element of 2 e g n to be o good if some extension of 8 to n g is invariant in c where c n c jg the property of being q good is preserved by conjugacy in gin and gallagher shows that lirr g i 13 l is equal to the number of classes of g in which consist of good elements somewhat less well known is the corresponding result for irreducible brauer characters with respect to some prime p if 8 e ibr n is g invariant we intend to count the elements of ibr g t9 i e the irreducible brauer characters of g whose restrictions to n are multiples of 8 in view of the fact that iibr g equals the number of p regular classes of g it is reasonable to guess that iibr gl f l is the number of e good p regular

a self stabilized algorithm for enforcing constraints in multibody systems a new algorithm is developed for the enforcement of constraints within the framework of nonlinear flexible multibody system modeled with the finite element approach the proposed algorithm exactly satisfies the constraints at the displacement and velocity levels and furthermore it achieves nonlinear unconditional stability by imposing the vanishing of the work done by the constraint forces when combined with specific discretizations of the inertial and elastic forces identical convergence rates are observed for the displacements velocities and lagrange multipliers the proposed algorithm is closely related to the stabilized index 2 or ggl method although no additional multipliers are introduced in the present approach these desirable characteristics are obtained without resorting to numerically dissipative algorithms if high frequencies are present in the system i e the system is physically stiff dissipative schemes become necessary the proposed algorithm is extended to deal with this situation

a new energy and momentum conserving algorithm for the non linear dynamics of shells a numerical time integration scheme for the dynamics of non linear elastic shells is presented that simultaneously and independent of the time step size inherits exactly the conservation laws of total linear total angular momentum as well as total energy the proposed technique generalizes to non linear shells recent work of the authors on non linear elastodynamics and is ideally suited for long term large scale simulations the algorithm is second order accurate and can be immediately extended with no modification to a fourth order accurate scheme the property of exact energy conservation induces a strong notion of non linear numerical stability which manifests itself in actual simulations

singularities and regularities on line pictures via symmetrical trapezoids an algorithm that decomposes a line image into singular and regular regions is presented we define a contour trapezoid as the building block of regular regions and postulate a maximal trapezoid set as the core of regular regions then we describe an algorithm that calculates a maximal trapezoid set of a polygon and show how to use it to find a skeleton of a polygonal approximation of a contour experiments are explained to show the behavior of the new concept on real images as compared to previous algorithms

ordered structural shape matching with primitive extraction by mathematical morphology abstract structural shape matching procedures begin by decomposing the shapes to be matched into primitive parts and extracting the properties of and relationships among these primitives the resultant structural descriptions are matched to structural models usually via a tree search whose time is exponential in the number of primitives in this paper we introduce a new fast method of structural shape matching called ordered structural matching which has polynomial time complexity instead of exponential the approach presented also uses mathematical morphology to rapidly decompose the shapes into primitives to be used in the matching the primitives so produced are pieces of the original shape but not necessarily those pieces that a human would select the method has been tested on the toy task of determining which plastic shapes match the shapes of the holes in a child s six sided toy box it is also directly applicable to the inspection and manipulation of certain airplane parts

robust integration schemes for flexible multibody systems a framework for the development of robust time integration schemes for nonlinear flexible multibody systems is presented the proposed schemes are designed to meet four specific requirements nonlinear unconditional stability of the scheme a rigorous treatment of both geometric and material nonlinearities exact satisfaction of the constraints and the presence of high frequency numerical dissipation specific algorithms are presented for rigid bodies cables beams shells and elasto dynamics the kinematic nonlinearities are treated in a rigorous manner for all elements and the material nonlinearities can be handled when the constitutive laws stem from the existence of a strain energy density function the treatment of the constraint equations associated with the six lower pair joints are presented as well the efficiency and robustness of the proposed approach is demonstrated with specific numerical examples

on fully ramified brauer characters let z be a normal subgroup of a finite group let p 5 be a prime and let ibr z be an irreducible g invariant p brauer character of z suppose that g e for some ibr g then g z is solvable in other words a twisted group algebra over an algebraically closed field of characteristic not 5 with a unique class of simple modules comes from a solvable group

dot pattern processing using voronoi neighborhoods a sound notion of the neighborhood of a point is essential for analyzing dot patterns the past work in this direction has concentrated on identifying pairs of points that are neighbors examples of such methods include those based on a fixed radius k nearest neighbors minimal spanning tree relative neighborhood graph and the gabriel graph this correspondence considers the use of the region enclosed by a point s voronoi polygon as its neighborhood it is argued that the voronoi polygons possess intuitively appealing characteristics as would be expected from the neighborhood of a point geometrical characteristics of the voronoi neighborhood are used as features in dot pattern processing procedures for segmentation matching and perceptual border extraction using the voronoi neighborhood are outlined extensions of the voronoi definition to other domains are discussed

non linear dynamics of three dimensional rods exact energy and momentum conserving algorithms the long term dynamic response of non linear geometrically exact rods under going finite extension shear and bending accompanied by large overall motions is addressed in detail the central objective is the design of unconditionally stable time stepping algorithms which exactly preserve fundamental constants of the motion such as the total linear momentum the total angular momentum and for the hamiltonian case the total energy this objective is accomplished in two steps first a class of algorithms is introduced which conserves linear and angular momentum this result holds independently of the definition of the algorithmic stress resultants second an algorithmic counterpart of the elastic constitutive equations is developed such that the law of conservation of total energy is exactly preserved conventional schemes exhibiting no numerical dissipation symplectic algorithms in particular are shown to lead to unstable solutions when the high frequencies are not resolved compared to conventional schemes there is little if any additional computational cost involved in the proposed class of energy momentum methods the excellent performance of the new algorithm in comparison to other standard schemes is demonstrated in several numerical simulations

reasoning about pictures and similarity retrieval for image information systems based on sk set knowledge representation spatial reasoning and similarity retrieval are two important functions of any image information system good spatial knowledge representation for images is necessary to adequately support these two functions in this paper we propose a new spatial knowledge representation called the sk set based on morphological skeleton theories spatial reasoning algorithms which achieve more accurate results by directly analysing skeletons are described sk set facilitates browsing and progressive visualization we also define four new types of similarity measures and propose a similarity retrieval algorithm for performing image retrieval moreover using sk set as a spatial knowledge representation will reduce the storage space required by an image database significantly

global shape analysis by k syntactic similarity the k syntactic similarity approach is couched in graphical representation terms and its ability to provide global recognition capability while retaining a low time complexity is explored one potential application domain that of composite shape decomposition into approximately convex subshapes is described this is shown to be equivalent to finding cycles within a particular graph the approach yields valid decompositions in many cases of interest and is capable of identifying those cases where additional semantic considerations are necessary for proper analysis the permissible graph structures representing composite shapes given a reasonable set of relations are determined experimental results on nonideal data are given

on groups of central type a finite group is said to be of central type if it possesses an irreducible complex character which takes the value zero on all noncentral elements equivalently the degree of this character is the square root of the index of the center in 1964 iwahori and matsumoto 15 conjectured that a group of central type must be solvable the paper of liebler and yellen 16 aims to prove this but there is a gap in their proof as explained below nevertheless they do correctly obtain substantial information about a minimal counterexample to the conjecture the aim of this paper is to fill the gap in the liebler yellen proof using as they do the classification of finite simple groups and to provide further information about which solvable groups can have central type we show for instance that every normal subgroup of the central factor group of a solvable group of central type has the property that its system normalizers have square index it is interesting to contrast this restrictive condition with the result of gagola that every solvable group is embeddable in the central factor group of a group of central type see 6 theorem 1 2 the arguments in 16 show that a minimal counterexample g to the iwahori matsumoto conjecture must have the following structure if k z is any minimal normal subgroup of g z where z z g the center then k is abelian k z is a 2 group s cg k is the maximal solvable normal subgroup of g and any minimal normal subgroup his of g s is the direct product of a number l of copies of gl 3 2 indeed the liebler yellen methods can be used to show that the sylow 2 subgroup of k considered as an h s module is a product o f copies of a gl 3 2 module of dimension 4 this module having a unique minimal submodule which is trivial and an irreducible factor module of dimension 3 the minimal submodules are amalgamated in the product

computing conforming partitions of orthogonal polygons with minimum stabbing number abstract let p be an orthogonal polygon with n vertices a partition of p into rectangles is called conforming if it results from cutting p along a set of interior disjoint line segments each having both endpoints on the boundary of p the stabbing number of a partition of p into rectangles is the maximum number of rectangles stabbed by any orthogonal line segment inside p in this paper we consider the problem of finding a conforming partition of p with minimum stabbing number we first give an o n log n time algorithm to solve the problem when p is a histogram for an arbitrary orthogonal polygon even with holes we give an integer programming formulation of the problem and show that a simple rounding results in a 2 approximation algorithm for the problem finally we show that the problem is np hard if p is allowed to have holes

energy decaying scheme for non linear beam models abstract this paper is concerned with the time integration of the equations of motion describing the non linear dynamic response of beams desirable characteristics of integration schemes for structural dynamics problems include unconditional stability accuracy and high frequency numerical dissipation several schemes exist that present all these features when applied to linear problems though the application of those schemes to non linear problems is often successful proofs of unconditional stability are rarely derived a finite difference integration scheme is derived in this paper for the non linear dynamic response of beams though of a finite difference nature the proposed scheme mimics the integration scheme obtained by applying the time discontinuous galerkin methodology to a single degree of freedom linear oscillator a formal proof of unconditional stability for the non linear problem is derived based on an energy decay argument numerical examples using the proposed scheme are given and the results are compared with the predictions of other available schemes the accuracy of the proposed scheme and its high frequency numerical dissipation characteristics are demonstrated in these examples

division based analysis of symmetry and its application a computational method das is proposed for symmetry analysis of a planar figure closed by a simply connected curve das determines both the symmetric axis and the symmetric point pairs on the curve consistently based on the duality of two geometric plane divisions the delaunay triangulation and the voronoi diagram

the searchlight scheduling problem the problem of searching for a mobile robber in a simple polygon by a number of searchlights is considered a searchlight is a stationary point which emits a single ray that cannot penetrate the boundary of the polygon the direction of the ray can be changed continuously and a point is detected by a searchlight at a given time if and only if it is on the ray a robber is a point that can move continuously with unbounded speed first it is shown that the problem of obtaining a search schedule for an instance having at least one searchlight on the polygon boundary can be reduced to that for instances having no searchlight on the polygon boundary the reduction is achieved by a recursive search strategy called the one way sweep strategy then various sufficient conditions for the existence of a search schedule are presented by using the concept of a searchlight visibility graph finally a simple necessary and sufficient condition for the existence of a search schedule for instances having exactly two sea

relative sensitivity of a family of closet point graphs in computer vision applications abstract various graph theoretic definitions of neighborhood have been used in the past in computer vision and clustering applications in this paper we study the properties of a set of four related closest point graphs using monte carlo methods i the delaunay triangulation dt and its dual voronoi tessellation ii the gabriel graph gg iii the relative neighborhood graph rng and iv the minimum spanning tree mst we examine the suitability of these graphs in the detection of structure in noisy images using the hough transform we also explore each graph s structural stability under random positional noise delaunay triangulation is shown to be the least sensitive to such noisy conditions

extraction of parametric descriptions of circular gcs from a pair of contours for 3 d shape recognition this paper addresses the issue of recognizing 3 d three dimensional shapes of objects from their 2 d contour pairs a shape model that is represented by a family of spheres of varying radii with their centers on its axis is developed for the shape class of circular generalized cones gcs with a space curved axis the quasi invariant property of the shape model is defined and is used to recover the 3 d shapes of the object class by solving the problem of stereo matching between their contour pairs the recovered shapes are represented by a set of their parametric primitives and spatial relations between them so that they may be used for recognition even under occluded environment

region extraction from complex shapes an algorithm is described which extracts primitive regions i e convex spiral shaped and biconcave lens from complex shapes the interior region bounded by the shape is decomposed by first slicing it into a set of convex subregions and then rotating and dissolving the various boundaries between subregions until a satisfactory decomposition is obtained the same algorithm also is used to decompose the exterior region between the shape and its convex hull the algorithm has been implemented as an algol w computer program for the univac 90 80 and results of running the program are presented for a wide variety of complex shapes these results compare favorably with the experience reported by previous programs

above the glauberman correspondence let s be a finite solvable group and suppose s acts on the finite group n and they have coprime orders then the celebrated glauberman correspondence provides a natural bijection from the set irrs n of irreducible characters of n which are invariant under the action of s to the set irr cn s of all irreducible characters of the centralizer of s in n suppose further that the semidirect product sn is a normal subgroup of a finite group g let irrs n and let irr cn s be its glauberman correspondent we prove that there is a bijection with good compatibility properties from the set irr g of the irreducible characters of g above to irr ng s such that in the case when s is a p group for some prime p it preserves fields of values and schur indices over qp the field of p adic numbers using this result we also prove a strengthening of the mckay conjecture for all p solvable groups

a first order energy dissipative momentum conserving scheme for elasto plasticity using the variational updates formulation abstract in a previous paper l noels l stainier j p ponthot an energy momentum conserving algorithm using the variational formulation of visco plastic updates int j numer methods engrg 65 2006 904 942 the authors demonstrated the efficiency of the variational formulation of elasto plastic updates to develop energy momentum conserving time integration algorithms indeed within such a framework the stress tensor always derives from an incremental potential even when plastic behavior is considered therefore the verification of the conservation of energy in the non linear range can easily be demonstrated the sum of the reversible stored energy and irreversible dissipated energy exactly corresponds to the work of the external forces applied to the structure although this formulation was shown to be accurate and robust the introduction of numerical dissipation for high frequency numerical modes can be necessary to simulate complex phenomena in this work we propose a modification of the variational updates framework to introduce this numerical property leading to a new energy dissipative momentum conserving time integration algorithm for elasto plasticity

development of simple models for the elastic forces in the absolute nodal co ordinate formulation abstract the objective of this study is to develop simple and accurate elastic force models that can be used in the absolute nodal co ordinate formulation for the analysis of two dimensional beams these force models which account for the coupling between bending and axial deformations are derived using a continuum mechanics approach without the need for introducing a local element co ordinate system four new different force models that include different degrees of complexity are presented it is shown that the vector of the elastic forces can be significantly simplified as compared to the elastic force model developed for the absolute nodal co ordinate formulation using a local element frame 1 despite the simplicity of the new models they account for elastic non linearity in the strain displacement relationship therefore they lead to more accurate results as compared to the more complex models developed using the local frame method which does not account for the non linearities in the strain displacement relationships numerical results are presented in order to demonstrate the use of the new models and test their performances in the analysis of large deformations of flexible multibody systems

morphological decomposition of 2 d binary shapes into convex polygons a heuristic algorithm in many morphological shape decomposition algorithms either a shape can only be decomposed into shape components of extremely simple forms or a time consuming search process is employed to determine a decomposition in this paper we present a morphological shape decomposition algorithm that decomposes a two dimensional 2 d binary shape into a collection of convex polygonal components a single convex polygonal approximation for a given image is first identified this first component is determined incrementally by selecting a sequence of basic shape primitives these shape primitives are chosen based on shape information extracted from the given shape at different scale levels additional shape components are identified recursively from the difference image between the given image and the first component simple operations are used to repair certain concavities caused by the set difference operation the resulting hierarchical structure provides descriptions for the given shape at different detail levels the experiments show that the decomposition results produced by the algorithm seem to be in good agreement with the natural structures of the given shapes the computational cost of the algorithm is significantly lower than that of an earlier search based convex decomposition algorithm compared to nonconvex decomposition algorithms our algorithm allows accurate approximations for the given shapes at low coding costs

energy preserving decaying schemes for non linear beam dynamics using the helicoidal approximation abstract we develop two unconditionally stable displacement based time stepping schemes for the non linear dynamic response of beams the first algorithm guarantees the exact discrete conservation of energy and momentum the second is associated with an energy decay inequality that achieves control of the unresolved frequencies by means of a numerical dissipation mechanism both schemes emanate from a weak form of the equations of dynamic equilibrium referred to a fixed pole space and time discretizations are based on the exponential parameterization of motion this implies that the beam reference line and the trajectories of the beam nodes are helicoids in space the exponential mapping approach allows a unified treatment of translations and rotations greatly simplifying the derivation of the algorithms and their analysis the capabilities and performance of the new schemes are demonstrated and discussed with the aid of numerical simulations

shape description and recognition using the high order morphological pattern spectrum abstract shape analysis and recognition is an important issue in modern image processing and computer vision it needs to solve three problems possibility sensitivity and robustness to deal with the third one this paper proposes the high order morphological pattern hp spectrum which relies upon the difference between two different sized alternating sequential morphological transformations on the original image the hp spectrum is characterized by the translating invariance and rotating invariance for the isotropic structuring element it is also proved that the higher order components of hp spectrum for a noisy image are exactly identical to these for the noise free image under certain conditions also the results of the experiments conducted have shown that the hp spectrum shows the strongest robustness in a noisy environment

some sequential algorithms for a generalized distance transformation based on minkowski operations a generalized distance transformation gdt of binary images and the related medial axis transformation mat are discussed these transformations are defined in a discrete space of arbitrary dimension and arbitrary grids the gdt is based on successive morphological operations using alternatively n arbitrary structuring elements n is called the period of the gdt the gdt differs from the classical distance transformations based on a point to point distance however the well known chessboard city block and hexagonal distance transformations are special cases of the one period gdt whereas the octagonal distance transformation is a special case of the two period gdt in this paper both one and two period gdts are discussed different sequential algorithms are proposed for computing such gdts these algorithms need a maximum of two scannings of the image the computation of the mat is also discussed

a method for shift rotation and scale invariant pattern recognition using the form and arrangement of pattern specific features abstract a new computer based method for visual pattern recognition is described the process extracts shape features from binary edge images represented in either real valued or discrete coordinates both separate and overlapping features are extracted maximizing their completeness and continuity without using templates or mathematical feature descriptions these features and their arrangement are encoded in a shift rotation and scale invariant manner and used to recognize incoming patterns from a set of previously encoded patterns stored in memory new patterns may be automatically classified and stored in memory allowing the system to learn and generalize without operator intervention testing shows the system to be completely shift rotation and scale invariant and insensitive to local image distortion

an intrinsic beam model based on a helicoidal approximation part ii linearization and finite element implementation the helicoidal beam model developed in the first part of this work is applied here to the development of a mixed finite element for space curved and twisted beams undergoing large displacements and finite rotations starting from the governing weak form expressed by the principle of virtual work a consistent linearization is obtained in the following and a novel updated lagrangian finite element implementation is thoroughly discussed the unique features and the distinguishing properties previously claimed for the helicoidal model are shown here to imply remarkable numerical consequences for this purpose meaningful example problems regarding the non linear static response of beams are addressed in the following and the results are compared with those available from the literature furthermore a finite element in time for the rigid body dynamic problem is developed within the framework of the helicoidal geometry the underlying philosophy of this novel finite element for dynamics is the realization of the helicoidal decomposition of the rigid body motion within a time step

binary shape recognition using the morphological skeleton transform abstract binary image representation by its morphological skeleton transform has been proposed in the past as an information preserving representation in this paper this skeleton representation is adopted as the start point for the development of a binary shape recognition scheme a skeleton matching algorithm is presented that efficiently characterizes the similarity between two skeletons as a distance measure this skeleton matching algorithm resembles the well known from speech processing elastic matching technique

efficient shape matching through model based shape recognition abstract an efficient shape matching method for shape recognition is proposed it first uses a polygonal approximation technique to describe a shape then using the proposed matching algorithm based on some polygonal attributes the dissimilarity measure between an input shape and its reference model is obtained the input shape can be classified into the class model which has the minimum dissimilarity measure with it in addition it can provide the best matching orientation information for the input shape and its model so that further applications such as automated inspection and assembly can be effectively performed the proposed shape matching is invariant to translation rotation and scale changes of a shape experiments using noisy shapes and real images are performed and the recognition results demonstrate that the proposed method is very effective

integration of elastic multibody systems by invariant conserving dissipating algorithms i formulation abstract this work presents a novel methodology for the dynamic analysis of general non linear flexible multibody systems in part i we develop the 6 d compact representation of motion for those body models which motion may be described by a displacement field plus an independent rotation field this approach explores the fundamental properties of rigid body motion and in particular the coupled nature of linear and angular quantities in both kinematics and dynamics inspiring a novel parameterization technique based on the exponential map using the proposed approach we derive the governing equations for the case of multibody systems composed by rigid bodies and geometrically non linear beams connected by holonomic constraints these equations provide the starting point for the derivation of a class of numerical algorithms characterized by non conventional conservation properties in part ii of this work we develop the algorithms and illustrate their properties with the aid of some numerical applications

an objective finite element approximation of the kinematics of geometrically exact rods and its use in the formulation of an energy momentum conserving scheme in dynamics we present in this paper a new finite element formulation of geometrically exact rod models in the three dimensional dynamic elastic range the proposed formulation leads to an objective or frame indifferent under superposed rigid body motions approximation of the strain measures of the rod involving finite rotations of the director frame in contrast with some existing formulations this goal is accomplished through a direct finite element interpolation of the director fields defining the motion of the rod s cross section furthermore the proposed framework allows the development of time stepping algorithms that preserve the conservation laws of the underlying continuum hamiltonian system the conservation laws of linear and angular momenta are inherited by construction leading to an improved approximation of the rod s dynamics several numerical simulations are presented illustrating these properties copyright 2002 john wiley sons ltd

on the design of energy preserving and decaying schemes for flexible nonlinear multi body systems abstract energy preserving schemes achieve unconditional stability for nonlinear systems by establishing discrete energy preservation statements several schemes have been presented by various authors within drastically different frameworks finite difference schemes based on a mid point approximation galerkin and time discontinuous galerkin approximations of the equations of motion written in the symmetric hyperbolic form finite elements in time and 2 stage fsal runge kutta methods furthermore different types of parameterization of finite rotations were used in the various formulations this paper presents a unified finite difference framework which readily allows comparing the various schemes and their respective properties numerical examples are presented and show that the predictions of two of these schemes are in very close agreement with each other

an intrinsic beam model based on a helicoidal approximation part i formulation the focus of the present work is directed towards the one dimensional non linear analysis of space curved and twisted beams undergoing large displacements and finite rotations according to cosserat s model a beam is intended here as a continuum generated by the rigid motion of a cross section along a curve the novelty of the proposed methodology is implied in the assumption that the reference line of the beam both in the undeformed and in the deformed configurations is a helicoid in space this formulation radically departs from the classical beam models based on polynomial interpolations of the independent fields in fact within the framework of helicoidal geometry a powerful description of space curved beam kinematics with large displacements and finite rotations can be developed furthermore the beam model developed herein can be proved to enjoy several invariance properties that make it particularly attractive for non linear analysis the formulation discussed in this work adheres to a mixed variational principle the independent fields being the generalized displacements and the sectional stress resultants in a companion paper we address the linearization of the governing weak form the finite element implementation of the proposed methodology with a novel incremental treatment of finite rotations and the development of a helicoidal model for rigid body dynamics using finite elements in time

computational complexity of art gallery problems we study the computational complexity of the art gallery problem originally posed by klee and its variations specifically the problem of determining the minimum number of vertex guards that can see an n wall simply connected art gallery is shown to be np hard the proof can be modified to show that the problems of determining the minimum number of edge guards and the minimum number of point guards in a simply connected polygonal region are also np hard as a byproduct the problem of decomposing a simple polygon into a minimum number of star shaped polygons such that their union is the original polygon is also shown to be np hard

binary object representation and recognition using the hilbert morphological skeleton transform abstract a binary shape representation called the hilbert morphological skeleton transform hmst is introduced this representation combines the morphological skeleton transform mst with the clustering capabilities of the hilbert transform the hmst preserves the skeleton properties including information preservation progressive visualization and compact representation then an object recognition algorithm the hilbert skeleton matching algorithm hsma is introduced this algorithm performs a single sweep over the hmst s and renders the similarity between them as a distance measure testing the hsma against the skeleton matching algorithm sma and invariant moments revealed that the hsma algorithm achieves slightly better object recognition rates while substantially reducing the complexity in an experiment of 14 400 shape matches the hsma achieved a 90 36 recognition rate as opposed to 89 76 for the sma and 89 49 for invariant moments on the other hand the hsma improved the sma processing more than 40