Following a brief discussion on Gitter, I've decided to open an issue here but I'm not 100% sure if this is a bug or intended behavior. The following script compares the usage of origin and extent when the limits are fixed to the same intervals and same axis direction:

import numpy as np
import matplotlib.pyplot as plt

image = np.arange(100).reshape((10, 10))

subplot = 0

fig = plt.figure(figsize=(8, 8))

for extent in [None, [1, 9, 1, 9]]:
    for origin in ['lower', 'upper']:
        subplot += 1
        ax = fig.add_subplot(2, 2, subplot)
        ax.imshow(image, interpolation='nearest', origin=origin,
                  extent=extent)
        ax.set_xlim(0, 10)
        ax.set_ylim(0, 10)
        ax.set_title('extent={0} origin={1}'.format(extent, origin),
                     fontsize=8)

fig.savefig('thumbs.png')

The output is:

As you can see, when no extent is specified, the origin keyword has no impact on the result whereas it does when the extent is specified.

There is either a bug here, or something that exists for historical reasons that deserves its own documentation section.

In any case, the documentation for origin doesn't make much sense:

origin : ['upper' | 'lower'], optional, default: None
    Place the [0,0] index of the array in the upper left or lower left
    corner of the axes. If None, default to rc `image.origin`.

the concept of 'upper left' or 'lower left' is tricky since the axes can be made to go in either direction, so whether [0,0] is at the upper or lower corner visually depends on the direction of the axes.

It seems that when extent is not specified, origin simply means that the y limits are flipped but this can be reverted by setting ylim. When extent is present, the array is truly flipped vertically.

cc @tacaswell @ngoldbaum @WeatherGod