Include border when generating basin markers for watershed. (#7362)

Updated the Segment human cells in mitosis (link to stable):

- removed the very last figure, which doesn't add much value;
- added a few words about the watershed segmentation step;
- fixed the way markers are computed, so that basins touching the image border are included. You can see the difference especially if you look at the RHS vertical border of the image.

Co-authored-by: Lars Grüter <lagru+github@mailbox.org>

doc/examples/applications/plot_human_mitosis.py

@@ -21,10 +21,9 @@
 import numpy as np
 from scipy import ndimage as ndi
 
-from skimage import color, feature, filters, measure, morphology, segmentation, util
-from skimage.data import human_mitosis
+import skimage as ski
 
-image = human_mitosis()
+image = ski.data.human_mitosis()
 
 fig, ax = plt.subplots()
 ax.imshow(image, cmap='gray')
@@ -70,7 +69,7 @@
 # To separate these three different classes of pixels, we
 # resort to :ref:`sphx_glr_auto_examples_segmentation_plot_multiotsu.py`.
 
-thresholds = filters.threshold_multiotsu(image, classes=3)
+thresholds = ski.filters.threshold_multiotsu(image, classes=3)
 regions = np.digitize(image, bins=thresholds)
 
 fig, ax = plt.subplots(ncols=2, figsize=(10, 5))
@@ -90,8 +89,8 @@
 
 cells = image > thresholds[0]
 dividing = image > thresholds[1]
-labeled_cells = measure.label(cells)
-labeled_dividing = measure.label(dividing)
+labeled_cells = ski.measure.label(cells)
+labeled_dividing = ski.measure.label(dividing)
 naive_mi = labeled_dividing.max() / labeled_cells.max()
 print(naive_mi)
 
@@ -112,12 +111,12 @@
 ax[0].imshow(image)
 ax[0].set_title('Original')
 ax[0].set_axis_off()
-ax[2].imshow(cells)
-ax[2].set_title('All nuclei?')
-ax[2].set_axis_off()
 ax[1].imshow(dividing)
 ax[1].set_title('Dividing nuclei?')
 ax[1].set_axis_off()
+ax[2].imshow(cells)
+ax[2].set_title('All nuclei?')
+ax[2].set_axis_off()
 plt.show()
 
 #####################################################################
@@ -140,7 +139,9 @@
 higher_threshold = 125
 dividing = image > higher_threshold
 
-smoother_dividing = filters.rank.mean(util.img_as_ubyte(dividing), morphology.disk(4))
+smoother_dividing = ski.filters.rank.mean(
+    ski.util.img_as_ubyte(dividing), ski.morphology.disk(4)
+)
 
 binary_smoother_dividing = smoother_dividing > 20
 
@@ -152,7 +153,7 @@
 
 #####################################################################
 # We are left with
-cleaned_dividing = measure.label(binary_smoother_dividing)
+cleaned_dividing = ski.measure.label(binary_smoother_dividing)
 print(cleaned_dividing.max())
 
 #####################################################################
@@ -163,38 +164,43 @@
 # ==============
 # To separate overlapping nuclei, we resort to
 # :ref:`sphx_glr_auto_examples_segmentation_plot_watershed.py`.
-# To visualize the segmentation conveniently, we colour-code the labelled
-# regions using the `color.label2rgb` function, specifying the background
-# label with argument `bg_label=0`.
+# The idea of the algorithm is to find watershed basins as if flooded from
+# a set of `markers`. We generate these markers as the local maxima of the
+# distance function to the background. Given the typical size of the nuclei,
+# we pass ``min_distance=7`` so that local maxima and, hence, markers will lie
+# at least 7 pixels away from one another.
+# We also use ``exclude_border=False`` so that all nuclei touching the image
+# border will be included.
 
 distance = ndi.distance_transform_edt(cells)
 
-local_max_coords = feature.peak_local_max(distance, min_distance=7)
+local_max_coords = ski.feature.peak_local_max(
+    distance, min_distance=7, exclude_border=False
+)
 local_max_mask = np.zeros(distance.shape, dtype=bool)
 local_max_mask[tuple(local_max_coords.T)] = True
-markers = measure.label(local_max_mask)
+markers = ski.measure.label(local_max_mask)
 
-segmented_cells = segmentation.watershed(-distance, markers, mask=cells)
+segmented_cells = ski.segmentation.watershed(-distance, markers, mask=cells)
+
+#####################################################################
+# To visualize the segmentation conveniently, we colour-code the labelled
+# regions using the `color.label2rgb` function, specifying the background
+# label with argument `bg_label=0`.
 
 fig, ax = plt.subplots(ncols=2, figsize=(10, 5))
 ax[0].imshow(cells, cmap='gray')
 ax[0].set_title('Overlapping nuclei')
 ax[0].set_axis_off()
-ax[1].imshow(color.label2rgb(segmented_cells, bg_label=0))
+ax[1].imshow(ski.color.label2rgb(segmented_cells, bg_label=0))
 ax[1].set_title('Segmented nuclei')
 ax[1].set_axis_off()
 plt.show()
 
 #####################################################################
-# Additionally, we may use function `color.label2rgb` to overlay the original
-# image with the segmentation result, using transparency (alpha parameter).
-
-color_labels = color.label2rgb(segmented_cells, image, alpha=0.4, bg_label=0)
+# Make sure that the watershed algorithm has led to identifying more nuclei:
 
-fig, ax = plt.subplots(figsize=(5, 5))
-ax.imshow(color_labels)
-ax.set_title('Segmentation result over raw image')
-plt.show()
+assert segmented_cells.max() > labeled_cells.max()
 
 #####################################################################
 # Finally, we find a total number of