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It was asked in an exam why a color video compress better than a black and white (grayscale) video using MPEG but can't find anything explaining it.

In other words, we would apparently get a better compression ratio when compressing color videos than when compressing BW videos.

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    $\begingroup$ What do you mean by "compress better", the final size is smaller or the ratio final size over initial size is smaller ? $\endgroup$ – François Aug 17 '15 at 13:13
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    $\begingroup$ Ratio original - compressed chanel is better. It is rather hard to compress BW video worse than color. Not meaningful video at least with this compression scheme. $\endgroup$ – Evil Aug 17 '15 at 13:42
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    $\begingroup$ Who says so, where? $\endgroup$ – Raphael Aug 17 '15 at 14:31
  • $\begingroup$ @Raphael it's from a question in an exam. Do you think the initial statement could be wrong? $\endgroup$ – Stéphane Bruckert Aug 17 '15 at 15:08
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    $\begingroup$ If the context was not given in the exam, it certainly was in the course. Please recheck your material. $\endgroup$ – Raphael Aug 18 '15 at 8:28
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Human eye is very sensitive to luminance change and order of magnitude less sensitive to chrominance change.
MPEG under the hood is based on JPEG transform, so you have 8x8 blocks of DCT.
It blurs a bit the whole block approximating it. Colour space changes to YUV or YCbCr, to encode two channels of colour and one of luminance.
Luminance (grayscale if it was colour) is not compressed as much as new created two colours. These colours are fitted more loosely than luminance.
The most heavy tricks are in colour space and luminance is preserved with lower compression (and less stages).

If you have BW frame it cannot be dealt with high compression as this faster degrades quality. MPEG was not created to deal with BW data. Origins of this codec are from times when grayscale tv was appended colour on top of existing frame.
Here I mean origins, not the same scheme as bandwidth was smaller at this time, I am referring to colour space and compression over chrominance.

MPEG popular scheme is 4:2:2 which encodes four parts of luminance (BW) and two times two colour parts. Colour is encoded as differences, because there are two channels and three colours.
So simply 50% of data is well preserved luminance and 50% are three colours with higher compression ratio. Compressed better means greater ratio of original vs processed channel.
Luminance takes (taking it simple as luminance is part of these colours) roughly equal space as colour info.

Different codecs are using different strategies, I referred to MPEG, not some new mixed schemes.

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  • $\begingroup$ I would have thought most MPEG/H264 etc videos would be 4:2:0, i.e. one Cb+Cr pair for every 2x2 pixels of Y, not 4:2:2 (which is more of a TV format which pre-dated affordable storage for line data). $\endgroup$ – Simon F Aug 17 '15 at 13:49
  • $\begingroup$ In common usage, "black and white" means greyscale, not "an image in which every pixel is either black or white". $\endgroup$ – David Richerby Aug 17 '15 at 13:50
  • $\begingroup$ H264 is not MPEG. If you specify MPEG-4 with H264 it is There are slight differences in origins of tv and codecs. Sorry for confusion as it was different over countries. Even though, H264 is using different codding scheme - entropy predicates. I tried to simply address the question not give full history of codecs and schemes. Also it is easier to give extendible example than give hard proof of approximation conpression in crossection with human perception. $\endgroup$ – Evil Aug 17 '15 at 14:09

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