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

Author: Michaël Sdika
Journal: Math. Comp. 88 (2019), 2827-2856
MSC (2010): Primary 65D07, 65D18, 37C05, 62H35, 68U10
Published electronically: March 5, 2019
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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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Additional Information

Michaël Sdika
Affiliation: Université Lyon, INSA-Lyon, Université Claude Bernard Lyon 1, UJM-Saint Etienne, CNRS, Inserm, CREATIS UMR 5220, U1206, F-69000, Lyon, France

Received by editor(s): June 23, 2017
Received by editor(s) in revised form: December 8, 2017, November 6, 2018, and November 25, 2018
Published electronically: March 5, 2019
Article copyright: © Copyright 2019 American Mathematical Society