Opening and Closing

Morphological openings yB and closings $B are the consecutive application of erosion and dilation:

with B = {—b} the transposed structuring element.

In order to understand the behavior of gray scale openings and closings, it is useful to consider the image f as a topographic surface: Pixels with low gray-levels correspond to valleys, pixels with high gray-levels correspond to mountains. A morphological opening removes all bright features that cannot contain the structuring element; "it razes the elevations." A morphological closing removes all dark features that cannot contain the structuring element; "it fills the depressions in the surface." The opening and closing of a retinal image are shown in Fig. 7.6: The opening removes the bright patterns (exudates) without enlarging the dark ones (Fig. 7.6(b)). The closing removes the dark patterns

Figure 7.6: Opening and closing of a retinal image (detail) with a circular SE.

Figure 7.6: Opening and closing of a retinal image (detail) with a circular SE.

(hemorrhages, vessels, microaneurysms) without enlarging the bright ones; but the shape of the bright patterns are altered, the spaces between the exudates are also filled (Fig. 7.6(c)).

Furthermore, any increasing, idempotent, and antiextensive transformation is called algebraic opening. Any increasing, idempotent, and extensive transformation is called algebraic closing.

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