Recent literature has reported the theory of symbolic dynamic filtering (SDF) of one-dimensional time-series data and its various applications for anomaly detection and pattern recognition. This paper extends the theory of SDF in the two-dimensional domain, where symbol sequences are generated from image data (i.e., pixels). Given the symbol sequence, a probabilistic finite state automaton (PFSA), called the D-Markov machine, is constructed on the principles of Markov random fields to incorporate the spatial information in the local neighborhoods of a pixel. The image analysis algorithm has been experimentally validated on a computer-controlled fatigue test apparatus that is equipped with a traveling optical microscope and ultrasonic flaw detectors. The surface images of test specimens, made of a polycrystalline alloy, are analyzed to detect and quantify the evolution of fatigue damage. The results of two-dimensional SDF analysis are in close agreement with those obtained from analysis of one-dimensional time-series data from the ultrasonic sensor, which are simultaneously generated from the same test specimen.
['Aparna Subbu', 'Abhishek Srivastav', 'Asok Ray', 'Eric Keller']
Symbolic dynamic filtering for image analysis: theory and experimental validation