Toward the Assessment of Intrinsic Geometry of Implicit Brain MRI Manifolds

Karim Makki,Boulbaba Ben Amor,Douraied Ben Salem

doi:10.1109/access.2021.3113611

Abstract

Principal and Gaussian curvatures are commonly used intrinsic metrics for geometric morphometrics analysis: to assess morphometric changes in brain geometry (developmental neuroimaging studies), to quantify shape deformation (organ motion assessment), or to analyze shape variability across subjects in musculoskeletal studies (statistical shape analysis of bones). However, most of existing algorithms for estimating curvatures act on explicit surfaces (triangle meshes), making them time consuming and sensitive to parameterization and neighborhood size. In this paper, we present a suite of fast and parameterization-free algorithms to estimate second order morphometric parameters given an implicit representation for the surface and without any loss of accuracy. We first show results for direct comparisons of our algorithms with a suite of popular algorithms for estimating curvatures of surfaces represented by triangular meshes. Then, in the context of brain imaging, methods were validated against developmental brain MRI data in which surface based analysis has very often failed. We also provided a modified version of the algorithm that can deal with a Freesurfer output surface mesh, and which was evaluated using an adult brain with more complicated folding patterns. Our algorithm provided a more realistic measures of intrinsic curvature for the white matter (mostly ranged between ±0.07 mm−2) which confirms its robustness. As compared to mesh-based algorithms, our algorithm reduces computation times from a few minutes to only a few seconds, showing a decrease by a factor of up to 7.

Highlights

F Or most of existing algorithms for estimating curvatures of 2D surfaces embedded in 3D space, the surface is given by an explicit form 1 [1], [2]
The fact that implicit models have already been successfully employed in computer vision applications [12], [13], in particular in medical imaging, see for instance the representation of blood vessel surface implicitly in [14], see the work of Mémoli et al introducing implicit brain imaging [15], we were surprised to find that a little attention has been devoted to the determination of intrinsic properties of thin brain structures without the need to parameterize the surface somewhere
To avoid duplication of efforts such as mesh post-processing steps, usually required to perform brain feature extraction with Freesurfer, we provide an algorithm acting directly on segmented volumes, and generating a smooth surface mesh, together with its texture feature maps

Summary

Introduction

F Or most of existing algorithms for estimating curvatures of 2D surfaces embedded in 3D space, the surface is given by an explicit form 1 [1], [2]. More precisely, to study motion, growth, and inter-subject variability in anatomical structures, the common starting point is a ground truth binary segmentation (e.g. of brain [3], organs [4], tumors [5], muscles [6], bones and surrounding tissues [7], etc.). Under such circumstances, an alternative solution to directly estimate curvature from binary segmentations suggests the representation of surfaces by an implicit form [8]–[11], allowing the computations to be performed in a cartesian grid.

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Conclusion