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•Introduce HyperSPHARM for simultaneous parameterization of multiple disjoint objects.•Show that HyperSPHARM possesses greater computational efficiency than SPHARM.•Employ isotropic ...sampling along 4D sphere for HyperSPHARM interpolation.•Employ HyperSPHARM as both a data smoothing and an object classification technique.
Image-based parcellation of the brain often leads to multiple disconnected anatomical structures, which pose significant challenges for analyses of morphological shapes. Existing shape models, such as the widely used spherical harmonic (SPHARM) representation, assume topological invariance, so are unable to simultaneously parameterize multiple disjoint structures. In such a situation, SPHARM has to be applied separately to each individual structure. We present a novel surface parameterization technique using 4D hyperspherical harmonics in representing multiple disjoint objects as a single analytic function, terming it HyperSPHARM. The underlying idea behind HyperSPHARM is to stereographically project an entire collection of disjoint 3D objects onto the 4D hypersphere and subsequently simultaneously parameterize them with the 4D hyperspherical harmonics. Hence, HyperSPHARM allows for a holistic treatment of multiple disjoint objects, unlike SPHARM. In an imaging dataset of healthy adult human brains, we apply HyperSPHARM to the hippocampi and amygdalae. The HyperSPHARM representations are employed as a data smoothing technique, while the HyperSPHARM coefficients are utilized in a support vector machine setting for object classification. HyperSPHARM yields nearly identical results as SPHARM, as will be shown in the paper. Its key advantage over SPHARM lies computationally; HyperSPHARM possess greater computational efficiency than SPHARM because it can parameterize multiple disjoint structures using much fewer basis functions and stereographic projection obviates SPHARM’s burdensome surface flattening. In addition, HyperSPHARM can handle any type of topology, unlike SPHARM, whose analysis is confined to topologically invariant structures.
Here, we describe a novel method for volumetric segmentation of the amygdala from MRI images collected from 35 human subjects. This approach is adapted from open-source techniques employed previously ...with the hippocampus (Suh et al., 2011; Wang et al., 2011a,b). Using multi-atlas segmentation and machine learning-based correction, we were able to produce automated amygdala segments with high Dice (Mean = 0.918 for the left amygdala; 0.916 for the right amygdala) and Jaccard coefficients (Mean = 0.850 for the left; 0.846 for the right) compared to rigorously hand-traced volumes. This automated routine also produced amygdala segments with high intra-class correlations (consistency = 0.830, absolute agreement = 0.819 for the left; consistency = 0.786, absolute agreement = 0.783 for the right) and bivariate (r = 0.831 for the left; r = 0.797 for the right) compared to hand-drawn amygdala. Our results are discussed in relation to other cutting-edge segmentation techniques, as well as commonly available approaches to amygdala segmentation (e.g., Freesurfer). We believe this new technique has broad application to research with large sample sizes for which amygdala quantification might be needed.
We present a novel surface parameterization technique using hyperspherical harmonics (HSH) in representing compact, multiple, disconnected brain subcortical structures as a single analytic function. ...The proposed hyperspherical harmonic representation (HyperSPHARM) has many advantages over the widely used spherical harmonic (SPHARM) parameterization technique. SPHARM requires flattening 3D surfaces to 3D sphere which can be time consuming for large surface meshes, and can't represent multiple disconnected objects with single parameterization. On the other hand, HyperSPHARM treats 3D object, via simple stereographic projection, as a surface of 4D hypersphere with extremely large radius, hence avoiding the computationally demanding flattening process. HyperSPHARM is shown to achieve a better reconstruction with only 5 basis compared to SPHARM that requires more than 441.
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