Classifying Image Sequences with the Markov Chain Structure and Matrix Normal Distributions

We consider the problem of classifying image sequences to several classes. Such problems arise in numerous applications, e.g., when a task to be completed requires that all sub-tasks are properly executed. In order to derive realistic classifiers for such complicated problems, we assume that images in the sequence form a Markov chain, while the conditional probability density function of transitions has the matrix normal distribution, i.e., it has the covariance matrix being the Kronecker product of inter-rows and inter-columns covariance matrices. Under these assumptions we derive the Bayes classifier for image sequences and its empirical version that is based on applying the plug-in rule. We also provide interpretable versions of such classifiers at the expense of additional assumptions. The proposed classifier is tested on the sequence of images from the laboratory experiments of detecting stages of an additive manufacturing process. Finally, we state conclusions and (partial) explanations on why the problem of classifying sequences of images is (much) more difficult than that of classifying individual images.