Automatic clustering of inks in cultural heritage artifacts via optimal selection of graph modularity

We present an automatic clustering algorithm for hyperspectral imagery of cultural heritage artifacts: the Selden Map and the Gough Map, both medieval artifacts imaged in the collections at the Bodleian Library of Oxford University. Unlike "traditional" remotely sensed hyperspectral data, these images are of man-made objects using specific materials meant to visually show feature differences and similarities. Consequently, the data are inherently non-Gaussian and potentially very non-linear in the spectral domain. First, we explore the effective graph representations for hyperspectral images, then optimally select the graph modularity to find community structures for a ROI within the scene. By utilizing the eigenvector of the modularity matrix associated with the largest positive eigenvalue for group labeling, we recursively identify multi-level subgroups existing in the graph, producing a variable level of detail cluster-map based on a cluster tree strategy. The generated non-linear decision boundaries are allowed to take any shape with no limits to cluster size. The clustering metric is determined by optimally selecting a high modularity and the largest positive eigenvalue, as well as considering the magnitude of the entry in the leading eigenvector to make each division more accurate and robust. As a result, the optimal number of clusters are found to best characterize the data. Compared to the traditional clustering methods, such as K-means, the graph modularity-based method can extract perceptually important non-local properties of an object, thus yielding semantically more meaningful cluster groups and better discriminating subtle spectral differences between varied pigments. For the Selden Map, we investigate subtle differences in black inks used to denote navigation routes. For the Gough Map, we look at a specific feature under investigation by historians: the castle depicting London. Our results demonstrate the effectiveness of the method as the clustering results explain and match the actual spectra well. This research aims to aid historians in analysis of pigment composition and further facilitate the study in inference of the creation and the evolving timeline of these artifacts.