[Python] How to efficiently retrieve xy-coordinates from image

I have an image img with 1000 rows and columns each.
Now I would like to consider each pixel as x- and y-coordinates and extract the respective value.

An illustrated example of what I want to achieve:



In theory, the code snippet below should work. But it is super slow (I stopped the execution after some time).

img = np.random.rand(1000,1000)
xy = np.array([(x, y) for x in range(img.shape[1]) for y in range(img.shape[0])])
xy = np.c_[xy, np.zeros(xy.shape[0])]
for i in range(img.shape[0]):
for j in range(img.shape[1]):
xy[np.logical_and(xy[:,1] == i, xy[:,0] == j),2] = img[i,j]


Is there a faster way (e.g. some numpy magic) to go from one table to the other?

Thanks in advance!

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