Continuous Symmetries of Non-rigid Shapes

Carmi Grushko, M.Sc. Thesis Seminar
Wednesday, 13.6.2012, 14:30
Taub 401
Prof. R. Kimmel

Our world is known for its abundance of symmetric structures - in the fields of the animal kingdom, in astronomy, mathematics and chemistry, to name a few. The existence of symmetry in 3D shapes is of great interest when such applications as efficient storage, comparison and lookup are considered. Traditionally, only symmetries which are a composition of rotations and reflections were considered. These symmetries, termed extrinsic, have limited use in non-rigid shapes, as they are easily lost when the shape is deformed. A different approach, treating 3D shapes as metric spaces, allows the definition of intrinsic symmetries, which offer a way for symmetry detection in deformable, non-rigid shapes. In this work we present a method to compute intrinsic, continuous symmetries of 3D shapes, based on a general-purpose isometry-finding algorithm. We further explore non-Euclidean intrinsic continuous symmetries, and in particular, we demonstrate an algorithm for the detection of affine-invariant intrinsic continuous symmetry.

Back to the index of events