Shan Shan

Graduate Student
Department of mathematics
Duke University

email: sshan at math dot duke dot edu

ariaDNE: A Robustly Implemented Algorithm for Dirichlet Normal Energy

Shan Shan     Shahar Z. Kovalsky     Julie M. Winchester     Doug M. Boyer     Ingrid Daubechies


Paper       Supplementary       Code


The Dirichlet energy of the normal measures how much a 3D surface bends; DNE, a discretized version for 3D meshes, is effective for biological studies of morphological surfaces. Recent studies found that the DNE algorithm is sensitive to various surface preparation procedures, raising concerns regarding comparability and objectivity when utilizing DNE in morphological research. We provide a robustly implemented algorithm for computing the Dirichlet normal energy (ariaDNE) on 3D meshes. We show that ariaDNE is much more stable than DNE when preparation-related mesh surface attributes such as resolution (polygon count), mesh representation (i.e., a different set of points/nodes or triangles representing the same continuous surface) and noise are varied through simulation. We also show that the effects of smoothing and boundary faces are more limited on ariaDNE than DNE. Further, ariaDNE retains the potential of DNE for biological studies, illustrated by it effectively differentiating species by dietary preferences. AriaDNE can be a useful tool to uniformly quantify shape on samples of surface meshes collected with different instruments or at different resolutions, and prepared by varying procedures. To facilitate the field to move towards this goal, the supplementary materials provide ariaDNE values for specimens used in previously published DNE analyses. Scripts for computing ariaDNE can be found by link within this manuscript.

ariaDNE for previously published DNE analysis