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3 Sobel operator acts locally on the image and only detects
edges at small scales. If an object with a jagged boundary is present, as
shown in Figure (a), the Sobel operator will find the
edges at each spike and twist of the perimeter as in
Figure (b). The operator is sensitive to high frequency
noise in the image and will generate only local edge data instead of
recovering the global structure of a boundary. Furthermore, smooth transitions
in contrast that occur over too large a spatial scale to fit in the 3 3 window of the Sobel operator will not be detected.
Sobel edge detection.
(a) The original intensity image. (b) The Sobel edge map.