generalizing the hough transform to detect arbitrary shapes abstract the hough transform is a method for detecting curves by exploiting the duality between points on a curve and parameters of that curve the initial work showed how to detect both analytic curves 1 2 and non analytic curves 3 but these methods were restricted to binary edge images this work was generalized to the detection of some analytic curves in grey level images specifically lines 4 circles 5 and parabolas 6 the line detection case is the best known of these and has been ingeniously exploited in several applications 7 8 9 we show how the boundaries of an arbitrary non analytic shape can be used to construct a mapping between image space and hough transform space such a mapping can be exploited to detect instances of that particular shape in an image furthermore variations in the shape such as rotations scale changes or figure ground reversals correspond to straightforward transformations of this mapping however the most remarkable property is that such mappings can be composed to build mappings for complex shapes from the mappings of simpler component shapes this makes the generalized hough transform a kind of universal transform which can be used to find arbitrarily complex shapes

efficient algorithms for finding the centers of conics and quadrics in noisy data abstract we present efficient algorithms for finding the centers of conics and quadrics of known parameters in noisy or scarce data the problem arises in applications where a conic or quadric of known parameters such as a circle of known radius is extracted from a scene or part common applications include locating an object in a noisy scene and determining the correspondence between a manufactured part and its intended shape although the original problem is nonlinear and usually requires an iterative method for its solution we reduce it to the well known problem of minimizing a nonhomogeneous quadratic expression on the unit sphere in the case of closed conics and quadrics such as circles ellipses spheres and ellipsoids we obtain the solution in just one iteration and no starting estimate is required furthermore we prove that the solution obtained by our method is the global minimum solution to the problem for hyperbolas and hyperboloids we describe a gauss seidel algorithm for which we give a lyapunov type proof of convergence we also describe an initialization algorithm to obtain starting estimates close to the global minimum solution furthermore every iteration of this algorithm satisfies all constraints we give numerical results showing a rapid convergence of the algorithm in just two iterations we apply our method in a metrology application to accurately determine the cutting radius of a tool we compare the results of our method in just one iteration for closed conics and two iterations for hyperbolas against multiple iterations of newton s method our comparison suggests that they are similar

majorization algorithms for inspecting circles ellipses squares rectangles and rhombi in several disciplines as diverse as shape analysis location theory quality control archaeology and psychometrics it can be of interest to fit a circle through a set of points we use the result that it suffices to locate a center for which the variance of the distances from the center to a set of given points is minimal in this paper we propose a new algorithm based on iterative majorization to locate the center this algorithm is guaranteed to yield a series of nonincreasing variances until a stationary point is obtained in all practical cases the stationary point turns out to be a local minimum numerical experiments show that the majorizing algorithm is stable and fast in addition we extend the method to fit other shapes such as a square an ellipse a rectangle and a rhombus by making use of the class of lp distances and dimension weighting in addition we allow for rotations for shapes that might be rotated in the plane we illustrate how this extended algorithm can be used as a tool for shape recognition

application of gradient descent method to the sedimentary grain size distribution fitting existence of a least squares solution for a sum of several weighted normal functions is proved the gradient descent gd method is used to fit the measured data i e the laser grain size distribution of the sediments with a sum of three weighted lognormal functions the numerical results indicate that the gd method is not only easy to operate but also could effectively optimize the parameters of the fitting function with the error decreasing steadily meanwhile the overall fitting results are satisfactory as a new way of data fitting the gd method could also be used to solve other optimization problems

motion recovery by integrating over the joint image manifold recovery of epipolar geometry is a fundamental problem in computer vision the introduction of the joint image manifold jim allows to treat the recovery of camera motion and epipolar geometry as the problem of fitting a manifold to the data measured in a stereo pair the manifold has a singularity and boundary therefore special care must be taken when fitting it four fitting methods are discussed direct algebraic geometric and the integrated maximum likelihood iml based method the first three methods are the exact analogues of three common methods for recovering epipolar geometry the more recently introduced iml method seeks the manifold which has the highest support in the sense that the largest measure of its points are close to the data while computationally more intensive than the other methods its results are better in some scenarios both simulations and experiments suggest that the advantages of iml manifold fitting carry over to the task of recovering epipolar geometry especially when the extent of the data and or the motion are small

unbiased estimation of ellipses by bootstrapping a general method for eliminating the bias of nonlinear estimators using bootstrap is presented instead of the traditional mean bias we consider the definition of bias based on the median the method is applied to the problem of fitting ellipse segments to noisy data no assumption beyond being independent identically distributed is made about the error distribution and experiments with both synthetic and real data prove the effectiveness of the technique

algorithms for projecting points onto conics we study the problem of projecting 2d points onto quadratic curves ellipses hyperbolas parabolas we investigate various projection algorithms focusing on those that are mathematically proven to produce or converge to correct results in all cases our tests demonstrate that those may be still unfit for practical use due to large computational errors we present two new algorithms that are not only theoretically proven to converge but achieve nearly perfect accuracy

robust ellipse fitting via half quadratic and semidefinite relaxation optimization ellipse fitting is widely applied in the fields of computer vision and automatic manufacture however the introduced edge point errors especially outliers from image edge detection will cause severe performance degradation of the subsequent ellipse fitting procedure to alleviate the influence of outliers we develop a robust ellipse fitting method in this paper the main contributions of this paper are as follows first to be robust against the outliers we introduce the maximum correntropy criterion into the constrained least square cls ellipse fitting method and apply the half quadratic optimization algorithm to solve the nonlinear and nonconvex problem in an alternate manner second to ensure that the obtained solution is related to an ellipse we introduce a special quadratic equality constraint into the aforementioned cls model which results in the nonconvex quadratically constrained quadratic programming problem finally we derive the semidefinite relaxation version of the aforementioned problem in terms of the trace operator and thus determine the ellipse parameters using semidefinite programming some simulated and experimental examples are presented to illustrate the effectiveness of the proposed ellipse fitting approach

embedding a quantum nonsingular quadric in a quantum p3 a definition of regularity has been given for non commutative graded algebras and results of artin schelter tate and van den bergh classify the regular algebras of global dimension three that are generated by degree one elements our purpose is to classify a certain class of quadratic regular algebras of global dimension four letsbe a twisted homogeneous coordinate ring of a nonsingular quadricq p3 our interest is in algebrasrsuch that there is an embedding proj s proj r in this paper we classify all the quadratic regular algebrasrof global dimension four which have the same hilbert series as that of the polynomial ring on four variables and which map ontosvia a graded degree zero homomorphism our approach makes use of the point modules ofrand their associated geometric data we classify the algebrasraccording to their point scheme pand corresponding automorphism aut p those algebrasrwhich are determined by p belong to at most a five parameter family but those which are not determined by p belong to at most a four parameter family in the first case pis either p3or consists ofqtogether with a linel while in the second casep q it is also proved that under certain sufficient conditions the zero locus of the defining relations of a quadratic regular algebra of global dimension four is the graph of an automorphism

the multiparametric non standard deformation of an 1 the authors introduce a multiparametric generalization of the non standard r matrix if sl n applying the method of faddeev reshetikhin takhtajan 1990 to the r matrix they construct the quantum group associated to it the new feature of this quantum group is that upon a certain choice of the parameters there can be nilpotent elements in it which is a sign of some hidden superstructure

algebraic aspects of the quantum yang baxter equation in this paper we examine a variety of algebraic contexts in which the quantum yang baxter equation arises and derive methods for generating new solutions from given ones the solutions we describe are encoded in objects which have a module and a comodule structure over a bialgebra our work here is based in part on the ideas of dr1 dr2 suppose that r m m m m is a solution to the quantum yang baxter equation where m is a finite dimensional vector space over a field k in dr2 it was shown that r can be derived from a left h module structure and a right h comodule structure on m for some bialgebra h over k also see yet maj1 maj2 frt2 the module and comodule structure satisfy a natural compatibility condition m together with these structures is called a left quantum yang baxter h module every left quantum yang baxter module gives rise to a solution to the quantum yang baxter equation in a natural way we study the category hyb of left quantum yang baxter h modules and show that many of the familiar constructions in the module category hm can be made in hyb through these constructions solutions to the quantum yang baxter equation can be combined in various ways to generate new ones we place particular emphasis on the tensor product of objects of hyb and ways in which the tensor algebra t m of an object m of hyb can be viewed as an object of hyb using the tensor algebra we are able to extend certain solutions when dim m 2 to the quantum plane we turn the tensor algebra t m of an object m of hyb into an object of hyb by giving it a module algebra and a comodule algebra structure module algebra and comodule algebra structures play a very important role in this paper in section 9 we develop a calculus for uq sl2 starting with a right k slq 2 comodule algebra structure on the quantum plane k x y q where k slq 2 is the coordinate ring of quantum slq 2 over k this calculus has been described in other ways m s sud the right comodule algebra structure on k x y q accounts for the left uq sl2 module algebra structure on k x y q described in m s we show how the basic irreducible representations of tak follow by the calculus a module algebra action or comodule algebra action is a natural vehicle for extending structure on a submodule or subcomodule respectively to the subalgebra it generates the calculus and the solutions to the quantum yang baxter equation we describe in this paper are determined in this manner on small structures two dimensional in this case we believe that many more results will follow from this circle of ideas in section 2 we discuss basic aspects of coalgebra and bialgebras used in the sequel a good general reference for this is sweedler s book sb on hopf algebras in section 3 we review the quantum yang baxter equation in connection with quantum yang baxter modules the a r construction of faddeev reshetikhin and takhtajan frt is considered in this light and examined in detail in when r arises from two commuting operators even though this particular r is rather simple the algebra structure of a r is surprisingly complex using the scratchpad computer algebra system we determine the algebra structure of a r in an interesting specific case showing that our particular example has a finite non commutative groeb

matrix element bialgebras determined by quadratic coordinate algebras abstract we develop the theory of manin s construction of quantum groups from finitely generated quadratic algebras in general this construction yields a bialgebra with matrix comultiplication we give formulae for the relations in the algebra and sufficient conditions for the existence of an antipode and for polynomiality of the algebra these are more systematic than the calculational approach of previous treatments

statistical bias of conic fitting and renormalization introducing a statistical model of noise in terms of the covariance matrix of the n vector we point out that the least squares conic fitting is statistically biased we present a new fitting scheme called renormalization for computing an unbiased estimate by automatically adjusting to noise relationships to existing methods are discussed and our method is tested using real and synthetic data

least squares based fitting of paraboloids a technique for reconstructing a class of quadric surfaces from 3d data is presented the technique is driven by a linear least squares based fitting mechanism previously such fitting was restricted to recovery of central quadrics here extension of that basic mechanism to allow recovery of one commonly occurring class of non central quadric the elliptic paraboloids is described the extension uses an indirect solution approach that involves introducing a variable to the basic mechanism that is a function of a quadric surface invariant results from fitting real and synthetic data are also exhibited

a class of methods for fitting a curve or surface to data by minimizing the sum of squares of orthogonal distances given a family of curves or surfaces in rs an important problem is that of finding a member of the family which gives a best fit to m given data points a criterion which is relevant to many application areas is orthogonal distance regression where the sum of squares of the orthogonal distances from the data points to the surface is minimized for certain types of fitting problem attention has recently focussed on the use of an iteration process which forces orthogonality to hold at every iteration and uses steps of gauss newton type within this framework a number of different methods has recently emerged and the purpose of this paper is to place these methods into a unified framework and to make some comparisons

improved approximate methods for calculating frequency response function matrix and response of mdof systems with viscoelastic hereditary terms as we know it is difficult and unnecessary to obtain all the eigenpairs of a large scaled viscoelastic nonviscous or hysteretic damping systems which means that the mode truncation scheme is generally used and the mode truncated error is therefore introduced this study is aimed at eliminating the influence of the unavailable modes on the dynamic response of mdof systems with viscoelastic hereditary terms the energy dissipation terms of the system depend on the past history of motion via convolution integrals over some kernel functions therefore the system is a nonviscously damped system which has been considered as the most generalized damping model within the scope of a linear mechanical analysis to approximate frequency response function frf matrix and response without using the unavailable modes we suggest two methods which attempt to approximate the influence of the unavailable modes in terms of the lower modes and system matrices by using the first one or two terms of neumann expansion of the contribution of the unavailable modes in contrast with the frf matrix approximated in terms of the first two terms of neumann expansion these procedures cannot be extended to further high order terms since all of them will be affected by the frequency dependent variation of damping matrix from previous terms finally an example is shown that the two presented methods can make the mode truncated error reduce and may be used to approximate the influence of nonviscous modes contributed to frf matrix due to the fact that the nonviscous modes are difficult to be obtained accurately even if a small scaled model is used for some eigensolution methods

eliminating the modal truncation problem encountered in frequency responses of viscoelastic systems increasing the number of degrees of freedom used in finite element analysis for mechanical and structural systems with viscoelastic damping the need to consider the modal truncation problem of viscoelastic systems is more than ever before the higher modes may be unnecessary to obtain in dynamic analysis for engineering applications for viscoelastic systems the modal truncation problem may be more frequently encountered since the nonviscous modes are difficult or even impossible to be found accurately even if a small scaled problem is considered for some eigensolution methods this study aims at eliminating the influence of the higher modes on the frequency responses of viscoelastically damped systems a method is presented by making the equilibrium equations of motion into a subspace equation spanned in terms of the columns of a projection basis obtained by considering the use of the contribution of the lower modes and the first two terms of the neumann expansion of the contribution of the unavailable modes finally three example studies are provided to illustrate the effectiveness of the derived results it is shown that the proposed method can reduce the modal truncation error significantly

unscented transformation based estimation of parameters of nonlinear models using heteroscedastic data this paper addresses the issue of estimating the parameters of nonlinear models using heteroscedastic data a weighted least squares problem formulation where the sum of the mahalanobis distance for all measurements is minimized forms the framework of this paper determining the mahalanobis distance requires the gradient of the cost function with respect to the noisy measurements which can be computationally expensive and infeasible for model which are discontinuous a derivative free approach to determine the mahalanobis distance as an error metric is proposed using the unscented transformation the advantages of using the proposed approach include a black box approach to evaluate the gradient weighted objective function precluding the need for analytical gradients and an improved estimation of the covariance numerical results for various applications such as triangulation using radar measurements ellipse and super ellipse fitting demonstrate the benefits of the proposed approach heteroscedastic data resulting from real x ray images are also used to illustrate the potential of the proposed approach highlightsderivative free approach of solving gradient weighted least squares problems improved approximation of the geometric distance for curve fitting improved performance of proposed technique demonstrated on three benchmarks monte carlo used to benchmark the reduction in bias in estimated parameters relevant to model fitting problems with heteroscedastic data

new improved series expansion for solving the moving oscillator problem a new method able to evaluate the dynamic stress response of an elastic beam subject to moving oscillators is presented the proposed procedure improves the convergence and accuracy of the conventional eigenfunction series expansion of beam response taking into account the gravitational inertial and damping effects due to the moving oscillators the improvement of the conventional solution is obtained by means of an extension to continuous systems of the dynamic correction method originally proposed for discretized structures the proposed method is able to account for the truncated higher order eigenfunctions by adding a pseudo static term to the conventional series expansion numerical results are presented to demonstrate the capability of the method to accurately determine the discontinuity and jump in bending moment and shear force distributions respectively

the isolated quantum group of the gl2 family abstract quantum analogs of gl 2 are parameterized by pgl 2 orbits in the commuting variety of the projective linear group pgl 2 the quantum group corresponding to the orbit constituting the second connected component of the commuting variety has previously received little attention this paper investigates ring theoretical properties of its coordinate ring

vibration of multi span timoshenko beams to a moving force abstract a method of modal analysis is proposed in this paper to investigate the forced vibration of multi span timoshenko beams the ratio of the radius of gyration of the cross section to one span length is defined as a parameterr the effect ofron the first modal frequency of a beam is studied a concentrated force traversing on the beam is used as an example the effects of span number rotary inertia and shear deformation on the maximum moment the maximum deflection and the critical velocity of a beam are examined the results are compared with those of a multi span bernoulli euler beam

consistent multiparameter quantisation of gl n the author describes a manifold of quantum group structures on the vector space of the universal enveloping algebra of gl n and on its dual the space of polynomials in n2 variables the dimension of the manifold is n2 n 2 2

duals of pointed hopf algebras in this paper we study the duals of some finite dimensional pointed hopf algebras working over an algebraically closed field k of characteristic 0 in particular we study pointed hopf algebras with coradical k for a finite abelian group and with associated graded hopf algebra of the form b v k where b v is the nichols algebra of v iv igi k k yd as a corollary to a general theorem on duals of coradically graded hopf algebras we have that the dual of b v k is b w k where w iwgi i k k yd this description of the dual is used to explicitly describe the drinfel d double of b v k we also show that the dual of a nontrivial lifting a of b v k which is not itself a radford biproduct is never pointed for v a quantum linear space of dimension 1 or 2 we describe the duals of some liftings of b v k we conclude with some examples where we determine all the irreducible finite dimensional representations of a lifting of b v k by computing the matrix coalgebras in the coradical of the dual

homological aspects of noetherian pi hopf algebras and irreducible modules of maximal dimension abstract we prove that a noetherian hopf algebra of finite global dimension possesses further attractive homological properties at least when it satisfies a polynomial identity this applies in particular to quantized enveloping algebras and to quantized function algebras at a root of unity as well as to classical enveloping algebras in positive characteristic in all three cases we show that these algebras are auslander regular and macaulay we derive representation theoretic consequences concerning the coincidence of the non azumaya and singular loci for each of the above three classes of algebras

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

least squares orthogonal distances fitting of circle sphere ellipse hyperbola and parabola the least squares fitting minimizes the squares sum of error of fit in predefined measures by the geometric fitting the error distances are defined with the orthogonal or shortest distances from the given points to the geometric feature to be fitted for the geometric fitting of circle sphere ellipse hyperbola parabola simple and robust nonparametric algorithms are proposed these are based on the coordinate description of the corresponding point on the geometric feature for the given point where the connecting line of the two points is the shortest path from the given point to the geometric feature to be fitted

a correction method for the analysis of continuous linear one dimensional systems under moving loads a new correction procedure for dynamic analysis of linear proportionally damped continuous systems under traveling concentrated loads is proposed both cases of non parametric moving forces and parametric moving mass loads are considered improvement in the evaluation of the dynamic response is obtained by separating the contribution of the low frequency lf modes from that of the high frequency hf modes the former is calculated as usual by classical modal analysis while the latter is taken into account using a new series expansion of the corresponding particular solution the advantage of the suggested method is immediately shown in the calculation of the stress distribution since it is able to capture the stress discontinuities due to the nature of the applied loads themselves numerical results are presented to discuss the convergence of the proposed series and to show the accuracy of the calculated response compared to the classical series expansion solution

quantum groups and quantum determinants abstract we construct function coordinate algebras of multi parameter quantum deformations of g sl n gl n so n o n and sp n when g is of rank l the obtained function algebra has 1 l l 1 2 continuous parameters and some discrete parameters whose values are roots of unity to do this we introduce a notion of co quasitriangular bialgebras and study their group like elements quantum determinants

revisiting the moving force problem abstract the problem of the vibration of a beam subject to a travelling force is considered the purpose of the study is to develop simple tools for finding the maximum deflection of a beam for any given velocity of the travelling force it is shown that for given boundary conditions there exists a unique response velocity dependence function a technique to determine this function is suggested which is based on the assumption that the maximum beam response can be adequately approximated by means of the first beam mode to illustrate this the maximum response function is calculated analytically for a simply supported ss beam and constructed numerically for a clamped clamped beam the effect of the higher modes on the maximum response is investigated and the relative error of the one mode approximation for a ss beam is constructed the estimates obtained substantiate the assumption about adequacy of the one mode approximation in a wide range of velocities in particular the relative error in the neighborhood of the velocity that results in the largest response is less than one percent

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

ellipse fitting using the finite rate of innovation sampling principle standard approaches for ellipse fitting are based on the minimization of algebraic or geometric distance between the given data and a template ellipse when the data are noisy and come from a partial ellipse the state of the art methods tend to produce biased ellipses we rely on the sampling structure of the underlying signal and show that the x and y coordinate functions of an ellipse are finite rate of innovation fri signals and that their parameters are estimable from partial data we consider both uniform and nonuniform sampling scenarios in the presence of noise and show that the data can be modeled as a sum of random amplitude modulated complex exponentials a low pass filter is used to suppress noise and approximate the data as a sum of weighted complex exponentials the annihilating filter used in fri approaches is applied to estimate the sampling interval in the closed form we perform experiments on simulated and real data and assess both objective and subjective performances in comparison with the state of the art ellipse fitting methods the proposed method produces ellipses with lesser bias furthermore the mean squared error is lesser by about 2 to 10 db we show the applications of ellipse fitting in iris images starting from partial edge contours and to free hand ellipses drawn on a touch screen tablet

robust ellipse fitting based on sparse combination of data points ellipse fitting is widely applied in the fields of computer vision and automatic industry control in which the procedure of ellipse fitting often follows the preprocessing step of edge detection in the original image therefore the ellipse fitting method also depends on the accuracy of edge detection besides their own performance especially due to the introduced outliers and edge point errors from edge detection which will cause severe performance degradation in this paper we develop a robust ellipse fitting method to alleviate the influence of outliers the proposed algorithm solves ellipse parameters by linearly combining a subset of more accurate data points formed from edge points rather than all data points which contain possible outliers in addition considering that squaring the fitting residuals can magnify the contributions of these extreme data points our algorithm replaces it with the absolute residuals to reduce this influence moreover the norm of data point errors is bounded and the worst case performance optimization is formed to be robust against data point errors the resulting mixed l1 l2 optimization problem is further derived as a second order cone programming one and solved by the computationally efficient interior point methods note that the fitting approach developed in this paper specifically deals with the overdetermined system whereas the current sparse representation theory is only applied to underdetermined systems therefore the proposed algorithm can be looked upon as an extended application and development of the sparse representation theory some simulated and experimental examples are presented to illustrate the effectiveness of the proposed ellipse fitting approach

a method for solving the multiple ellipses detection problem in this paper the multiple ellipses detection problem on the basis of a data points set coming from a number of ellipses in the plane not known in advance is considered an ellipse is considered as a mahalanobis circle with some positive definite matrix a very efficient method for solving this problem is proposed this method very successfully combines the well known direct least squares method and the ransac algorithm with a realistic statistical model of multiple ellipses in the plane the method is illustrated and tested on numerous synthetic and real world applications the method was also compared with other similar methods in the case when a data points set comes from a number of ellipses with clear edges the proposed method gives results similar to other known methods however when a data points set comes from a number of ellipses with noisy edges the proposed method performs significantly better than the other methods we should emphasize the advantage and utility of the proposed methods in a variety of applications such as medical image analysis and ultrasound image segmentation highlightsransac based method for solving the multiple ellipses detection problem is proposed the proposed method shows high efficiency the method has the potential to solve real time applications data is considered as a realization of a realistic statistical model pseudocodes of all proposed algorithms are provided

invariant fitting of planar objects by primitives the determination of invariant characteristics is an important problem in pattern recognition many invariants are known which have been obtained by the method of normalization in this paper we introduce a new approach of fitting planar objects by primitives using the method of normalization e g fitting by lines triangles rectangles circles ellipses super quadrics etc objects and primitives are described by features for example by moments the main advantage is that the normalization process provides us with a canonical frame of the object and the primitive therefore the fit is invariant with respect to the transformation used by this new method an analytical fitting of non analytical objects can be achieved for example fitting by polygons furthermore the numerical effort can be reduced drastically by normalizing of the object and the primitive

ellipse fitting for imaged cross sections of a surface of revolution this paper addresses the problem of accurately fitting the elliptical projections of the cross sections of a surface of revolution sor with the given intrinsic matrix of a camera by the new approach proposed in this paper the image points of the sor cross sections are fitted under the two geometric constraints which are derived from the configuration characteristics of sor it is demonstrated by comparison with other previous methods that our method can fit the elliptical projections of sor cross sections more accurately and robustly in this paper we also describe the applications of the algorithm in euclidean reconstruction of sor and pose estimation for sor shaped object such as spacecraft we accurately fit the imaged cross sections of a surface of revolution the ellipses can be fitted under the circular point and orthogonality constraints an effective optimization is elaborately designed the method can serve for reconstruction and localization of a surface of revolution

orthogonal distance fitting of implicit curves and surfaces dimensional model fitting finds its applications in various fields of science and engineering and is a relevant subject in computer machine vision and coordinate metrology in this paper we present two new fitting algorithms distance based and coordinate based algorithm for implicit surfaces and plane curves which minimize the square sum of the orthogonal error distances between the model feature and the given data points each of the two algorithms has its own advantages and is to be purposefully applied to a specific fitting task considering the implementation and memory space cost and possibilities of observation weighting by the new algorithms the model feature parameters are grouped and simultaneously estimated in terms of form position and rotation parameters the form parameters determine the shape of the model feature and the position rotation parameters describe the rigid body motion of the model feature the proposed algorithms are applicable to any kind of implicit surface and plane curve in this paper we also describe algorithm implementation and show various examples of orthogonal distance fit

ellifit an unconstrained non iterative least squares based geometric ellipse fitting method a novel ellipse fitting method which is selective for digital and noisy elliptic curves is proposed in this paper the method aims at fitting an ellipse only when the data points are highly likely belong to an ellipse this is achieved using the geometric distances of the ellipse from the data points the proposed method models the non linear problem of ellipse fitting as a combination of two operators with one being linear numerically stable and easily invertible while the other being non linear but unique and easily invertible operator as a consequence the proposed ellipse fitting method has several salient properties like unconstrained stable non iterative and computationally inexpensive the efficacy of the method is compared against six contemporary and recent algorithms based on the least squares formulation using five experiments of diverse practical challenges like digitization incomplete ellipses and gaussian noise up to 30 three of the experiments comprise of a total of 44 400 ellipses positive test data while the other two are tested on 320 000 non elliptic conics negative test data the results show that the proposed method is quite selective to elliptic shapes only and provides accurate fitting results indicating potential application in medical robotics object detection and other image processing industrial applications

a new family of mode superposition methods for response calculations abstract a new family of mode superposition methods for the computation of the forced response of proportionally damped systems with and without rigid body modes is investigated the method may be considered to be an extension of the mode acceleration method it allows response calculations to be done with a very small subset of the modes of the system numerical examples are given for systems of order 20 and 40 execution times and number of modes required for convergence are recorded the particular order of the method among the family which takes the shortest time is determined for the example systems time savings with the new method are realized compared to the existing mode displacement and mode acceleration methods the method is expected to be particularly suitable for large systems

dynamic response of a beam with a crack subject to a moving mass abstract an iterative modal analysis approach is developed to determine the effect of transverse cracks on the dynamic behavior of simply supported undamped bernoulli euler beams subject to a moving mass the presence of crack results in higher deflections and alters the beam response patterns in particular the largest deflection in the beam for a given speed takes longer to build up and a discontinuity appears in the slope of the beam deflected shape at the crack location crack effects become more noticeable as crack depth increases the effect of the inertia force due to the moving mass is in general qualitatively similar and additive to the effect of the crack the exact effect of crack and mass depends on the speed time crack size crack location and the moving mass level other approximate methods namely a stationary mass model and a single iteration technique are also evaluated the stationary mass approach is useful for light moving masses