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<p>Examines the localization criterion for edge detection and determine the probability density function describing the edge location error. Canny (1986) defines the measure of localization as the reciprocal of the root-mean-square edge location error and formulates an expression of this measure for local maximum detectors. However, Tagare and deFigueiredo (1990) point out that an incorrect assumption is made in the calculation. The same procedure is used by Sarkar and Boyer (1991) for their localization measure for zero-crossing detectors. We modify the analysis and obtain a closed-form solution of the probability density function of the edge location error. Examination of the density function indicates the variance of the edge location error does not exist, and hence cannot be used directly as a measure of localization.</p>
edge detection; errors; probability; feature extraction; image segmentation; edge location error; local maximum detectors; zero-crossing edge detectors; localization criterion; probability density function; root-mean-square error; closed-form solution; variance; localization measure; feature extraction; image processing; image segmentation

V. Greco and J. Koplowitz, "On the Edge Location Error for Local Maximum and Zero-Crossing Edge Detectors," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 16, no. , pp. 1207-1212, 1994.
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