Keypoint-Guided Optimal Transport with Applications in Heterogeneous Domain Adaptation A Mathematical Deductions

A.1 Proof of Proposition 1 Proposition 1 in the paper is for the case that p Given the marginal distributions p and q, we say that the transport plan π Π(p, q) preserves the matching of a keypoint pair with index (i, j) K, if π satisfies one of the following conditions: 1. The left part of Fig. A-1 illustrates these conditions. Then, the transport plan π = M π with π Π(p, q; M) preserves the matching of keypoint pairs with index in K. For the other points (corresponding to the last three cases in Eq. (A-1)), we set M Proof: For any (i, j) K, we next prove that π preserves the matching of keypoint pair (i, j). This means that π preserves the matching of keypoint pairs with index in K. A.2 Linear Programming for Solving KPG-RL We cast the matrix G (resp.