EFFECT OF SAMPLING, QUANTIZATION AND NOISE ON THE PERFORMANCE OF THE 2ND DIRECTIONAL DERIVATIVE EDGE DETECTOR

Berzins [2] and De Vriendt [14] studied the processes that influence the performance of the Laplacian and the second directional derivative edge detector in the continuous domain. In this paper the influence of sampling, quantization and noise is studied in the discrete domain for the second directional derivative edge detector. The results are compared with those for the Laplacian edge detector. The smoothing and derivative operations are implemented by FIR digital filters. Two sampling processes are considered: a square aperture and a Gaussian smoothing process. The influence of sampling can be limited by increasing the spread a of the smoothing filter. Though, sigma should not be chosen too large because of the influence of nearby edges. The quantization of the intensity function introduces an uncertainty in the edge location. The uncertainty is larger than the error due to sampling if the step height is small. We also prove that the second directional derivative is less sensitive to noise than the Laplacian. An increase of sigma slightly reduces the variation of the edge location.