On an Application of Lattice Integral Transforms in Image Processing

The lattice integral transforms have been introduced to generalize lower and upper fuzzy for lattice-valued functions that are used approximate original from below above. They defined in complete analogy with classical transforms, particularly, the product of a function relation called kernel is integrated by Sugeno-like integral. In article, we first investigate conditions under which preserve (reverse) constant functions, appears be fundamental presumption successful approximation functions. Further, show how can applied image processing, more specifically, non-linear filtering, compression/decompression, opening/closing images. We demonstrate filters based on popular median filter as well minimum maximum filters, also opening closing using morphological erosion dilation. illustrate proposed methods various selected