Pasha Hosseinbor A, Chung Moo K, Koay Cheng Guan, Schaefer Stacey M, van Reekum Carien M, Schmitz Lara Peschke, Sutterer Matt, Alexander Andrew L, Davidson Richard J
Waisman Laboratory for Brain Imaging and Behavior, University of Wisconsin-Madison, Madison, WI, USA.
Waisman Laboratory for Brain Imaging and Behavior, University of Wisconsin-Madison, Madison, WI, USA; Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, WI, USA.
Med Image Anal. 2015 May;22(1):89-101. doi: 10.1016/j.media.2015.02.004. Epub 2015 Mar 9.
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.
基于图像的脑部分割通常会产生多个不相连的解剖结构，这给形态形状分析带来了重大挑战。现有的形状模型，如广泛使用的球谐（SPHARM）表示，假设拓扑不变性，因此无法同时对多个不相交的结构进行参数化。在这种情况下，必须将SPHARM分别应用于每个单独的结构。我们提出了一种新颖的表面参数化技术，使用4D超球谐函数将多个不相交的物体表示为单个解析函数，称之为HyperSPHARM。HyperSPHARM背后的基本思想是将整个不相交的3D物体集合进行球极投影到4D超球面上，随后用4D超球谐函数同时对它们进行参数化。因此，与SPHARM不同，HyperSPHARM允许对多个不相交的物体进行整体处理。在一个健康成人大脑的成像数据集中，我们将HyperSPHARM应用于海马体和杏仁核。HyperSPHARM表示被用作一种数据平滑技术，而HyperSPHARM系数则用于支持向量机设置中进行物体分类。正如本文将展示的，HyperSPHARM产生的结果与SPHARM几乎相同。它相对于SPHARM的关键优势在于计算方面；HyperSPHARM比SPHARM具有更高的计算效率，因为它可以使用少得多的基函数对多个不相交的结构进行参数化，并且球极投影避免了SPHARM繁重的表面扁平化。此外，与SPHARM不同，HyperSPHARM可以处理任何类型的拓扑结构，SPHARM的分析仅限于拓扑不变的结构。
