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Is it possible to conceive of a system that would use a stationary camera with a fish-eye lens to effectively provide the same images as a camera that was actually panning and tilting.

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Yes, but you pay for it in resolution. – drxzcl Apr 12 '11 at 20:47

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The results would be pretty awful. The distortion from a fish eye lens would result in images that look ridiculous compared to image stitching. Although your results of the stitched images vary based on the quality of your lens, all fisheye images I've ever seen result in vertical lines looking bowed.

http://wiki.panotools.org/Fisheyes

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Thanks @Dave. Couldn't the bowing and distortion be corrected in software? – Zippy Apr 12 '11 at 21:35
I haven't tried that, but it seems plausible that you could do some correction in software. Here's something that the google told me about: fisheyelensreview.com/defishing-software/… – Dave Apr 12 '11 at 21:58
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It is a matter of recalculating the image projection, and has been done in software, so the short answer is yes - it's possible. Whether it's worth it would require some more knowledge.

An example is using Hugin to remap fisheye images.

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It's instructive to look at the cost of pixels on camera versus the cost of lenses & motors. For some applications like robot situational awareness it's a good tradeoff. – Tim Williscroft Apr 15 '11 at 0:19

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