Augmented Symmetry Transforms

"Perfect symmetries are all alike; every imperfect symmetry is imperfect in its own way." - adapted from Leo Tolstoy\´s "Anna Karenina". Symmetry has been playing an increasing role in 3D shape processing. Recently introduced planar reflective symmetry transform(PRST) has been found useful for canonical coordinate frame determination, shape matching, retrieval, and segmentation. Guided by the intuition that every imperfect symmetry is imperfect in its own way, we investigate the possibility of incorporating more information into symmetry transforms like PRST. As a step in this direction, the concept of augmented symmetry transform is introduced; we obtain a family of symmetry transforms indexed by a parameter. While the original PRST measures how much the symmetry is broken, the augmented PRST also gives some information about how it is broken. Several approaches to calculating the augmented transform are described. We demonstrate that the augmented transform is useful for shape retrieval.