Is ProPhoto RGB with gamma 1.8 optimized for color reproduction?

[jc1]

Hi all,
 
Any idea why gamma 1.8 was chosen and not 1.0 or 2.2 for ProPhoto RGB? Or was there any historical reason for that?
 
I am wondering if ProPhoto RGB Color Space is optimized with Gamma 1.8 for color reproduction when converting to a smaller color space such as Adobe RGB or sRGB?
 
Thanks
 
jc

[madmanchan]

The shape of the encoding curve should have no impact on color reproduction capabilities when converting to another space, as long as you have enough precision in your calculations. You can try this for yourself by defining custom ProPhoto-based color spaces in Photoshop (using whatever gamma values you want, including 1.0 and 2.2).

You don't often see linear encodings preferred for file formats (like jpegs) because of the limited bit depth (usually 8-bit). That would result in quantization problems in the shadows.

[digitaldog]

Dug this up from Chris Murphy on the CS list:

> Anyone know the rational why Kodak used the same working space gamma?

ROMM (ProPhoto) has an 8bpc and 16bpc implementation, and with the 
limited precision offered with 8bpc with such a huge space,  going 
from XYZ to RGB back to XYZ could produce significant errors in 
blacks. The steeper the TRC (tone response curve), the bigger the 
reversal error. So a TRC defined with gamma 1.8 was chose, largely 
for reversibility. It's a useful characteristic because, of course, 
we convert captures into that space for editing and then we convert 
them out of the space for output.

[jc1]

Thanks for the input.
 
I agree that gamma encoding would reduce the error due to quantization, especially near the shadow and highlight areas.
 
But on the hand, I think gamma encoding scheme does has certain impact on color reproduction. This effect is insignificant when converting from a smaller color space to a larger color space. However, when conversion is performed with ProPhoto to either Adobe RGB or sRGB color space, regardless of 8-bit or 16-bit precision, it does affect color reproduction to certain degree.
 
So, if color reproduction is influenced by the gamma curve, my point is, with 16-bit work flow, gamma 1.8 may not be the best choice for better color reproduction.

jc
 

[bjanes]

Dug this up from Chris Murphy on the CS list:

> Anyone know the rational why Kodak used the same working space gamma?

ROMM (ProPhoto) has an 8bpc and 16bpc implementation, and with the 
limited precision offered with 8bpc with such a huge space,  going 
from XYZ to RGB back to XYZ could produce significant errors in 
blacks. The steeper the TRC (tone response curve), the bigger the 
reversal error. So a TRC defined with gamma 1.8 was chose, largely 
for reversibility. It's a useful characteristic because, of course, 
we convert captures into that space for editing and then we convert 
them out of the space for output.

That explanation sounds reasonable. One can check the quantization error with various tone curves by using Bruce Lindbloom's companding calculator, as outlined in his write up of his BetaRGB (look at the analysis for gray scale). The ideal tone curve for limiting visible quantization errors is L*, which is uniformly perceptual.

Results using the method outlined by Bruce for Gamma 2.2, 1.8, and 1.0 are shown below. A gamma of 1.8 gives less error in the shadows at the expense of the increased error for the midtone values. Since the definition of ROMM (ProPhotoRGB) includes a linear segment for the extreme shadows in order to minimize reversibility errors, the extent of this advantage is questionable. The companding calculator shows a pure gamma function whose slope is infinite at an L* of zero.

A linear ramp (gamma 1.0) gives large quantization errors, especially in the shadows. However, as Eric points out, the quantization error is related to the precision of the encoding. With 16 bpc encoding, a linear ramp is able to encode the output of current digital sensors down to the last electron for most current sensors. With 16 bit ROMM I doubt that the 1.8 slope makes any significant difference as compared to 2.2.

Regards,

Bill

[madmanchan]

Yes, the choice of primaries affects color reproduction, and in particular the choice of gamut mapping method (when mapping from one space, like ProPhoto, to another space, like a display, or printer, or sRGB) affects color reproduction. 

But aside from quantization error, the choice of gamma encoding (1.8, 2.2, sRGB, 1.0, etc.) has no impact on the color reproduction capabilities.  In fact, conceptually the first thing that happens in an ICC-based workflow is the transformation from the RGB encoding space back to the Profile Connection Space (a.k.a., PCS, usually D50-relative XYZ or CIE L*a*b*) before conversion/mapping to the desired output space.  So the encoding is basically irrelevant as long as you can get safely back to the PCS.

[jc1]

Hi,

Thanks for the replies, messages are understood. But I would like to look at it from a different prospective.

I have to wait for some bug fix for the software utility I am currently using before further analysis can be carried out.

jc

[jc1]

Results using the method outlined by Bruce for Gamma 2.2, 1.8, and 1.0 are shown below. A gamma of 1.8 gives less error in the shadows at the expense of the increased error for the midtone values. Since the definition of ROMM (ProPhotoRGB) includes a linear segment for the extreme shadows in order to minimize reversibility errors, the extent of this advantage is questionable. The companding calculator shows a pure gamma function whose slope is infinite at an L* of zero.

Bruce' gamma optimization was based on gray axis(L=0 to 100, a=b=0), that is my understanding.
 
Due to the characteristic of an absolute color space and that ProPhoto has 2 imaginary primaries,  gray scale may not be the only limiting factor for gamma optimization. If we are interested in converting these imaginary colors back to the visible color space, then the gamma value does play an important role besides reducing quantization error.
 
Gamma affects the distribution of data points. The L values (of Lab) for the blue primary (B=0 to 255, R=G=0) are close to zero (shadow area) and that are greatly affected by the chosen gamma value. Hence, they could have been clipped to zero before they can be useful if such factor is not taken into account.

jc

[bjanes]

Gamma affects the distribution of data points. The L values (of Lab) for the blue primary (B=0 to 255, R=G=0) are close to zero (shadow area) and that are greatly affected by the chosen gamma value. Hence, they could have been clipped to zero before they can be useful if such factor is not taken into account.

I think that is why ProPhotoRGB includes a linear segment for the deep shadows.

Regards,

Bill

[madmanchan]

Yes, having a gamma encoding curve with an infinite slope at zero is not a great idea ...