Expectation Maximization and its Application in Modeling, Segmentation and Anomaly Detection

摘要

Expectation Maximization (EM) is a general purpose algorithm for solving maximum likelihood estimation problems in a wide variety of situations best described as incomplete data problems. The incompleteness of the data may arise due to missing data, truncated distributions, etc. One such case is a mixture model, where the class association of the data is unknown. In these models, the EM algorithm is used to estimate the parameters of parametric mixture distributions along with their probabilities of occurrence. In this thesis, the EM algorithm is employed to estimate different mixture models for raw single and multi-band electro-optical Infra Red (IR) data. The EM update equations for single and multi-band Gaussian and single-band Gamma and Beta mixture models are discussed. Gaussian mixture models are used for the raw image segmentation of single and multi-band imagery. Three different anomaly detection techniques based on EM-based image segmentation are discussed and evaluated. The Gamma and Beta mixture models are used to model the detection statistic of two different anomaly detectors. An adaptive CFAR (Constant False Alarm Rate) threshold selection based on the mixture model of the detection statistic has been implemented to determine potential target locations. These mixture models of detection statistics can also be used for multi-sensor or multi-algorithm fusion. The algorithms have been evaluated using single-band mid-wave IR airborne imagery for mine and mine field detection problems.