Overlay contour plot on imshow

I am having trouble producing an overlay with contour plot and imshow.

import numpy as np
import matplotlib.pyplot as plt

%matplotlib inline

def f(x, y):
    return (1 - x / 2 + x ** 5 + y ** 3 ) * np.exp(-x ** 2 - y ** 2)

n = 100
x = np.linspace(-3, 3, 3 * n)
y = np.linspace(-3, 3, 3 * n)
X, Y = np.meshgrid(x, y)
Z = f(X, Y)
plt.figure(figsize=(8,6))
plt.imshow(Z, interpolation='nearest', cmap=plt.cm.hot, origin='lower')
contours = plt.contour(X, Y, f(X,Y), 10, colors='black')
plt.clabel(contours, inline=1, fontsize=10)
plt.xticks([])
plt.yticks([])
plt.savefig('overlay_image.pdf', dpi=72)
plt.show()

The resulting picture has the contour plot forced into the bottom left hand corner:

How is it possible to get a contour overlay on top of the image?

You need to set the extent of the imshow, so that the coordinates line up with those used in the contour plot.

From the imshow docs:

extent : floats (left, right, bottom, top), optional

The bounding box in data coordinates that the image will fill. The image is stretched individually along x and y to fill the box.

So you could use:

extent = x.min(), x.max(), y.min(), y.max()
plt.imshow(Z, interpolation='nearest', 
           cmap=plt.cm.hot, origin='lower',
           extent=extent)