On 12/10/2011 04:30 PM, Warp wrote:

> but instead analyze the image and try to
> figure out the path that the camera took during the exposure, and then just
> "undo" that movement?

Basically, yes.

Camera shake is basically a spatial convolution. When you convolve 
something in the spatial domain, you multiply it in the frequency 
domain. In other words, some [spatial] frequencies are amplified, while 
others are attenuated. If you can figure out /exactly/ how the spectrum 
was altered, in theory you can apply the reverse alteration, and get 
back the original image. Mathematically, that's quite a simple 
operation. It's called "deconvolution".

Out here in the Real World, there are several very big problems.

1. How to figure out the exact path of the camera shake, using only the 
blurry image? Without knowing the original image [that's kind of the 
whole point], it's mathematically impossible to get the "correct" 
answer. Instead, you must apply various heuristics.

2. Some frequencies may have been attenuated so much that they get lost 
in the noise floor of the signal. If you try to amplify them back up, 
you just get signal noise. Other frequencies may have been reduced to 
zero amplitude. Now you must /guess/ what the original was. Again, 
heuristics.

3. If the image has lossy compression, the "lost" data is probably the 
exact information you need in order to unblur the image.

4. The blurring may not be uniform over the entire image. For example, 
if the camera rotates, one corner might be near the center of rotation 
and hardly blurred at all, while the opposite corner might be severely 
blurred. Now calculating the blur just had a whole lot harder. (Let's 
not even dwell on how objects at different distances from the camera 
move by different amounts if the camera's viewpoint changes.)

5. Any signal noise on top of the blurred image throws the analysis off. 
For example, if the lens has dust on it, or there was static on the CCD 
or whatever.

Fairly obviously, the worse the blur, the harder it is to unblur. More 
extreme blur basically means more frequencies have been filtered out and 
have to be amplified / guessed.

I note in passing that this technique also works for image focus as well 
as motion blur.

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