Multiscale Analysis from 1D Parametric Geometric Decomposition of Shapes

This paper deals with the construction of a non parametric multiscale analysis from a 1D parametric decomposition of shapes where the elements of the decomposition are geometric primitives. We focus on the case of linear structures in shapes but our construction readily extends to the case of any geometric primitives. One key point of the construction is that it is truly multiscale in the sense that a higher level is a sublevel of a lower one and that it preserves symmetries of shapes. We made some experiments to show the simplification it provides on classical shapes. Results are promising.