Symmetry Detection in Geometric Models

PUNTIS (LO1506), SGS-2019-016Symmetry occurs very commonly in real world objects as well as in artificially created geometric models. The knowledge about symmetry of a given object can be very useful in many applications in computer graphics and geometry processing, such as compression, object alignment, symmetric editing or completion of partial objects. In order to use the symmetry of any object in any given application, it first needs to be found. In this work, we provide some background about symmetry in general and about different types of symmetry, mainly in 3D objects. Then we focus on the task of automatic symmetry detection in 3D objects and we also describe the link between symmetry detection and the problem of registration. Most importantly, we present our own contribution in these fields. First, we show a new method of evaluating consensus in RANSAC surface registration together with a thorough analysis of various distance metrics for rigid transformations that can be used in this new approach. Afterwards, we provide an analysis of different representations of the space of planes in context of symmetry plane detection. At last, we propose a new, robust, fast and flexible method for symmetry plane detection based on a novel differentiable symmetry measure