Hi!

On 1/12/06, M. Adam Davis <stienman@gmail.com> wrote:
>
> How the camera captures the image is relevant, but your explanation
> does not prove that one could not obtain sub-pixel resolution from
> multiple shots of the same subject.
>
> I don't see a reason why it's not possible.

Well, the problem really is much more complex, and related to filtering.

First, an example. You take a photo of a pattern of white vertical lines
on a black background, and each pixel takes exactly 1 line and the
background surrounding it. You see each pixel with the same value (at
half the brightness of the line). If you move the camera to the side,
always you get 1 line per pixel (with some line entering from the left as
another leaves at the right), so you always obtain the same image.
How can you reconstruct the original pattern?

Into the details, you can describe the process like:

* The original image ("infinite resolution") goes through the lenses system.
  The lens actually low-pass filters the image, convolutioning the image
  with the diffraction spot of the lens.
* Then, the image is sampled by the sensor, using rectangular pixels.
  This applies another filter to the image (convolution with a box filter),
  and then aliases the remaining high frequencies to the lower bands.

Now, the aliasing effect can be reduced taking new images (of the
*same* data) with the sensor at another (fractional-pixel) position.

An then you can equalize the new image using an optimal inverse
filter.

Problem is, there are *some* frequencies that are highly attenuated
by the filters (even some that are zeroed), so you can not restore the
original information.

To solve this problem, you can move the camera perpendicular to the
image, so the sampling frequency changes. But the reconstruction
process can be *very* difficult, and this can only be done if the image
is very far away, so moving the camera don't change the scene imaged.

    Daniel.

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