A Comparison of Spherical Harmonic and Sliding Semilandmark Analyses as Methods for Three‐Dimensional Shape Evaluation
A Comparison of Spherical Harmonic and Sliding Semilandmark Analyses as Methods for Three‐Dimensional Shape Evaluation
复制标题
球谐函数和滑动半地标分析作为三维形状评估方法的比较
DOI：
10.1096/fasebj.2020.34.s1.05335
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Sylvester, Adam D.
中科院分区：
文献类型：
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作者：
Goldstein, Deanna M.;Harper, Christine M.;Sylvester, Adam D.
量化形态变异的能力是生物学研究不可或缺的一部分。在几何形态测量 (GM) 分析中使用滑动半地标可以在三个维度上评估整个骨骼形态。然而，当结构缺乏明显的地标放置的同源特征时，滑动半地标分析很难完成。在这种情况下，球谐函数 (SPHARM) 提供了另一种形状分析方法。在这里，我们通过将非洲猿和现代人类跟骨滑动半地标分析的结果进行比较来评估 SPHARM 方法。对现代人类 (n=20)、黑猩猩 (n=20) 和大猩猩 (n=20) 跟骨进行表面扫描。对于 GM 分析，1007 个滑动半地标均匀分布在每个跟骨的外表面。滑动半地标以最小化薄板样条插值函数相对于更新的 Procrustes 平均值的弯曲能量。然后使用广义 Procrustes 分析来对齐最终的地标配置。对于 SPHARM 分析，表面模型被映射到球体表面（参数化），然后分解为球谐函数的加权和。由于球谐函数为量化形状提供了标准化基础，因此调和函数的系数可以用作形状描述符。使用 Procrustes 坐标和 SPHARM 系数的主成分 (PC) 分析总结跟骨形状变化。通过计算均方根 (RMS) 和每个物种的平均样本的表面模型之间的最大距离，以及 PC 扭曲的表面模型，对沿着 PC 1-3 产生与平均值的两个标准偏差进行比较。滑动半地标和 SPHARM 都沿着前两个 PC 分析不同的物种。对于这两项分析，非洲猿和现代人类沿着 PC1 分开。物种平均值之间的平均 RMS 为 0.25 毫米。两次分析的平均表面模型之间的最大表面距离均小于 0.23 毫米。所有相应 PC 翘曲之间的平均 RMS 为 0.82 毫米。 PC 经线之间的最大表面距离均小于 1 毫米。尽管两次分析得出的 PC 图之间存在微小差异，但物种之间的形态学差异相同。 SPHARM 和基于滑动半地标的 PC 扭曲和物种平均值表面模型之间的主要差异出现在锐边周围，尽管这些差异很小，但使用 SPHARM 分析较少定义这些边缘。总体而言，SPHARM 提供了与滑动半地标分析相同的形状表示，使其成为评估三个维度形状的可比较方法。支持或资助信息该项目得到了 NSF 拨款 # BCS ‐ 1824630 的支持。
The ability to quantify morphological variation is integral to biological research. The use of sliding semilandmarks in geometric morphometric (GM) analyses allows for the evaluation of whole bone morphology in three dimensions. A sliding semilandmark analysis, however, is difficult to complete when structures lack obvious homologous features for landmark placement. Spherical harmonics (SPHARM) offers an alternative method for shape analysis in such cases. Here we evaluate the SPHARM method by comparing results to those from a sliding semilandmark analysis of the calcaneus in African apes and modern humans.Modern human (n=20), chimpanzee (n=20), and gorilla (n=20) calcanei were surface scanned. For the GM analysis, 1007 sliding semilandmarks were evenly distributed across the external surface of each calcaneus. Semilandmarks were slid to minimize the bending energy of the thin plate spline interpolation function relative to an updated Procrustes average. Final landmark configurations were then aligned using Generalized Procrustes Analysis. For the SPHARM analysis, surface models were mapped onto the surface of a sphere (parameterization), and then decomposed into a weighted sum of spherical harmonic functions. Because the spherical harmonics provide a standardized basis for quantifying shape, coefficients of the harmonic functions can be used as shape descriptors. Calcaneal shape variation was summarized using a principal components (PC) analysis of the Procrustes coordinates and SPHARM coefficients. Analyses were compared through calculation of the root mean square (RMS) and maximum distance between surface models of the average specimen from each species, as well as surface models of PC warps created two standard deviations from the average along PCs 1–3.Both sliding semilandmark and SPHARM analyses separate species along the first two PCs. For both analyses, African apes and modern humans separate along PC1. Average RMS between species averages was 0.25 mm. Maximum surface distances between average surface models from the two analyses were all less than 0.23 mm. Average RMS between all respective PC warps was 0.82 mm. Maximum surface distances between PC warps were all less than 1 mm. Although there were minor differences between PC plots produced from the two analyses, the same general morphological distinctions between species were identified. The primary differences between SPHARM and sliding semilandmark‐based surface models of PC warps and species averages occur around sharp edges, which are less defined using the SPHARM analysis, although these differences are small. Overall, SPHARM provides the same shape representation as a sliding semilandmark analysis, making it a comparable method for the evaluation of shape in three dimensions.Support or Funding InformationThis project was supported by NSF grant # BCS ‐ 1824630.