15 bit color space conversion errors

In the previous post, I reported on the location of the worst errors that resulted from taking this 8-bit sRGB image:

and converting it to Adobe (1998) RGB and back many times, using double precision floating point precision for the intermediate calculations, and quantizing the result to 8 bit per color plane unsigned integers after every conversion.

In this post, I’d like to look at the error image if the post-conversion quantizing is 15 bits and 100 iterations are performed.  Here’s the error image in CIELab DeltaE, normalized so that the worst case error, 0.14 DeltaE is full scale, and with a gamma of 2.2:

Pretty dark, huh? That means that most of the errors are much less than the worst ones. Let’s lighten the image by two stops:

And zoom in on the upper left corner:

and the lower right corner:

You can see that many of the worst errors occur in the same places as they did with 8 bits per color plane. It’s a good thing they’re so much smaller.