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The Sobel Operator

The 3 $\times$ 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 $\times$3 window of the Sobel operator will not be detected.

Figure 2.1: Sobel edge detection. (a) The original intensity image. (b) The Sobel edge map.
(a) & (b)
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Tony Jebara