AxIoU: An Axiomatically Justified Measure for Video Moment Retrieval

TL;DR

This paper introduces AxIoU, a new evaluation measure for Video Moment Retrieval that addresses limitations of existing metrics by considering rank positions and localization quality, and is grounded in formal axioms.

Contribution

We propose AxIoU, an axiomatic evaluation measure for VMR that overcomes rank insensitivity and binarization issues of current metrics, with theoretical justification and empirical validation.

Findings

AxIoU satisfies key axioms for VMR evaluation.

AxIoU correlates well with existing metrics and is stable across data variations.

It provides a more nuanced assessment of localization quality.

Abstract

Evaluation measures have a crucial impact on the direction of research. Therefore, it is of utmost importance to develop appropriate and reliable evaluation measures for new applications where conventional measures are not well suited. Video Moment Retrieval (VMR) is one such application, and the current practice is to use R@$K,\theta$ for evaluating VMR systems. However, this measure has two disadvantages. First, it is rank-insensitive: It ignores the rank positions of successfully localised moments in the top-$K$ ranked list by treating the list as a set. Second, it binarizes the Intersection over Union (IoU) of each retrieved video moment using the threshold $\theta$ and thereby ignoring fine-grained localisation quality of ranked moments. We propose an alternative measure for evaluating VMR, called Average Max IoU (AxIoU), which is free from the above two problems. We show that AxIoU satisfies two important axioms for VMR evaluation, namely, \textbf{Invariance against Redundant Moments} and \textbf{Monotonicity with respect to the Best Moment}, and also that R@$K,\theta$ satisfies the first axiom only. We also empirically examine how AxIoU agrees with R@$K,\theta$, as well as its stability with respect to change in the test data and human-annotated temporal boundaries.