重心法による円の中心位置の計測誤差

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  • Measurement Errors of Centroid Methods of Center Location of a Circle
  • ジュウシンホウ ニ ヨル エン ノ チュウシン イチ ノ ケイソク ゴサ

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We conducted an experiment to evaluate measuring methods of the center location of a circle by using simulated images of various sizes of circles. In the experiment results we found that the variances of the measurement errors of the centroid methods oscillate on a one-pixel cycle in diameter. This paper reports an analysis of the dependence of the location measurement accuracy of centroid methods on the diameter of a circular target. Two centroid methods : weighted centroid method (WCM), and unweighted centroid method using a binary image created by thresholding (BCM) are investigated. Since variances of the measurement errors by both WCM and BCM are unable to be obtained analytically, those are obtained by numerical integration. The results of the numerical integration show that the variances of the measurement errors by WCM can be expressed by the combination of the inverse proportion to the cube of the diameter and the oscillation on a one-pixel cycle in diameter. On the other hand, the variances of the measurement errors by BCM should approximate to the combination of the inverse proportion to the diameter and the oscillation on a one-pixel cycle in diameter.

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