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I love computational photography.

For a better understanding of how this works, watch the video at: http://graphics.stanford.edu/papers/lfcamera/

Totally! Array cameras and coded apertures ahoy. I'm convinced that CompPhoto stuff has a lot to offer - now that we've seen the technology can work, even on a DIY level, it's time to get it in the hands of people that will actually use it. Mobile phones are a good way to do that. Glad to see Pelican going this way.
I would love to build one of these myself.

Anyone up for building a photography research lab??

I have ideas and experience. We've met IRL...
In fact, I'm even working on some of the super-low-budget stuff we talked about at FOO East.
Oh, awesome! I can't wait to hear more.
I'm curious whether this is actually going to work in practice, because the see-throughish behavior leads me to think that there's a large separation distance between the individual cameras in the experiments (perhaps the test cameras are too large to bring them, say, 0.2 mm apart) whereas this would not be the case on a tiny cellphone camera.
Yeah, that's correct. The video has almost absolutely nothing to do with the actual content.
First the picture shows a finished conventional camera module, packaged and including the focus, zoom drives, cable and connector. The concept camera apparently doesn't need any PCB or link to the camera.

The limit on cellphone cameras isn't optical it's computational - the CPU and battery power isn't there to stream more than VGA resolution movies at 60fps, so how is it going to do the image combination for this?

The computational limits are very rapidly disappearing. Check Anandtech's story on the new ARM A15 processors. We are seeing generational leaps in processing power very frequently.
The video is fascinating, but a complete fabrication in terms of actual consumer products. The plank at 2:50 is an excellent example: to see past the plank entirely, the camera array would have to be wider than the plank. Probably 6 inches or so, in that case.

We may see it, and multiple smaller lenses could indeed solve the crappy-focus problems, and still keep the resolution high. But until I see a legitimate demonstration, I highly doubt the shiny through-occlusion tracking will work as well in any product using it. Better than current cameras, certainly - it can still track depth - but nothing like their examples.

I agree, I'm not sure I can comprehend a situation in which capturing the central figure with such high visibility is worth destroying the rest of the video frame.

edit - Maybe it would be good for scientists tracking animals, however the distance they shoot from would require a very wide array of cameras.

Do you think a sports franchise would be interested in being able to show slow motion "see-through" shots? How about tracking people in a crowd especially when you can pick which person after the fact, there might be some government somewhere that might care to do that on every street corner.

Or much more simple and $$$. Track every people in CVS so you can figure out which one stole the razor blades.

So, a lens is a mechanism for doing a significant amount of computation. All this does is move some of that computation from optics to software.

If you take out some of the optics from a real lens you get a blurry image too. That doesn't mean the remaining lenses aren't doing something useful -- or that the output is bad. It just needs further processing.

Post-processing, you end up with interesting images.

More examples: http://www.refocusimaging.com/gallery/

I'd be interested in what this kind of array could do if it could be used to take cinema-quality video with your examples level of post-processing.
I was confused about that as well. It feels as though Engadget just found a video of something superficially similar and tagged it on, because it seems irrelevant to the technology they're describing.
Does this have any connection to the multi-lensed eyes of insects?
No,with insects, every lens on their eyes is like a single pixel, and looking in a different direction - this combines multiple images and they're looking in the same direction.