Colourized Film

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I'm wondering whether the colours in this sort of film footage are accurate or not. I would have thought that with the sort of advanced computer-aided technology that exists in the modern era, old black and white film can be analysed in such a way that the various shades of grey might be accurately assigned to their correct original colours.

On the other hand, while researching the topic fairly recently, I was surprised to read that the colourizers simply tried to find out from other sources what colour certain items and objects were, and where such information was lacking, simply employed their own judgement and imagination.

Or maybe the two methods have co-existed side by side?

The 'Digital Colorization' section of this Wikipedia article seems to suggest something closer to the latter scenario, namely that a good deal of subjective judgment is involved:

https://en.wikipedia.org/wiki/Film_colorization

Decades ago I overheard mom, dad, and neighbors of their same (depression and WWII) generation snearing at a "colorized" movie they had just seen on TV...colorized from a nineteen Forties black and white original. Lamenting how the street mail boxes were the wrong color. They were actually kelly green, but were blue in the movie. So yes...the folks who do colorization often dont get things right if it was from before their time.

AFAIK there's no way of telling what the original colours were from the tones in a black and white picture. I don't think the information is there, just as stereo information isn't there in a mono sound recording. So the information has to come from elsewhere.

I was very impressed with the colourisations they did on some of the Laurel & Hardy shorts. I gather they went to great lengths to make sure the colours the chose were authentic.

Yes, the principle of this technique is similar to that of Hand Coloring. It is common for orange to be confused with yellow and blue with purple.

A red dress in an old movie might be black in a black and white movie. I remember early colorization where it was easy to tell. Some frames, where there is a fade from one scene to another can be especially hard to get right. When Disney was still hand drawing every frame there was a job called “in-betweener”. A main artist would draw something like every 20th frame defining the look and action of a character another artist was employed to draw the frames “in-between” to make the illusion of movement fluid.
Now there are computer programs that do the in-betweener’s job.
In a similar way, a frame of old black and white film can be hand colored and a computer can figure out how to color neighboring frames based on that. Also the color used to be added on top of the existing grey levels but now a color can be used to replace a grey on a piece of clothing or face, etc.

There are formulas, given a color level for Red, Blue, Green (RBG) and using the eye’s sensitivity to each color a grey level may be determined. Many modern color screens have tiny patches that glow red or blue or green. What we see and interpret as thousands of colors are caused by light from those three colors.

For example:
0.299 ∙ Red + 0.587 ∙ Green + 0.114 ∙ Blue

If you fool around with that formula you will see that different combinations of RGB can result in the same grey level.

To reverse the formula you would need a sure fire way to get the original RGB from grey level but if one grey level can result from two different RGB the reverse formula cannot be done reliably without some tie breaker. In some cases there may be color publicity photos to use as reference. Or newspaper reports saying “she looked stunning in her red dress”. Or the costume might still exist (but colors fade with time).

Note:
The actual relationship between grey level and RGB is even more complicated than the above formula for a number of technical reasons.

https://en.m.wikipedia.org/wiki/Grayscale