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====== Otsu et al. (2018), part 4 ======

In the [[gsoc:otsu2018_3|previous part]] I mentioned that reflectances reconstructed using this method can exceed the [0, 1] range and violate conservation of energy. Indeed, I could simply ask it for an imaginary color and get a weird, unphysical spectrum.

What's interesting is that this doesn't happen in practice, when upsampling real data. Out of almost 1300 reflectances I tested, I found only one bad reconstruction. Using the original clustering, the result for ''magenta'' from ''BabelColor Average'' colorchecker reflects 100,6% of light at 730 nm. Clipping this value to 100% creates a tiny color difference, orders of magnitude smaller than the [[https://en.wikipedia.org/wiki/Just-noticeable_difference|just-noticeable difference]]. 

[{{ gsoc:otsu2018_error.png?400 |You can see the small difference between the clipped and unclipped reflectances in the upper right corner of the figure. (Click to enlarge.)}}]

Many methods have this property of being able to create perfect metamers, so looking at ΔE's isn't very interesting. In a future post I'll take a look at MSE (mean square error), which quantizes differences between spectra themselves, and compare a few methods.