German tank variant: estimate resolution of camera given cropped photo sizes

Make whatever assumptions you like, but I like the flavor of nonparametric techniques.

I have a list of the $x_i$ by $y_i$ resolutions of a number of photos, all cropped from photos taken at the same size (by the same sensor, of course). What would be a good way to measure $a$ and $b$, the width and height of the sensor, respectively?

• Is it possible some photos may have the orientation "swapped" (taken in portrait mode on something that has a landscape orientation)? If not, it seems pretty simple -- the width must be at least as wide as the widest observed image, similarly for height. If we can make some reasonable guesses about the ratio of longest side to shortest side in the original resolution (the aspect ratios seem to belong to a fairly limited range - indeed to a fairly limited set of values), then we can incorporate that information. ... (ctd) – Glen_b May 25 '15 at 5:57
• (ctd) ... Do we also bring in the fact that actual devices tend to use a limited number of different possible pixels-per-side (e.g. 1751 probably isn't an observed number of pixels on a side)? – Glen_b May 25 '15 at 6:03
• @Glen_b: yes to both. – Simon Kuang May 25 '15 at 6:49
• With external information of that kind (like prior probabilities across a distribution of possible heights and widths in pixels). I'd be inclined to take a Bayesian approach. – Glen_b May 25 '15 at 7:31