Mapping images into ordinal networks

Determining liquid crystal properties with ordinal networks and machine learning

“…After obtaining the typical textures from the mesophases present in our samples, we average the image pixels over the three RGB layers to represent each texture as a simple array M = {y u t } u=1,...,Ny t=1,...,Nx , where y u t represents the average pixel intensity at column t and line u, while N x and N y are respectively the image width and height. We then map these two-dimensional arrays into ordinal networks [28,29]. To illustrate this method, We have made node sizes proportional to the occurring frequency of their associated ordinal patterns and used a grayscale color map to highlight edge weights (the darker the shade, the higher the weight).…”

“…The first step of the algorithm is to partition the matrix M into overlapping submatrices of size d x × d y (the embedding dimensions). While other choices are certainly possible [20,28,30], it is common to set d x = d y = 2 when dealing with images [28]. For this choice, the matrix M is partitioned into four submatrices {w q p } q=1,...,ny p=1,...,nx (with…”

“…Figure 1b depicts visualizations of ordinal networks mapped from textures collected around the transition between the mesophases chiral smectic A and cholesteric of an 8CB sample doped with 3.26% of R811. We have used d x = d y = 2 in these examples and in all other results of this work, which in turn constrains our ordinal networks to have up to 24 nodes and 416 edges [28]. Furthermore, we have used the numerical implementation of ordinal networks available in the Python module ordpy [29].…”

“…The Shannon entropy of this ordinal distribution defines the permutation entropy that, together with statistical complexity [21,22], are the most commonly used quantifiers associated with the Bandt-Pompe symbolization method [23]. Beyond counting ordinal patterns, recent developments related to the Bandt-Pompe approach have shown that analyzing transitions among ordinal patterns as complex networks can be even more effective for characterizing datasets [24][25][26][27][28]. These ordinal networks were also originally proposed for mapping time series into complex networks [24] and only very recently have been extended to produce a map between images and complex networks [28].…”

“…Beyond counting ordinal patterns, recent developments related to the Bandt-Pompe approach have shown that analyzing transitions among ordinal patterns as complex networks can be even more effective for characterizing datasets [24][25][26][27][28]. These ordinal networks were also originally proposed for mapping time series into complex networks [24] and only very recently have been extended to produce a map between images and complex networks [28].…”