Eroded Otsu-labeling

This operation segments and labels an image using blurring, Otsu-thresholding, binary erosion and masked Voronoi-labeling.

After bluring and thresholding using Otsu’s method, iterative binary erosion is applied. Objects in the eroded image are labeled using connected component labeling and these labels are dilated to fit again into the initial binary image using masked-Voronoi labeling.

This function is similar to voronoi_otsu_labeling. It is intended to deal better in cases where labels of objects swapping into each other if objects are dense. Like when using Voronoi-Otsu-labeling, small objects may disappear when applying this operation.

This function is inspired by a similar implementation in Java by Jan Brocher (Biovoxxel) in the Biovoxxel toolbox. Big thanks Jan!

from skimage.data import cells3d
import pyclesperanto_prototype as cle
import napari_segment_blobs_and_things_with_membranes as nsbatwm

image = cells3d()
image.shape

(60, 2, 256, 256)

We just crop out a 2D slice.

nuclei = cle.asarray(image[30, 1])
nuclei

cle._ image shape (256, 256) dtype float32 size 256.0 kB min 1091.0 max 58327.0

labels = cle.eroded_otsu_labeling(nuclei, number_of_erosions=11, outline_sigma=4)
labels

cle._ image shape (256, 256) dtype uint32 size 256.0 kB min 0.0 max 17.0

Parameter: number_of_erosions

If the specified number of erosions is too small, sticky objects will be labeled together.

labels = cle.eroded_otsu_labeling(nuclei, number_of_erosions=5, outline_sigma=4)
labels

cle._ image shape (256, 256) dtype uint32 size 256.0 kB min 0.0 max 16.0

If too many erosions are configured, objects may disappear.

labels = cle.eroded_otsu_labeling(nuclei, number_of_erosions=20, outline_sigma=4)
labels

cle._ image shape (256, 256) dtype uint32 size 256.0 kB min 0.0 max 3.0

Parameter: outline_sigma

With this outline, you can control the denoising before thresholding. If this value is too low, objects may have noisy edges and holes lead to more object-splits.

labels = cle.eroded_otsu_labeling(nuclei, number_of_erosions=5, outline_sigma=1)
labels

cle._ image shape (256, 256) dtype uint32 size 256.0 kB min 0.0 max 37.0

If this value is too high, object outlines may be not fitting to the original objects anymore.

labels = cle.eroded_otsu_labeling(nuclei, number_of_erosions=11, outline_sigma=10)
labels

cle._ image shape (256, 256) dtype uint32 size 256.0 kB min 0.0 max 11.0