Group-wise cortical correspondence via sulcal curve-constrained entropy minimization

Abstract

We present a novel cortical correspondence method employing group-wise registration in a spherical parametrization space for the use in local cortical thickness analysis in human and non-human primate neuroimaging studies. The proposed method is unbiased registration that estimates a continuous smooth deformation field into an unbiased average space via sulcal curve-constrained entropy minimization using spherical harmonic decomposition of the spherical deformation field. We initialize a correspondence by our pair-wise method that establishes a surface correspondence with a prior template. Since this pair-wise correspondence is biased to the choice of a template, we further improve the correspondence by employing unbiased ensemble entropy minimization across all surfaces, which yields a deformation field onto the iteratively updated unbiased average. The specific entropy metric incorporates two terms: the first focused on optimizing the correspondence of automatically extracted sulcal landmarks and the second on that of sulcal depth maps. We also propose an encoding scheme for spherical deformation via spherical harmonics as well as a novel method to choose an optimal spherical polar coordinate system for the most efficient deformation field estimation. The experimental results show evidence that the proposed method improves the correspondence quality in non-human primate and human subjects as compared to the pair-wise method.

Fig. 1

Schematic overview of the proposed method

Fig. 2

Displacement encoding (a) and estimated deformation field (sampling of a continuous representation) with sulcal depth maps (b). A spherical displacement is encoded as change in spherical angles after rotation onto the equator for arclength preservation, which avoids a distorted displacement representation. The deformation field is estimated by extrapolation using spherical harmonic decomposition.

Fig. 3

Visual comparison of correspondence results. The colored template surface (first column) is propagated to a selected, representative example surface via initial spherical mapping (second), pair-wise correspondence (third), and group-wise correspondence (fourth). The arrows indicate areas of visual differences across the correspondence methods.

Fig. 4

Sulcal curve agreement by initial spherical mapping (left), pair-wise correspondence (middle), and group-wise correspondence (right). The arrows indicate improved agreement in the group-wise as compared to the pair-wise correspondence.

Fig. 5

Reconstruction errors (a) and cumulative coefficient load for elevation (b) and azimuth (c) displacements. No major differences are observed for the elevation displacements, whereas for the azimuth displacements, the total amount of the coefficient load significantly decreases for the optimal pole selection.