Learning a Restricted Bayesian Network for Object Detection

Abstract

Many classes of images have the characteristics of sparse structuring of statistical dependency and the presence of conditional independencies among various groups of variables. Such characteristics make it possible to construct a powerful classifier by only representing the stronger direct dependencies among the variables. In particular, a Bayesian network compactly represents such structuring. However, learning the structure of a Bayesian network is known to be NP complete. The high dimensionality of images makes structure learning especially challenging. This paper describes an algorithm that searches for the structure of a Bayesian network based classifier in this large space of possible structures. The algorithm seeks to optimize two cost functions: a localized error in the log-likelihood ratio function to restrict the structure and a global classification error to choose the final structure of the Network. The final network structure is restricted such that the search can take advantage of pre-computed estimates and evaluations. We use this method to automatically train detectors of frontal faces, eyes, and the iris of the human eye. In particular, the frontal face detector achieves state-of-the-art performance on the MIT-CMU test set for face detection.