Legendre矩的一种有效算法

Ｌｅｇｅｎｄｒｅ正交矩的模式识别、图像分析等许多领域有成功的应用,然而,由于正交矩的复杂性,目前有关正交矩快速算法的研究很少,从而在一定程度上影响了它的应用,对此,作者对Ｌｅｇｅｎｄｒｅ多项式进行了研究,获得了一些新的有效的性质,它们能够显著地减少矩计算中的运算量。     

三维正交矩的快速算法

给出一种针对一类特殊三维物体－多面体的Ｌｅｇｅｎｄｒｅ正交知匠有效算法。首先利用高斯公式,将矩定义中的体积积分转化为表面积分,这使得矩计算中的运算量减少一个数量级。其次,为计算面积积分,彩格林公式将其转化为围线积分,后者可以方便地用迭代方法求出。文中介绍的方法能显著地减少三维正交矩的运算量。     

基于Legendre多项式的随机连续系统的Markov参数估计

本文在讨论连续Ｗｉｓｅｎｒ过程的Ｌｅｇｅｎｄｒｅ多项式逼近值的相关性和Ｗｉｅｎｅｒ过程扰动下连续线性系统基于该正交多项的最小二乘估计有偏性后，提出了无偏一致的且数估计误差方差最小的Ｍａｒｋｏｖ估计（最小方差估计）算法，并给出本文方法的仿真结果。     

基于不规则三角网的等值线填充算法

现有基于不规则三角网的等值线填充算法较少,且不能精确判断区域颜色。对此给出一种通过不规则三角网快速填充等值线图的算法,搜索出所有开区域轮廓,通过围成区域等值线属性值与不同颜色的对应关系确定区域颜色,采用深度优先的方法对开区域及其内部的多级封闭区域进行矢量填充。对不同数据源运行该算法,并与其他算法进行比较,根据对比结果可知该算法比现有算法更适合于基于三角网生成的等值线图精确填充。     

Chebyshev-Fourier矩的快速计算方法

给出了求解Chebyshev-Fourier正交矩及其反变换的快速算法．和其它类型的正交矩相比，Chebyshev-Fourier正交矩不仅表达形式简单，而且具有更好的图像描述能力和鲁棒性．利用Clenshaw递推公式，作者实现了一维Fourier变换及多项式求和运算的快速计算，大大减少了复指数运算的次数，降低了计算复杂度，从而加快了Chebyshev-Fourier矩正、反变换的运算时间．图像的重建结果表明，该算法和直接计算方法具有相同的精度和稳定性，但效率更高．     

正交Gaussian-Hermite矩的应用

分析了正交Gaussian Hermite矩的一些性质 ,指出它在运动检测中的应用 ,并提出运动检测中正交Gaussian Hermite矩的最佳参数的估计方法 .最后我们给出了对比实验结果 .实验表明我们的方法是有效的 .     

正交傅里叶—梅林矩的一种高效算法*

提出了一种高效计算图像正交傅里叶—梅林矩的算法。该算法通过消除正交多项式中的阶乘项和提取该图像矩的公共项以提高图像矩值的计算性能。实验分析表明,与传统的直接计算方法相比,该算法可有效节省计算时间,尤其是在计算高阶连续矩情况下性能更好。     

基于四边形网格剖分的可计算区域填充方法

针对在一定形状限制条件下的可形变填充问题,提出一种可计算填充方法。对目标区域和填充样板进行四边形网格剖分。给出在样板拼接、边界、旋转、最小形变等约束条件下的整型规划,使用填充样板在填充区域中进行离散拼接,并通过全局优化迭代样板形变,以达到理想的填充效果。实验结果表明,该填充方法对目标区域的有效覆盖率以及边缘拟合度与约束限制无直接关系,在指定约束条件下,能较好地达到区域填充效果。     

Krawtchouk矩旋转不变性的分析

矩是基于区域的形状描述子,相对于基于轮廓的描述子例如傅立叶、链码描述子等,对于不连通的图像形状描述和对噪声的鲁棒性等方面有着更良好的性能.正交矩又可分为连续正交矩和离散正交矩,Krawtchouk矩是离散正交矩中的一种,和连续正交矩不同,基于离散正交矩本身的离散特性,更适合于对数字图像的处理.但同其他离散矩一样,Krawtchou矩并不具备天然的几何不变性(旋转、缩放和平移),这也从一定程度上限制了Krawtchouk矩的应用.为使Krawtchouk矩得到更广泛的应用,对Krawtchouk旋转不变矩的构造进行详细分析和实验,比较出更适合用于浮游植物的Krawtchouk旋转不变矩.     

一种新的快速计算Legendre矩的方法

正交矩在模式识别，图像分析等领域有成功的应用，但由于正交矩的复杂性，有关正交矩的快速算法研究尚未得到很好的解决，该文提出一种 新的快速计算Ｌegendre矩的方法，该方法把基于像素点的二维Ｌegendre矩转换为线段的形式来计算，在计算出所有线段的积分后，使用扩展的Ｈatamian滤波方法来计算一维的Ｌegendre矩。结果显示新的算法有效地降低了计算的复杂度，并且，该方法能用于处理任意形状的物体。     

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.     

一种新的灰度图像Legendre矩的快速算法

Legendre正交矩在模式识别和图像分析等领域有着广泛的应用，但由于计算的复杂性，相关的快速算法尚未得到很好的解决，已有方法均局限于二值图像．文章提出了一种灰度图像的Legendre正交矩的快速算法，借助于Legendre多项式的递推公式推导出计算一维Legendre矩的递归公式．利用该关系式，一维Legendre矩Lp可以用一系列初始值L1(a)，a＜p，Lo(a)，a＜p-1来得到．而二维Legendre矩pq可以利用一维算法进行计算,为了降低算法复杂度，文中采用基于Systolic阵列的快速算法进行计算L1(a)，Lo(a),与直接方法相比，快速算法可以大幅度减少乘法的次数，从而达到了降低算法复杂度的目的。     

Functional approximation for inversion of Laplace transforms via polynomial series

A method for finding the inverse of Laplace transforms using polynomial series is discussed. It is known that any polynomial series basis vector can be transformed into Taylor polynomials by use of a suitable transformation. In this paper, the cross product of a polynomial series basis vector is derived in terms of Taylor polynomials, and as a result the inverse of the Laplace transform is obtained, using the most commonly used polynomial series such as Legendre, Chebyshev, and Laguerre. Properties of Taylor series are first briefly presented and the required function is given as a Taylor series with unknown coefficients. Each Laplace transform is converted into a set of simultaneous linear algebraic equations that can be solved to evaluate Taylor series coefficients. The inverse Laplace transform using other polynomial series is then obtained by transforming the properties of the Taylor series to other polynomial series. The method is simple and convenient for digital computation. Illustrative examples are also given,     

An efficient method for the computation of Legendre moments

Legendre moments are continuous moments, hence, when applied to discrete-space images, numerical approximation is involved and error occurs. This paper proposes a method to compute the exact values of the moments by mathematically integrating the Legendre polynomials over the corresponding intervals of the image pixels. Experimental results show that the values obtained match those calculated theoretically, and the image reconstructed from these moments have lower error than that of the conventional methods for the same order. Although the same set of exact Legendre moments can be obtained indirectly from the set of geometric moments, the computation time taken is much longer than the proposed method.     

Radial shifted Legendre moments for image analysis and invariant image recognition

The rotation, scaling and translation invariant property of image moments has a high significance in image recognition. Legendre moments as a classical orthogonal moment have been widely used in image analysis and recognition. Since Legendre moments are defined in Cartesian coordinate, the rotation invariance is difficult to achieve. In this paper, we first derive two types of transformed Legendre polynomial: substituted and weighted radial shifted Legendre polynomials. Based on these two types of polynomials, two radial orthogonal moments, named substituted radial shifted Legendre moments and weighted radial shifted Legendre moments (SRSLMs and WRSLMs) are proposed. The proposed moments are orthogonal in polar coordinate domain and can be thought as generalized and orthogonalized complex moments. They have better image reconstruction performance, lower information redundancy and higher noise robustness than the existing radial orthogonal moments. At last, a mathematical framework for obtaining the rotation, scaling and translation invariants of these two types of radial shifted Legendre moments is provided. Theoretical and experimental results show the superiority of the proposed methods in terms of image reconstruction capability and invariant recognition accuracy under both noisy and noise-free conditions.     

Accurate and speedy computation of image Legendre moments for computer vision applications

A novel algorithm that permits the fast and accurate computation of the Legendre image moments is introduced in this paper. The proposed algorithm is based on the block representation of an image and on a new image representation scheme, the Image Slice Representation (ISR) method. The ISR method decomposes a gray-scale image as an expansion of several two-level images of different intensities (slices) and thus enables the partial application of the well-known Image Block Representation (IBR) algorithm to each image component. Moreover, using the resulted set of image blocks, the Legendre moments’ computation can be accelerated through appropriate computation schemes. Extensive experiments prove that the proposed methodology exhibits high efficiency in calculating Legendre moments on gray-scale, but furthermore on binary images. The newly introduced algorithm is suitable for the computation of the Legendre moments for pattern recognition and computer vision applications, where the images consist of objects presented in a scene.