Performance analysis of line and circle tting in digital images

Fitting lines and circles to a sequence of pixels, where the t is determined by minimizing the distance between the pixel coordinates and the tted line or circle, is a commonly used procedure in image analysis and computer vision. In this paper we derive analytic expressions for the variance of the estimated parameters as a function of image noise. We verify the analytic expresssions by comparing what they predict by what we actually observed in over 600,000 experiments. For lines we varied line orientation, length, width, center (speciied to sub-pixel precision), and noise level. For circles we varied radius, arc angle, ribbon width, starting direction, center (speciied to sub-pixel coordinates), and noise level. The experimental results indicated that the analytic expression underestimated the variance between 10% to 15%. This means that they are good enough to use so that if a line or circle parameter must be estimated with a given precision, or a given requirement, it is possible to determine what line length or what circular arc angle and radius are needed to guarantee with high probability that the estimate will meet the requirements for a given image noise variance.