Ink Detection from Surface Topography of the Herculaneum Papyri

Abstract

Reading the Herculaneum papyri is challenging because both the scrolls and the ink, which is carbon-based, are carbonized. In X-ray radiography and tomography, ink detection typically relies on density- or composition-driven contrast, but carbon ink on carbonized papyrus provides little attenuation contrast. Building on the morphological hypothesis, we show that the surface morphology of written regions contains enough signal to distinguish ink from papyrus. To this end, we train machine learning models on three-dimensional optical profilometry from mechanically opened Herculaneum papyri to separate inked and uninked areas. We further quantify how lateral sampling governs learnability and how a native-resolution model behaves on coarsened inputs. We show that high-resolution topography alone contains a usable signal for ink detection. Diminishing segmentation performance with decreasing lateral resolution provides insight into the characteristic spatial scales that must be resolved on our dataset to exploit the morphological signal. These findings inform spatial resolution targets for morphology-based reading of closed scrolls through X-ray tomography.

Figures (3)

• Figure 1: Representative profilometry overview for three samples from PHerc. 250. Each row shows a distinct letter. From left to right: (i) full 3D render of the measured topography; (ii) 2D heightmap with topographic contours; (iii) aligned brightfield image with visible ink. Axes are in µm; height color bars share the same scale within each row.
• Figure 2: Qualitative examples across three papyri. Rows from top to bottom are $\epsilon$ on PHerc. 248, $\kappa$ on PHerc. 250, and $\eta$ on PHerc. 500P2. Columns from left to right are (i) topographic map converted to uint16 image, (ii) nnU-Net model prediction, and (iii) brightfield photo. The grid structure visible in the heightmap is the lattice of fibers composing the papyrus substrate.
• Figure 3: Segmentation performance (Dice) as a function of effective lateral sampling (pixel size, µm). Orange boxes: nnU-Net models trained and evaluated at matched resolution. Blue boxes: a single nnU-Net trained at 0.34µm evaluated on inputs downsampled to coarser pixel sizes and upsampled to the native grid. Boxes show the median and interquartile range across $n=14$ cases; whiskers extend to the most extreme non-outlier values (Tukey, $1.5\times\mathrm{IQR}$; outliers omitted). The dashed horizontal line marks $\mathrm{Dice}=0.70$ as a reference overlap threshold.