Fuzzy Hit-or-Miss Transform Using Uninorms

Abstract

The Hit-or-Miss transform (HMT) is a morphological operator which has been successfully used to identify shapes and patterns satisfying certain geometric restrictions in an image. Recently, a novel HMT operator, called the fuzzy morphological HMT, was introduced within the framework of the fuzzy mathematical morphology based on fuzzy conjunctions and fuzzy implication functions. Taking into account that the particular case of considering a t-norm as fuzzy conjunction and its residual implication as fuzzy implication functions has proved its potential in several applications, in this paper, the case when residual implications derived from uninorms and a general fuzzy conjunction, possibly a t-norm or the same uninorm, is deeply analysed. In particular, some theoretical results related to properties desirable for the applications are proved. Finally, some experimental results are presented showing the potential of this choice of operator to detect shapes and patterns in images.