The science of thermography deals with the non-destructive evaluation of materials through the application of heat and the observation of cooling patterns. By examining the surface temperature cooling pattern of heated metals via a sequence of infra-red images, sub-surface defects can be detected. The thermal cooling patterns vary according to a thermal time-constant which appears in the solution to the heat conduction equation. This thermal time-constant is different for the cooling patterns over defective areas compared to non-defective areas. Because of the nature of heat, the actual cooling patterns contain noise, and the defects must be detected from noisy infra-red images.; In this dissertation the thermal time-constant is estimated and classified by various signal estimation and detection algorithms which take the thermal noise into account. As a result of this estimation or classification, a thermal image can be segmented into defective and non-defective areas. Four standard algorithms are used: the Extended Kalman Filter (EKF), the Generalized Maximum Likelihood (GML) algorithm, a Likelihood-Ratio Test (LRT), and the Expectation-Maximization (EM) algorithm. In addition two entirely original algorithms are developed and implemented based upon a recursive solution to the heat conduction equation. In each case simulation experiments are performed and the results of the experiments are presented.
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