Understanding NetPBM's PNM nonlinear RGB color space for converting to grayscale

Question

I am trying to understand how to properly work with the RGB values found in PNM formats in order to inevitably convert them to Grayscale.

Researching the subject, it appears that if the RGB values are nonlinear, then I would need to first convert them to a linear RGB color space, apply my weights, and then convert them back to the same nonlinear color space.

There appears to be an expected format http://netpbm.sourceforge.net/doc/ppm.html:

In the raster, the sample values are "nonlinear." They are proportional to the intensity of the ITU-R Recommendation BT.709 red, green, and blue in the pixel, adjusted by the BT.709 gamma transfer function.

So I take it these values are nonlinear, but not sRGB. I found some thread topics around ImageMagick that say they might save them as linear RGB values.

Am I correct that PNM specifies a standard, but various editors like Photoshop or GIMP may or may not follow it?

From http://netpbm.sourceforge.net/doc/pamrecolor.html

When you use this option, the input and output images are not true Netpbm images, because the Netpbm image format specifies a particular color space. Instead, you are using a variation on the format in which the sample values in the raster have different meaning. Many programs that ostensibly use Netpbm images actually use a variation with a different color space. For example, GIMP uses sRGB internally and if you have GIMP generate a Netpbm image file, it really generates a variation of the format that uses sRGB.

Else where I see this http://netpbm.sourceforge.net/doc/pgm.html:

Each gray value is a number proportional to the intensity of the pixel, adjusted by the ITU-R Recommendation BT.709 gamma transfer function. (That transfer function specifies a gamma number of 2.2 and has a linear section for small intensities). A value of zero is therefore black. A value of Maxval represents CIE D65 white and the most intense value in the image and any other image to which the image might be compared.

BT.709's range of channel values (16-240) is irrelevant to PGM.

Note that a common variation from the PGM format is to have the gray value be "linear," i.e. as specified above except without the gamma adjustment. pnmgamma takes such a PGM variant as input and produces a true PGM as output.

Most sources out there assume they are dealing with linear RGB and just apply their weights and save, possibly not preserving the luminance. I assume that any complaint renderer will assume that these RGB values are gamma compressed... thus technically displaying different grayscale "colors" than what I had specified. Is this correct? Maybe to ask it differently, does it matter? I know it is a loaded question, but if I can't really tell if it is linear or nonlinear, or how it has been compressed or expected to be compressed, will the image processing algorithms (binarization) be greatly effected if I just assume linear RGB values?

Answer 1

There may have been some confusion with my question, so I would like to answer it now that I have researched the situation much further.

To make a long story short... it appears like no one really bothers to re-encode an image's gamma when saving to PNM format. Because of that, since almost everything is sRGB, it will stay sRGB as opposed to the technically correct BT.709, as per the spec.

I reached out to Bryan Henderson of NetPBM. He held the same belief and stated that the method of gamma compression is not as import as knowing if it was applied or not and that we should always assume it is applied when working with PNM color formats.

To reaffirm the effect of that opinion in regard to image processing, please read "Color-to-Grayscale: Does the Method Matter in Image Recognition?", 2012 by Kanan and Cottrell. Basically if you calculate the Mean of the RGB values you will end up in one of three situations: Gleam, Intensity', or Intensity. After comparing the effects of different grayscale conversion formulas, taking into account when and how gamma correction was applied, he discovered that Gleam and Intensity' where the best performers. They differ only by when the gamma correction was added (Gleam has the gamma correction on the input RGB values, while Intensity' takes in linear RGB and applies gamma afterwords). Sadly you drop from 1st and 2nd place down to 8th when no gamma correction is added, aka Intensity. It's interesting to note that it was the simple Mean formula that worked the best, not one of the more popular grayscale formulas most people tout. All of that to say that if you use the Mean formula for converting PNM color to grayscale for image processing applications, you will ensure great performance since we can assume some gamma compression will have been applied. My comment about ImageMagick and linear values appears only to apply to their PGM format.

I hope that helps!

Answer 2

There is only one way good way to convert colour signal to greyscale: going to linear space and add light (and so colour intensities). In this manner you have effective light, and so you can calculate the brightness. Then you can "gamma" correct the value. This is the way light behave (linear space), and how the brightness was measured by CIE (by wavelength).

On television it is standard to build luma and then black and white images) from non-linear R,G,B. This is done because simplicity and the way analog colour television (NTSC and PAL) worked: black and white signal (for BW television) as main signal, and then adding colours (as subcarrier) to BW image. For this reason, the calculations are done in non linear space.

Video could use often such factors (on non-linear space), because it is much quick to calculate, and you can do it easily with integers (there are special matrix to use with integers).

For edge detection algorithms, it should not be important which method you are using: we have difficulty to detect edge with similar L or Y', so we do no care if computers have similar problem.

Note: our eyes are non linear on detecting light intensities, and with similar gamma as phosphors on our old televisions. For this reason using gamma corrected value is useful: it compress the information in a optimal way (or in "analog-TV" past: it reduce perceived noise).

So you if you want Y', do with non linear R',G',B'. But if you need real grey scale, you need to calculate real greyscale going to linear space. You may see differences especially on mid-greys, and on purple or yellow, where two of R,G,B are nearly the same (and as maximum value between the three).

But on photography programs, there are many different algorithms to convert RGB to greyscale: we do not see the world in greyscale, so different weight (possibly non linear) could help to make out some part of image, which it is the purpose of greyscale photos (by remove distracting colours).

Note Rec.709 never specified the gamma correction to apply (the OETF on the standard is not useful, we need EOTF, and often one is not the inverse of the other, for practical reasons). Only on a successive recommendation this missing information were finally provided. But because many people speak about Rec.709, the inverse of OETF is used as gamma, which it is incorrect.

How to detect: classical yellow sun on blue sky, choosing yellow and blue with same L. If you see sun in grey image, you are transforming with non-linear space (Y' is not equal). If you do no see the sun, you transform linearly.