Find the intersection of two segmentations

When segmenting an image, you may want to combine multiple alternative segmentations. The skimage.segmentation.join_segmentations() function computes the join of two segmentations, in which a pixel is placed in the same segment if and only if it is in the same segment in both segmentations.

import numpy as np
import matplotlib.pyplot as plt

from skimage.filters import sobel
from skimage.measure import label
from skimage.segmentation import slic, join_segmentations, watershed
from skimage.color import label2rgb
from skimage import data

coins = data.coins()

# Make segmentation using edge-detection and watershed.
edges = sobel(coins)

# Identify some background and foreground pixels from the intensity values.
# These pixels are used as seeds for watershed.
markers = np.zeros_like(coins)
foreground, background = 1, 2
markers[coins < 30.0] = background
markers[coins > 150.0] = foreground

ws = watershed(edges, markers)
seg1 = label(ws == foreground)

# Make segmentation using SLIC superpixels.
seg2 = slic(
    coins,
    n_segments=117,
    max_num_iter=160,
    sigma=1,
    compactness=0.75,
    channel_axis=None,
    start_label=0,
)

# Combine the two.
segj = join_segmentations(seg1, seg2)

# Show the segmentations.
fig, axes = plt.subplots(ncols=2, nrows=2, figsize=(9, 5), sharex=True, sharey=True)
ax = axes.ravel()
ax[0].imshow(coins, cmap='gray')
ax[0].set_title('Image')

color1 = label2rgb(seg1, image=coins, bg_label=0)
ax[1].imshow(color1)
ax[1].set_title('Sobel+Watershed')

color2 = label2rgb(seg2, image=coins, image_alpha=0.5, bg_label=-1)
ax[2].imshow(color2)
ax[2].set_title('SLIC superpixels')

color3 = label2rgb(segj, image=coins, image_alpha=0.5, bg_label=-1)
ax[3].imshow(color3)
ax[3].set_title('Join')

for a in ax:
    a.axis('off')
fig.tight_layout()
plt.show()