Design and analysis of fuzzy morphological algorithms for image processing

Abstract

A general paradigm for lifting binary morphological algorithms to fuzzy algorithms is employed to construct fuzzy versions of classical binary morphological operations. The lifting procedure is based upon an epistemological interpretation of both image and filter fuzzification. Algorithms are designed via the paradigm for various fuzzifications and their performances are analyzed to provide insight into the kind of liftings that produce suitable results. Algorithms are discussed for three image processing tasks: shape detection, edge detection, and clutter removal. Detailed analyses are given for the effect of noise and its mitigation owing to fuzzy approaches. It is demonstrated how the fuzzy hit-or-miss transform can be used in conjunction with a decision procedure to achieve word recognition.

Interval-Valued and Intuitionistic Fuzzy Mathematical Morphologies as Special Cases of $\mathbb{L}$ -Fuzzy Mathematical Morphology

“…Researchers in fuzzy mathematical morphology (FMM) have devised fuzzy inclusion and intersection measures by relaxing the notions of crisp inclusion and intersection measure [7,45,71,72,88]. Large classes of fuzzy inclusion measures and fuzzy intersection measures can be constructed in terms of fuzzy implications and conjunctions [80].…”

“…Various researchers have presented fuzzy inclusion measures [7,45,71,72,88]. A certain fuzzy inclusion measure Inc F induces an operator E F : F (X) × F (X) → F (X) via the following definition [56]:…”

A fuzzy morphological hit-or-miss transform for grey-level images: A new approach

“…In this work, these researchers suggest to use as indicator for fuzzified set inclusion 1 the family of functions 1] function satisfying six conditions that can be found in [57] and [58]. In [57] the authors proposed several families of λ-functions that were used in various applications [58].…”

“…A first attempt to extend the HMT transform to grey-level images that adds fuzzy logic elements without first binarizing the image appears in 1997 with the work of D. Sinha, P. Sinha and E.R. Dougherty [58].…”

Fuzzy Hit-or-Miss Transform Using the Fuzzy Mathematical Morphology Based on T-norms

“…In this framework, the analysis of the fuzzy Hit-or-Miss transform (FHMT) is much narrower. Sinha et al in [36] discussed a FHMT based on his FMM to achieve word recognition. In such a paper, no properties are analysed but they indicated how to choose the structuring elements.…”