5. Morphological filtering

Unlike filters defined in other areas of image processing (by convolution, for example), morphological filters are defined by algebraic properties: a filter is an increasing, idempotent operator. Immediate examples are algebraic openings (which are also anti-extensive) and algebraic closures (which are also extensive). If (γ _i ) is a family of openings, ${\vee }_i{\mathrm{\gamma }}_i$ is also an opening and therefore a morphological filter. Similarly, if $\left({\mathrm{\phi }}_i\right)$ is a family...