Analysis of Partial Axial Symmetry on 3D Surfaces and Its Application in the Restoration of Cultural Heritage Objects

Abstract

Symmetry is a ubiquitous concept that can help to understand the structure of real objects. One of the main challenging problems in the analysis of symmetry is the robustness against high partiality, i.e., when the support of the symmetry in the input geometry is small. In this paper, we address the problem of finding the partial axial symmetry of 3D objects through the analysis of surface descriptors with invariance to partiality. These descriptors are used to reduce the search space of axial symmetric correspondences, and allows us to design an effective and efficient algorithm to detect the generator axis of the symmetry. Our algorithm collects enough evidence of the presence of the axial symmetry in a consensus-based approach. Our algorithm can also identify the support of the axial symmetry. Our experiments show the robustness of our method in challenging scenarios. We show that our method is good to generate plausible restorations of damaged cultural heritage objects.