Reflection imaging spectroscopy is a useful technique to remotely identify and map minerals and vegetation. Here we report on the mapping and identification of artists' materials in paintings using this method. Visible and infrared image cubes of Picasso's Harlequin Musician are collected using two hyperspectral cameras and combined into a single cube having 260 bands (441 to 1680 nm) and processed using convex geometry algorithms. The resulting 18 spectral end members are identified by comparison with library spectra, fitting by nonlinear mixing, and using results from luminescence imaging spectroscopy. The results are compared with those from X-ray fluorescence spectrometry, polarized light microscopy, and scanning electron microscopy-energy dispersive spectrometry (SEM/EDS). This work shows the potential of reflection imaging spectroscopy, in particular if the shortwave infrared region is included along with information from luminescence imaging spectroscopy.