skimage2.morphology.max_tree_local_maxima#

skimage2.morphology.max_tree_local_maxima(image, connectivity=1, parent=None, tree_traverser=None)[source]#

Determine all local maxima of the image.

The local maxima are defined as connected sets of pixels with equal gray level strictly greater than the gray levels of all pixels in direct neighborhood of the set. The function labels the local maxima.

Technically, the implementation is based on the max-tree representation of an image. The function is very efficient if the max-tree representation has already been computed. Otherwise, it is preferable to use the function local_maxima.

Parameters:

imagendarray: The input image for which the maxima are to be calculated.
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.
parentndarray, int64, optional: The value of each pixel is the index of its parent in the ravelled array.
tree_traverser1D array, int64, optional: 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).

Returns:

local_maxndarray, uint64: Labeled local maxima of the image.

See also

skimage.morphology.local_maxima
skimage.morphology.max_tree

References

[1]

Vincent L., Proc. “Grayscale area openings and closings, their efficient implementation and applications”, EURASIP Workshop on Mathematical Morphology and its Applications to Signal Processing, Barcelona, Spain, pp.22-27, May 1993.

[2]

Soille, P., “Morphological Image Analysis: Principles and Applications” (Chapter 6), 2nd edition (2003), ISBN 3540429883. DOI:10.1007/978-3-662-05088-0

[3]

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

[4]

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

[5]

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 an image (quadratic function with a maximum in the center and 4 additional constant maxima.

>>> w = 10
>>> x, y = np.mgrid[0:w,0:w]
>>> f = 20 - 0.2*((x - w/2)**2 + (y-w/2)**2)
>>> f[2:4,2:4] = 40; f[2:4,7:9] = 60; f[7:9,2:4] = 80; f[7:9,7:9] = 100
>>> f = f.astype(int)

We can calculate all local maxima:

>>> maxima = max_tree_local_maxima(f)

The resulting image contains the labeled local maxima.