Efficient Point Process Inference for Large-Scale Object Detection Supplemental Material

Abstract

where α = max(|D(ui)|, |D(uj)|)+ ; is a small positive number. For notational simplicity, we denoteD(xi) = D(ui)xi, V (xi, xj) = V (ui, uj)xixj , V̂ (xi, xj) = V̂ (ui, uj)xixj , andR(xi, xj) = R(ui, uj)xixj . Lemma 1. If X∗ is the global optimum of E(X),R(xi, xj) < To,∀ xi ∼ xj , xi, xj ∈ X∗. Proof. If there exists a pair xi ∼ xj , xi, xj ∈ X∗ such thatR(xi, xj) ≥ To, then E(X∗) > 0 = E(0) (5) where 0 is a all-zero vector of length N . This is because V (xi, xj) = K (K g(R(ui, uj)) and K sup(D(ui)) ∀ui, uj). This contradicts the fact that X∗ is a global minimizer of E(X). Lemma 2. If X∗ is the global optimum of Ê(X),R(xi, xj) < To,∀ xi ∼ xj , xi, xj ∈ X∗.

Cite this paper

@inproceedings{Pham2016EfficientPP, title={Efficient Point Process Inference for Large-Scale Object Detection Supplemental Material}, author={Tung Thanh Pham and Seyed Hamid Rezatofighi and Ian D. Reid}, year={2016} }