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.