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

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

on the stable module category of a self injective algebra let a be a finite dimensional self injective algebra we study the dimensions of spaces of stable homomorphisms between indecomposable amodules which belong to auslander reiten components of the form za or zao rk the results are applied to representations of finite groups over fields of prime characteristic especially blocks of wild representation type we are interested in homological properties of modules for self injective algebras an important invariant of a finite dimensional algebra is its stable auslander reiten quiver and during the past years it has played a crucial role for classification problems of self injective algebras of finite or tame representation type we call a stable component quasi serial if it is of the form zaoo or zaoo rk if a is any tame algebra then most of its auslander reiten components are homogeneous tubes by cb hence are quasi serial moreover it seems that for self injective algebras of wild type most components of the stable auslander reiten quiver are quasi serial for a block of a group algebra which is of wild representation type all components are of this form see e2 therefore it is important to understand homological properties of quasi serial components if a is a finite dimensional self injective algebra and x y are a modules then we denote the stable homomorphisms from x to y by hom x y following the terminology in ri if m is a module in a quasi serial stable component c then the quasi length of m is the number of the row to which m belongs the module m is quasi simple if it has quasi length one that is if it lies at the end of the component the first two chapters contain basic facts on dimensions of spaces of stable homomorphisms this is intended to provide tools which may be of more general use in chapter 3 we prove the following general results suppose f is an equivalence of the stable module category of a consider stable homomorphisms hom m fm for modules m in a quasi serial component c we prove that the dimension of hom m fm is weakly increasing as a function of the quasi length of m except possibly when tq 1 f t on c see 3 3 moreover we study the cases when f is and f qs in more detail we show that if c is a tube then the dimensions of hom m rsm for m e c are unbounded 3 5 in general if c is a component of the form za which is not fixed by q and the dimensions of hom m tsm are bounded then hom x r mx 0 received by the editors june 4 1996 and in revised form october 2 1997 2000 mathematics subject classification primary 18g25 secondary 16g70 20c20

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

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

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 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

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

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

supersymmetric boundary conditions in mathcal n 4 super yang mills theory we study boundary conditions in mathcal n 4 super yang mills theory that preserve one half the supersymmetry the obvious dirichlet boundary conditions can be modified to allow some of the scalar fields to have a pole at the boundary the obvious neumann boundary conditions can be modified by coupling to additional fields supported at the boundary the obvious boundary conditions associated with orientifolds can also be generalized in preparation for a separate study of how electric magnetic duality acts on these boundary conditions we explore moduli spaces of solutions of nahm s equations that appear in the presence of a boundary though our main interest is in boundary conditions that are lorentz invariant to the extent possible in the presence of a boundary we also explore non lorentz invariant but half bps deformations of neumann boundary conditions we make preliminary comments on the action of electric magnetic duality deferring a more serious study to a later paper

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

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

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

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

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

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

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