Any grayscale image can be considered as a topographic surface. If this surface is flooded from its minima, and the merging of waters from different sources are prevented, and the image will be partitioned into two different sets, namely the catchment basins and the watershed lines. If this transform is applied to the image gradient, the catchment basins should theoretically correspond to the homogeneous gray-level regions (segments) of this image.

However, the image gets over-segmented using this transform in practice, because of noise or local irregularities in the gradient image. To prevent over-segmentation, a pre-defined set of markers are used and the flooding of the surface starts from these markers. Hence, the following are the steps in segmentation of an image by the watershed transformation:

• Find the markers and the segmentation criterion (the function that is to be used to split the regions, often it is the contrast/gradient)
• Run a marker-controlled watershed algorithm with these two elements

Now let's use the scikit-image implementation of the morphological watershed algorithm to separate the foreground coins from the background. The first step is to find an elevation map using the sobel gradient of the image, as demonstrated in the following code block:

elevation_map = sobel(coins)
fig, axes = pylab.subplots(figsize=(10, 6))
axes.imshow(elevation_map, cmap=pylab.cm.gray, interpolation='nearest')
axes.set_title('elevation map'), axes.axis('off'), pylab.show()

Next, the markers of the background and the coins are computed, based on the extreme parts of the histogram of gray values, as demonstrated in the following code block:

markers = np.zeros_like(coins)
markers[coins < 30] = 1
markers[coins > 150] = 2
print(np.max(markers), np.min(markers))
fig, axes = pylab.subplots(figsize=(10, 6))
a = axes.imshow(markers, cmap=plt.cm.hot, interpolation='nearest')
plt.colorbar(a)
axes.set_title('markers'), axes.axis('off'), pylab.show()

The next screenshot shows the output of the earlier code block, the heatmap of the markers array:

Finally, the watershed transform is used to fill regions of the elevation map starting from the markers determined, as demonstrated in the next code block:

segmentation = morphology.watershed(elevation_map, markers)
fig, axes = pylab.subplots(figsize=(10, 6))
axes.imshow(segmentation, cmap=pylab.cm.gray, interpolation='nearest')
axes.set_title('segmentation'), axes.axis('off'), pylab.show()

The following image shows the output of the code block, the resulting segmented binary image using the morphological watershed algorithm:

This last method works even better, and the coins can be segmented and labeled individually, as shown in the following code block:

segmentation = ndi.binary_fill_holes(segmentation - 1)
labeled_coins, _ = ndi.label(segmentation)
image_label_overlay = label2rgb(labeled_coins, image=coins)
fig, axes = pylab.subplots(1, 2, figsize=(20, 6), sharey=True)
axes[0].imshow(coins, cmap=pylab.cm.gray, interpolation='nearest')
axes[0].contour(segmentation, [0.5], linewidths=1.2, colors='y')
axes[1].imshow(image_label_overlay, interpolation='nearest')
for a in axes:
 a.axis('off')
pylab.tight_layout(), pylab.show()

The next screenshot shows the output of this code block, the segmented coins with the watershed lines (contours), and the labeled coins, respectively: