Nonlinear unmixing of hyperspectral reflectance data is one of the key problems in quantitative imaging of painted works of art. The approach presented is to interrogate a hyperspectral image cube by first decomposing it into a set of reflectance curves representing pure basis pigments and second to estimate the scattering and absorption coefficients of each pigment in a given pixel to produce estimates of the component fractions. This two-step algorithm uses a deep neural network to qualitatively identify the constituent pigments in any unknown spectrum and, based on the pigment(s) present and Kubelka-Munk theory to estimate the pigment concentration on a per-pixel basis. Using hyperspectral data acquired on a set of mock-up paintings and a well-characterized illuminated folio from the 15th century, the performance of the proposed algorithm is demonstrated for pigment recognition and quantitative estimation of concentration.
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