Protonotarios, Emmanouil D.; (2016) Quantification of Order in Point Patterns. Doctoral thesis , UCL (University College London).

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Abstract

Pattern attributes are important in many disciplines, e.g. developmental biology, but there are few objective measures of them. Here we concentrate on the attribute of order in point patterns and its objective measurement. We examine perception of order and develop analysis algorithms that quantify the attribute in accordance with perception of it. Based on pairwise ranking of point patterns by degree of order, we show that judgements are highly consistent across individuals and that the perceptual dimension has an interval scale structure, spanning roughly 10 just-noticeable differences (jnds) between disorder and order. We designed a geometric algorithm that estimates order to an accuracy of half a jnd by quantifying the variability of the spaces between points. By anchoring the output of the algorithm so that Poisson point processes score on average 0, and perfect lattices score 10, we constructed an absolute interval scale of order. We demonstrated its utility in biology by quantifying the order of the Drosophila dorsal thorax epithelium during development. The psychophysical scaling method used relies on the comparison of stimuli with similar levels of order yielding a discrimination-based scale. As with other perceptual dimensions, an interesting question is whether supra-threshold perceptual differences are consistent with this scale. To test that we collected discrimination data, and data based on comparison of perceptual differences. Although the judgements of perceptual differences were found to be consistent with an interval scale, like the discrimination judgements, no common interval scale that could predict both sets of data was possible. Point patterns are commonly displayed as arrangements of dots. To examine how presentation parameters (dot size, dot numbers, and pattern area) affect discrimination, we collected discrimination data for ten presentation conditions. We found that discrimination performance depends on the ratio ‘dot diameter / average dot spacing’.

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