A Landmark-free Approach for Surface Asymmetry Detection and Profile Drawings from Bilaterally Symmetrical Geometry

Bilaterally symmetrical objects represent a large and important proportion of archaeological artifacts and biological objects. The identification of the plane of symmetry plays a vital role in quantifying surface asymmetry and producing profile drawings in archaeology and anthropology. The correct recognition of symmetry provides evidence to allow experts to restore damaged artifacts, assess consistency in artifact manufacture, and examine morphological variability in human development. With the increasing availability of archaeological and anthropological three-dimensional (3D) meshes, landmark-based and landmark-free morphometric methods for detecting planes of symmetry have both been proposed. However, the landmark-based approach requires manual identification of landmark locations, and hence they are time-consuming and prone to error. Additionally, the landmark-independent morphometric method is influenced by missing data. This study presents an effective landmark-free approach to approximate the best-fitted plane of symmetry from nearly bilaterally symmetrical objects by means of finding the plane with the minimum geometric differences between the original and mirrored meshes. Subsequently, a global and regional method is carried out to quantify surface asymmetry, reducing the effect of the size and orientation of 3D meshes on gross asymmetry detection. Finally, profile drawings are produced by computing the intersections of the plane of symmetry and 3D meshes. Both synthetic and real objects are used to evaluate the effectiveness and robustness of the proposed method. Our results show the approximated plane of symmetry generated by the proposed method is consistent with that determined by anatomical landmarks, and no significant differences in asymmetry ratio representing the degree of gross asymmetry are found between the landmark-based and proposed methods. These results demonstrate that the proposed method provides a suitable plane of symmetry from a bilaterally symmetrical object with small geometric distortion or simple missing geometry, thereby speeding up asymmetry detection and profile drawings.