1 research outputs found
Objective, Probabilistic, and Generalized Noise Level Dependent Classifications of sets of more or less 2D Periodic Images into Plane Symmetry Groups
Crystallographic symmetry classifications from real-world images with
periodicities in two dimensions (2D) are of interest to crystallographers and
practitioners of computer vision studies alike. Currently, these
classifications are typically made by both communities in a subjective manner
that relies on arbitrary thresholds for judgments, and are reported under the
pretense of being definitive, which is impossible. Moreover, the computer
vision community tends to use direct space methods to make such classifications
instead of more powerful and computationally efficient Fourier space methods.
This is because the proper functioning of those methods requires more periodic
repeats of a unit cell motif than are commonly present in images analyzed by
the computer vision community. We demonstrate a novel approach to plane
symmetry group classifications that is enabled by Kenichi Kanatani's Geometric
Akaike Information Criterion and associated Geometric Akaike weights. Our
approach leverages the advantages of working in Fourier space, is well suited
for handling the hierarchic nature of crystallographic symmetries, and yields
probabilistic results that are generalized noise level dependent. The latter
feature means crystallographic symmetry classifications can be updated when
less noisy image data and more accurate processing algorithms become available.
We demonstrate the ability of our approach to objectively estimate the plane
symmetry and pseudosymmetries of sets of synthetic 2D-periodic images with
varying amounts of red-green-blue and spread noise. Additionally, we suggest a
simple solution to the problem of too few periodic repeats in an input image
for practical application of Fourier space methods. In doing so, we effectively
solve the decades-old and heretofore intractable problem from computer vision
of symmetry detection and classification from images in the presence of noise.Comment: 74 pages, 12 figures, 56 table