Analysis of a Spatio-Temporal Clustering Algorithm for Counting People in a Meeting

This paper proposes an algorithm that, given a time interval and the positions of people’s faces located by a face detector, automatically deter mines the number of people present at a meeting. It should be noted that such a face detec tor often times produces noise and false positives, rendering the analysis of its res ults increasingly difficult. In any given frame, false positives may appear, and legitimate fac s can go unnoticed, which calls for the use of statistical methods in the algorit hm. Exploiting clustering patterns based on temporal and spati al lignments of the detected faces, our algorithm employs the expectation-maxim ization (EM) algorithm [4] for mixture models and K-Means clustering algorithm [8]. Th e Gaussian mixture model [2] is used to estimate the probability density functi on of the data points; its parameters are then optimized using the EM algorithm, whose performance is in turn enhanced by its joint use with the K-Means algorithm. Also, b y performing random restarts in the final model verification stage of the algorith m, different estimates are sampled using different parameters, and the most consisten t result is chosen, under the assumption that an incorrect parameter set will have incons istent fitting. The results from this combination of algorithms and the samp le training data set indicate the existence of the optimal set of parameters that produces estimates with locally minimum standard deviation and percentage error. Finally, a stand-alone module will first be trained with a dat a set for which the ground truth is available for calculation of percentage err ors. It will also implement an automatic, but simplified, model verification procedure wit h the parameters obtained from the data set.