Landmark-based spherical quasi-conformal mapping for hippocampal surface registration.

Abstract

<h4>Background</h4>The cognitive decline induced by Alzheimer's disease (AD) is closely related to changes in hippocampal structure captured by magnetic resonance imaging (MRI). To accurately analyze the morphological changes of the hippocampus induced by AD, it is necessary to establish a one-to-one surface correspondence to compare the morphological measurements across different hippocampal surfaces. However, most existing landmark-based registration methods cannot satisfy both landmark matching and diffeomorphism under large deformations. To address these challenges, we propose a landmark-based spherical registration method via quasi-conformal mapping to establish a one-to-one correspondence between different hippocampal surfaces.<h4>Methods</h4>In our approach, we use the eigen-graph of the hippocampal surface to extract the intrinsic and unified landmarks of all the hippocampal surfaces and then realize the parameterization process from the hippocampal surface to a unit sphere according to the barycentric coordinate theory and the triangular mesh optimization algorithm. Finally, through the local stereographic projection, the alignment of the landmarks is achieved based on the quasi-conformal mapping on a two-dimensional (2D) plane under the constraints of Beltrami coefficients which can effectively control the topology distortion.<h4>Results</h4>We verified the proposed registration method on real hippocampus data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database and created AD and normal control (NC) groups. Our registration algorithm achieved an area distortion index (ADI) of 0.4362e-4±0.7800e-5 in the AD group and 0.5671e-4±0.602e-5 in the NC group, and it achieved an angle distortion index (E_angle) of 0.6407±0.0258 in the AD group and 0.6271±0.0194 in the NC group. The accuracy of support vector machine (SVM) classification for the AD <i>vs.</i> NC groups based on the morphological features extracted from the registered hippocampal surfaces reached 94.2%.<h4>Conclusions</h4>This landmark-based spherical quasi-conformal mapping for hippocampal surface registration algorithm can maintain precise alignment of the landmarks and bijectivity in the presence of large deformation.