Linear versus Lattice Fuzzy Transforms: Image Algebra Representation, Observations, and Results in Image Denoising
Peter Sussner, Tiago Schuster · 2018
The linear fuzzy transform (FT) has found a great variety of applications whereas the two versions of the lattice FT seem to have found almost no applications at first glance. However, a closer look at lattice FTs reveals their relationship to operators of mathematical morphology which are widely used in image processing and analysis including image noise filtering. This paper compares linear and lattice FTs in terms of some properties and experimental results in image noise reduction. Moreover, we show that both linear as well as lattice FTs can be expressed in terms of image-template products in the mathematical theory of image algebra.