Levelings in vector spaces

This paper focuses on a novel class of morphological filters called levelings and their extension to vector spaces. Unlike many filtering techniques reported in the literature, levelings suppress details while preserving perfectly the contours of the remaining objects. This feature makes them ideal tools for simplifying images in a large set of applications. They are particularly useful as preprocessing films for segmentation and coding. However when dealing with color images, new colors may be introduced if each color component is treated separately. In order to solve this drawback two extensions of scalar levelings to vector spaces are presented.