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There is already a succesful question How did they color old black and white movies? on this site. Very general and correspondingly in general answered. Let me please narrow it down to just the photograpy (i.e. no time dimension) and more specified starting point:

What is the algorithm to color the greyscale HD picture given the colors at various points on greyscale original?

Note: Yes, I am aware that the original colors can't be restored any more.

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  • $\begingroup$ Welcome to DSP.SE! Doesn't that question and its answer tell you that already? ... by using vector masks to indicate regions of uniform color on a few keyframes, and interpolating between them. Then a color transform is applied to each mask. And then the last paragraph on automating the process. $\endgroup$
    – Peter K. ♦
    Commented Dec 9, 2015 at 14:13
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    $\begingroup$ Thanks for the comment. I have read that, but I was looking for more detailed answer, if it would be possible. $\endgroup$
    – Victor Pira
    Commented Dec 9, 2015 at 14:23
  • $\begingroup$ I'll leave the question open. Let's see what answers you get (or not). $\endgroup$
    – Peter K. ♦
    Commented Dec 9, 2015 at 14:56

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This can be useful to you: Oscar Dalmau Cedeño, Mariano Rivera, Teresa Alarcón: Bayesian Scheme for Interactive Colourization, Recolourization and Image/Video Editing. Comput. Graph. Forum 29(8): 2372-2386, 2010. ISSN: 0167-7055

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This is one of the most important papers in this area: Colorization using Optimization.

You may found additional information with code here

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