Deriche Edge Detection

The Deriche output, on the other hand, can be adjusted with the $\alpha$ scale parameter to filter out high frequency noise and pixelization from the image by linking adjacent edges into long, smooth, continuous contours. This allows the edge map to reflect the dominant structures in the image. The effect of small and large $\alpha$ (the scale parameter) is shown in Figure (a) and Figure (b). Furthermore, the computation is not limited to a small window and can find edges which change gradually. Thus, the outline of the trees as separate whole objects is found instead of the outline of the leaves.

  

Figure 2.2: Deriche edge detection at multiple scales (a) Deriche edge map at a small scale. (b) Deriche edge map at a large scale.

Despite its complexity, the Deriche technique, as with all other edge detectors, has its limits. While a human is capable of isolating objects and uses contextual knowledge of the scene to determine boundaries, the Deriche operator sometimes confuses the edges of nearby objects and links them into a single contour. The detection of erroneous phantom edges is also another problem as pointed out by Kelly and Levine [21].

The most significant disadvantage in using the Deriche operator and other complex edge detection schemes is in their computational cost. The Deriche extraction of edges from an image can take orders of magnitude more time when compared to the Sobel operator. If a real-time system is desired, image processing must be performed in fractions of a second. Deriche edge detection would simply be too time consuming on contemporary workstations.