In this paper, we have extended the approach defined in [Segmentation of Discrete Curves into Fuzzy Segments, Segmentation of Discrete Curves into Fuzzy Segments, extented version] to a multiorder analysis. The approach is based on the arithmetical definition of discrete lines [G?om?trie discr?te, calculs en nombre entiers et algorithmique] with variable thickness. We provide a framework to analyse a digital curve at different levels of thickness. The extremities points of a segment provided at a high resolution are tracked at lower resolution in order to refine their locations. The high resolution level is automatically defined from the stability of the number of segments between two consecutive levels. The method is threshold-free and automatically provides a partitioning of a digital curve into its meaningful parts.