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On Achievable Accuracy in Edge Localization
July 1992 (vol. 14 no. 7)
pp. 777-781

Edge localization occurs when an edge detector determines the location of an edge in an image. The authors use statistical parameter estimation techniques to derive bounds on achievable accuracy in edge localization. These bounds, known as the Cramer-Rao bounds, reveal the effect on localization of factors such as signal-to-noise ratio (SNR), extent of edge observed, scale of smoothing filter, and a priori uncertainty about edge intensity. By using continuous values for both image coordinates and intensity, the authors focus on the effect of these factors prior to sampling and quantization. They also analyze the Canny algorithm and show that for high SNR, its mean squared error is only a factor of two higher than the lower limit established by the Cramer-Rao bound. Although this is very good, the authors show that for high SNR, the maximum-likelihood estimator, which is also derived, virtually achieves the lower bound.

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Index Terms:
image intensity; S/N ratio; picture processing; pattern recognition; achievable accuracy; edge localization; statistical parameter estimation; Cramer-Rao bounds; smoothing filter; image coordinates; sampling; quantization; Canny algorithm; maximum-likelihood estimator; filtering and prediction theory; parameter estimation; pattern recognition; picture processing; statistical analysis
Citation:
R. Kakarala, A.O. Hero, "On Achievable Accuracy in Edge Localization," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 14, no. 7, pp. 777-781, July 1992, doi:10.1109/34.142913
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