The Morphological Reconstruction

In order to avoid these alterations of contours, like the ones caused by openings and closings shown in Fig. 7.6, the morphological reconstruction can be used.

The morphological reconstruction by dilation works with two images: a marker f and a mask g. The marker image is dilated, then the point-wise minimum with g is calculated, then the result is dilated once again, and so on. This process is iterated until idempotence. Let sg1^ f = 8B f A g. The morphological reconstruction can then be written as:

Rg(f) = sgro)(f) with 8f)(f) = 8« [8f-1)(f)] (7.3)

With s(g1) f = eBf v g, the reconstruction by erosion can be defined analogously:

Rg (f) = egro)(f) with ef)(f) = ef [ef-1)(f)] (7.4)

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