From autocorrelation to unsupervised learning; searching for aperiodic tilings (quasicrystals) in images via patch-hashing.

摘要

"Arguably much of the understanding of the world around us is based on the perception and recognition of shared or repeated structures, and so is our sense of beauty [Thompson 1961]" I'll explain step-by-step how we started by identifying repeated patterns as patches in images by eye, then searching for similar instances via mathematical correlation, then, to avoid strong human bias we moved to autocorrelation, incorporating rotation and mirroring degrees of freedom, using Python and numba (@jit). I'll then explain how we moved to standard forms of unsupervised machine learning with rotation and reflection invariance so that we could expand our search to a larger and more diverse database of (Physics STM) images. I will cover in detail how, using Python, we implemented patch searching, image hashing using discrete cosine transforms, then finally geometrical hashing based on positions of atoms and clusters. THOMPSON, D. W. 1961. On Growth and Form. Cambridge.

說明