A hit-or-miss transform for multivariate images

The hit-or-miss transform (HMT) is considered to be among the fundamental operations in the morphological toolbox. Initially, it was defined for binary images, as a morphological approach to the problem of template matching, whereas its extension to grey-level data has been problematic, leading to multiple definitions, that have been only recently unified by means of a common theoretical foundation. In this paper, we generalise these definitions to the case of multivariate images, and propose a vectorial HMT, allowing the detection of objects over multiple image channels. Moreover, in order to counter the operator’s extreme sensitivity to variations, rank order filters as well as synthetic structuring functions are studied in the context of multivariate data. We additionally present examples of the use of the suggested operator in combination with colour images.