Wavelet-Based Multiscale Initial Flow For Improved Atlas Estimation in the Large Diffeomorphic Deformation Model Framework

Fleur Gaudfernau (1, 2) , Eléonore Blondiaux (3) , Stéphanie Allassonnière (1, 2) , Erwan Le Pennec (4)

1 HeKA - Health data- and model- driven Knowledge Acquisition
2 CRC (UMR_S_1138 / U1138) - Centre de Recherche des Cordeliers
3 CHU Trousseau [APHP]
4 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

Modelling the mean and variability in a population of images, a task referred to as atlas estimation, remains very challenging, especially in a clinical setting where deformations between images can occur at multiple scales. In this paper, we introduce a coarse-to-fine strategy for atlas estimation in the Large Deformation Diffeomorphic Metric Mapping framework, based on a finite parametrization of the subjects' velocity field. Using the Haar Wavelet Transform, a multiscale representation of the initial velocity fields is computed in order to optimize the template-to-subject deformations in a coarse-to-fine fashion. This reparametrization preserves the reproducing kernel Hilbert space structure of the velocity fields, enabling the algorithm to perform efficiently gradient descent. Numerical experiments on three different datasets, including a dataset of abnormal fetal brain images, show that compared to the original algorithm, the coarse-to-fine strategy reaches higher performance and yields template images that preserve important details while avoiding unrealistic features.

Mots clés: Deformable template model; Atlas estimation; Diffeomorphic deformations; Haar Wavelet; Coarse-to-fine algorithm

Domaines: Traitement du signal et de l'image [eess.SP]

Fleur Gaudfernau, Eléonore Blondiaux, Stéphanie Allassonnière, Erwan Le Pennec. Wavelet-Based Multiscale Initial Flow For Improved Atlas Estimation in the Large Diffeomorphic Deformation Model Framework. 2022. ⟨hal-03620367⟩