Unbiased Longitudinal Brain Atlas Creation Using Robust Linear Registration And Log-Euclidean Framework For Diffeomorphisms

Abstract

We present a new method to create a diffeomorphic longitudinal (4D) atlas composed of a set of 3D atlases each representing an average model at a given age. This is achieved by generalizing atlasing methods to produce atlases unbiased with respect to the initial reference up to a rigid transformation and ensuring diffeomorphic deformations thanks to the Baker-Campbell-Hausdorff formula and the log-Euclidean framework for diffeomorphisms. Subjects are additionally weighted using an asymmetric function to closely match specified target ages. Creating a longitudinal atlas also implies dealing with subjects with large brain differences that can lead to registration errors. This is overcome by a robust rigid registration based on polar decomposition. We illustrate these techniques for the creation of a 4D pediatric atlas, showing their ability to create a temporally consistent atlas.

Regional brain development analysis through registration using anisotropic similarity, a constrained affine transformation

“…However, the unbiasing steps does not take into account affine (global) transformations leading to atlases unbiased up to an affine transformation only. Our method, developed in [38] and available in Anima-Scripts (open source scripts for medical image processing: github.com/Inria-Visages/Anima-Scripts-Public/ -RRID:SCR_017072), takes advantage of the log-Euclidean framework developed in [39] and the Baker-Campbell-Hausdorff formula, mentioned in [40] and [41], allowing to average compositions of affine transformations and diffeomorphisms. This adjustment leads to the creation of atlases up to a rigid transformation.…”

Online Atlasing Using an Iterative Centroid

“…1. An affine registration that outputs a transformation matrix B which is decomposed through polar decomposition into a rigid part R and a stretching part S as depicted in Legouhy et al [10]. 2.…”

“…In the following experiments, we evaluate the quality of the iterative centroid atlas and its divergence with respect to direct atlasing, here a method developed in Legouhy et al [10] available in Anima-Scripts 2 based on Guimond et al [8].…”

“…We first introduce the iterative centroid method and its specificities for image atlasing in Section 2. Then in Section 3, we present experiments comparing how the atlases built using direct atlasing (here a modified Guimond et al method [10]) and with our method differ from each other as they include more and more subjects. We demonstrate with three different metrics that the iterative centroid and direct atlases diverge only by a small amount in terms of transformations and that their intensity based features do not vary.…”

Regional brain development analysis through registration using anisotropic similarity, a constrained affine transformation

“…in [32], takes advantage of the log-Euclidean framework developed in [33] and the 185 Baker-Campbell-Hausdorff formula, mentionned in [34] and [35], allowing to average the 186 composition of an affine transformations and a diffeomorphism. This adjustment leads 187 to the creation of atlases up to a rigid transformation.…”