Critical kernels constitute a general framework settled in the category of abstract complexes for the study of parallel thinning in any dimension. It allows to easily design parallel thinning algorithms which produce new types of skeletons, with specific geometrical properties, while guaranteeing their topological soundness. In this paper, we demonstrate that it is possible to define a skeleton based on the Euclidean distance, rather than on the common discrete distances, in the context of critical kernels. We provide the necessary definitions as well as an efficient algorithm to compute this skeleton.