4 ms·

This looks very similar to what I came up for pik, consequently used as main default colorspace of JPEG XL, i.e., XYB. Also butteraugli's XYB has similar ideas

This looks very similar to what I came up for pik, consequently used as main default colorspace of JPEG XL, i.e., XYB. Also butteraugli's XYB has similar ideas, but is slightly more expensive to calculate due to the biased logarithm in the compression function (instead of cubic root), but possibly scales better for HDR (say above 200 nits). JPEG XL's XYB includes more red and less green in S-receptor modeling (for the blue-yellow axis). If I look at literature of LMS receptor spectra, it makes me wonder why there is so much green in Oklab. When I optimized similar for XYB, the optimization would favor adding slightly more red for the S than green. S component in JPEG XL XYB before non-linearity: 0.24 * R + 0.20 * G + 0.56 * B S component in Oklab before non-linearity: 0.05 * R + 0.26 * G + 0.63 * B Given the similarity of Oklab and XYB I suspect (but i'm not completely sure) that JPEG XL's format is powerful enough to model Oklab, too. Very very likely it can perfectly model the M1 matrix and the cubic root. I believe for M2 there may be some need for approximations. There JPEG XL can have local variations for M2 from chroma-from-luma fields, but likely luma needs to be slightly different from Oklab.

JyrkiAlakuijala 6y ago
Another rather substantial difference is in M2 matrix of Oklab. In my experiments I don't see S-participation in colors with high spatial frequency. Because in image compression a lot of information is in high spatial frequency, one gets favorable image compression when M2 matrix is without S contribution in Luma. We use just [b b 0, a -a 0, -0.5 * c, -0.5 * c, c] in the M2 phase in JPEG XL. The two 0s there don't bring S reception into Luma and redness-greenness observations. This difference can be because Oklab is based on XYZ which is based on 2 degree color samples. XYB is based on about 0.03 degree color samples. Perception seems to be different there -- to me it looks like S is not yet integrated into Luma experience at that resolution. In butteraugli color modeling is more complex: it is divided into high spatial frequency and low spatial frequency. S is brought only to the low spatial frequency color transforms. (Frequency separation there is by Laplacian pyramid.)
- JyrkiAlakuijala 6y ago
  One more interesting and substantial difference between Oklab and XYB is that XYB includes biases before the nonlinearity, i.e., one can consider the M1 matrix as a homogeneous matrix. These biases make the receptive model (more) linear close to zero, and the non-linearity ramps up when one goes further into high intensity. The idea there is to model the spontaneous opsin isomerization in the receptors. I believe sRGB approximated this by gluing a small linear ramp into the nonlinearity with if-then-logic.
  - bjornornorn 6y ago
    Not that familiar with XYB and its properties. Is there anywhere I can read more? Found some specifications, but not anything on its properties. I think this might be a case where the requirements for image editing and image compression are different. For image editing, especially when working with HDR images, I think it is better to just have a simple power function, since this makes less assumptions on the exact viewing conditions. E.g a user might want to adjust exposure while editing an image, and if the prediction of hue changes when the exposure is altered, that would be confusing (which happen if more complex non-linearities are used). When compressing final images though, that wouldn’t be an issue in the same way.
    - jacobolus 6y ago
      I would consider just continuing to use the CIELAB adjusted cube root function, with a linear part near zero. It has been used widely for 45 years and people understand it pretty well. It is plenty fast to implement (just takes one extra conditional move or the like and one FMA).
      - JyrkiAlakuijala 6y ago
        We don't need to use something just because it is old. CIELAB is based on 2 degree samples of color. Colors work differently at smaller angles due to the different densities of receptors, particularly the larger size and lower density of S receptors. Pixels on most recent monitors are about 0.02 degrees, 100x smaller in angle, 10'000x smaller in area than what the old color research is based on.
JyrkiAlakuijala 6y ago
Ops. I believe I confused linear XYZ that enters the Oklab M1 matrix with the linear sRGB that enters the JPEG XL XYB's M1 matrix. When one converts them into the same space first, XYB and Oklab are likely even more similar with each other.

JyrkiAlakuijala 6y ago

Another rather substantial difference is in M2 matrix of Oklab. In my experiments I don't see S-participation in colors with high spatial frequency. Because in image compression a lot of information is in high spatial frequency, one gets favorable image compression when M2 matrix is without S contribution in Luma. We use just [b b 0, a -a 0, -0.5 * c, -0.5 * c, c] in the M2 phase in JPEG XL. The two 0s there don't bring S reception into Luma and redness-greenness observations. This difference can be because Oklab is based on XYZ which is based on 2 degree color samples. XYB is based on about 0.03 degree color samples. Perception seems to be different there -- to me it looks like S is not yet integrated into Luma experience at that resolution. In butteraugli color modeling is more complex: it is divided into high spatial frequency and low spatial frequency. S is brought only to the low spatial frequency color transforms. (Frequency separation there is by Laplacian pyramid.)

JyrkiAlakuijala 6y ago
One more interesting and substantial difference between Oklab and XYB is that XYB includes biases before the nonlinearity, i.e., one can consider the M1 matrix as a homogeneous matrix. These biases make the receptive model (more) linear close to zero, and the non-linearity ramps up when one goes further into high intensity. The idea there is to model the spontaneous opsin isomerization in the receptors. I believe sRGB approximated this by gluing a small linear ramp into the nonlinearity with if-then-logic.
- bjornornorn 6y ago
  Not that familiar with XYB and its properties. Is there anywhere I can read more? Found some specifications, but not anything on its properties. I think this might be a case where the requirements for image editing and image compression are different. For image editing, especially when working with HDR images, I think it is better to just have a simple power function, since this makes less assumptions on the exact viewing conditions. E.g a user might want to adjust exposure while editing an image, and if the prediction of hue changes when the exposure is altered, that would be confusing (which happen if more complex non-linearities are used). When compressing final images though, that wouldn’t be an issue in the same way.
  - jacobolus 6y ago
    I would consider just continuing to use the CIELAB adjusted cube root function, with a linear part near zero. It has been used widely for 45 years and people understand it pretty well. It is plenty fast to implement (just takes one extra conditional move or the like and one FMA).
    - JyrkiAlakuijala 6y ago
      We don't need to use something just because it is old. CIELAB is based on 2 degree samples of color. Colors work differently at smaller angles due to the different densities of receptors, particularly the larger size and lower density of S receptors. Pixels on most recent monitors are about 0.02 degrees, 100x smaller in angle, 10'000x smaller in area than what the old color research is based on.

JyrkiAlakuijala 6y ago

Ops. I believe I confused linear XYZ that enters the Oklab M1 matrix with the linear sRGB that enters the JPEG XL XYB's M1 matrix. When one converts them into the same space first, XYB and Oklab are likely even more similar with each other.