Oscillation of the Measurement Accuracy of the Center Location of an Ellipse on a Digital Image

Abstract. Circular targets are often utilized in photogrammetry and a circle on a plane is projected as an ellipse onto an oblique image. This paper reports an experiment conducted to investigate whether the measurement accuracy of the center location of an ellipse on a digital image oscillates as its dimension increases. The experiment was executed by the Monte Carlo simulation using 1024 synthesized images of which the centers were randomly distributed in one pixel for each ellipse. We investigated four typical measurement methods: intensity-weighted centroid method, non-iterative ellipse fitting, iterative ellipse fitting with the star operator, and least-squares matching. Three flattenings 0.00, 0.25, 0.50, and three rotation angles 0.0°, 22.5°, 45.0° were investigated in the experiment. The experiment results clearly show that the measurement accuracy by all the investigated methods would oscillate as the dimension of an ellipse increases. The measurement accuracy by the intensity-weighted centroid method and the non-iterative ellipse fitting would oscillate smoothly, while that by the least-squares matching would oscillate considerably roughly. It would be impossible to determine the cycle of the oscillation except the measurement accuracy by the intensity-weighted centroid method and the non-iterative ellipse fitting when the rotation angle of an ellipse is 0.0° and 45.0°. The experiment results indicate that the flattening and the rotation angle of an ellipse would affect the cycle of the oscillation as well.