Accurate calculation of Zernike moments
Accurate calculation of Zernike moments
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DOI：
10.1016/j.ins.2013.01.012
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发表时间：
2013-06
期刊：
影响因子：
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通讯作者：
C. Singh;Ekta Walia;R. Upneja
中科院分区：
文献类型：
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作者：
C. Singh;Ekta Walia;R. Upneja
Zernike矩是一种非常有效的全局图像描述子，在数字图像处理中有着广泛的应用。数字化过程损害了矩的准确性，因此，它的几个属性受到影响。离散误差主要有两种，即几何误差和数值积分误差。在本文中，我们提出了两个新的算法，消除这些错误。第一种算法是先精确计算单位圆盘上的几何矩，然后利用几何矩与零几何矩的关系计算零几何矩。该算法计算量大，对高阶矩不稳定，因此，我们提出了基于高斯积分的第二种算法。第二种算法同时减小了两种误差，其精度随着高斯积分次数的增加而增加。所提出的算法被观察到提供非常准确的ZMs，这导致在改进的图像重建，减少重建误差和改进的旋转和尺度不变性。详尽的实验提供了支持，以提高准确性的ZMs和时间复杂度分析进行现有的和提出的方法。
Zernike moments (ZMs) are very effective global image descriptors which are used in many digital image processing applications. The digitization process compromises the accuracy of the moments and therefore, several of its properties are affected. There are two major discretization errors, namely, the geometric error and numerical integration error. In this paper we propose two new algorithms which eliminate these errors. The first algorithm performs the exact computation of geometric moments (GMs) over a unit disk and then uses GMs-to-ZMs relationship to compute the latter. This algorithm is computationally more expensive and it becomes numerically instable for higher order moments, therefore, we develop a second algorithm based on Gaussian quadrature numerical integration. The second algorithm reduces both the errors simultaneously and its accuracy increases as the degree of Gaussian quadrature numerical integration increases. The proposed algorithms are observed to provide very accurate ZMs which result in improved image reconstruction, reduction in reconstruction error and improvement in rotation and scale invariance. Exhaustive experiments are provided to support improved accuracy of ZMs and time complexity analysis is performed for the existing and the proposed methods.