Spradley Jackson P, Pampush James D, Morse Paul E, Kay Richard F
Department of Evolutionary Anthropology, Duke University, Durham, North Carolina, 27708.
Department of Anthropology, University of Florida, Gainesville, Florida.
Am J Phys Anthropol. 2017 May;163(1):94-109. doi: 10.1002/ajpa.23188. Epub 2017 Feb 20.
Dirichlet normal energy (DNE) is a metric of surface topography that has been used to evaluate the relationship between the surface complexity of primate cheek teeth and dietary categories. This study examines the effects of different 3D mesh retriangulation protocols on DNE. We examine how different protocols influence the DNE of a simple geometric shape-a hemisphere-to gain a more thorough understanding than can be achieved by investigating a complex biological surface such as a tooth crown.
We calculate DNE on 3D surface meshes of hemispheres and on primate molars subjected to various retriangulation protocols, including smoothing algorithms, smoothing amounts, target face counts, and criteria for boundary face exclusion. Software used includes R, MorphoTester, Avizo, and MeshLab. DNE was calculated using the R package "molaR."
In all cases, smoothing as performed in Avizo sharply decreases DNE initially, after which DNE becomes stable. Using a broader boundary exclusion criterion or performing additional smoothing (using "mesh fairing" methods) further decreases DNE. Increasing the mesh face count also results in increased DNE on tooth surfaces.
Different retriangulation protocols yield different DNE values for the same surfaces, and should not be combined in meta-analyses. Increasing face count will capture surface microfeatures, but at the expense of computational speed. More aggressive smoothing is more likely to alter the essential geometry of the surface. A protocol is proposed that limits potential artifacts created during surface production while preserving pertinent features on the occlusal surface.
狄利克雷正态能量（DNE）是一种表面形貌度量，已被用于评估灵长类颊齿表面复杂性与饮食类别之间的关系。本研究考察了不同的三维网格重新三角剖分协议对DNE的影响。我们研究不同协议如何影响一个简单几何形状——半球体的DNE，以便比通过研究诸如牙冠等复杂生物表面能更全面地理解。
我们在半球体的三维表面网格以及经过各种重新三角剖分协议处理的灵长类磨牙上计算DNE，这些协议包括平滑算法、平滑量、目标面数量以及边界面排除标准。使用的软件包括R、MorphoTester、Avizo和MeshLab。DNE使用R包“molaR”进行计算。
在所有情况下，Avizo中执行的平滑操作最初会使DNE急剧下降，之后DNE变得稳定。使用更宽泛的边界排除标准或执行额外的平滑操作（使用“网格光顺”方法）会进一步降低DNE。增加网格面数量也会导致牙齿表面的DNE增加。
不同的重新三角剖分协议对于相同表面会产生不同的DNE值，并且不应在荟萃分析中合并使用。增加面数量会捕捉表面微观特征，但以计算速度为代价。更激进的平滑操作更有可能改变表面的基本几何形状。提出了一种协议，该协议在保留咬合面上相关特征的同时，限制表面生成过程中产生的潜在伪影。
