Extinction transform

Include <mln/morpho/extinction_transform.hpp>

Image{I}
image_concrete_t<I> minima_extinction_transform(I ima, Neighborhood nbh)

Image{I}
image_concrete_t<I> maxima_extinction_transform(I ima, Neighborhood nbh)

The notion of extinction of a local extremum is based on the h-extrema (see. Opening and Closing by Dynamic). The extinction value of a bassin corresponds its dynamic when it merges with another basin. By definition, the lowest image minima / highest image maxima, have an extinction equal to the difference between the highest and lowest image grey scale values.

Let Mₜ be a regional maximum at level t of an image f, and 𝓟 any path linking a pixel p of Mₜ to a pixel q of a regional maximum Mₜ’ higher than Mₜ. In [Soi13], its extinction of Mₜ is defined as:

\[\min_{\mathcal{P} = \{p, \cdots, q\}} \left\{ \max_{x \in \mathcal{P}} (f(p) - f(x)) \right\}\]

Note

Pixels that do not belong to a local extremum are set to 0.

Extinction transform of a 1D signal. Red arrows show the extinction value of each minima.

Parameters:

• f – Input image 𝑓

• nbh – Elementary structuring element.

Returns:

An image whose type is deduced from the input image

Exception:

N/A

Notes

Complexity

References

[Soi13]

Soille, P. (2013). Morphological image analysis: principles and applications. Springer Science & Business Media.