Elementary factorisation of Box spline subdivision

Cédric Gérot (1)

1 GIPSA-AGPIG - GIPSA - Architecture, Géométrie, Perception, Images, Gestes

When a subdivision scheme is factorised into lifting steps, it admits an in–place and invertible implementation, and it can be the predictor of many multiresolution biorthogonal wavelet transforms. In the regular setting where the underlying lattice hierarchy is defined by Z s and a dilation matrix M, such a factorisation should deal with every vertex of each subset in Z s /M Z s in the same way. We define a subdivision scheme which admits such a factorisation as being uniformly elementary factorable. We prove a necessary and sufficient condition on the directions of the Box spline and the arity of the subdivision for the scheme to admit such a factorisation, and recall some known keys to construct it in practice.

Domaines: Algèbre commutative [math.AC]; Traitement du signal et de l'image [eess.SP]; Géométrie algorithmique [cs.CG]

Cédric Gérot. Elementary factorisation of Box spline subdivision. Advances in Computational Mathematics, 2019, 45 (1), pp.153-171. ⟨10.1007/s10444-018-9612-x⟩. ⟨hal-01775340⟩