Monocular depth foundations predict domain-general relative depth but lack absolute scale; a handful of sparse metric anchors from a range sensor can calibrate them to metric depth, an attractive alternative to metric-supervised training. Existing sparse-anchor calibration methods, however, assume the anchors are clean, whereas real sensors produce outliers that are present with the wrong value -- time-of-flight multipath, mixed pixels -- not merely missing. We show that the established residual-on-CFA calibration recipe collapses under such outliers, and that the strongest publicly deployed method, VI-Depth, has a structural multipath blind spot: robust to missing anchors, it falls behind an unprotected baseline on three of four datasets when anchors are present but wrong. We propose Multipath-Robust Anchor Calibration (MRAC), a parameter-free, inference-time wrapper that gates anchors by foundation consistency -- a Theil--Sen fit and a median-absolute-deviation test against the foundation's own relative-depth ordering -- before a single call to the calibration head. MRAC adds no learned parameters, runs its selection in $\approx 50\,μ$s on CPU, and serves anchor budgets $K \in [5,200]$ from one checkpoint. On a $320$-cell benchmark with a same-backbone, same-architecture control, MRAC strictly wins $84\%$ of same-backbone cells across all four outlier families and, against VI-Depth, wins all twelve corrupted multipath cells and all sixteen KITTI cells, reducing KITTI multipath AbsRel by $3.2\times$ ($0.489$ to $0.151$) at zero retraining.
Coherent Point Drift (CPD) is widely used for rigid point cloud registration because of its soft correspondences and closed-form parameter updates. However, CPD's target-side marginal constraint forces every observation, including outliers, to receive exactly unit probability mass. This assumption degrades registration accuracy under heavy outliers and partial overlap. Optimal transport (OT) methods can handle missing mass through unbalanced formulations, but require hand-tuned annealing schedules. In this paper, we propose Sinkhorn-CPD, which replaces CPD's target-side marginal constraint with dual Kullback-Leibler penalties, allowing the algorithm to discard outliers on both sides. The resulting formulation is a fully unbalanced entropic optimal transport problem, which can be efficiently solved by generalized Sinkhorn iterations. Moreover, Sinkhorn-CPD preserves the closed-form Procrustes and variance updates of CPD. In our method, the variance sigma^2 plays the role of the entropic regularization parameter, which induces an automatic annealing schedule from diffuse to sharp correspondences without manual temperature tuning. Experiments on synthetic, cross-category, and scan-to-CAD benchmarks show that Sinkhorn-CPD achieves state-of-the-art accuracy, with strong robustness to outliers and partial overlap.