A Locally Linear Method for Enforcing Temporal Smoothness in Serial Image Registration - Longitudinal Registration and Shape Modeling - page 11

A Locally Linear Method for Enforcing
Temporal Smoothness in Serial Image
Registration

B

Ernst Schwartz 1 , 2(

) , Andras Jakab 1 , 2 , Gregor Kasprian 2 ,
Lilla Zollei 3 , and Georg Langs 1 , 2

1 CIR Lab, Department of Biomedical Imaging and Image-Guided Therapy,
Medical University of Vienna, Vienna, Austria
[e-mail]
2 Department of Biomedical Imaging and Image-Guided Therapy,
Medical University of Vienna, Vienna, Austria
3 Laboratory for Computational Neuroimaging,
Martinos Center for Biomedical Imaging, Massachusetts General Hospital,
Boston, USA

Abstract. Deformation fields obtained from image registration are com-
monly used for deriving measurements of morphological changes between
reference and follow-up images. As the underlying image matching prob-
lem is ill-posed, the exact shape of these deformation fields is often
dependent on the regularization method. In longitudinal and cross-
sectional studies this effect is amplified if time between acquisitions
varies and smoothness between serial deformations is neglected. Existing
solutions suffer from high computational costs, strong modeling assump-
tions and the bias towards a single reference image. In this paper, we
propose a computationally ecient solution to this problem via a tem-
poral smoothing formulation in the one-parameter subgroup of diffeo-
morphisms parametrized by stationary velocity fields. When applied to
modeling fetal brain development, the proposed regularization results in
smooth deformation fields over time and high data fidelity.

1 Introduction

Accurately estimating the deformation of an anatomical structure as a function
of time or age from a set of examples is central to the analysis of developmental
[ 1 ] and degenerative processes [ 2 ]. Finding a temporal deformation field that rep-
resents the underlying process well, and at the same time captures the variability
in the training population requires regularization.
Modelling fetal brain development [ 3 , 4 ] is particularly challenging. The reg-
ularization method has substantial impact on the resulting deformation due

This research was supported by the Austian National Bank (14812, FETALMOR-
PHO), the Austrian Science Fund (P 22578-B19, PULMARCH), and the European
Union (FP7-ICT-2009-5/257528, KHRESMOI and FP7-ICT-2009-5/318068, VIS-
CERAL).