  Kubelka-Munk (K-M) theory has been successfully used to estimate pigment
concentrations in the pigment mixtures of modern paintings in spectral imagery.
In this study the single-constant K-M theory has been utilized for the
classification of green pigments in the Selden Map of China, a navigational map
of the South China Sea likely created in the early seventeenth century.
Hyperspectral data of the map was collected at the Bodleian Library, University
of Oxford, and can be used to estimate the pigment diversity, and spatial
distribution, within the map. This work seeks to assess the utility of
analyzing the data in the K/S space from Kubelka-Munk theory, as opposed to the
traditional reflectance domain. We estimate the dimensionality of the data and
extract endmembers in the reflectance domain. Then we perform linear unmixing
to estimate abundances in the K/S space, and following Bai, et al. (2017), we
perform a classification in the abundance space. Finally, due to the lack of
ground truth labels, the classification accuracy was estimated by computing the
mean spectrum of each class as the representative signature of that class, and
calculating the root mean squared error with all the pixels in that class to
create a spatial representation of the error. This highlights both the
magnitude of, and any spatial pattern in, the errors, indicating if a
particular pigment is not well modeled in this approach.
