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Figure 2
(a) Method to quantify structural features. For each q value, the intensity along the angular direction, [I(\chi)], can be analyzed. The standard deviation of this entire curve ([\sigma_{\chi}]) can be compared with the average of the `local' standard deviations along this curve ([\langle \sigma_{\rm{loc}} \rangle]). The ratio of these quantities provides a measure of whether [I(\chi)] is structured: one expects [\langle \sigma_{\rm{loc}} \rangle / \sigma_{\chi} \approx 1] for an isotropic curve and [\langle \sigma_{\rm{loc}} \rangle / \sigma_{\chi} \,\lt\, 1] for an anisotropic curve. The histograms (right) of [\sigma_{\chi}] and [\langle \sigma_{\rm{loc}} \rangle / \sigma_{\chi}] (accumulated across all q) provide a signature of the overall structure in the image. (b) Method to classify images. When the [\langle \sigma_{\rm{loc}} \rangle / \sigma_{\chi}] histogram is peaked near 1.0, the background can be inferred to be isotropic. When the [\sigma_{\chi}] histogram is skewed (relative to the [\langle \sigma_{\rm{loc}} \rangle / \sigma_{\chi}] histogram), one can infer the presence of sharp anisotropic peaks in the data.

IUCrJ
Volume 4| Part 4| July 2017| Pages 455-465
ISSN: 2052-2525
https://doi.org/10.1107/S2052252517006212