refined moment calculation using image block representation this paper deals with effective calculation of moments of binary images recently spiliotis and mertzios see ibid vol 7 p 1609 15 nov 1998 published a method based on image block representation ibr we propose a refinement of their method which yields exact results and performs even more effectively

exact and fast algorithm for two dimensional image wavelet moments via the projection transform wavelet moments are perfect representations of moments in multiresolution wavelet domain which integrates the theory of moment invariants into wavelet analysis however the calculations of moments are very complicated in terms of computational complexity so it is difficult to implement them in real time an exact and fast projection based algorithm for two dimensional wavelet moments is presented in this paper in our approach the computation of a two dimensional wavelet moment of order of r is performed in r 1 different one dimensional spaces since only additions are required to perform the projection transform the total computational complexity can be greatly reduced

efficient parallel algorithms for the computation of two dimensional image moments abstract moments constitute an important set of parameters for image analysis the low order moments contain significant information about a simple object they have been used in finding the location and orientation of an object moment invariants have been used as features for pattern recognition to compute moments of a two dimensional image a large number of multiplications and additions are required in a direct approach multiplications which are the most time consuming operations in simple processors can be completely avoided in the proposed algorithms for low order moments in this paper parallel algorithms are proposed for efficient implementation in processor arrays the basic idea is to decompose a 2 d moment into many vertical moments and a horizontal moment and to use the data parallelism for the vertical moments and the task parallelism for the horizontal moment

high order moment computation of gray level images describes an efficient approach to calculate geometric moments of a 2 d gray level image it is shown both theoretically and experimentally that the new method compares favorably with previous techniques especially for high order moments

two dimensional local moment surface fitting and their fast computation abstract it is proved that local moments are related to their surface fitting coefficients by a linear transform and by this the surface fitting based feature extraction is converted into the computation of 2d local moments a npt recursive method is proposed to compute 2d local moments quickly and then to efficiently implement surface fitting the new method has a novel advantage that its computational complexity for both 2d local moment computation and surface fitting is independent of the mask size which much efficiently speed up the feature extraction

the revised fundamental theorem of moment invariants a revised fundamental theorem of moment invariants for pattern recognition which corrects the fundamental theorem proposed by m k hu 1962 is presented the correction affects neither similitude scale nor rotation invariants derived using the original theorem but it does affect features invariant to general linear transformations four of the latter invariants were presented originally by hu these are revised to take the correction to the fundamental theorem into account furthermore these four invariants are combined to yield three new invariants which are additionally invariant to changes in the illumination of an image

shape sensitivity analysis of large deformation frictional contact problems sensitivity analysis of large displacement multi body two dimensional contact problems with friction is developed in the paper the incremental path dependent sensitivity problem is derived by direct differentiation of the discretized equations governing the direct problem in view of finite deformations due attention is paid to spatial and nominal contact tractions and to proper formulation of the contact laws within the penalty approach for these reasons an extended node to segment contact element is used to model the frictional contact interactions as the finite elasto plastic deformations of the contacting bodies are considered the numerical procedures for computation of all the necessary characteristic formulae of the solid elements for both the direct and the sensitivity problem are automatically derived and generated using the symbolic algebra package acegen numerical examples of shape and parameter sensitivity analysis illustrate the approach

design sensitivity analysis for rate independent elastoplasticity abstract a new incremental direct differentiation method for design sensitivity analysis of structures with rate independent elastoplastic behavior is presented we formulate analytical sensitivity expressions that are consistent with numerical algorithms for elastoplasticity that use implicit methods to integrate the constitutive equations and return mappings to enforce the consistency conditions the sensitivity expressions can be evaluated with only a modest increase in computational expense beyond the cost of simulation combined with the inherent advantages of implicit integration strategies this represents a significant improvement over previous sensitivity formulations for history dependent materials first order sensitivity expressions involving the complete set of design variables including shape design variables are derived for a generic response functional the reduced form of the consistent tangent stiffness matrix obtained at the end of each time or load step in the finite element procedure is used to update the response sensitivities for that time step no iterations are needed in the sensitivity computations a numerical example demonstrates the accuracy and efficiency of the new sensitivity analysis method for an elastoplastic analysis problem explicit sensitivities from the new method are confirmed by finite difference estimates

real time computation of two dimensional moments on binary images using image block representation this work presents a new approach and an algorithm for binary image representation which is applied for the fast and efficient computation of moments on binary images this binary image representation scheme is called image block representation since it represents the image as a set of nonoverlapping rectangular areas the main purpose of the image block representation process is to provide an efficient binary image representation rather than the compression of the image the block represented binary image is well suited for fast implementation of various processing and analysis algorithms in a digital computing machine the two dimensional 2 d statistical moments of the image may be used for image processing and analysis applications a number of powerful shape analysis methods based on statistical moments have been presented but they suffer from the drawback of high computational cost the real time computation of moments in block represented images is achieved by exploiting the rectangular structure of the blocks

pattern recognition by affine moment invariants abstract the paper deals with moment invariants which are invariant under general affine transformation and may be used for recognition of affine deformed objects our approach is based on the theory of algebraic invariants the invariants from second and third order moments are derived and shown to be complete the paper is a significant extension and generalization of recent works several numerical experiments dealing with pattern recognition by means of the affine moment invariants as the features are described

computing geometric moments using morphological erosions abstract geometrical moments have proven to be very nice features to describe a binary shape for its further recognition in this paper we present a new method based on morphological operations to compute these important features for this the shape is decomposed into a partition of disks under d 8 double summations used in the computation of the moments are substituted by the sum of the moments of each disk of the partition it is shown that these last moments can be computed in terms of simple formulae function of the centers and radii of the disks and that the values obtained are exactly the same as if a double sum were used besides once the partition is obtained moment computation using this approach is very fast

sensitivity of forming processes to shape parameters abstract shape sensitivity analysis is presented for metal forming processes described in terms of the flow approach 1 the direct differentiation method is employed to derive the sensitivity expressions the continuum approach is adopted so that both the equilibrium equations and response functional are differentiated before discretization the necessary derivatives with respect to shape design variables are calculated making use of the framework already available for isoparametric elements control volume approach in finite element implementation a system of equations is obtained which has the same system matrix as the equilibrium problem the right hand side is calculated by partially differentiating the internal and external forces with respect to the design parameters the procedure is illustrated by calculating sensitivities of some independent and dependent variables with respect to the die angle in an extrusion problem and to the roll radius in a plane rolling

beyond the flow decomposition barrier we introduce a new approach to the maximum flow problem this approach is based on assigning arc lengths based on the residual flow value and the residual arc capacities our approach leads to an o min n 2 3 m 1 2 m log n 2 m log u time bound for a network with n vertices m arcs and integral arc capacities in the range 1 u this is a fundamental improvement over the previous time bounds we also improve bounds for the gomory hu tree problem the parametric flow problem and the approximate s t cut problem

fast computation of moment invariants abstract the subject of moment invariants has found wide application in pattern recognition since it was proposed in the present paper we propose a fast algorithm for the calculation of moment invariants firstly we propose using green s theorem for double integral to transform moment calculation to a simple integration along the boundary which reduces the complexity from o n 2 to o n secondly the relation between the monomials for successive pixels along a curve is analysed and the pascal triangle matrix transform is proposed to calculate the monomials for a pixel from those for the preceding one an iterative algorithm is thus proposed for moment calculation which needs no multiplications and the number of additions needed is reduced to o n moreover a very simple systolic structure is proposed to implement the pascal triangle transformation and the proposed algorithm can thus be realized by simple hardware to further accelerate the calculation comparison of the computational complexity with some known methods is also given which shows that our algorithm significantly reduces the complexity

improved moment invariants for shape discrimination abstract moment invariants have been frequently used as features for shape recognition they are computed based on the information provided by both the shape boundary and its interior region although several fast algorithms for computing traditional moment invariants have been proposed none has ever shown the theoretical results of moment invariants computed based on the shape boundary only this paper proposes improved moment invariants computed using the shape boundary only which tremendously reduces computations the new moment invariants called improved moment invariants are mathematically proved to be invariant to scaling translation and rotation graphical plots of the first two improved moment invariants for six country maps and four industrial tools using improved moment invariants are also given the results suggest that improved moment invariants can be used as effective features for shape discrimination or recognition

efficient algorithms for geometric graph search problems in this paper we show that many graph search problems can be solved quite efficiently for a geometric intersection graph of horizontal and vertical line segments we first extract several basic operations for depth first search and breadth first search on a graph then we present data structures for the intersection graph in terms of which those operations can be implemented in an efficient manner the data structures enable us to solve various graph search problems besides depth first search and breadth first search specifying the results obtained in this paper for an intersection graph of n horizontal and vertical segments with m pairs of intersecting segments we obtain algorithms with the following complexity where n min m n log n i depth first search and breadth first search can be executed in o n log n time and o n space ii the biconnected components can be found in o n log n time and o n space iii a maximum matching and a maximum independent set can be found in o

a fast algorithm for the computation of axial moments and its application to the orthogonal fitting of curves this paper describes a fast algorithm to compute local axial moments used in the detection of objects of interest in images the basic idea is the elimination of redundant operations while computing axial moments for two neighboring angles of orientation the main result is that the complexity of the recursive computation of axial moments becomes independent of the total number of computed moments at a given point i e it is of the order o n where n is the size of the data set this result is of great importance in computer vision since many feature extraction methods rely on the computation of axial moments the use of this algorithm for fast object skeletonization in images by orthogonal regression fitting is described in detail with the experimental results confirming the theoretical computational complexity

a general approach to moment calculation for polygons and line segments abstract the calculation of moments from the boundary of a solid digital area is a quite useful technique used in pattern recognition a straightforward way of doing the calculation that does not have any numerical instabilities is presented all the symmetries available in moment calculations are preserved and it is shown how different moment formulas are related to each other this includes relations between different moments and the relationships among different methods for calculating moments finally a direct relation between the moment expansion of a polygonal area and a stick figure made from one dimensional lines embedded in a two dimensional plane is derived

image normalization by complex moments the role of moments in image normalization and invariant pattern recognition is addressed the classical idea of the principal axes is analyzed and extended to a more general definition the relationship between moment based normalization moment invariants and circular harmonics is established invariance properties of moments as opposed to their recognition properties are identified using a new class of normalization procedures the application of moment based normalization in pattern recognition is demonstrated by experiment

invariant image recognition by zernike moments the problem of rotation scale and translation invariant recognition of images is discussed a set of rotation invariant features are introduced they are the magnitudes of a set of orthogonal complex moments of the image known as zernike moments scale and translation invariance are obtained by first normalizing the image with respect to these parameters using its regular geometrical moments a systematic reconstruction based method for deciding the highest order zernike moments required in a classification problem is developed the quality of the reconstructed image is examined through its comparison to the original one the orthogonality property of the zernike moments which simplifies the process of image reconstruction make the suggest feature selection approach practical features of each order can also be weighted according to their contribution to the reconstruction process the superiority of zernike moment features over regular moments and moment invariants was experimentally verified

an efficient algorithm for computation of shape moments from run length codes or chain codes abstract moments are very useful for shape analysis zero to third order moments have been used for computer vision applications such as shape recognition and orientation they can serve for composition of the well known moment invariants used as desirable features as well as for the detection of the location and the principal axis direction of a shape the shape is often represented by a binary image and its moments can be obtained by use of fast algorithms considering the shape as a discrete point array in this paper a new algorithm based on the double integral formulation is presented the shape is considered as a continuous region and the contribution of boundary points is used for fast computation of shape moments this method can be used to calculate moments from either the run length codes or the chain codes of shape

exact and fast computation of geometric moments for gray level images geometric moments are widely used in image processing and pattern recognition while several methods have been proposed exact geometric moment s computation for gray level images is still unavailable in this paper exact values of geometric moments are calculated using mathematical integration of the monomial terms over digital image pixels this method removed the numerical approximation errors involved in conventional methods a fast algorithm is proposed to accelerate the moment s computations the method is extended to compute the three dimensional moments a comparison with other conventional methods is performed the obtained results explained the superiority of the proposed method

simple and fast computation of moments abstract in this paper we address the problem of efficient computation of moments from the boundary of a digital area boundary based computation is superior to usual region based approaches as the data dimension of boundary representations is substantially smaller than that of region representations we investigate the inter order relationship of moments one of our results is that moments of higher order can be computed from moments of lower order based on this relationship a simple iterative algorithm is proposed for the computation of moments from a polygonal approximation of the boundary in comparison with a direct computation method our algorithm is simpler to program the memory requirement is minimum simulation results show that a speed up of factor 8 can be achieved using our algorithm a special version of the algorithm can be utilized to compute moments from the run length chain code of the boundary our algorithm can be applied to compute the most popular geometric moments as well as other types of moments like legendre zernike rotational and complex moments

fast computation of geometric moments using a symmetric kernel this paper presents a novel set of geometric moments with symmetric kernel sgm obtained using an appropriate transformation of image coordinates by using this image transformation the computational complexity of geometric moments gm is reduced significantly through the embedded symmetry and separability properties in addition it minimizes the numerical instability problem that occurs in high order gm computation the novelty of the method proposed in this paper lies in the transformation of gm kernel from interval 0 to interval 1 1 the transformed gm monomials are symmetry at the origin of principal cartesian coordinate axes and hence possess symmetrical property the computational complexity of sgm is reduced significantly from order o n 4 using the original form of computation to order o n 3 for the proposed symmetry separable approach experimental results show that the percentage of reduction in computation time of the proposed sgm over the original gm is very significant at about 75 0 and 50 0 for square and non square images respectively furthermore the invariant properties of translation scaling and rotation in hu s moment invariants are maintained the advantages of applying sgm over gm in zernike moments computation in terms of efficient representation and computation have been shown through experimental results

principal component analysis of speech spectrogram images abstract recent research has demonstrated that spectrograms containing human speech utterances can be analyzed using image processing techniques to yield a high recognition rate in particular fourier descriptors fds have been proved very useful for characterizing the boundary of segmented isolated words containing the english semivowels w y 1 and r this study examines the appropriateness of fds combined with 17 other general features for classifying objects contained in binary spectrogram images principal components pcs are used for feature reduction on a speaker dependent data set consisting of 80 sounds representing 20 speakerdependent words containing english semivowels with only eight features including four 32 point fds and four general features obtained from principal component analysis a 97 5 recognition rate was obtained 1997 pattern recognition society published by elsevier science ltd

recognitive aspects of moment invariants moment invariants are evaluated as a feature space for pattern recognition in terms of discrimination power and noise tolerance the notion of complex moments is introduced as a simple and straightforward way to derive moment invariants through this relation properties of complex moments are used to characterize moment invariants aspects of information loss suppression and redundancy encountered in moment invariants are investigated and significant results are derived the behavior of moment invariants in the presence of additive noise is also described

a new fast algorithm for moment computation abstract a new fast algorithm for the computation of discrete image moments is presented the procedure is based on a discrete analogon of green s theorem and is much faster than the method introduced earlier by zakaria et al the new scheme produces exact results unlike methods based on the continuous green s theorem

efficient and accurate computation of geometric moments on gray scale images a novel algorithm that permits the fast and accurate computation of geometric moments on gray scale images is presented in this paper the proposed algorithm constitutes an extension of the ibr algorithm introduced in the past which was applicable only for binary images a new image representation scheme the isr intensity slice representation which represents a gray scale image as an expansion of several two level images of different intensity values enables the partially application of the ibr algorithm to each image component moreover using the resulted set of image blocks the geometric moments computation can be accelerated through appropriate computation schemes

calculation of moment invariants via hadamard transform abstract the calculation of moment invariants via the hadamard transform is proposed first of all the relationship between moments and coefficients of a hadamard transformed image is established moments can then be calculated from these coefficients via addition and shift operations except for a negligible amount of multiplication operations furthermore based on the relationship among moments the higher order ones can be computed from the lower order ones for the simply connected binary image regions the amount of computation can be further reduced by projecting the original two dimensional 2d image to the x and y direction one dimensional 1d arrays and tracing the object s boundary to get the values simulation results indicate that the amount of computation required for the proposed algorithm is only about 50 of li s algorithm

nonlinear structural design sensivitity analysis for path dependent problems part 1 general theory abstract two procedures direct differentiation and adjoint structure for design sensitivity analysis of nonlinear structural systems with path dependent effects are described in this paper continuum formulation is used and both geometric and material nonlinearities are included in the derivations incremental nonlinear analysis based on the total lagrangian concept is adopted the reference volume concept is used to unify the shape and nonshape design problems to show the generality of the theory the derived expressions are reduced to some special cases that have been treated previously in the literature in part 2 of the paper a few analytical example problems will be solved to demonstrate the use of the design sensitivity analysis theory the theory has also beendiscretized elsewhere using finite element approximations for implementation into structural analysis programs these developments offer a firm foundation for design optimization of complex structural systems

shape optimization and preform design in metal forming processes abstract a continuum sensitivity analysis is presented for the computation of the shape sensitivity of finite hyperelastic viscoplastic deformations involving contact with friction using a direct differentiation method weak shape sensitivity equations are developed that are consistent with the kinematic analysis constitutive sub problem as well as the analysis of the contact friction sub problem used in the solution of the direct deformation problem the shape sensitivities are defined in a rigorous sense and the linear sensitivity analysis is performed in an infinite dimensional continuum framework the direct deformation and the sensitivity deformation problems are implemented using the finite element method the shape sensitivity analysis is validated by a comparison of the results with those obtained from the solution of the perturbed direct deformation problem i e using finite differences finite dimensional gradients of objective functions are then computed using the results of the shape sensitivity analysis for the purpose of preform design and shape optimization in metal forming the effectiveness of the proposed methodology is demonstrated by solving practical shape optimal design problems in forging processing

fast computation of legendre moments of polyhedra abstract the three dimensional 3d orthogonal moments are an efficient tool for object reconstruction and 3d image analysis however until now 3d orthogonal moments have not been analysed in detail from the point of view of reducing the computational complexity in this paper we present a recursive algorithm for fast computation of legendre moments of polyhedra first a gaussian theorem is employed to transform the volume integral into a surface one the double integral can then be deduced from the simple integral by a green s theorem finally the recursive relationship is investigated as one can see the proposed method decreases the computational complexity tremendously

decomposition of binary images a survey and comparison we present an overview of the most important methods that decompose an arbitrary binary object into a union of rectangles we describe a run length encoding and its generalization decompositions based on quadtrees on mathematical morphology on the distance transform and a theoretically optimal decomposition based on a maximal matching in bipartite graphs we compare their performance in image compression in moment computation and in linear filtering we show that the choice is always a compromise between the complexity and time memory consumption we give advice how to select an appropriate method in particular cases

a novel feature extraction method for image recognition based on similar discriminant function sdf abstract the extraction of image features is the most fundamental and important problem in image recognition in this paper a similarity measure of matrices is first presented and a similar discriminant function sdf of images is established based on the discriminant function we further propose a novel feature extraction method for image recognition for each class of training image samples an optimal projection axis maximizing the similarity among these training image samples for the class is calculated unlike the common methods of feature extraction we extract a projective feature vector for a training image sample by projecting the image on the optimal projection axis of the class itself and a set of projective feature vectors for a testing image sample by projecting the image on all the optimal projection axes finally a hierarchical classifier in the optimal discriminant space is designed to recognize images in order to test the efficiency of our method it is used to recognize human faces and english characters experimental results have shown that our method has good recognition performance and the extracted projective feature vectors contain more recognition information than commonly used image features

colored noise enhanced stability in a tumor cell growth system under immune response in this paper we investigate a mathematical model for describing the growth of tumor cell under immune response which is driven by cross correlation between multiplicative and additive colored noises as well as the nonzero cross correlation in between the expression of the mean first passage time mfpt is obtained by virtue of the steepest descent approximation it is found i when the noises are negatively cross correlated 0 then the escape is slower than in the case with no correlation moreover in the case of positive cross correlation the escape time has a maximum for a certain intensity of one of the noises i e the maximum for mfpt identifies the noise enhanced stability of the cancer state ii the effect of the cross correlation time 3 on the mfpt is completely opposite for 0 and 0 iii the self correlation times 1 and 2 of colored noises can enhance stability of the cancer state while the immune rate can reduce it

shape and non shape structural sensitivity analysis for problems with any material and kinematic non linearity abstract the general problem of sizing material selection load parameter and shape sensitivity of non linear structural response is considered the non linear sensitivity path is followed by an incremental strategy employing the continuum based updated lagrangian description the resulting finite element equations are derived both the direct differentiation and adjoint structure strategies are considered the merits of using the consistent tangent matrix for sensitivity calculations are indicated the formulation employs the so called reference volume concept and may be seen as a further attempt to unify the shape and non shape sensitivity analysis procedures

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

fast computation of 2 d image moments using biaxial transform abstract in this paper a new transform is introduced this transform is based on dividing the image into four quadrants the transform can be generated by adding or subtracting the gray levels of each two axially symmetric points in the original image the addition or subtraction is dependent on the quadrant position the newly transformed quadrants can then be used to compute the moments only one quadrant of transformed image is needed to compute the moments of specific orders this can lead to considerable savings in both processing time as well as storage other advantages of this transform such as image reconstruction and using multiple filters on the same image frame to remove noise are also explored

radial and angular moment invariants for image identification radial and angular moments of images are presented and methods are shown for deriving moment functions that are invariant with respect to rotation translation reflection and size changes without the aid of the theory of algebraic invariants hu s invariants are expressed in terms of these radial and angular moments and it is claimed that this facilitates visual inspection of invariance properties

computation of volume and surface body moments abstract the paper presents explicit formulae for calculation of surface moments for polytopes in r n we describe also efficient algorithms for calculation of 3d body volume and surface moments the algorithms are based on explicit formulae for moment calculation and take advantages of shape polygonal representation they use only coordinates of the body vertices and faces orientation

the moment calculation of polyhedra abstract this paper proposes a novel approach to calculate polyhedra moments at first the gaussian theorem is used to convert a volume integral into a surface one by which we decrease the moment computational complexity from o n 3 to o n 2 then an iterative method is proposed to calculate the surface integral finally some comparison shows that the computational complexity of the new method is independent of voxel numbers of polyhedra therefore the new moment computation is more efficient

computing horizontal vertical convex shape s moments on reconfigurable meshes abstract zero to third order moments are very useful tools for analysing 2 d two dimensional shapes given an n n digital image this paper presents a novel constant time parallel algorithm for computing a horizontal vertical convex shape s moments each row column in the shape without holes on an n n reconfigurable mesh in the sense of the product of time and the number of processors used our algorithm is time and cost optimal

on the efficient computation of 2 d image moments using the discrete radon transform abstract in this paper a fast algorithm for the computation of two dimensional image moments is proposed in our approach a new discrete radon transform drt is used for the major part of the algorithm the new drt preserves an important property of the continuous radon transform that the regular or geometric moments can be directly obtained from the projection data with this property the computation of two dimensional 2 d image moments can be decomposed to become a number of one dimensional 1 d ones hence it reduces greatly the computational complexity the new drt algorithm can be applied with a recursive approach such that the number of multiplication required is further reduced however the number of addition will then be increased it suits to the situation where the effort for realizing multiplication is much greater than addition comparisons of the present approaches with some known methods show that the proposed algorithms significantly reduce the complexity and computation time

efficient moment computation over polygonal domains with an application to rapid wedgelet approximation many algorithms in image processing rely on the computation of sums of pixel values over a large variety of subsets of the image domain this includes the computation of image moments for pattern recognition purposes or adaptive smoothing and regression methods such as wedgelets in the first part of the paper we present a general method which allows the fast computation of sums over a large class of polygonal domains the approach relies on the idea of considering polygonal domains with a fixed angular resolution combined with an efficient implementation of a discrete version of green s theorem the second part deals with the application of the new methodology to a particular computational problem namely wedgelet approximation our technique results in a speedup of o 10 3 by comparison to preexisting implementations a further attractive feature of our implementation is the instantaneous access to the full scale of wedgelet minimizers we introduce a new scheme that replaces the locally constant regression underlying wedgelets by basically arbitrary local regression models due to the speedup obtained by the techniques explained in the first part this scheme is computationally efficient and at the same time much more flexible than previously suggested methods such as wedgelets or platelets in the final section we present numerical experiments showing the increase in speed and flexibility

fast algorithm for the computation of moment invariants abstract moment invariants have been used as feature descriptors in a variety of object recognition applications when assuming a continuous image function moments calculated using a double integral formulation are invariant to variations in translation rotation and size of the object however due to the recursive nature of the calculations and the limited speed of microprocessors the moments were not computable in real time in this paper we present fast invariant moment computations using the delta method as a means of scene representation this method computes moments of contiguous images by using the contribution of each line rather than individual pixel

design sensitivity analysis of elastoplastic structures an iterative and incremental algorithm is presented for the design sensitivity analysis dsa of elastoplastic structures geometrical non linearity is included in the formulation and the structure may be subjected to a cyclic loading the key concept is discussed using an elastoplastic truss it is shown that the design sensitivity coefficients dscs are path dependent and discontinuous at the time at which yielding takes place in a member yield time in the proposed algorithm the yield time is considered to be a function of the design variables in this way the discontinuity in the dscs at the material transition points can be overcome in a simple and routine way incremental response analysis and dsa are carried out simultaneously using the newton raphson type iterative procedure since the proposed algorithm is completely consistent with the analysis procedure it can be implemented into an existing code for structural analysis application to distributed parameter structures with kinematic and or isotropic hardening is discussed using the von mises yield condition and the elastic predictor radial return method dsa is carried out for a ten bar truss with a piecewise linear constitutive relation it is shown that the dscs found using the proposed method agree quite well with those calculated by the central difference method finally an alternate method without any iteration for dsa is proposed and the results from the two methods are compared

fast computation of legendre and zernike moments this paper presents recursive algorithms for fast computation of legendre and zernike moments of a grey level image intensity distribution for a binary image a contour integration method is developed for the evaluation of legendre moments using only the boundary information a method for recursive calculation of zernike polynomial coefficients is also given a square to circular image transformation scheme is introduced to minimize the computation involved in zernike moment functions the recursive formulae can also be used in inverse moment transforms to reconstruct the original image from moments the mathematical framework of the algorithms is given in detail and illustrated with binary and grey level images

class of self limiting growth models in the presence of nonlinear diffusion the source term in a reaction diffusion system in general does not involve explicit time dependence a class of self limiting growth models dealing with animal and tumor growth and bacterial population in a culture on the other hand are described by kinetics with explicit functions of time we analyze a reaction diffusion system to study the propagation of spatial front for these models

a cascade optimization methodology for automatic parameter identification and shape process optimization in metal forming simulation computer simulations of metal forming processes using the finite element method fem are today well established this form of simulation uses an increasing number of sophisticated geometrical and material models relying on a certain number of input data which are not always readily available the aim of inverse problems which will be considered here is to determine one or more of the input data relating to these forming process simulations thereby leading to a desired result in this paper we will focus on two categories of such inverse problems the first category consists of parameter identification inverse problems these involve evaluating the material parameters for material constitutive models that would lead to the most accurate results with respect to physical experiments i e minimizing the difference between experimental results and fem simulations the second category consists of shape process optimization inverse problems these involve determining the initial geometry of the specimen and or the shape of the forming tools as well as some parameters of the process itself in order to provide the desired final geometry after the forming process these two categories of inverse problems can be formulated as optimization problems in a similar way i e by using identical optimization algorithms in this paper we intend firstly to solve these two types of optimization problems by using different non linear gradient based optimization methods and secondly to compare their efficiency and robustness in a variety of numerical applications

affine curve moment invariants for shape recognition this paper presents a method of affine curve moment invariants for shape recognition the proposed method extends affine moment invariants from an area domain to a curve domain first a new type of curve moments is defined on a parameterized boundary description of an object a set of affine moment invariants are then derived based on the theory of algebraic invariants the proposed moment invariants only deal with pixels on a shape boundary and are mathematically proven to be invariant under arbitrary affine transformations furthermore after a parameterized object boundary description is acquired through curve fitting the newly defined curve moments can be represented by an integration of the fitting function so that the computation of moment invariants can be obtained from either one by one computation of boundary pixels or a direct integration of the fitting function which makes the computation efficient while at the same time reducing noise effect affine curve moment invariants work well in recognition of affine deformed objects which is demonstrated by processing various 2 d shapes under affine transformations

a new fast method for computing legendre moments abstract this paper presents a new algorithm for fast and accurate computation of legendre moments for a binary image by use of a green s theorem we transform a surface integral to a simple integration along the boundary the inter order relationship of legendre moments is then investigated as a result the moments of higher order can be deduced from those of lower order based on this relationship an iterative method is proposed to calculate the legendre moments from a polygonal approximation of the boundary comparison with known methods shows that our algorithm is almost as efficient as the existing method but is more accurate

3 d moment forms their construction and application to object identification and positioning the 3 d moment method is applied to object identification and positioning a general theory of deriving 3 d moments invariants is proposed the notion of complex moments is introduced complex moments are defined as linear combinations of moments with complex coefficients and are collected into multiplets such that each multiplet transforms irreducibly under 3 d rotations the application of the 3 d moment method to motion estimation is also discussed using group theoretic techniques various invariant scalars are extracted from compounds of complex moments via clebsch gordon expansion twelve moment invariants consisting of the second order and third order moments are explicitly derived based on a perturbation formula it is shown that the second order moment invariants can be used to predict whether the estimation using noisy data is reliable or not the new derivation of vector forms also facilities the calculation of motion estimation in a tensor approach vectors consisting of the third order moments can be derived in a similar manner

a novel algorithm for fast computation of zernike moments abstract zernike moments zms have been successfully used in pattern recognition and image analysis due to their good properties of orthogonality and rotation invariance however their computation by a direct method is too expensive which limits the application of zms in this paper we present a novel algorithm for fast computation of zernike moments by using the recursive property of zernike polynomials the inter relationship of the zernike moments can be established as a result the zernike moment of order n with repetition m znm can be expressed as a combination of zn 2 m and zn 4 m based on this relationship the zernike moment znm for n m can be deduced from zmm to reduce the computational complexity we adopt an algorithm known as systolic array for computing these latter moments using such a strategy the multiplication number required in the moment calculation of zmm can be decreased significantly comparison with known methods shows that our algorithm is as accurate as the existing methods but is more efficient

an adaptive method for image registration abstract the paper deals with the registration of images with non linear local geometric distortions it describes a new approach to the determination of a mapping function from given coordinates of control points the processed image is recursively divided into subregions of various size and shape according to the distortion character each subregion is then transformed by a simple local transformation the described method enables the registration with optional accuracy a practical use of this method is presented and a comparison of its accuracy and computing complexity with previously published methods is given

efficient computation of local geometric moments local moments have attracted attention as local features in applications such as edge detection and texture segmentation the main reason for this is that they are inherently integral based features so that their use reduces the effect of uncorrelated noise the computation of local moments when viewed as a neighborhood operation can be interpreted as a convolution of the image with a set of masks nevertheless moments computed inside overlapping windows are not independent and convolution does not take this fact into account by introducing a matrix formulation and the concept of accumulation moments this paper presents an algorithm which is computationally much more efficient than convolving and yet as simple

on image analysis by moments research has been performed investigating the use of moments for pattern recognition in recent years the basic problem of the influence of discretization and noise on moment accuracy as object descriptors has been barely investigated in this paper the detailed error analysis involved in the moment method is discussed several new techniques to increase the accuracy and efficiency of moment descriptor are proposed we utilize these results for the problem of image reconstruction from the orthogonal legendre moments computed from discrete and noisy data the automatic selection of an optimal number of moments is also discussed

an alternative approach to computing shape orientation with an application to compound shapes we consider the method that computes the shape orientation as the direction that maximises the integral of the length of projections taken to the power of 2n of all the straight line segments whose end points belong to the shape to a line that has the slope we show that for n 1 such a definition of shape orientation is consistent with the shape orientation defined by the axis of the least second moment of inertia for n 1 this is not the case and consequently our new method can produce different results as an additional benefit our approach leads to a new method for computation of the orientation of compound objects

two new algorithms for efficient computation of legendre moments orthogonal moments have been successfully used in the field of pattern recognition and image analysis however the direct computation of orthogonal moments is very expensive in this paper we present two new algorithms for fast computing the two dimensional 2d legendre moments the first algorithm consists of transforming the pixel based calculation of legendre moments into the line segment based calculation after all line segment moments have been calculated hatamian s filter method is extended to calculate the one dimensional legendre moments the second algorithm is directly based on the double integral formulation the 2d shape is considered as a continuous region and the contribution of the boundary points is used for fast calculation of shape moments the numerical results show that the new algorithms can decrease the computational complexity tremendously furthermore they can be used to treat any complicated objects

fast algorithm for generation of moment invariants abstract moment invariants are important shape descriptors in computer vision the method of decomposing the trigonometric function is suggested to obtain various moment invariants based on this method the multi filter algorithm is introduced as an efficient way to generate large numbers of moment invariants a great deal of repeated computation on sub polynomial is avoided general explicit constructions of basic moment invariants are also provided furthermore the proposed magnitude normalized method makes invariants more stable and easier for classification

a shape recognition scheme based on relative distances of feature points from the centroid abstract in this paper a simple but efficient scheme to recognize shapes is proposed in our scheme all of the boundary points are used to calculate the centroid of an object then the distance between each feature point and the centroid is computed we have shown that the time complexity of our shape matching algorithm is o m where m is the number of feature points the most important advantage of our method is its independence to translation rotation and scaling of objects

fast computation of krawtchouk moments the paper describes the calculation of the krawtchouk moments kms from an image which is a computationally demanding task we present two original methods that use the outputs of cascaded digital filters in deriving kms the first approach uses the digital filter outputs to form geometric moments gms and the kms are obtained via gms the second method uses a direct relationship to obtain kms from the digital filter outputs this is possible thanks to the formulation of krawtchouk polynomials in terms of binomial functions which are equivalent to the digital filter outputs in this study the performance of the proposed techniques is compared with other existing methods of kms calculation the experimental study shows that the first and the second proposed techniques perform 57 and 87 faster than the recurrence method for a real image of a size 128 128 pixels which performs a significant improvement

cross correlation enhanced stability in a tumor cell growth model with immune surveillance driven by cross correlated noises the transient properties of a tumor cell growth model with immune surveillance driven by cross correlated multiplicative and additive noises are investigated the explicit expression of extinction rate from the state of a stable tumor to the state of extinction is obtained based on the numerical computations we find the following i the intensity of multiplicative noise d and the intensity of additive noise enhance the extinction rate for the case of 0 i e denotes cross correlation intensity between two noises but for the case of 0 a critical noise intensity d or exists at which the extinction rate is the smallest d and at first weaken the extinction rate and then enhance it ii the immune rate and the cross correlation intensity play opposite roles on the extinction rate i e enhances the extinction rate of the tumor cell while weakens the extinction rate of the tumor cell namely the immune rate can enhance the extinction of the tumor cell and the cross correlation between two noises can enhance stability of the cancer state

tangent operators and design sensitivity formulations for transient non linear coupled problems with applications to elastoplasticity tangent operators and design sensitivities are derived for transient non linear coupled problems the solution process and the formation of tangent operators are presented in a systematic manner and sensitivities for a generalized response functional are formulated via both the direct differentiation and adjoint methods the derived formulations are suitable for finite element implementations analyses of systems with materials that exhibit history dependent response may be obtained directly by applying the analyses of transient non linear coupled systems rate independent elastoplasticity is investigated as a case study and a problem with an analytical solution is analysed for demonstration purposes

on image analysis by the methods of moments various types of moments have been used to recognize image patterns in a number of applications a number of moments are evaluated and some fundamental questions are addressed such as image representation ability noise sensitivity and information redundancy moments considered include regular moments legendre moments zernike moments pseudo zernike moments rotational moments and complex moments properties of these moments are examined in detail and the interrelationships among them are discussed both theoretical and experimental results are presented

moment based methods for polygonal approximation of digitized curves object shape representation plays an important role in the area of image processing pattern recognition and computer vision in the past two decades many algorithms have been suggested for creating approximated polygons in this study two new polygonal approximation methods based on the geometric moments and the orthogonal moments defined in terms of legendre polynomials are proposed the difference between the moments defined by the initial contour and those of the approximated polygon is taken as the objective function each algorithm provides various polygonal approximation results with different number of line segments for different application situations for a given error bound we can determine the optimal polygon with a minimum number of line segments the procedures are applied to some digital curves and better results are obtained in comparison with some known methods

sensitivity analysis for frictional contact problems in the augmented lagrangian formulation direct differentiation method of sensitivity analysis is developed for frictional contact problems as a result of the augmented lagrangian treatment of contact constraints the direct problem is solved simultaneously for the displacements and lagrange multipliers using the newton method the main purpose of the paper is to show that this formulation of the augmented lagrangian method is particularly suitable for sensitivity analysis because the direct differentiation method leads to a non iterative exact sensitivity problem to be solved at each time increment the approach is applied to a general class of three dimensional frictional contact problems and numerical examples are provided involving large deformations multibody contact interactions and contact smoothing techniques

a new computation of geometric moments abstract geometric moments gms have been successfully used in pattern recognition and object orientation determination however their computation is too expensive which limits the application of gms in this paper a new method is proposed to calculate geometric moments firstly the pixel based calculation of gms is converted into the line segment based calculation then a new approach is proposed to calculate the line segment integrals after line segment integrals are calculated hatamian s filter method is introduced to calculate gms which further simplifies the moment calculation finally this method is compared with the known results which show that our method can calculate any complicated object moments and also efficiently reduces both addition and multiplication complexity

translation and scale invariants of legendre moments abstract by convention the translation and scale invariant functions of legendre moments are achieved by using a combination of the corresponding invariants of geometric moments they can also be accomplished by normalizing the translated and or scaled images using complex or geometric moments however the derivation of these functions is not based on legendre polynomials this is mainly due to the fact that it is difficult to extract a common displacement or scale factor from legendre polynomials in this paper we introduce a new set of translation and scale invariants of legendre moments based on legendre polynomials the descriptors remain unchanged for translated elongated contracted and reflected non symmetrical as well as symmetrical images the problems associated with the vanishing of odd order legendre moments of symmetrical images are resolved the performance of the proposed descriptors is experimentally confirmed using a set of binary english chinese and latin characters in addition to this a comparison of computational speed between the proposed descriptors and the aforesaid geometric moments based method is also presented

structural shape sensitivity analysis relationship between material derivative and control volume approaches the material derivative and control volume approaches for structural shape design sensitivity analysis are presented analyzed and compared starting with a continuum formulation and a general response functional needing sensitivity analysis the two approaches are derived it is shown that the final design sensitivity expression for one approach can be obtained from the final expression for the other thus the two approaches are theoretically equivalent discretizations of the continuum expressions are presented and it is shown that the two approaches can lead to different implementations for numerical calculations a unified interpretation is developed in which the explicit design variations partial derivatives with respect to the design variables of the internal and external forces are the major calculations needed to implement the design sensitivity analysis the discretized forms of the continuum sensitivity expressions are also compared with the ones obtained by starting with the discretized model ab initio this comparison shows that these two approaches lead to similar expressions for numerical calculations therefore the exact same procedures can be used for computer implementations for both of the approaches the presented analyses give insights for implementation of the design sensitivity analysis theory with the finite element analysis programs

a new approach to the maximum flow problem all previously known efficient maximum flow algorithms work by finding augmenting paths either one path at a time as in the original ford and fulkerson algorithm or all shortest length augmenting paths at once using the layered network approach of dinic an alternative method based on the preflow concept of karzanov is introduced a preflow is like a flow except that the total amount flowing into a vertex is allowed to exceed the total amount flowing out the method maintains a preflow in the original network and pushes local flow excess toward the sink along what are estimated to be shortest paths the algorithm and its analysis are simple and intuitive yet the algorithm runs as fast as any other known method on dense graphs achieving an o n 3 time bound on an n vertex graph by incorporating the dynamic tree data structure of sleator and tarjan we obtain a version of the algorithm running in o nm log n 2 m time on an n vertex m edge graph this is as fast as any known method for any graph density and faster on graphs of moderate density the algorithm also admits efficient distributed and parallel implementations a parallel implementation running in o n 2 log n time using n processors and o m space is obtained this time bound matches that of the shiloach vishkin algorithm which also uses n processors but requires o n 2 space

fast and exact computation of cartesian geometric moments using discrete green s theorem abstract green s theorem evaluates a double integral over a planar object by a simple integration along the boundary of the object it can be used in fast computation of cartesian geometric moments of two dimensional binary objects since the object shape is totally determined by the boundary li and shen pattern recognition 24 807 813 1991 used an approximation of green s theorem to deal with discrete objects this method is fast but not accurate in this paper we present a discrete version of green s theorem which evaluates a double sum over a two dimensional discrete object by a simple summation along the discrete boundary of the object by using the discrete green s theorem we propose a new algorithm for fast computation of the geometric moments the new algorithm is faster than the previous methods and gives exactly the same results as if a double sum were used the importance of the exact computation is discussed by examining the accuracy of hu s moment invariants and some other moment based shape features which are frequently used in various shape description and pattern recognition tasks a fast method for computing moments of regions in gray level images using the discrete green s theorem is also presented we show that the moments of this type are useful in structural texture analysis

a computational method for design sensitivty analysis of elastoplastic structures abstract design sensitivity analysis of structural systems having elastoplastic material behavior is developed using the continuum formulation and its implementation into a finite element program is described the main idea is to develop a computational procedure for design sensitivity analysis based on the response obtained by an incremental load approach for non linear response analysis where the elastoplatic time independent constitutive model is employed to account for the plastic material behavior i e kinematic hardening and isotropic hardening discontinuities in the design sensitivity coefficients are investigated and a procedure is proposed to alleviate them the control reference domain approach is used to treat shape and non shape design variables simultaneously the direct variation method is adopted for this path dependent problem to obtain the design sensitivity expression for the response variables analytical examples are used to demonstrate the developed sensitivity procedure and gain insights for numerical implementation the design sensitivity expression is discretized to implement it into a computer program using the isoparametric formulation of finite element analysis numerical examples are presented to calculate the design sensitivity coefficients and compare them with those using the central finite difference method

fast discrete w transforms via computation of moments a novel approach to compute all four types of discrete w transform dwt is proposed by using kernel transforms and taylor expansions a dwt is approximated by a linear sum of discrete moments this enables us to use computational techniques developed for computing moments to compute dwts efficiently the amount of multiplications used in our method is o nlog sub 2 n log sub 2 log sub 2 n and is superior to the o nlog sub 2 n in the conventional dwt the proposed algorithm achieves a simple computational structure and naturally deals with any sequence lengths

shape design sensitivity analysis of viscoplastic structures abstract design sensitivity analysis of nonlinear viscoplastic structures is developed in the continuum form starting from hamilton s principle constitutive models based on internal variable theory are incorporated in response analysis such models are described by a set of first order nonlinear differential equations with respect to time and some of them allow development of the yield surface the direct variation method is employed to obtain the sensitivity of the response discretization of the analysis and sensitivity equations and computer implementation aspects are discussed the discretized equations are implemented into a computer program and two numerical examples are solved to demonstrate the theory in the numerical examples only material nonlinearity under quasi static loading history is considered and the explicit integration method is employed to integrate the constitutive equations and their design variations the accuracy and efficiency of the developed sensitivity analysis are compared with the central finite difference method cyclic loading and loading rate effects are studied and discussed to show the general applicability of the developed sensitivity formulation

shape ellipticity from hu moment invariants in this paper we derive an explicit formula which uses the first two hu moment invariants to compute a shape ellipticity measure i e to evaluate how much a planar shape differs from an ellipse the ellipticity measure computed by this formula is invariant with respect to translation rotation and scaling transformations also the highest possible value is obtained if and only if the shape considered is an ellipse several experiments are also provided to confirm the theoretical observations a by product of the derivations made in this paper is an implicit interpretation of geometric shape meaning of the second hu moment invariant a formula which connects the shape ellipticity and the first hu moment invariant both having a well understood behavior and the second hu moment invariant is derived