Unsupervised detection of ruptures in spatial relationships in video sequences based on log-likelihood ratio

In this work, we propose a new approach to automatically detect ruptures in spatial relationships in video sequences, based on low-level primitives, in unsupervised manner. The spatial relationships between two objects of interest are modeled using angle and distance histograms as examples. The evolution of the spatial relationships during time is estimated from the distances between two successive angle or distance histograms and then considered as a temporal signal. The evolution of a spatial relationship is modeled by a linear Gaussian model. Then, two hypotheses “without change” and “with change” are considered, and a log-likelihood ratio is computed. The distribution of the log-likelihood ratio, given that H0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_0$$\end{document} is true, is estimated and used to compute the p value. The comparison of this p value to a significance level α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}, expressing the probability of false alarms, allows us to detect significant ruptures in spatial relationships during time. In addition, this approach is generalized to detect multiple object events such as merging, splitting, and other events that contain ruptures in their spatial relationships evolution. This work shows that the description of spatial relationships across time is a promising step toward event detection.