A novel algorithm for fast computation of Zernike moments

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, Z_nm, can be expressed as a combination of Z_n−2,m and Z_n−4,m. Based on this relationship, the Zernike moment Z_nm, for n>m, can be deduced from Z_mm. 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 Z_mm can be decreased significantly. Comparison with known methods shows that our algorithm is as accurate as the existing methods, but is more efficient.     

A fast algorithm for computing parametric rational functions

An algorithm for fast computation of a class of parametric rational functions whose coefficients are assumed to be affine functions of some underlying parameters is described. The algorithm has been implemented in Microsoft Quick BASIC 4.0. Execution times are minimal     

A fast algorithm for computing sparse visibility graphs

AnO(¦E¦log² n) algorithm is presented to construct the visibility graph for a collection ofn nonintersecting line segments, where ¦E¦ is the number of edges in the visibility graph. This algorithm is much faster than theO(n ²)-time andO(n ²)-space algorithms by Asanoet al., and by Welzl, on sparse visibility graphs. Thus we partially resolve an open problem raised by Welzl. Further, our algorithm uses onlyO(n) working storage.     

A fast algorithm for computing sparse visibility graphs

AnO(¦E¦log² n) algorithm is presented to construct the visibility graph for a collection ofn nonintersecting line segments, where ¦E¦ is the number of edges in the visibility graph. This algorithm is much faster than theO(n ²)-time andO(n ²)-space algorithms by Asanoet al., and by Welzl, on sparse visibility graphs. Thus we partially resolve an open problem raised by Welzl. Further, our algorithm uses onlyO(n) working storage.     

A fast algorithm for computing a histogram on reconfigurable mesh

The reconfigurable mesh captures salient features from a variety of sources, including the content addressable array parallel processor, the CHiP, the polymorphic-torus network and the bus automaton. It consists of an array of processors interconnected by a reconfigurable bus system. The bus system can be used to dynamically obtain various interconnection patterns between the processors. In this paper, we present a fast algorithm for computing the histogram of an N×N image with h grey levels in O(min{√h+log*(N/h),N}) time on an N×N reconfigurable mesh assuming each PE has a constant amount of local memory. This algorithm runs on the PARBUS and MRN/LRN models. In addition, histogram modification can be performed in O(√h) time on the same model. A variant of out algorithm runs in O(min{√h+log log(N/h),N}) time on an N×N RMESH in which each PE has constant storage. This result improves the known time and memory bounds for histogramming on the RMESH model     

Efficient region segmentation on compressed gray images using quadtree and shading representation

Image segmentation, which partitions the image into homogeneous regions, is a fundamental operation in image processing. Suppose the input gray image with size N×N has been compressed into the compressed image via quadtree and shading representation. Assume that the number of blocks in the representation is B, commonly B<N² due to the compression effect. This paper first derives some closed forms for computing the mean/variance of any block and for calculating the two statistical measures of any merged region in O(1) time. It then presents an efficient O(Bα(B))-time algorithm for performing region segmentation on the compressed image directly where α(B) is the inverse of the Ackerman's function and is a very slowly growing function. With the same time complexity, our results extend the pioneering results by Dillencourt and Samet from the map image to the gray image. In addition, with four real images, experimental results show that our proposed algorithm has about 55.4% execution time improvement ratio when compared to the previous fastest region-segmentation algorithm by Fiorio and Gustedt whose O(N²)-time algorithm is run on the original N×N gray image.     

基于局部灰度占比的粘连细胞分割方法

针对医学细胞图像中的粘连现象,对采集到的细胞图像进行均值聚类、二值化、空洞填充、距离变换等预处理操作后,根据距离变换图像的像素灰度值来选取实现粘连细胞分割的最佳阚值,在分析重叠或粘连细胞图像的局部像素特征的基础上,对距离变换处理后图片的局部灰度占比分布进行了全面的分析和处理.实验结果表明,该方法简单易行,具有较好的分割效果.     

A fast and fully automatic registration approach based on point features for multi-source remote-sensing images

Automatic registration of multi-source remote-sensing images is a difficult task as it must deal with the varying illuminations and resolutions of the images, different perspectives and the local deformations within the images. This paper proposes a fully automatic and fast non-rigid image registration technique that addresses those issues. The proposed technique performs a pre-registration process that coarsely aligns the input image to the reference image by automatically detecting their matching points by using the scale invariant feature transform (SIFT) method and an affine transformation model. Once the coarse registration is completed, it performs a fine-scale registration process based on a piecewise linear transformation technique using feature points that are detected by the Harris corner detector. The registration process firstly finds in succession, tie point pairs between the input and the reference image by detecting Harris corners and applying a cross-matching strategy based on a wavelet pyramid for a fast search speed. Tie point pairs with large errors are pruned by an error-checking step. The input image is then rectified by using triangulated irregular networks (TINs) to deal with irregular local deformations caused by the fluctuation of the terrain. For each triangular facet of the TIN, affine transformations are estimated and applied for rectification. Experiments with Quickbird, SPOT5, SPOT4, TM remote-sensing images of the Hangzhou area in China demonstrate the efficiency and the accuracy of the proposed technique for multi-source remote-sensing image registration.     

An evolutionary gray gradient algorithm for multilevel thresholding of brain MR images using soft computing techniques

The conventional two dimensional (2-D) histogram based Otsu’s method gives unreliable results while considering multilevel thresholding of brain magnetic resonance (MR) images, because the edges of the brain regions are not preserved due to the local averaging process involved. Moreover, some of the useful pixels present inside the off-diagonal regions are ignored in the calculation. This article presents an evolutionary gray gradient algorithm (EGGA) for optimal multilevel thresholding of brain MR images. In this paper, more edge information is preserved by computing 2-D histogram based gray gradient. The key to our success is the use of the gray gradient information between the pixel values and the pixel average values to minimize the information loss. In addition, the speed improvement is achieved. Theoretical formulations are derived for computing the maximum between class variance from the 2-D histogram of the brain image. A first-hand fitness function is suggested for the EGGA. A novel adaptive swallow swarm optimization (ASSO) algorithm is introduced to optimize the fitness function. The performance of ASSO is validated using twenty three standard Benchmark test functions. The performance of ASSO is better than swallow swarm optimization (SSO). The optimum threshold value is obtained by maximizing the between class variance using ASSO. Our method is tested using the standard axial T₂ − weighted brain MRI database of Harvard medical education using 100 slices. Performance of our method is compared to the Otsu’s method based on the one dimensional (1-D) and the 2-D histogram. The results are also compared among four different soft computing techniques. It is observed that results obtained using our method is better than the other methods, both qualitatively and quantitatively. Benefits of our method are – (i) the EGGA exhibits better objective function values; (ii) the EGGA provides us significantly improved results; and (iii) more computational speed is achieved.     

A simple and fast algorithm for computing exponentials of power series

As was initially shown by Brent, exponentials of truncated power series can be computed using a constant number of polynomial multiplications. This note gives a relatively simple algorithm with a low constant factor.     

A fast algorithm for computing a longest common increasing subsequence

Let A=〈a₁,a₂,…,am〉 and B=〈b₁,b₂,…,bn〉 be two sequences, where each pair of elements in the sequences is comparable. A common increasing subsequence of A and B is a subsequence 〈ai₁=bj₁,ai₂=bj₂,…,ail=bjl〉, where i₁<i₂<?<il and j₁<j₂<?<jl, such that for all 1?k<l, we have aik<aik+1. A longest common increasing subsequence of A and B is a common increasing subsequence of the maximum length. This paper presents an algorithm for delivering a longest common increasing subsequence in O(mn) time and O(mn) space.     

A fast algorithm for computing minimum routing cost spanning trees

Communication networks have been developed based on two networking approaches: bridging and routing. The convergence to an all-Ethernet paradigm in Personal and Local Area Networks and the increasing heterogeneity found in these networks emphasizes the current and future applicability of bridging. When bridging is used, a single active spanning tree needs to be defined. A Minimum Routing Cost Tree is known to be the optimal spanning tree if the probability of communication between any pair of network nodes is the same. Given that its computation is a NP-hard problem, approximation algorithms have been proposed.We propose a new approximation Minimum Routing Cost Tree algorithm. Our algorithm has time complexity lower than the fastest known approximation algorithm and provides a spanning tree with the same routing cost in practice. In addition, it represents a better solution than the current spanning tree algorithm used in bridged networks.     

A fast recursive algorithm based on fuzzy 2-partition entropy approach for threshold selection

The fuzzy c-partition entropy approach for threshold selection is an effective approach for image segmentation. The approach models the image with a fuzzy c-partition, which is obtained using parameterized membership functions. The ideal threshold is determined by searching an optimal parameter combination of the membership functions such that the entropy of the fuzzy c-partition is maximized. It involves large computation when the number of parameters needed to determine the membership function increases. In this paper, a recursive algorithm is proposed for fuzzy 2-partition entropy method, where the membership function is selected as S-function and Z-function with three parameters. The proposed recursive algorithm eliminates many repeated computations, thereby reducing the computation complexity significantly. The proposed method is tested using several real images, and its processing time is compared with those of basic exhaustive algorithm, genetic algorithm (GA), particle swarm optimization (PSO), ant colony optimization (ACO) and simulated annealing (SA). Experimental results show that the proposed method is more effective than basic exhaustive search algorithm, GA, PSO, ACO and SA.     

基于阈值动态分配空闲灰度级的红外图像增强

分析了直方图均衡化增强算法的优缺点,并结合红外图像的特点对其简并的缺点提出了改进措施.利用全局灰度均值法得到阈值,并依据该阈值将图像灰度分为背景段和目标段,接着将空闲灰度级动态分配给背景段和目标段,最后利用局域直方图均衡化方法对背景段和目标段分别进行增强,从而达到减少简并可能性的目的.     

A novel approach to the fast computation of Zernike moments

This paper presents a novel approach to the fast computation of Zernike moments from a digital image. Most existing fast methods for computing Zernike moments have focused on the reduction of the computational complexity of the Zernike 1-D radial polynomials by introducing their recurrence relations. Instead, in our proposed method, we focus on the reduction of the complexity of the computation of the 2-D Zernike basis functions. As Zernike basis functions have specific symmetry or anti-symmetry about the x-axis, the y-axis, the origin, and the straight line y=x, we can generate the Zernike basis functions by only computing one of their octants. As a result, the proposed method makes the computation time eight times faster than existing methods. The proposed method is applicable to the computation of an individual Zernike moment as well as a set of Zernike moments. In addition, when computing a series of Zernike moments, the proposed method can be used with one of the existing fast methods for computing Zernike radial polynomials. This paper also presents an accurate form of Zernike moments for a discrete image function. In the experiments, results show the accuracy of the form for computing discrete Zernike moments and confirm that the proposed method for the fast computation of Zernike moments is much more efficient than existing fast methods in most cases.     

Distributed computing model for processing remotely sensed images based on grid computing

With advances in remote-sensing technology, the large volumes of data cannot be analyzed efficiently and rapidly, especially with arrival of high-resolution images. The development of image-processing technology is an urgent and complex problem for computer and geo-science experts. It involves, not only knowledge of remote sensing, but also of computing and networking. Remotely sensed images need to be processed rapidly and effectively in a distributed and parallel processing environment. Grid computing is a new form of distributed computing, providing an advanced computing and sharing model to solve large and computationally intensive problems. According to the basic principle of grid computing, we construct a distributed processing system for processing remotely sensed images. This paper focuses on the implementation of such a distributed computing and processing model based on the theory of grid computing. Firstly, problems in the field of remotely sensed image processing are analyzed. Then, the distributed (and parallel) computing model design, based on grid computing, is applied. Finally, implementation methods with middleware technology are discussed in detail. From a test analysis of our system, TARIES.NET, the whole image-processing system is evaluated, and the results show the feasibility of the model design and the efficiency of the remotely sensed image distributed and parallel processing system.     

A fast algorithm for computing integrals in function spaces: Financial applications

The paper describes a fast and general numerical algorithm for computing path integrals in function spaces. Efficiency is ensured by use of FFT-based procedures as the primary element of the algorithm. The total number of operations required by the algorithm can be shown to be proportional to the total number of discretization nodes. A number of financial applications of the algorithm are considered, including pricing European and American style interest rate options, path dependent options, and index amortization swaps.     

A fast algorithm for computing least-squares cross-validations for nonparametric conditional kernel density functions

Nonparametric conditional density functions are widely used in applied econometric and statistical modelling because they provide enriched information summaries of the relationships between dependent and independent variables. Although least-squares cross-validation is considered to be the best criterion for bandwidth selection of the kernel estimator of the conditional density, the number of computations required for this procedure grows exponentially as the number of observations increases. A fast algorithm is proposed to reduce this computational cost, and its accuracy and efficiency are verified via numerical experiments. A practical application is also presented to demonstrate the algorithm’s potential usefulness.