Diffeomorphic B-spline vector fields with a tractable set of inequalities

Sdika, Michaël

doi:10.1090/mcom/3419

Diffeomorphic B-spline vector fields with a tractable set of inequalities
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Math. Comp. 88 (2019), 2827-2856 Request permission

Abstract:

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.

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