Newsgroups: sci.image.processing
Path: cantaloupe.srv.cs.cmu.edu!europa.chnt.gtegsc.com!howland.reston.ans.net!Germany.EU.net!Munich.Germany.EU.net!eso.org!news
From: ndevilla@eso.org (Nicolas Devillard)
Subject: Re : Resolution
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Message-ID: <1995Jun26.140757.8933@eso.org>
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Organization: ESO - European Southern Observatory, Garching by Munich
Date: Mon, 26 Jun 1995 14:07:57 GMT
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Ron Tomlin (RKTR49A@prodigy.com) wrote:
: Is there away to take a image, say from a frame grabber and zoom in 
: without losing the resolution ?

Perry West answer was :

> Once an image has been digitized in a frame grabber, there is a finite 
> amount of information present in the digitized image.  In this sense, 
> we are equating resolution with information content.  No amount of 
> additional processing can add information not present.
>  That is, you can add useful resolution.  Zooming with interpolation may make the
> image better for viewing for some purposes, but it does not add information.

This I will moderate by sending you back to information theory and Shannon theorem. If a signal has a maximum frequency of Fc, and is sampled with frequency Fe > 2.Fc (Shannon condition or sampling theorem), the WHOLE signal can be ideally reconstructed from its samples (NO LOSS of information at all). According to this, in good conditions, you could increase your resolution till an upper limit of Fc. But this is mathematically ideal, thus not so true in reality :


1. First of all, the sampling frequency of an image is limited by the pixels size in the captor. No matter your processing, you will never go further this limit. This means that details above this limit will not be resolved. The condition Fe > 2.Fc is not respected. You rather have Fc = Fe/2, that is : the maximum spatial frequency you can resolve depends on your captor cut-off frequency.

2. The captors do not really sample, they are blocker-samplers, they integrate the intensity on a surface. This means the signal spectrum undergoes a non-harmless transformation.

3. Even if the Shannon condition is respected (i.e. you take picture of low-frequency objects), the reconstruction of the signal must be undertaken by an ideal filter, which needs an infinity of samples. This leads to aliasing and Gibbs phenomena.

But :

Provided your image has not so high frequencies,
Provided your take into account the integration on your captor,
Provided you use the best interpolation kernels, and prove the ringing in the image domain is limited to an epsilon strictly inferior to your quantization step,

You could reconstruct any higher resolution image than your original.

This seems like getting out information of nowhere, but as information theory has not been disproved, it works well !

Let's take an example :
If you magnify low-frequency images (big uniform patterns, with slow transitions from one gray level to another), pixels are not getting out of nowhere, they rather reflect the frequency distribution in the image, and thus are full part of the signal.

If you magnify a highly detailed picture, for example a car seen from a 100 meters far with a standard CCD camera, you will not be able to reconstruct the license plate number because its frequency was above the cut-off frequency of your detector, and thus escapes the Shannon condition.

In other words : the higher your bandwidth, the higher the quality of the reconstructed signal. The same theorem applies on loudspeakers or CD players... or anything that undergoes sampling.

Once more, for more detailed information, have a look on Shannon theory or more precisely in the image domain, 'Digital Image Warping' as I quotated in the previous answer.

Hope it reminded you of something,
Friendly,
Nicolas Devillard


