Conclusions (pre-6/4/19)
(Update: The newly-developed LHTSS method is a better choice than ILLSS when requiring the reflectance curves to fall strictly between 0 and 1. It matches the Munsell colors better and takes about 60% of the computational effort of ILLSS. See the 6/4/2019 update on the next page for more information.)
In summary, the method that best matches paint and pigment colors found commercially and in nature is the ILLSS (Iterative Least Log Slope Squared) method. It suffers, however, from very large computational requirements. If efficiency is more important, then the ILSS (Iterative Least Slope Squared) method is the preferred one. A third alternative that is midway between the match quality and computing effort is LLSS (Least Log Slope Squared), but be aware that some reflectance curves can end up with values >1. I would not recommend the LSS (Least Slope Squared) method, despite its spectacular computational efficiency, because it can give reflectance curves with physically meaningless negative values. The following table summarizes the three suggested methods:
| Algorithm Name | Computational Effort | Comments | Link to Matlab Code |
| ILSS (Iterative Least Slope Squared) | Relatively little. | Very fast, but tends to undershoot reflectance curve peaks, especially for bright red and purple colors. Always returns reflectance values in the range 0-1. | link |
| LLSS (Least Log Slope Squared) | About 12 times that of ILSS. | Better quality matches overall, but tends to overshoot peaks in the yellow region. Some reflectance values can be >1, especially for bright red colors. | link |
| ILLSS (Iterative Least Log Slope Squared) | About 20 times that of ILSS. | Best quality matches. Tends to overshoot peaks in the yellow region. Always returns reflectance values in the range 0-1. | link |
__________________________________
Update 9/26/2018: I’ve added a new page that presents an even faster way to generate reflectance curves from sRGB values. It is as fast as the fastest methods presented above, guarantees reflectance values in the 0-1 range, but produces reflectance curves that are not as smooth or realistic as the slower, higher quality reconstruction methods. Nevertheless, it permits good quality subtractive mixture with little computational overhead. (This new method is the result of the idea being suggested to me by Brien Dieterle, who asked me to help find a way to implement the idea.)
__________________________________
Update 10/2/2018: I have recently added a new page that shows how to apply these methods to the color space called Recommendation ITU-R BT.2020-2 (10/2015), or Rec. 2020 for short.
________________________________________
Update 5/23/2019: I’ve recently applied the reflectance reconstruction ideas presented here to the subject of chromatic adaptation, and have written a paper called “Chromatic Adaptation Transform by Spectral Reconstruction,” which was published in the journal Color Research and Application (citation: Burns SA. Chromatic adaptation transform by spectral reconstruction. Color Res Appl. 2019;44(5):682-693). Please contact me if you’d like a copy of this paper.
Navigation
The presentation is spread over several web pages. Click the Next Page or Previous Page links to move sequentially. To access a page directly, use these links:
1. Introduction
2. Computing an sRGB triplet from a Reflectance Curve
3. Linear Least Squares (LLS) Method
4. Least Slope Squared (LSS) Method
5. Least Log Slope Squared (LLSS) Method
6. Iterative Least Log Slope Squared (ILLSS) Method
7. Iterative Least Slope Squared (ILSS) Method
8. Comparison of Methods
9. Conclusions (pre-6/4/19) (this page)
10. Update 6/4/19: Least Hyperbolic Tangent Slope Squared (LHTSS) Method