טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentCarmi Grushko
SubjectContinuous Symmetries of Non-rigid Shapes
DepartmentDepartment of Computer Science
Supervisor Full Professor Kimmel Ron
Full Thesis textFull thesis text - English Version


Abstract

    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 symmetries in 3D shapes is of great interest when such applications as efficient storage, comparison and search are considered.

    Traditionally, only symmetries which are a composition of rotations and reflections were studied. 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 thesis 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.

    Finally, we develop an efficient algorithm to solve dense, low-dimensional linear min-max problems, which directly improves the performance of the previously mentioned general-purpose isometry-finding algorithm.