Invariant SPHARM Shape Descriptors for Complex Geometry in MR Region of Interest Analysis

Abstract

In earlier work, we have shown the importance of including 3D shape characteristics when analyzing regions of interest (ROIs) in magnetic resonance imaging (MRI) data. Spherical harmonics (SPHARM) based ROI shape descriptors were proposed and shown to provide important complementary information to traditionally used simple volumetric ROI measures. In this paper we extend our SPHARM shape parameterization technique by using functions defined on concentric spherical shells. We then propose the use of a novel radial transform to obtain unique features even under independent rotations of the constituting shells. These enhanced features enable the analysis of 3D ROIs with complex topologies including those with possible disconnections (e.g. ventricles). We validate the proposed 3D shape descriptors on synthetic data and demonstrate their sensitivity to subtle shape changes in the presence of inter-subject variability. We also apply our approach to real MRI data and detect significant shape changes in the left and right thalamus in Parkinson's disease (PD) patients when compared against normal volunteers, complementing the observed volumetric changes.

SPHARM-Based Spatial fMRI Characterization With Intersubject Anatomical Variability Reduction

“…However, the process of obtaining these coefficients by direct computation of the triple integral is not efficient and would be computationally very expensive for larger ROIs. An alternate practical approach for computing (6) is to use multiple concentric spherical shells [27]. We first define , the spherical harmonic expansion of the function for a specific value of as (7) The individual function , can be visualized as the intersection between the function and a spherical shell of radius (see Fig.…”

“…Earlier work on SPHARM features that utilize shells in the manner described above derive the invariant shape features directly from (7), [24], [24], but this derived representation is not unique [24], possibly resulting in two very distinct shapes having the exact same feature vectors. To address this problem, we incorporate a radial transform [27] (8)…”

“…The shape parameterization employed in [26] was limited to convex topologies which significantly limited its applicability. In [27], we proposed an enhanced more powerful version of that earlier SPHARM-based feature representation which had the ability of handling arbitrarily complex ROI shapes including those with disjoint topologies. These enhanced features simultaneously overcame the topology limitation of our original work in [26] as well as addressed the non-unique representation problem by employing a radial transform across the SPHARM features that were derived for each of the concentric spheres within the 3-D structural MR volume [27].…”

“…In [27], we proposed an enhanced more powerful version of that earlier SPHARM-based feature representation which had the ability of handling arbitrarily complex ROI shapes including those with disjoint topologies. These enhanced features simultaneously overcame the topology limitation of our original work in [26] as well as addressed the non-unique representation problem by employing a radial transform across the SPHARM features that were derived for each of the concentric spheres within the 3-D structural MR volume [27]. In this current paper, we extend our work and present two novel contributions; first, we derive similar unique invariant SPHARM-based features for full 3-D real valued data (as opposed to our earlier work on binary ROI masks only) and then employ these new features for representing 3-D functional information in fMRI data.…”

Invariant 3D spharm features for characterizing fMRI activations in ROIs while minimizing effects of intersubject anatomical variability

“…This approach, however, could not detect independent rotations of a shape along the shells, thereby resulting in a non-unique representation [7]. In order to overcome this limitation, we have recently proposed a unique radial transform [9].…”