A Multivariate Hit-or-Miss Transform for Conjoint Spatial and Spectral Template Matching

The Hit-or-Miss transform is a well-known morphological operator for template matching in binary and grey-level images. However it cannot be used straightforward in multivalued images (such as colour or multispectral images) since Mathematical Morphology needs an ordering relation which is not trivial on multivalued spaces. Moreover, existing definitions of the Hit-Or-Miss Transform in grey-level use only spatial templates (or structuring elements) which could be insufficient for some feature extraction problems. In this paper, we propose a multivariate Hitor-Miss Transform operator which combines spatial and spectral patterns to perform template matching. We illustrate its relevance with an application in the remote sensing field, the extraction of coastline from very high (spatial) resolution images.