Segmentation of Small-Field-of-Viewstar Images Based on Kittler Minimum Error Algorithm
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摘要: 小视场星图易受光照不均和噪声影响，常用阈值分割算法存在处理效果不佳或效率较低的不足. 针对星图灰度的高斯分布特征，基于贝叶斯最小误差理论，提出利用Kittler最小误差分割算法处理小视场星图. 以视频测量机器人为测量平台，以 "优度法"、区域一致性、区域对比度和时间复杂度为评价指标，对比了常用的阈值分割算法和一维最大熵法，验证了Kittler算法在确保星图良好分割的同时，星图处理效率可以提高70%左右. 基于半仿真星图和真实星图的室内试验表明，Kittler算法可以准确提取星点质心坐标，水平和垂直方向均方根误差分别为0.025像素和0.019像素；采用该算法的野外天文定位实测表明，经纬度内符合平均精度分别优于0.015 s和0.22″，外符合精度分别优于0.025 s和0.35″，可以满足一等天文测量的精度要求.
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关键词:
- 天文测量 /
- 高斯分布 /
- 图像分割 /
- Kittler最小误差法 /
- 小视场星图
Abstract: Compared with conventional images, small-field-of-view star images are more susceptible to the impacts of uneven illumination and measurement noises. Meanwhile, the traditional threshold segmentation algorithm has poor processing effect or efficiency. In terms of the Gaussian distribution of star image gray, the Kittler minimum error segmentation algorithm was used to process star images on the basis of Bayesian minimum error theory. By the use of the video measuring robot, several commonly-used threshold segmentation algorithms and one-dimensional maximum entropy algorithm are compared and analyzed in terms of goodness methods, regional consistency, regional contrast ratio and time complexity. It is indicated that the Kittler minimum error segmentation algorithm can achieve a satisfied segmentation of the small-field-of-view star images, and improves astronomical data processing efficiency significantly withthe average computation timereduced by about 70%. Laboratory experiments for semi-simulation star map and real star mapshow that the proposed algorithm can extract star points and obtain centroid coordinates accurately,whose horizontal and vertical root mean square errors are 0.025 and 0.019 pixels, respectively. Furthermore, extensive field experiments show that the astronomical longitude and latitude calculated by the proposed algorithm can meet first-class astronomical survey accuracy requirements, whose average internal accordant accuracy is better than 0.015 s and 0.22″ respectively, and external accordant accuracy is better than 0.025 s and 0.35″ respectively. -
表 1 星图阈值分割算法效果评价
Table 1. Resultevaluation of star image threshold segmentation algorithms
项目 局部阈值法 全局阈值法 Bernsen算法 Niblack算法 迭代法 Otsu算法 一维最大熵 Kittler算法 区域一致性 0.9969 0.9979 0.9981 0.9983 1.0000 1.0000 区域对比度 0.0452 0.2133 0.2199 0.2175 0.3494 0.3688 时间复杂度 $O({n^2})$ $O({n^2})$ $O(n)$ $O(n)$ $O(n\log \;n)$ $O(n)$ 处理时间/s 22.394 770.592 17.052 19.385 77.037 17.428 
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表 2 星点提取精度误差表
Table 2. Errors of star extraction accuracy
图号 一维最大熵法 Kittler算法 $\Delta x$ $\Delta y$ x y x y 1 1266.588 992.759 1266.453 992.682 0.136 0.077 2 1259.350 964.614 1259.418 964.593 −0.068 0.021 3 1186.383 1005.017 1186.308 1005.155 0.075 −0.138 4 1258.316 793.991 1258.277 793.930 0.038 0.061
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表 3 野外天文测量精度指标
Table 3. Accuracy index of astronomical survey
经纬度 一等 二等 三等 纬度/(") 0.30 0.50 1.00 经度/s 0.02 0.04 0.08
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表 4 内符合精度
Table 4. Internal accordant accuracy
经度 纬度 项目 值/s 项目 值/（″） 最大值 ±0.017 最大值 ±0.26 最小值 ±0.010 最小值 ±0.16 平均值 ±0.012 平均值 ±0.20
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表 5 外符合精度
Table 5. External accordant accuracy
经度 纬度 项目 值/s 项目 值/（″） 最大差值 0.038 最大差值 0.52 最小差值 0.001 最小差值 0.02 RMSE 0.023 RMSE 0.33
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表 6 野外实测结果
Table 6. Fieldtest results
测站号 时段号 经度/s 纬度/（″） 经度中误差/s 经度真误差/s 纬度中误差/（″） 经度真误差/（″） A 1 **.4906 **.7465 0.014 0.038 0.170 0.087 2 **.4797 **.6368 0.011 0.027 0.185 −0.023 B 1 **.6291 **.6844 0.010 −0.025 0.215 0.464 2 **.6438 **.3932 0.015 −0.011 0.159 0.173 注：**表示坐标的整数部分.
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