Ink Detection from Surface Topography of the Herculaneum Papyri

Giorgio Angelotti; Federica Nicolardi; Paul Henderson; W. Brent Seales

cs.CVMar 29, 2026

Ink Detection from Surface Topography of the Herculaneum Papyri

Authors: Giorgio Angelotti, Federica Nicolardi, Paul Henderson, W. Brent Seales

Organizations: Vesuvius Challenge, USA · Universit`a degli Studi di Napoli Federico II, Italy · University of Glasgow, Scotland, UK · EduceLab, University of Kentucky, USA

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 & tables

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 $\mathrm{\SIUnitSymbolMicro m}$ ; 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,

\mathrm{\SIUnitSymbolMicro m}

). Orange boxes: nnU-Net models trained and evaluated at matched resolution. Blue boxes: a single nnU-Net trained at

0.34\text{\,}\mathrm{\SIUnitSymbolMicro m}

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.

Lateral pixel size	Pixel size sensitivity (n=14)		Model trained at $0.34\text{\,}\mathrm{\SIUnitSymbolMicro m}$		Z-binned test inputs ( $\Delta z=\Delta x$ , n=14)
	Median [Q1, Q3]	Mean $\pm$ s.d.	Median [Q1, Q3]	Mean $\pm$ s.d.	Median [Q1, Q3]	Mean $\pm$ s.d.
$0.34\text{\,}\mathrm{\SIUnitSymbolMicro m}$	0.890 [0.864, 0.905]	0.881 $\pm$ 0.039	0.899 [0.866, 0.913]	0.889 $\pm$ 0.038	0.864 [0.808, 0.900]	0.839 $\pm$ 0.075
$0.68\text{\,}\mathrm{\SIUnitSymbolMicro m}$	0.817 [0.775, 0.831]	0.803 $\pm$ 0.068	0.881 [0.857, 0.906]	0.877 $\pm$ 0.042	0.817 [0.755, 0.843]	0.792 $\pm$ 0.085
$1.02\text{\,}\mathrm{\SIUnitSymbolMicro m}$	0.754 [0.698, 0.784]	0.748 $\pm$ 0.068	0.758 [0.670, 0.786]	0.736 $\pm$ 0.091	0.742 [0.701, 0.787]	0.744 $\pm$ 0.080
$1.36\text{\,}\mathrm{\SIUnitSymbolMicro m}$	0.586 [0.483, 0.644]	0.570 $\pm$ 0.143	0.634 [0.557, 0.670]	0.611 $\pm$ 0.104	0.596 [0.507, 0.645]	0.586 $\pm$ 0.139
$2.04\text{\,}\mathrm{\SIUnitSymbolMicro m}$	0.516 [0.421, 0.559]	0.493 $\pm$ 0.093	0.494 [0.341, 0.604]	0.455 $\pm$ 0.208	0.499 [0.451, 0.541]	0.486 $\pm$ 0.083

Table 1: Dice versus lateral pixel size across three settings: (i) pixel size sensitivity (nnU-Net trained and evaluated at matched resolutions); (ii) a model trained at

0.34\text{\,}\mathrm{\SIUnitSymbolMicro m}

evaluated on degraded input; and (iii) matched-resolution evaluation on z-binned heightmaps (

\Delta z=\Delta x

) to emulate isotropic voxels. Values are median [Q1, Q3] and mean

\pm

s.d. Only models at or finer than

1.02\text{\,}\mathrm{\SIUnitSymbolMicro m}

exceed the

\mathrm{Dice}=0.70

reference threshold.

Held-out papyrus	n	Median [Q1, Q3]	Mean $\pm$ s.d.
PHerc. 248	5	0.757 [0.733, 0.812]	0.777 $\pm$ 0.059
PHerc. 250	5	0.817 [0.755, 0.822]	0.789 $\pm$ 0.053
PHerc. 500P2	4	0.475 [0.454, 0.482]	0.461 $\pm$ 0.035

Table 2: Leave-one-papyrus-out generalization at native lateral sampling (

0.34\text{\,}\mathrm{\SIUnitSymbolMicro m}

). For each held-out papyrus, an nnU-Net was trained on all samples from the other two papyri and evaluated on all samples from the held-out papyrus. Values are median [Q1, Q3] and mean

\pm

s.d. across samples from the held-out papyrus. Pooled across all held-out samples (

n=14

), the mean Dice is 0.691.

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Complete virtual unwrapping and reading of a rolled Herculaneum papyrus

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Cultural Heritage Computed Tomography

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The carbonized papyri from Herculaneum preserve the only large-scale library to survive from classical antiquity, but many unopened rolls remain unread because physical opening risks irreversible damage. X-ray computed microtomography (

μ

CT) and virtual unwrapping offer a non-invasive route to their texts, yet previous work on sealed Herculaneum scrolls has recovered only localized readings or limited surface regions. Here, using high-resolution phase-contrast

μ

CT acquired on the BM18 beamline at the European Synchrotron Radiation Facility (ESRF), together with improved computational unrolling and machine learning, we achieve the complete virtual unwrapping and reading of PHerc. 1667 under explicit coverage and papyrological-review criteria. This makes PHerc. 1667 the first Herculaneum papyrus to be fully digitally unrolled and read for extended scholarly study without physical opening. In PHerc. Paris 4, the optimized scan protocol makes ink directly visible in the tomographic volume, allowing three-dimensional ink segmentation and independent validation of surface-conditioned ink recovery. In PHerc. 139, we recover title and author-attribution evidence identifying the scroll as Philodemus, On Gods, Book 8. These results move virtual unwrapping of the Herculaneum scrolls beyond isolated demonstrations towards a scalable framework for systematic recovery of the still-unopened library.

Abstract

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