Skeleton is a widely addressed topic in binary image processing and object or shape representation. The difficulty raised by the discrete nature of images has led to different classes of methods. Among the most popular ones, distance based methods led to the important notion of centers of maximal balls (CMB), and mathematical morphology based methods led both to an efficient computation of CMB and to a completely different class of approaches, relying on homotopic thinning. Skeleton by influence zones (SKIZ) is another important related problem, often addressed using tools from mathematical morphology.

When imprecision has to be explicitly modeled, then objects become fuzzy sets and all the previous approaches for skeleton and SKIZ have to be extended to deal with fuzzy sets and to cope with spatial imprecision. This chapter gives an overview of the main existing definitions of fuzzy skeleton and fuzzy SKIZ, including some derived from grey level image processing, and proposes a few novel definitions.