GROUT: Geometric Reasoning Over Unstructured Tessellations — Zero-Shot Semantic Segmentation of Mosaic Surfaces

Precise segmentation of tessellated surfaces is a critical prerequisite for the digital preservation, structural analysis, and restoration of mosaic heritage sites. However, traditional supervised learning approaches are hindered by the scarcity of annotated datasets, while general-purpose edge detectors often fail to distinguish between structural joints and material texture. In this work, we present GROUT (Geometric Reasoning Over Unstructured Tessellations), a deep learning framework capable of state-of-the-art segmentation without seeing a single real image during training ("Zero-Shot Sim2Real"). We introduce a novel procedural generator that simulates distinct tiling geometries—including Opus Vermiculatum and Opus Tessellatum—while modeling specific "hard negatives" such as zero-width butt-joints and monochromatic surfaces. We evaluate GROUT against traditional (Canny, Sobel) and deep learning edge detectors (HED, BDCN). Results demonstrate that while HED suffers from low recall and BDCN suffers from texture confusion (over-segmentation of stone grain), GROUT successfully disentangles complex grout networks from stone texture artifacts. Our EfficientNet-B3 U-Net, trained exclusively on 1,500 synthetic priors, generalizes directly to high-resolution archival photography with high semantic precision. Resources Code Repository: https://github.com/advancedtech-sk/GROUT Interactive Demo: https://huggingface.co/spaces/advancedtech-sk/GROUT