二维高斯分布光斑中心快速提取算法研究

在深入分析二维高斯分布公式的基础上,通过将光斑中心整像素坐标和亚像素坐标进行分离,推导出一种无需求解广义逆矩阵的高斯曲面解析算法,该方法综合利用窗口内的所有像素灰度信息,通过解析表达式直接计算高斯分布光斑的亚像素中心位置;并且对传统高斯曲面拟合法求解过程进行了优化,提出一种更加高效的定参高斯拟合法。与传统高斯曲面拟合法相比,提出的两种方法具有基本相同的稳定性和定位精度,但运行效率分别提高了278倍和78倍以上。

Fast Algorithms on Center Location of Two Dimensional Gaussian Distribution Spot

The Gaussian surface fitting (GSF) is considered to be an excellent target location algorithm with high precision. But it is too expensive in computation to be utilized in real-time applications, such as dynamic tracking, dynamic measurement and autonomous navigation. By dividing the coordinate of the spot center into integer pixel value and subpixel value, a new fast algorithm, named Gaussian surface analyzing (GSA) is deduced, in which the center is located with analytical formulas and the intensity values of all pixels in the region of interest (ROI). In addition, an improved version of the traditional GSF algorithm, called fixed-coefficient Gaussian fitting (FCGF) is proposed as well, in which the expensive computation of the generalized inverse matrix is avoided. Compared to the GSF, the GSA and the FCGF have similar performanece in accuracy and robustness, however their running time is no more than 1/278 and 1/78 of the GSF respectively.