Waterfall

Include <mln/morpho/waterfall.hpp>

template<typename I, typename N> auto waterfall(I ima, N nbh)

Implementation of the Waterfall algorithm [B94] described in [M15]. The Waterfall is an iterative process starting from a watershed segmentation and removing the watershed lines surrounded by watershed lines whose gradient is bigger. The resulting of the last iteration is the complete image domain.

Parameters:

ima – The input image
nbh – The neighborhood relationship considered to build the watershed segmentation

Returns:

A pair (tree, node_map) where tree is the hierarchical representation of the Waterfall and node_map is a mapping from a point of the image to a node of the tree. This node map is usually the initial watershed segmentation.

References

[B94]

Beucher, S. (1994). Watershed, hierarchical segmentation and waterfall algorithm. In Mathematical morphology and its applications to image processing (pp. 69-76). Springer, Dordrecht.

[M15]

Meyer, F. (2015, May). The waterfall hierarchy on weighted graphs. In International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing (pp. 325-336). Springer, Cham.

Example

// (1) Get an image
mln::image2d<std::uint8_t> input = ...;

// (2) Compute the gradient (here using the morphological gradient)
auto grad = mln::morpho::gradient(input, mln::se::disc(3));

// (3) Compute the waterfall hierarchy
auto [t, nodemap] = mln::morpho::waterfall(grad, mln::c8);

// (4) Compute the cut at level 4
t.horizontal_cut(4, nodemap);


Original image	Watershed segmentation on the gradient of the original image	Waterfall horizontal cut at level 4

template<typename I, typename S, typename N> auto waterfall_from_markers(I ima, S seeds, N nbh)

Implementation of the waterfall from user defined markers (instead of local minima in the previous implementation).

Parameters:

ima – The input image
seeds – Image of markers
nbh – The neighborhood relationship considered to build the watershed segmentation

Returns:

A pair (tree, node_map) where tree is the hierarchical representation of the Waterfall and node_map is a mapping from a point of the image to a node of the tree. This node map is usually the initial watershed segmentation.

// (1) Get an image
mln::image2d<std::uint8_t> input = ...;

// (2) Get the image of markers
mln::image2d<std::uint8_t> markers = ...;

// (3) Compute the gradient (here using the morphological gradient)
auto grad = mln::morpho::gradient(input, mln::se::disc(3));

// (4) Compute the waterfall hierarchy
auto [t, nodemap] = mln::morpho::waterfall_from_markers(grad, markers, mln::c8);

// (5) Compute the cut at level 4
t.horizontal_cut(4, nodemap);


Original image	Markers image

Watershed from markers	Waterfall horizontal cut at level 1