application of the fast multipole method for the evaluation of magnetostatic fields in micromagnetic computations micromagnetic simulations are elaborated to describe the magnetic dynamics in ferromagnetic bodies in these simulations most of the time is spent on the evaluation of the magnetostatic field in the magnetic material this paper presents a new numerical finite difference scheme for the evaluation of the magnetostatic field based on the fast multipole method fmm the interactions between finite difference cells are described in terms of far and near field interactions the far field computations are conducted using the spherical harmonic expansion of the magnetostatic field while the near field computations are accelerated using fast fourier transforms fft the performance of the presented fmm scheme is studied by comparing the scheme with a pure fft scheme the fmm scheme is more memory efficient and more flexible then the fft scheme it is accurate and still has a good time efficiency

efficient fmm accelerated vortex methods in three dimensions via the lamb helmholtz decomposition vortex methods are used to efficiently simulate incompressible flows using lagrangian techniques use of the fmm fast multipole method allows considerable speed up of both velocity evaluation and vorticity evolution terms in these methods both equations require field evaluation of constrained divergence free vector valued quantities velocity vorticity and cross terms from these these are usually evaluated by performing several fmm accelerated sums of scalar harmonic functions we present a formulation of vortex methods based on the lamb helmholtz decomposition of the velocity in terms of two scalar potentials in its original form this decomposition is not invariant with respect to translation violating a key requirement for the fmm one of the key contributions of this paper is a theory for translation for this representation the translation theory is developed by introducing conversion operators which enable the representation to be restored in an arbitrary reference frame using this form efficient vortex element computations can be made which need evaluation of just two scalar harmonic fmm sums for evaluating the velocity and vorticity evolution terms details of the decomposition translation and conversion formulae and sample numerical results are presented

locating dominating sets of functigraphs abstract a locating dominating set of a graph g is a dominating set of g such that every vertex of g outside the dominating set is uniquely identified by its neighborhood within the dominating set the location domination number of g is the minimum cardinality of a locating dominating set in g let g 1 and g 2 be two disjoint copies of a graph g and f v g 1 v g 2 be a function a functigraph f g f consists of vertex set v g 1 v g 2 and edge set e g 1 e g 2 u v v f u in this paper we study the variation of location domination number in passing from g to f g f and find its sharp lower and upper bounds we also study location domination number of functigraphs of complete graphs for all possible definitions of function f we also obtain location domination number of functigraphs of a family of spanning subgraph of the complete graphs

a fast solution method for three dimensional many particle problems of linear elasticity a boundary element method for solving three dimensional linear elasticity problems that involve a large number of particles embedded in a binder is introduced the proposed method relies on an iterative solution strategy in which matrix vector multiplication is performed with the fast multipole method as a result the method is capable of solving problems with n unknowns using only o n memory and o n operations results are given for problems with hundreds of particles in which n o 105 1998 john wiley sons ltd

image sequence coding by split and merge a method is described for reducing the information contained in an image sequence while retaining the information necessary for the interpretation of the sequence by a human observer the method consists of first locating the redundant information reducing the degree of redundancy and coding the result the sequence is treated as a single 3d data volume the voxels of which are grouped into several regions obtained by a 3d split and merge algorithm the information is coded by representing the borders of the regions using a pyramidal structure in the x y t space the coefficients of the approximating polynomials are coded in a straightforward manner for 256 256 pixel 25 frame s image sequences compressions allowing transmission rates near 64 kbit s are obtained

regular article a fast adaptive multipole algorithm in three dimensions we present an adaptive fast multipole method for the laplace equation in three dimensions it uses both new compression techniques and diagonal forms for translation operators to achieve high accuracy at a reasonable cost

segmentation through variable order surface fitting the solution of the segmentation problem requires a mechanism for partitioning the image array into low level entities based on a model of the underlying image structure a piecewise smooth surface model for image data that possesses surface coherence properties is used to develop an algorithm that simultaneously segments a large class of images into regions of arbitrary shape and approximates image data with bivariate functions so that it is possible to compute a complete noiseless image reconstruction based on the extracted functions and regions surface curvature sign labeling provides an initial coarse image segmentation which is refined by an iterative region growing method based on variable order surface fitting experimental results show the algorithm s performance on six range images and three intensity images

hybrid image segmentation using watersheds and fast region merging a hybrid multidimensional image segmentation algorithm is proposed which combines edge and region based techniques through the morphological algorithm of watersheds an edge preserving statistical noise reduction approach is used as a preprocessing stage in order to compute an accurate estimate of the image gradient then an initial partitioning of the image into primitive regions is produced by applying the watershed transform on the image gradient magnitude this initial segmentation is the input to a computationally efficient hierarchical bottom up region merging process that produces the final segmentation the latter process uses the region adjacency graph rag representation of the image regions at each step the most similar pair of regions is determined minimum cost rag edge the regions are merged and the rag is updated traditionally the above is implemented by storing all rag edges in a priority queue we propose a significantly faster algorithm which additionally maintains the so called nearest neighbor graph due to which the priority queue size and processing time are drastically reduced the final segmentation provides due to the rag one pixel wide closed and accurately localized contours surfaces experimental results obtained with two dimensional three dimensional 2 d 3 d magnetic resonance images are presented

fast single domain subdomain bem algorithm for 3d incompressible fluid flow and heat transfer in this paper acceleration and computer memory reduction of an algorithm for the simulation of laminar viscous flows and heat transfer is presented the algorithm solves the velocity vorticity formulation of the incompressible navier stokes equations in 3d it is based on a combination of a subdomain boundary element method bem and single domain bem the cpu time and storage requirements of the single domain bem are reduced by implementing a fast multipole expansion method the laplace fundamental solution which is used as a special weighting function in bem is expanded in terms of spherical harmonics the computational domain and its boundary are recursively cut up forming a tree of clusters of boundary elements and domain cells data sparse representation is used in parts of the matrix which correspond to boundary domain clusters pairs that are admissible for expansion significant reduction of the complexity is achieved the paper presents results of testing of the multipole expansion algorithm by exploring its effect on the accuracy of the solution and its influence on the non linear convergence properties of the solver two 3d benchmark numerical examples are used the lid driven cavity and the onset of natural convection in a differentially heated enclosure

polynomial approximation and vector quantization a region based integration the paper presents an adaptive scheme for image data compression it is a region based approach that suitably integrates two different approaches to image coding vector quantization vq and polynomial approximation pa the scheme is adaptive from the point of view of the human observer the perceptually most significant areas are those near edges or details in smoothed areas pa can be used with notable results but there vq must be employed to ensure high fidelity the two techniques exhibit a complementarity in both advantages and drawbacks pa is not efficient in compressing high frequency areas but yields the best results when applied to highly correlated data vq is unable to reach high compression ratios because of its low adaptability but is quite suitable for compressing uncorrelated data the means to achieve the integration of the two techniques is a control image containing information about edge and texture locations in the paper edge encoding and restoration are also addressed which are closely related to the proposed hybrid scheme block prediction is also utilized to further reduce the residual redundancy between vq blocks the exploitation of the best features of both approaches results in high compression factors and in perceivable good quality in particular bit rates range from 0 15 to 0 07 bpp main applications of this compression scheme are in the areas of very low bit rate image transmission and image archiving

a meshless method for unbounded acoustic problems in this paper an effective meshless method is proposed to solve time harmonic acoustic problems defined on unbounded domains to this end the near field is discretized by a set of nodes and the far field effect is taken into account by considering radiative boundary conditions the approximation within the near field is performed using a set of local residual free basis functions defined on a series of finite clouds for considering the far field effect a series of infinite clouds are defined on which another set of residual free bases satisfying the radiation conditions are considered for the approximation validation of the results is performed through solving some acoustic problems

fast multipole method for the biharmonic equation in three dimensions the evaluation of sums matrix vector products of the solutions of the three dimensional biharmonic equation can be accelerated using the fast multipole method while memory requirements can also be significantly reduced we develop a complete translation theory for these equations it is shown that translations of elementary solutions of the biharmonic equation can be achieved by considering the translation of a pair of elementary solutions of the laplace equations the extension of the theory to the case of polyharmonic equations in r 3 is also discussed an efficient way of performing the fmm for biharmonic equations using the solution of a complex valued fmm for the laplace equation is presented compared to previous methods presented for the biharmonic equation our method appears more efficient the theory is implemented and numerical tests presented that demonstrate the performance of the method for varying problem sizes and accuracy requirements in our implementation the fmm for the biharmonic equation is faster than direct matrix vector product for a matrix size of 550 for a relative l 2 accuracy e 2 10 4 and n 3550 for e 2 10 1 2

generalized hough transform using regions with homogeneous color a novel generalized hough transform algorithm which makes use of the color similarity between homogeneous segments as the voting criterion is proposed in this paper the input of the algorithm is some regions with homogeneous color these regions are obtained by first pre segmenting the image using the morphological watershed algorithm and then refining the resultant outputs by a region merging algorithm region pairs belonging to the object are selected to generate entries of the reference table for the hough transform every r table entry stores a relative color between the selected region pairs this is done in order to compute the color similarity and in turn generate votes during the voting process and some relevant information to recover the transformation parameters of the object based on the experimental results our algorithm is robust to change of illumination occlusion and distortion of the segmentation output it recognizes objects which were translated rotated scaled and even located in a complex environment

adaptive split and merge segmentation based on piecewise least square approximation the performance of the classic split and merge segmentation algorithm is severely hampered by its rigid split and merge processes which are insensitive to the image semantics the author proposes efficient algorithms and data structures to optimize the split and merge processes by piecewise least square approximation of image intensity functions this optimization aims at the unification of segment finding and edge detection the optimized split and merge algorithm is shown to be adaptive to the image semantics and hence improves the segmentation validity of the previous algorithms this algorithm also appears to work well on noisy sources since the optimization is done within the split and merge framework the better segmentation performance is achieved at the same order of time complexity as the previous algorithms

on edge detection edge detection is the process that attempts to characterize the intensity changes in the image in terms of the physical processes that have originated them a critical intermediate goal of edge detection is the detection and characterization of significant intensity changes this paper discusses this part of the edge detection problem to characterize the types of intensity changes derivatives of different types and possibly different scales are needed thus we consider this part of edge detection as a problem in numerical differentiation we show that numerical differentiation of images is an ill posed problem in the sense of hadamard differentiation needs to be regularized by a regularizing filtering operation before differentiation this shows that this part of edge detection consists of two steps a filtering step and a differentiation step following this perspective the paper discusses in detail the following theoretical aspects of edge detection 1 the properties of different types of filters with minimal uncertainty with a bandpass spectrum and with limited support are derived minimal uncertainty filters optimize a tradeoff between computational efficiency and regularizing properties 2 relationships among several 2 d differential operators are established in particular we characterize the relation between the laplacian and the second directional derivative along the gradient zero crossings of the laplacian are not the only features computed in early vision 3 geometrical and topological properties of the zero crossings of differential operators are studied in terms of transversality and morse theory

a parallel fast multipole accelerated integral equation scheme for 3d stokes equations in this paper we discuss a numerical scheme for the stokes equations in three dimensions it uses an integral equation formulation and is accelerated by the new version of fast multipole method first introduced by greengard and rokhlin in 1997 acta numerica 1997 6 229 269 the code is parallelized to solve problems of extremely large size the resulting numerical solver can be applied to stokes flows in complex geometry and also serves as a building block for solving the navier stokes equations of low to moderate reynold s numbers copyright 2006 john wiley sons ltd

using canny s criteria to derive a recursively implemented optimal edge detector a highly efficient recursive algorithm for edge detection is presented using canny s design 1 we show that a solution to his precise formulation of detection and localization for an infinite extent filter leads to an optimal operator in one dimension which can be efficiently implemented by two recursive filters moving in opposite directions in addition to the noise truncature immunity which results the recursive nature of the filtering operations leads with sequential machines to a substantial saving in computational effort five multiplications and five additions for one pixel independent of the size of the neighborhood the extension to the two dimensional case is considered and the resulting filtering structures are implemented as two dimensional recursive filters hence the filter size can be varied by simply changing the value of one parameter without affecting the time execution of the algorithm performance measures of this new edge detector are given and compared to canny s filters various experimental results are shown

second kind integral equations for the first kind dirichlet problem of the biharmonic equation in three dimensions a fredholm second kind integral equation skie formulation is constructed for the dirichlet problem of the biharmonic equation in three dimensions a fast numerical algorithm is developed based on the constructed skie its performance is illustrated via several numerical examples

integral equation methods for stokes flow and isotropic elasticity in the plane we present a class of integral equation methods for the solution of biharmonic boundary value problems with applications to two dimensional stokes flow and isotropic elasticity the domains may be multiply connected and finite infinite or semi infinite in extent our analytic formulation is based on complex variables and our fast multipole based iterative solution procedure requireso n operations wherenis the number of nodes in the discretization of the boundary the performance of the methods is illustrated with several large scale numerical examples

on the numerical solution of the biharmonic equation in the plane the biharmonic equation arises in a variety of problems in applied mathematics most notably in plane elasticity and in viscous incompressible flow integral equation methods are natural candidates for the numerical solution of such problems since they discritize the boundary alone are easy to apply in the case of free or moving boundaries and achieve superalgebraic convergence rates on sufficiently smooth domains regardless of shape in this paper we follow the work of mayo and greenbaum and make use of the sherman lauricella integral equation which is a fredholm equation with bounded kernel we describe a fast algorithm for the evaluation of the integral operators appearing in that equation when combined with a conjugate gradient like algorithm we are able to solve the discretized integral equation in an amount of time proportional to n where n is the number of nodes in the discretization of the boundary

identifying and locating dominating codes np completeness results for directed graphs let g v a be a directed asymmetric graph and c a subset of vertices and let b sub r sup v denote the set of all vertices x such that there exists a directed path from x to v with at most r arcs if the sets b sub r sup v spl cap c v spl isin v respectively v spl isin v spl bsol c are all nonempty and different we call c an r identifying code respectively an r locating dominating code of g in other words if c is an r identifying code then one can uniquely identify a vertex v spl isin v only by knowing which codewords belong to b sub r sup v and if c is r locating dominating the same is true for the vertices v in v spl bsol c we prove that given a directed asymmetric graph g and an integer k the decision problem of the existence of an r identifying code or of an r locating dominating code of size at most k in g is np complete for any r spl ges 1 and remains so even when restricted to strongly connected directed asymmetric bipartite graphs or to directed asymmetric bipartite graphs without directed cycles

a method to compute periodic sums in a number of problems in computational physics a finite sum of kernel functions centered at n particle locations located in a box in three dimensions must be extended by imposing periodic boundary conditions on box boundaries even though the finite sum can be efficiently computed via fast summation algorithms such as the fast multipole method fmm the periodized extension is usually treated via a different algorithm ewald summation accelerated via the fast fourier transform fft a different approach to compute this periodized sum just using a blackbox finite fast summation algorithm is presented in this paper the method splits the periodized sum in to two parts the first comprising the contribution of all points outside a large sphere enclosing the box and some of its neighbors is approximated inside the box by a collection of kernel functions sources placed on the surface of the sphere or using an expansion in terms of spectrally convergent local basis functions the second part comprising the part inside the sphere and including the box and its immediate neighborhood is treated via available summation algorithms the coefficients of the sources are determined by least squares collocation of the periodicity condition of the total potential imposed on a circumspherical surface for the box while the method is presented in general details are worked out for the case of evaluating electrostatic potentials and forces results show that when used with the fmm the periodized sum can be computed to any specified accuracy at a cost that is twice that of the free space fmm with the same accuracy several technical details and efficient algorithms for auxiliary computations are provided as are numerical comparisons

a scalar potential formulation and translation theory for the time harmonic maxwell equations we develop a computational method based on the debye scalar potential representation which efficiently reduces the solution of maxwell s equations to the solution of two scalar helmholtz equations one of the key contributions of this paper is a theory for the translation of maxwell solutions using such a representation since the scalar potential form is not invariant with respect to translations the translation theory is developed by introducing conversion operators which enable the representation of the electric and magnetic vector fields via scalar potentials in an arbitrary reference frame advantages of this representation include the fact that only two helmholtz equations need be solved and moreover the divergence free constraints are satisfied automatically by construction truncation error bounds are also presented the availability of a translation theory and error bounds for this representation can find application in methods such as the fast multipole method for illustration of the use of the representation and translation theory we implemented an algorithm for the simulation of mie scattering off a system of spherical objects of different sizes and dielectric properties using a variant of the t matrix method the resulting system was solved using an iterative method based on gmres the results of the computations agree well with previous computational and experimental results

morphological grayscale reconstruction in image analysis applications and efficient algorithms two different formal definitions of gray scale reconstruction are presented the use of gray scale reconstruction in various image processing applications discussed to illustrate the usefulness of this transformation for image filtering and segmentation tasks the standard parallel and sequential approaches to reconstruction are reviewed it is shown that their common drawback is their inefficiency on conventional computers to improve this situation an algorithm that is based on the notion of regional maxima and makes use of breadth first image scannings implemented using a queue of pixels is introduced its combination with the sequential technique results in a hybrid gray scale reconstruction algorithm which is an order of magnitude faster than any previously known algorithm

automatic image segmentation by dynamic region merging this paper addresses the automatic image segmentation problem in a region merging style with an initially oversegmented image in which many regions or superpixels with homogeneous color are detected an image segmentation is performed by iteratively merging the regions according to a statistical test there are two essential issues in a region merging algorithm order of merging and the stopping criterion in the proposed algorithm these two issues are solved by a novel predicate which is defined by the sequential probability ratio test and the minimal cost criterion starting from an oversegmented image neighboring regions are progressively merged if there is an evidence for merging according to this predicate we show that the merging order follows the principle of dynamic programming this formulates the image segmentation as an inference problem where the final segmentation is established based on the observed image we also prove that the produced segmentation satisfies certain global properties in addition a faster algorithm is developed to accelerate the region merging process which maintains a nearest neighbor graph in each iteration experiments on real natural images are conducted to demonstrate the performance of the proposed dynamic region merging algorithm

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

on a new class of codes for identifying vertices in graphs we investigate a new class of codes for the optimal covering of vertices in an undirected graph g such that any vertex in g can be uniquely identified by examining the vertices that cover it we define a ball of radius t centered on a vertex spl upsi to be the set of vertices in g that are at distance at most t from spl upsi the vertex spl upsi is then said to cover itself and every other vertex in the ball with center spl upsi our formal problem statement is as follows given an undirected graph g and an integer t spl ges 1 find a minimal set c of vertices such that every vertex in g belongs to a unique set of balls of radius t centered at the vertices in c the set of vertices thus obtained constitutes a code for vertex identification we first develop topology independent bounds on the size of c we then develop methods for constructing c for several specific topologies such as binary cubes nonbinary cubes and trees we also describe the identification of sets of vertices using covering codes that uniquely identify single vertices we develop methods for constructing optimal topologies that yield identifying codes with a minimum number of codewords finally we describe an application of the theory developed in this paper to fault diagnosis of multiprocessor systems

quantification of mr brain images by mixture density and partial volume modeling the problem of automatic quantification of brain tissue by utilizing single valued single echo magnetic resonance imaging mri brain scans is addressed it is shown that this problem can be solved without classification or segmentation a method that may be particularly useful in quantifying white matter lesions where the range of values associated with the lesions and the white matter may heavily overlap the general technique utilizes a statistical model of the noise and partial volume effect together with a finite mixture density description of the tissues the quantification is then formulated as a minimization problem of high order with up to six separate densities as part of the mixture this problem is solved by tree annealing with and without partial volume utilized the results compared and the sensitivity of the tree annealing algorithm to various parameters is exhibited the actual quantification is performed by two methods a classification based method called bayes quantification and parameter estimation results from each method are presented for synthetic and actual data

locating dominating codes bounds and extremal cardinalities in this work two types of codes such that they both dominate and locate the vertices of a graph are studied those codes might be sets of detectors in a network or processors controlling a system whose set of responses should determine a malfunctioning processor or an intruder here we present our contributions on l codes and h codes concerning bounds extremal values and realization theorems

minimizing the size of an identifying or locating dominating code in a graph is np hard let g v e be an undirected graph and c a subset of vertices if the sets br v c v v respectively v v c are all nonempty and different where br v denotes the set of all points within distance r from v we call c an r identifying code respectively an r locating dominating code we prove that given a graph g and an integer k the decision problem of the existence of an r identifying code or of an r locating dominating code of size at most k in g is np complete for any r

hierarchy in picture segmentation a stepwise optimization approach a segmentation algorithm based on sequential optimization which produces a hierarchical decomposition of the picture is presented the decomposition is data driven with no restriction on segment shapes it can be viewed as a tree where the nodes correspond to picture segments and where links between nodes indicate set inclusions picture segmentation is first regarded as a problem of piecewise picture approximation which consists of finding the partition with the minimum approximation error then picture segmentation is presented as an hypothesis testing process which merges only segments that belong to the same region a hierarchical decomposition constraint is used in both cases which results in the same stepwise optimization algorithm at each iteration the two most similar segments are merged by optimizing a stepwise criterion the algorithm is used to segment a remote sensing picture and illustrate the hierarchical structure of the picture

an image segmentation method based on network clustering model abstract network clustering phenomena are ubiquitous in nature and human society in this paper a method involving a network clustering model is proposed for mass segmentation in mammograms first the watershed transform is used to divide an image into regions and features of the image are computed then a graph is constructed from the obtained regions and features the network clustering model is applied to realize clustering of nodes in the graph compared with two classic methods the algorithm based on the network clustering model performs more effectively in experiments

an efficient computational method for solving fractional biharmonic equation in this paper we first introduce the fractional biharmonic equation and an orthogonal system of basis functions for the space of continuous functions on the interval 0 l generated by the shifted chebyshev polynomials moreover we propose a computational method based on the operational matrix of fractional derivatives of these basis functions for solving the fractional biharmonic equation the main characteristic behind this approach is that it reduces the problem under consideration to solving a system of algebraic equations which greatly simplifies the problem convergence of the shifted chebyshev polynomials expansion in two dimensions is investigated also the power of this manageable method is illustrated

a fast multipole method for the three dimensional stokes equations many problems in stokes flow and linear elasticity require the evaluation of vector fields defined in terms of sums involving large numbers of fundamental solutions in the fluid mechanics setting these are typically the stokeslet the kernel of the single layer potential or the stresslet the kernel of the double layer potential in this paper we present a simple and efficient method for the rapid evaluation of such fields using a decomposition into a small number of coulombic n body problems following an approach similar to that of fu and rodin y fu g j rodin fast solution methods for three dimensional stokesian many particle problems commun numer meth en 16 2000 145 149 while any fast summation algorithm for coulombic interactions can be employed we present numerical results from a scheme based on the most modern version of the fast multipole method h cheng l greengard v rokhlin a fast adaptive multipole algorithm in three dimensions j comput phys 155 1999 468 498 this approach should be of value in both the solution of boundary integral equations and multiparticle dynamics