Diffeomorphic B-Spline Vector Fields With a Tractable Set of Inequalities

Michaël Sdika (1, 2)

1 Service Informatique et développements
2 MYRIAD - Modeling & analysis for medical imaging and Diagnosis

B-spline diffeomorphic vector fields are objects of great interest in image processing and analysis, more specifically for the registration of medical images. In this paper, several conditions on the B-spline coefficients ensuring that a given B-spline vector field is a diffeomorphism are proposed. Some properties of vector fields satisfying these conditions are established showing that they are not too restrictive while having a reasonable computational complexity. This work opens the way to the development of practical image registration algorithms in two and three dimensions whose unknowns would be such diffeomorphic B-spline vector fields.

Domaines: Analyse numérique [math.NA]; Traitement des images [eess.IV]

Michaël Sdika. Diffeomorphic B-Spline Vector Fields With a Tractable Set of Inequalities. Mathematics of Computation, 2019, 88 (320), pp.2827--2856. ⟨10.1090/mcom/3419⟩. ⟨hal-01956237⟩