How to connect the points from a contour of a binary image - python-3.x

Question

I have a segmentation result stored in a binary image, from which i want to extract the contours. To do so, I compute the difference between the mask and the eroded mask. Hence, I am able to extract the pixels that are on the boundaries of my segmentation result. Here is a code snippet:
import numpy as np
from skimage.morphology import binary_erosion
from matplotlib import pyplot as plt
# mask is a 2D boolean np.array containing the segmentation result
contour_raw=np.logical_xor(mask,binary_erosion(mask))
contour_y,contour_x=np.where(contour_raw)
fig=plt.figure()
plt.imshow(mask)
plt.plot(contour_x,contour_y,'.r')
I end up with a collection of dots on the contours of the mask:
The troubles starts when I want to connect the dots. Doing a naive plot of the contours results of course in a disappointing results, because contour_x and contour_y are not sorted as I would like:
plt.plot(contour_x,contour_y,'--r')
And here is the result, with a focus on an arbitrary part of the figure to highlight the connection between the dots:
How is it possible to sort the contours coordinates contour_x and contour_y so that they are correctly ordered when I connect the dot? Furthermore, if my mask contains several independent connected component, I would like to obtain as many contours as there are connected components.
Thanks for your help!
Best,

Answer 1

I think combining a clustering and convex hull works in your case. For this example, I am generating three synthetic segments using make_blobs function and demonstrating each with a color:
import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import make_blobs
from sklearn.cluster import DBSCAN
from scipy.spatial import ConvexHull, convex_hull_plot_2d
X, y = make_blobs(n_samples=1000, centers=3, n_features=2, random_state=0, cluster_std=0.3)
plt.scatter(X[:,0], X[:,1], c=y)
Then, since segments are distributed in a two dimensional map, we can run density based clustering method to cluster them, and then by finding a convex hull around each cluster, we can find points surrounding those clusters coming with order:
# Fitting Clustering
c_alg = DBSCAN()
c_alg.fit(X)
labels = c_alg.labels_
for i in range(0, max(labels)+1):
ind = np.where(labels == i)
segment = X[ind, :][0]
hull = ConvexHull(segment)
plt.plot(segment[:, 0], segment[:, 1], 'o')
for simplex in hull.simplices:
plt.plot(segment[simplex, 0], segment[simplex, 1], 'k-')
However in your case Concave Hull should work not Convex Hull. There is a package alphashape in python that claimed to find Concave hulls in two-dimensional maps. More information here. The tricky part is to find the best alpha, but in this example, we can fit concave hulls using:
import alphashape
from descartes import PolygonPatch
fig, ax = plt.subplots()
for i in range(0, max(labels)+1):
ind = np.where(labels == i)
points = X[ind, :][0,:,:]
alpha_shape = alphashape.alphashape(points,5.0)
ax.scatter(*zip(*points))
ax.add_patch(PolygonPatch(alpha_shape, alpha=0.5))
plt.show()