Selection of optimal spectral metrics for classification of inks in historical documents using hyperspectral imaging data

Hyperspectral imaging has been increasingly used for non-destructive analysis of historical documents. Spectral reflectance data allow material identification and mapping using a library of reference spectra. Similarity metrics are crucial for quantifying the differences between reference and test spectra. Despite the apparent simplicity of the metrics, little work has been done on comparing their performance in the classification of historical inks. In this work, we propose three methods for selection of optimal spectral metrics, with an application to classification of historical inks. Hyperspectral images of laboratory and real historical samples are acquired in VNIR [400-1000 nm] and SWIR [900-1700 nm] spectral ranges. Two spectral reflectance libraries are obtained (one for each range) including eight inks: iron gall, sepia, and carbon-based inks, and some mixtures. Six spectral similarity metrics are used: RMSE, SAM, SID, SIDSAM, NS3, and JMSAM. Firstly, metrics values in laboratory samples are studied to determine the classification confidence threshold of each metric. Then, the optimal metrics found for classification are selected using diverse approaches: (1) considering the confidence threshold; (2) evaluating classification performance metrics; (3) studying the probability of spectral discrimination and the power of spectral discrimination of each metric. Finally, inks of historical samples are classified by searching through the spectral libraries using optimal spectral metrics. Our method can correctly identify inks in both laboratory and historical samples in a simple and semi-supervised way.