Edge location error for local maximum and zero-crossing edge detectors

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Abstract
In this paper we examine the localization criterion for edge detection and determine the density function describing the edge location error, i.e. the displacement of the detected edge position from the true edge location. Canny 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 point out that an incorrect assumption is made in the calculation. The same procedure is used by Sarkar and Boyer 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 can not be used as a measure of localization. A new localization measure is proposed, characterized by a percentile level on the absolute value of the edge location error.

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