image - "Standard" RGB to Grayscale Conversion

Question

I'm trying to write a converters algorithm that takes a JPEG image and returns its PGM (Portable Gray Map) version. The problem is that I can't understand how the "official" JPG->PGM convertitors work in terms of what value to assign to the final pixel (i guess, 0->255) starting from the classic RGB format.

At the beginning, I used this formula (it's the same used by OpenCV's CV_RGB2GRAY conversion):

0.30*R + 0.59*G + 0.11*B = val

I wrote a simple code to test my results: it takes a color image and its PGM version (already converted using GIMP). Then it converts the color image using the previous formula. The goal is to have a grayscale image that is pixel-to-pixel equal to the PGM input.

At this point, it does not return the same values. Can you help me?

Answer 1

The problem is that I can't understand how the "official" JPG->PGM convertitors work in terms of what value to assign to the final pixel (i guess, 0->255) starting from the classic RGB format.

There is likely a gamma adjustment in the conversion those "official" tools are using.
That is, it is not just a linear transform.

See this Wikipedia section for the details: Converting color to grayscale

I believe you want to use the formula for Csrgb.
Try it out and see if it matches the results you're expecting.

Basically, you'll do this:

1. Take R, G, B color (each in [0,1] range)
   • If they're in the range 0..255 instead, simply divide by 255.0
2. Compute Clinear = 0.2126 R + 0.7152 G + 0.0722 B
   • This is likely the linear transform you were applying before
3. Compute Csrgb according to it's formula, based on Clinear
   • This is the nonlinear gamma correction piece you were missing
   • Check out this WolframAlpha plot
   • Csrgb = 12.92 Clinear when Clinear <= 0.0031308
   • Csrgb = 1.055 Clinear1/2.4 - 0.055 when Clinear > 0.0031308