sklearn GaussianMixture on Images - scikit-learn

Question

I want to use Gaussian Mixture models to find the centers of multimodal distributions that look something like this:
To this end I want to use sklearn.mixture.GaussianMixture. This code regresses a mixture of Gaussian distributions to data. The way this is usually done like this:
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.colors import LogNorm
from sklearn import mixture
n_samples = 300
# generate random sample, two components
np.random.seed(0)
# generate spherical data centered on (20, 20)
shifted_gaussian = np.random.randn(n_samples, 2) + np.array([20, 20])
# generate zero centered stretched Gaussian data
C = np.array([[0., -0.7], [3.5, .7]])
stretched_gaussian = np.dot(np.random.randn(n_samples, 2), C)
# concatenate the two datasets into the final training set
X_train = np.vstack([shifted_gaussian, stretched_gaussian])
# fit a Gaussian Mixture Model with two components
clf = mixture.GaussianMixture(n_components=2, covariance_type='full')
clf.fit(X_train)
The point is, that the data is given as a list of 2D points that form a Gaussian cloud. My data is a little different - more like weighted x,y points. Given my image, I could do something like this:
import numpy, cv2
image = cv2.imread("double_blob.jpg")
xs, ys = np.meshgrid(list(range(image.shape[0])), list(range(image.shape[1])))
xs, ys = xs.flatten(), ys.flatten()
weights = image[xs, ys].flatten()
to get a list of x,y image coordinates and weights. But I don't know how I can feed this to the GaussianMixture function. Any ideas?

Answer 1

I have found a 'cheat' way of doing it:
from sklearn.mixture import GaussianMixture
data = cv.imread("dual_blob.jpg")
data = cv.normalize(data, None, 0, 255, cv.NORM_MINMAX)
gmm = GaussianMixture(n_components=2)
xs, ys = np.meshgrid(list(range(glint_size*2)), list(range(glint_size*2)))
xs, ys = xs.flatten(), ys.flatten()
gmm_data = [
np.array([[x, y]] * int(data[x, y])).transpose()
if int(data[x, y]) > 0
else -np.ones((2, 1))
for x, y in zip(xs, ys)
]
gmm_data = np.concatenate(gmm_data, axis=1)
gmm_data = gmm_data[gmm_data >= 0]
gmm_data = gmm_data.reshape(2, gmm_data.shape[0] // 2).transpose()
print(gmm_data)
gmm.fit(gmm_data)
centers = gmm.means_
Basically what it does is normalise the image to between 0 and 255. Then it goes over every pixel and creates as many points of that coordinate as the image value at that pixel. So if the pixel at [3, 7] has a value of 10, then [[3, 7], [3, 7],[3, 7],[3, 7],[3, 7],[3, 7],[3, 7],[3, 7],[3, 7],[3, 7]] gets added to the list of points for processing. This gives:
However this solution is so ugly. So I'm definitely keen to see if anyone has something better.