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Incompressible image registration using divergence-conforming B-splines

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Original languageEnglish
Title of host publicationMedical Image Computing and Computer Assisted Intervention – MICCAI 2019 - 22nd International Conference, Proceedings
EditorsDinggang Shen, Pew-Thian Yap, Tianming Liu, Terry M. Peters, Ali Khan, Lawrence H. Staib, Caroline Essert, Sean Zhou
Number of pages9
Publication statusAccepted/In press - 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11765 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


King's Authors


Anatomically plausible image registration often requires volumetric preservation. Previous approaches to incompressible image registration have exploited relaxed constraints, ad hoc optimisation methods or practically intractable computational schemes. Divergence-free velocity fields have been used to achieve incompressibility in the continuous domain, although, after discretisation, no guarantees have been provided. In this paper, we introduce stationary velocity fields (SVFs) parameterised by divergence-conforming B-splines in the context of image registration. We demonstrate that sparse linear constraints on the parameters of such divergence-conforming B-Splines SVFs lead to being exactly divergence-free at any point of the continuous spatial domain. In contrast to previous approaches, our framework can easily take advantage of modern solvers for constrained optimisation, symmetric registration approaches, arbitrary image similarity and additional regularisation terms. We study the numerical incompressibility error for the transformation in the case of an Euler integration, which gives theoretical insights on the improved accuracy error over previous methods. We evaluate the proposed framework using synthetically deformed multimodal brain images, and the STACOM’11 myocardial tracking challenge. Accuracy measurements demonstrate that our method compares favourably with state-of-the-art methods whilst achieving volume preservation.

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