Fig. 1. Self-dual image simplification removing all dark and bright connected components of pixels smaller than a given threshold (by processing each band separately). This is achieved by computing the alternating sequential filter of each band using 8-connected area openings and closings (see Eq. (15) for the case where λ=25).

Fig. 2. Four-connected self-dual reconstruction of the median filter of a rectangle corrupted by noisy black and white rectangles. The median filter has been computed within a 17×17 square window. It corresponds therefore to the rank filter ζ with ▪₁₇ and rank equal to 145. R^ν denotes the self-dual reconstruction (Eq. (16)) while R^ν′ refers to the alternative definition (Eq. (17)).

Fig. 3. Flat zones of the first band of the image shown in Fig. 1c (alternating self-dual 8-connected area opening and closing up to an area of 100 pixels). Although this filter ensures that all extrema of the filtered image are larger or equal to the size of the filter, flat zones belonging to non-extrema regions can be of arbitrary size in the filtered image.

Fig. 4. Flat zone based area filtering of a satellite image (compare with Fig. 1). In each filtering example, the 3 bands of the input image have been processed separately by the specified flat zone based filter.

Fig. 5. Flat zones of the first band of the image shown in Fig. 4c (flat zone area filter using a threshold value of 100 pixels). Each flat zone contains at least 100 pixels. Compare with the partition shown in Fig. 3.