CT scanning books

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DrAltaica
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CT scanning books

Post by DrAltaica »

I just read about Matti Kariluoma and Daniel Reetz(Any one else think he look like a young Adam Savage? I guess that explains his Mythbuster avatar....) and I caught this
What can you do with a light field? The lowest hanging fruit is computational refocusing. By computational refocusing, we mean focusing the image AFTER it is captured.
while I can't find any details on how their software does the refocusing I dought it is a simple as dual tomography.

I guess no one though of combining dual photography and Tomography are too obscure for anyone to put them together before?
spamsickle
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Re: CT scanning books

Post by spamsickle »

Is "I dought it is as simple as dual tomography" supposed to mean you doubt it is as simple, or you thought it is as simple?

Are you using software to do dual tomography?

I would think dual photography would have its own set of problems, chiefly matching a point on one image with the same point on another image. This is hard enough when the images are in focus (or so I've heard from those who are extracting depth information from stereo photographs). I'd think it would be even harder if the images were unfocused.

Edited to add: Never mind, I looked at your "dual photography" link, and it's something other than stereo photography, though they're probably related.
spamsickle
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Re: CT scanning books

Post by spamsickle »

Having followed all the links here, and checked out Daniel and Matti's work with the dozen camera array, I'm kind of confused.

The refocusing they do seems similar to the "dual photography" described in the Siggraph paper, but I'm not sure how either relates to book scanning. With your use of the term "tomography" are you proposing to scan a book without opening it? Because I don't think either D&M's work or the dual photography method would work without illuminating all the pages being scanned, and you can't really shine a light through the cover. Maybe a REALLY BRIGHT LIGHT...

Apologies in advance if I've misunderstood, but could you clarify?
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rob
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Re: CT scanning books

Post by rob »

Computational refocusing consists of taking many images at slightly different positions, and then computing a focus for those images. This is exactly the same principle that drives phased array radar, phased array speakers, phased array microphones, very long baseline interferometry, very long baseline arrays, etc.

The concept behind all of these applications is to take a large number of small elements, and computationally combine the outputs of those elements into a single output. Most often the computation involves detecting the phase difference of the signal in each element with respect to that of the neighboring elements, and using that information to construct or synthesize a result. You can computationally change the direction of each element by changing the calculations done on the phase difference -- this is called beamforming, which means computationally "forming" a beam from your phased array to the target or source.

It isn't quite tomography. Tomography involves taking multiple images through slices of an object at different angles, and then computing the structure of the sliced object. There is no beamforming involved here, and there is no changing of the calculations. The object is to get an accurate representation of the object by scanning through it: the tomographic device is both the source and the detector of the signal.

And yes, I studied the equations behind beamforming and tomography when I got my EE degree, and no, I've forgotten all the details :)
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spamsickle
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Re: CT scanning books

Post by spamsickle »

What kind of phase information can you get from a pixel? I kind of understand using a Fourier transform to go from 2D space to frequency, but as far as I know that doesn't provide any phase information either. This whole area of study is new to me.
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Re: CT scanning books

Post by rob »

Well, it's the phase difference that is important, and specifically the phase difference of the same image pixel in different images. This means the position of that pixel, so effectively you have to match the images up and then determine the difference in position in each matching pixel. I haven't done any imaging phased arrays, so I think at this point Daniel would have to step in. :)
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Re: CT scanning books

Post by daniel_reetz »

Rob's dead on, but this is a slightly different treatment.

Imagine you are standing in a field. Out in the field is a post. You know this because you can see it.

If you walk to the left, from your original position, and face the post again, you can still see it.

If you walk to the right, from your original position, and face the post again, again it is visible.

The obvious implication is that there was a ray of light going in one direction that hit you in the center, a ray of light that goes in another direction that you saw from the left, and another ray, from the right. By carefully choosing which rays (ie pixels) from each camera, you can reconstruct novel images using whichever rays you like. You know which rays you are choosing by the distance between the points of capture. The "light field" is another way of saying "a big bundle of rays with an X-Y position and a direction".

Matti and I did this in the crudest and fastest way we could, just to get up to speed. A lot of other people have it covered better, and some people have built much smaller, more sophisticated cameras. I particularly recommend the tutorial materials from Todor Georgiev.
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Re: CT scanning books

Post by daniel_reetz »

BTW, I desperately wish I'd done EE instead of Art. I am trying so hard to catch up with the math, and I find it very difficult.
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Re: CT scanning books

Post by StevePoling »

daniel_reetz wrote:BTW, I desperately wish I'd done EE instead of Art. I am trying so hard to catch up with the math, and I find it very difficult.
Don't feel too bad, even Feynman had to struggle from time to time with the math. Maybe I'm just ignorant, but I get the impression the math behind this light field stuff is pretty gnarly. 2nd year calc was cool, and i got the broad concepts, but the details kicked my butt. I liked vector analysis, but it didn't like me.

Single element antenna design requires solutions of partial differential equations, but phased-arrays just seemed like totally black magic. It looks like the light field work is that same sort of thing. Maybe it's easier b/c you're doing convolutions and fourier transforms and stuff. If so, the game works like this: you've got something intractible, you do a transform to some linear domain you can understand, do something there, then reverse-transform back to where it's gnarly. I'll ask my daughter what if she knows enough about tomography to explain it to me again.
wels
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Re: CT scanning books

Post by wels »

rob wrote:Well, it's the phase difference that is important, and specifically the phase difference of the same image pixel in different images. This means the position of that pixel, so effectively you have to match the images up and then determine the difference in position in each matching pixel. I haven't done any imaging phased arrays, so I think at this point Daniel would have to step in. :)
if I remember correctly, this is also used for subpixel registration of (two?) images (determining a subpixel-shift in x- and y-direction) ...

recently, I came across the idea of superresolution which would enable me to use a couple of cheap and low-res cameras to compute a higher resolution image from it ... (not to mention additional spatial information provided ...) but that's another topic/story, probably
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