Wavelet-based Detection and Classification of Local Symmetries
Zsuzsanna Püspöki, EPFL STI LIB

Seminar • 13 January 2014 • BM 4.233

Abstract
The ability to detect edges and local symmetry centers (or symmetric junctions) can be very useful for the quantitative analysis of microscopic images. For example, certain experiments in stem-cell research rely on the accurate detection of cell shape and extracellular structures (like tight junctions) that exhibit polygonal shapes. Also, in polycrystalline materials such as the hexagonal graphene, it is fundamental to detect line defects since they strongly affect the physical and chemical properties of grain boundaries. In this presentation, we describe an algorithm for the detection of local symmetries and their classification in a template-free fashion. The algorithm is based on the circular harmonic wavelet transform, which distributes the energy of the signal among a set of angular harmonics. Based on this angular distribution, we propose a measure of symmetry and a hypothesis test for local symmetry at each pixel. Using the noted measure, we also formulate an approximate maximum-likelihood classifier in terms of the orders of local symmetry. We provide experimental results on synthetic images, biological micrographs, and electron-microscopy images to demonstrate the performance of the algorithm.