Alpha 形状：跨形态多样的结构确定 3D 形状复杂度。
Alpha shapes: determining 3D shape complexity across morphologically diverse structures.
机构信息
Institute of Ageing and Chronic Disease, University of Liverpool, Liverpool, L7 8TX, UK.
Manchester X-ray Imaging Facility, University of Manchester, Manchester, M13 9PL, UK.
出版信息
BMC Evol Biol. 2018 Dec 5;18(1):184. doi: 10.1186/s12862-018-1305-z.
BACKGROUND
Following recent advances in bioimaging, high-resolution 3D models of biological structures are now generated rapidly and at low-cost. To use this data to address evolutionary and ecological questions, an array of tools has been developed to conduct shape analysis and quantify topographic complexity. Here we focus particularly on shape techniques applied to irregular-shaped objects lacking clear homologous landmarks, and propose a new 'alpha-shapes' method for quantifying 3D shape complexity.
METHODS
We apply alpha-shapes to quantify shape complexity in the mammalian baculum as an example of a morphologically disparate structure. Micro- computed-tomography (μCT) scans of bacula were conducted. Bacula were binarised and converted into point clouds. Following application of a scaling factor to account for absolute size differences, a suite of alpha-shapes was fitted per specimen. An alpha shape is formed from a subcomplex of the Delaunay triangulation of a given set of points, and ranges in refinement from a very coarse mesh (approximating convex hulls) to a very fine fit. 'Optimal' alpha was defined as the refinement necessary in order for alpha-shape volume to equal CT voxel volume, and was taken as a metric of overall 'complexity'.
RESULTS
Our results show that alpha-shapes can be used to quantify interspecific variation in shape 'complexity' within biological structures of disparate geometry. The 'stepped' nature of alpha curves is informative with regards to the contribution of specific morphological features to overall 'complexity'. Alpha-shapes agrees with other measures of complexity (dissection index, Dirichlet normal energy) in identifying ursid bacula as having low shape complexity. However, alpha-shapes estimates mustelid bacula as being most complex, contrasting with other shape metrics. 3D fractal dimension is identified as an inappropriate metric of complexity when applied to bacula.
CONCLUSIONS
Alpha-shapes is used to calculate 'optimal' alpha refinement as a proxy for shape 'complexity' without identifying landmarks. The implementation of alpha-shapes is straightforward, and is automated to process large datasets quickly. We interpret alpha-shapes as being particularly sensitive to concavities in surface topology, potentially distinguishing it from other shape complexity metrics. Beyond genital shape, the alpha-shapes technique holds considerable promise for new applications across evolutionary, ecological and palaeoecological disciplines.
背景
随着生物成像技术的最新进展，现在可以快速且低成本地生成高分辨率的生物结构 3D 模型。为了利用这些数据来解决进化和生态问题，已经开发了一系列工具来进行形状分析和量化地形复杂性。在这里，我们特别关注应用于缺乏明确同源标志点的不规则形状物体的形状技术，并提出了一种新的“alpha 形状”方法来量化 3D 形状复杂性。
方法
我们以哺乳动物阴茎骨为例，应用 alpha 形状来量化形态差异较大的结构的形状复杂性。对阴茎骨进行微计算机断层扫描 (μCT) 扫描。将阴茎骨二值化并转换为点云。在应用比例因子来解释绝对尺寸差异之后，为每个标本拟合一系列 alpha 形状。alpha 形状是由给定点集的 Delaunay 三角剖分的子复杂形状形成的，从非常粗糙的网格（逼近凸包）到非常精细的拟合，细化程度各不相同。“最优”alpha 被定义为使 alpha 形状体积等于 CT 体素体积所需的细化程度，并作为整体“复杂性”的度量。
结果
我们的结果表明，alpha 形状可用于量化具有不同几何形状的生物结构中种间形状“复杂性”的变化。alpha 曲线的“阶梯状”性质对于特定形态特征对整体“复杂性”的贡献具有信息性。alpha 形状与其他复杂性度量（解剖指数、Dirichlet 法向能量）一致，认为熊科阴茎骨的形状复杂性较低。然而，alpha 形状估计值认为鼬科阴茎骨的复杂性最高，与其他形状度量值形成对比。3D 分形维数被确定为应用于阴茎骨时不适当的复杂性度量。
结论
alpha 形状用于计算“最优”alpha 细化程度作为形状“复杂性”的代理，而无需识别标志点。alpha 形状的实现简单明了，并通过自动化处理快速处理大数据集。我们认为 alpha 形状特别敏感于表面拓扑的凹度，可能与其他形状复杂性度量区分开来。除了生殖器形状之外，alpha 形状技术在进化、生态和古生态等多个领域都有很大的应用潜力。
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