Recent advances have markedly improved the cross-scene generalization of relative depth estimation, yet its practical applicability remains limited by the absence of metric scale, local inconsistencies, and low computational efficiency. To address these issues, we present \emph{\textbf{M}idas \textbf{T}ouch for \textbf{D}epth} (MTD), a mathematically interpretable approach that converts relative depth into metric depth using only extremely sparse 3D data. To eliminate local scale inconsistencies, it applies a segment-wise recovery strategy via sparse graph optimization, followed by a pixel-wise refinement strategy using a discontinuity-aware geodesic cost. MTD exhibits strong generalization and achieves substantial accuracy improvements over previous depth completion and depth estimation methods. Moreover, its lightweight, plug-and-play design facilitates deployment and integration on diverse downstream 3D tasks. Project page is available at https://mias.group/MTD.
@article{arxiv.2605.11578,
title = {The Midas Touch for Metric Depth},
author = {Yu Ma and Zizhan Guo and Zuyi Xiong and Haoran Zhang and Yi Feng and Hongbo Zhao and Hanli Wang and Rui Fan},
journal= {arXiv preprint arXiv:2605.11578},
year = {2026}
}