skimage2.morphology.max_tree

skimage2.morphology.max_tree(image, connectivity=1)

Build the max tree from an image.

Component trees represent the hierarchical structure of the connected components resulting from sequential thresholding operations applied to an image. A connected component at one level is parent of a component at a higher level if the latter is included in the first. A max-tree is an efficient representation of a component tree. A connected component at one level is represented by one reference pixel at this level, which is parent to all other pixels at that level and to the reference pixel at the level above. The max-tree is the basis for many morphological operators, namely connected operators.

Parameters:

imagendarray

The input image for which the max-tree is to be calculated. This image can be of any type.

connectivityunsigned int, optional

The neighborhood connectivity. The integer represents the maximum number of orthogonal steps to reach a neighbor. In 2D, it is 1 for a 4-neighborhood and 2 for a 8-neighborhood. Default value is 1.

Returns:

parentndarray, int64

Array of same shape as image. The value of each pixel is the index of its parent in the ravelled array.

tree_traverser1D array, int64

The ordered pixel indices (referring to the ravelled array). The pixels are ordered such that every pixel is preceded by its parent (except for the root which has no parent).

References

[1]

Salembier, P., Oliveras, A., & Garrido, L. (1998). Antiextensive Connected Operators for Image and Sequence Processing. IEEE Transactions on Image Processing, 7(4), 555-570. DOI:10.1109/83.663500

[2]

Berger, C., Geraud, T., Levillain, R., Widynski, N., Baillard, A., Bertin, E. (2007). Effective Component Tree Computation with Application to Pattern Recognition in Astronomical Imaging. In International Conference on Image Processing (ICIP) (pp. 41-44). DOI:10.1109/ICIP.2007.4379949

[3]

Najman, L., & Couprie, M. (2006). Building the component tree in quasi-linear time. IEEE Transactions on Image Processing, 15(11), 3531-3539. DOI:10.1109/TIP.2006.877518

[4]

Carlinet, E., & Geraud, T. (2014). A Comparative Review of Component Tree Computation Algorithms. IEEE Transactions on Image Processing, 23(9), 3885-3895. DOI:10.1109/TIP.2014.2336551

Examples

We create a small sample image (Figure 1 from [4]) and build the max-tree.

>>> image = np.array([[15, 13, 16], [12, 12, 10], [16, 12, 14]])
>>> P, S = max_tree(image, connectivity=2)