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.