III Simposio de Postgrado 2025: Ingeniería, ciencia e innovación

57 02 *E-mail: ncaytuir@dcc.uchile.cl Nicolás Caytuiro ¹* Iván Sipiran ¹ ¹ Departamento de Ciencias de la Computación, Universidad de Chile Symmetrization of 3D Generative Models Resumen “Symmetry is what we see at a glance” – Blaise Pascal. Symmetry is ubiquitous in both natural and artificial objects, and it is a funda- mental property in geometry. It serves as a visual cue that helps humans perceive object structure and interpret spatial relationships [1, 2] . In computer vision – either in the 2D or 3D domain – symmetry has long been leveraged as a structural cons- traint to simplify complex visual tasks such as pose estimation, shape synthesis, and 3D reconstruction. Based on its mathematical definition, symmetry could be detected through finding the geometric invariance under the transformation of a symmetry group [3] . While current 3D generative models demonstrate strong performance in synthesi- zing shapes from 3D or depth data, explicitly generating symmetrical objects is rare- ly an architectural or experimental design objective. This remains true even though many objects in widely used 3D shape datasets exhibit clear reflection symmetry. This work aims to generate 3D objects that are both visually plausible and geome- trically symmetric using current generative models. We hypothesize that if a ge- nerative model is trained exclusively on partial structures (e.g., half-objects) and if the data distribution is sufficiently rich, the model should be capable of generating novel, varied half-objects that, once reflected, result in complete shapes that are both visually plausible and geometrically symmetric. To test this hypothesis, first, we introduce an evaluation protocol to assess symmetry in shapes generated by four 3D generative models. Then, we train these models from scratch on a novel dataset of half-objects, derived from the ShapeNet benchmark. Our results demonstrate that models trained on the half-objects dataset can generate novel partial shapes which, when reflected, produce complete objects that are both visually plausible and geometrically symmetric. These findings hi- ghlight the effectiveness of the proposed methodology in promoting symmetry preservation during the generative process. __References [1] Treder, M. Behind the Looking-Glass: A Review on Human Symmetry Perception. Symmetry (2010) [2] Li et al. Symmetry Strikes Back: From Single-Image Symmetry Detection to 3D Generation. arXiv (2024) [3] Mitra et al. Symmetry in 3D Geometry: Extraction and Applications. Computer Graphics Forum (2013)