From Kantorovitch Problem to Linear Sum Assignment Problem

Romain Raveaux (1)

1 RFAI - Reconnaissance des formes et analyse d'images

The goal of this technical report is to detail the link between the Linear Sum Assignment Problem (LSAP) and the Kantorovitch Problem (KP) also called Optimal Transport. This relation is not new and is reported in \cite{peyre2020computational}

Mots clés: Linear Sum Assignment; Kantorovitch; Optimal Transport; Matching

Domaines: Traitement des images [eess.IV]; Vision par ordinateur et reconnaissance de formes [cs.CV]

Romain Raveaux. From Kantorovitch Problem to Linear Sum Assignment Problem. [Intern report] Université de tours. 2021. ⟨hal-03388191v2⟩