DIFFEOMORPHIC B-SPLINE VECTOR FIELDS WITH A TRACTABLE SET OF INEQUALITIES

摘要

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.