Approximations of the diffeomorphic metric and their applications in shape learning

Statistical Shape Analysis of Large Datasets Based on Diffeomorphic Iterative Centroids

In this paper, we propose an approach for template-based shape analysis of large datasets, using diffeomorphic centroids as atlas shapes. Diffeomorphic centroid methods fit in the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework and use kernel metrics on currents to quantify surface dissimilarities. The statistical analysis is based on a Kernel Principal Component Analysis (Kernel PCA) performed on the set of initial momentum vectors which parametrize the deformations. We tested the approach on different datasets of hippocampal shapes extracted from brain magnetic resonance imaging (MRI), compared three different centroid methods and a variational template estimation. The largest dataset is composed of 1,000 surfaces, and we are able to analyse this dataset in 26 h using a diffeomorphic centroid. Our experiments demonstrate that computing diffeomorphic centroids in place of standard variational templates leads to similar shape analysis results and saves around 70% of computation time. Furthermore, the approach is able to adequately capture the variability of hippocampal shapes with a reasonable number of dimensions, and to predict anatomical features of the hippocampus, only present in 17% of the population, in healthy subjects.

Evolution of hippocampal shapes across the human lifespan

Aberrant hippocampal morphology plays an important role in the pathophysiology of aging. Volumetric analysis of the hippocampus has been performed in aging studies; however, the shape morphometry--which is potentially more informative in terms of related cognition--has yet to be examined. In this paper, we employed an advanced brain mapping technique, large deformation diffeomorphic metric mapping (LDDMM), and a dimensionality reduction approach, locally linear diffeomorphic metric embedding (LLDME), to explore age-related changes in hippocampal shape as delineated from magnetic resonance (MR) images of 302 healthy adults aged from 18 to 94 years. Compared with the hippocampal volumes, the hippocampal shapes clearly showed the nonlinear trajectory of biological aging across the human lifespan, where the variation of hippocampal shapes by age was characterized by a cubic polynomial. By integrating of LDDMM and LLDME, we were also able to illustrate the average hippocampal shapes in each individual decade. In addition, LDDMM and LLDME facilitated the identification of 63 years as a threshold beyond which hippocampal morphological changes were accelerated. Adults over 63 years of age showed the inward-deformation bilaterally in the head of the hippocampi and the left subiculum regardless of hippocampal volume reduction when compared to adults younger than 63. Hence, we demonstrated that the shape of anatomical structures added another dimension of structural morphological quantification beyond the volume in understanding aging.