Peter Moeck

Sagarika Menon, Peter Moeck

The computer program "Histropy" is an interactive Python program for the quantification of selected features of two-dimensional (2D) images/patterns (in either JPG/JPEG, PNG, GIF, BMP, or baseline TIF/TIFF formats) using calculations based on the pixel intensities in this data, their histograms, and user-selected sections of those histograms. The histograms of these images display pixel-intensity values along the x-axis (of a 2D Cartesian plot), with the frequency of each intensity value within the image represented along the y-axis. The images need to be of 8-bit or 16-bit information depth and can be of arbitrary size. Histropy generates an image's histogram surrounded by a graphical user interface that allows one to select any range of image-pixel intensity levels, i.e. sections along the histograms' x-axis, using either the computer mouse or numerical text entries. The program subsequently calculates the (so-called Monkey Model) Shannon entropy and root-mean-square contrast for the selected section and displays them as part of what we call a "histogram-workspace-plot." To support the visual identification of small peaks in the histograms, the user can switch between a linear and log-base-10 display scale for the y-axis of the histograms. Pixel intensity data from different images can be overlaid onto the same histogram-workspace-plot for visual comparisons. The visual outputs of the program can be saved as histogram-workspace-plots in the PNG format for future usage. The source code of the program and a brief user manual are published in the supporting materials as well as on GitHub. Instead of taking only 2D images as inputs, the program's functionality could be extended by a few lines of code to other potential uses employing data tables with one or two dimensions in the CSV format.

Andrew Dempsey, Peter Moeck

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.