[Atomic-S (OP)]

If a photograph is printed by a digital printer (e.g., inkjet), and if that printer works by placing, or not placing, a huge number of ink dots on paper, then is it possible in principle to recover an exact duplicate of the original file by scanning all those dots?

[Don_1]

No. There will always be a loss of picture quality regardless of the scanners capability.

[BenV]

What if the printer was of a higher resolution than the original image?

[Don_1]

Image quality would still be lost. It may not be discernable but any copy from an original photo will loose quality. If you copied the copy enough times, or attempted to enlarge the copy, you would be able to see the difference with the naked eye.

[lyner]

In principle you are right about regenerating a digital photo perfectly. (The digital version, that is).
But, firstly, you have to realise that the digital version has already been degraded due to sampling and quantisation.

Modern printers don't have "a dot or no dot". They have variable sized dots (digital values of size, of course). But let's ignore that problem. Take a simple black ink printer with simple dots which are arranged to have varying density for the greyscale.
If the dots are small enough to be able to identify each dot and the 'noise', in the form of fibres and muck on the paper, is small enough not to upset this then you could reconstruct the  original (digital) picture perfectly.
After all, this just comes down to a wacky method for recording digital signals.
You need to scan the picture with high enough resolution and reasonable quantisation so that you can actually identify the dot profiles. This gives you a chance to apply filtering (of the spacial kind) to recover as much information as possible about what was laid onto the paper.
The system for printing, of course, is not aimed at making the picture recoverable in this way but is aimed at making it 'look right'. For a start, they try to put the dots in patterns which your eye can't spot. They overlap the dots a lot to give you good dark greys and blacks. Basically, you don't want any gaps between dots for solid black. This means that the process would be very hard, if not impossible, in practice.
It also depends, ultimately, on the signal to noise ratio of the 'recorded' information. Given low enough noise, you can dig any signal out of what you can see.

[techmind]

What if the printer was of a higher resolution than the original image?

You also need to consider the tonal (eg greyscale) printing and scanning capabilites. The printer and/or scanner will often push near-blacks to black, so you loose detail/features in the shadows, similarly you may loose detail in the highlights.

Another consideration is that printers often use "halftoning" so you need an actual printer resolution many times higher than the basic file-resolution (pixel count) might lead you to believe. If you get proper photographic prints (of digital files) made in an in-store photolab, then they often use a continuous-tone process so each 300dpi pixel can reproduce the full range of red/green/blue or cmy without any halftoning.


As another poster said, no image (that isn't already quantised according to known rules) can be copied without some degree of degradation. The better the equipment and the more skilled the operator, the less degradation there will be - but there will always be some.

[lyner]

We're somewhere between Shannon and 'no chance at all', with this question.
Pictures aren't printed with reconstruction in mind so they will be hard / impossible to reconstruct.
But you could arrange a 'compatible' printing system which would look ok but not optimum and yet be 'machine readable' back to it's original. Why you'd want to is another matter.

[LeeE]

If you knew all the characteristics of the printer you would be able to come very close to reproducing the original data from which the picture was printed.  Of course, this does depend upon the resolution of the print being sufficient to cope with the resolution of the original data.

[Atomic-S (OP)]

Why you'd want to is another matter.

Such an image would be excellent for serious archival purposes, because even if its colors degraded some over many years, as long as they were discrete, the picture could be fully restored. Furthermore, such a picture, being in a very basic format, would not quickly become obsolete.

[lyner]

But it wouldn't achieve either job very well. You'd be best to store the data efficiently and print a picture to look nice.

[Don_1]

For archival purposes I doubt that loss of resolution would be a problem. The problem would be in the reprinting, if it were required.

If you do not have the original capture data (i.e. the downloaded information from the camera or camera's data card) or if the image predates digital capture, then you would need the largest possible print from the original data capture (or celluloid negative/transparency) and a very high quality scanner. In the case of a print, you would need a scanner of 1200dpi or higher and in the case of a transparency 2400dpi or higher.

The resulting digital image could then be enhanced using a programme such as Adobe Photoshop™. This will allow you to adjust the noise, contrast, colour saturation and white balance. But there will still be a loss of resolution.

Can I just add, that if you are intending on archiving photos which I presume are not your own, there could be an issue with copyright if you intend to use this archive for commercial purposes. The owner of the copyright, usually the photographer or photo library, would be legally entitled to royalties for any such commercial venture and even for some private use.

[lyner]

I assumed we were talking of archiving digital pictures. This could include scans of analog pictures at an appropriately chosen resolution and quality.