Global divergences between measures: from Hausdorff distance to Optimal Transport
Résumé
The data attachment formula is a key component of shape registration pipelines: computed at every step, its gradient is the vector field that drives a deformed model towards its target. Unfortunately, most classical formulas are at most semi-local: their gradients saturate and stop being informative above some given distance, with appalling consequences on the robustness of shape analysis pipelines. In this paper, we provide a unified view of three fidelities between measures that alleviate this problem: the Energy Distance from statistics; the (weighted) Hausdorff distance from computer graphics; the Wasserstein distance from Optimal Transport theory. Provided with efficient GPU routines and theoretical guarantees, these tools should allow the shape analyst to handle large deformations without hassle.
Origine | Fichiers produits par l'(les) auteur(s) |
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