Multivariate Component Tree

The component trees have been extended for multivariate images [Car19]. Right now, only the multivariate tree of shapes [Car15] (MToS) has been implemented in Pylene.

  • Include <mln/morpho/mtos.hpp>

auto mtos(image2d<rgb8> ima, point2d pstart);

Compute the multivariate tree of shapes and returns a pair (tree, node_map). See Component Trees (Overview) for more information about the representation of tree.

Parameters:

  • ima – The input image in RGB format.

  • pstart – The rooting point

Returns:

A tree of type component_tree<void> (no values are related to the nodes of the tree since they do not have a natural value) and a map from image point to node tree.

Notes

  • Before computing the MToS, the user should add a border to the image, with the values of this border set to the median value of the border of the original image.

  • The resulting nodemap has a domain size of 4d - 3 with d the input image domain.

  • The MToS not having values related to the nodes, the user has to compute a value for each node, such as the mean of each node (as shown below in example with the mean_node_accu accumulator).

Example

This example computes a grain filter, which removes all the node having an area inferior to 100.

#include <mln/accu/accumulators/count.hpp>
#include <mln/core/extension/padding.hpp>
#include <mln/core/image/ndimage.hpp>
#include <mln/morpho/mtos.hpp>
#include <mln/io/imread.hpp>

// Function to reduce the nodemap to the original image domain
mln::image2d<int> reduce_nodemap(mln::image2d<int> n);

// Function to get the median of the border values
mln::rgb8 get_median_on_border(mln::image2d<mln::rgb8> ima);

int main(void)
{
    mln::image2d<mln::rgb8> ima;
    mln::io::imread("lena.ppm", ima);

    // Adding a border
    const auto median = get_median_on_border(ima);
    ima.inflate_domain(1);
    constexpr int borders[2][2] = {{1, 1}, {1, 1}};
    mln::pad(ima, mln::PAD_CONSTANT, borders, median);

    // Compute the MToS
    auto [t, nm] = mln::morpho::mtos(to_process, {-1, -1}); // The rooting point is in the added border

    // Reduce the nodemap
    nm = reduce_nodemap(nm);

    // Remove the border
    ima.inflate_domain(-1);
    nm.inflate_domain(-1);

    // Compute the area of each node of the tree
    auto area = t.compute_attribute_on_points(nm, mln::accu::accumulators::count<int>());

    // Perform a grain filter on the tree
    t.filter(mln::morpho::CT_FILTER_DIRECT, nm, [&area](int n) { return area[n] >= 100; });

    // Compute the mean of the connected component of each nodes
    auto mean = t.compute_attribute_on_values(nm, ima, mln::accu::features::mean<>(), false);

    // Reconstruct the tree
    auto rec = t.reconstruct_from(nm, ranges::make_span(mean.data(), mean.size()));

    return 0;
}
../_images/depth_map.png ../_images/mtos_rec.png

The depth map resulting of the fusion of the trees (see [Car15] for more details)

The reconstructed image from the filtered tree

References

[Car19]

Edwin Carlinet and Thierry Géraud (2019). Introducing Multivariate Connected Openings and Closings. International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing. Springer, Cham. 215-227

[Car15] (1,2)

Edwin Carlinet and Thierry Géraud (2015). MToS: A tree of shapes for multivariate images. IEEE Transactions on Image Processing 24.12 5330-5342