On the morphological analysis of binary random fields

Modeling image data by means of random fields and developing statistical techniques for the processing and analysis of these random fields is an important problem in image processing and analysis. We theoretically formulate the problem of processing binary random fields by means of mathematical morphology. This may allow us employ mathematical morphology in order to develop new statistical techniques for the processing and analysis of random shapes modeled as binary random fields. Since morphological transformations of continuous space binary random fields are not measurable in general, we employ intermediate steps which require generation of an equivalent random closed set. The relationship between binary random fields and random closed sets is thoroughly investigated. As a by-product of this investigation, a number of useful new results, regarding separability of random closed sets, are presented