RT Journal Article
SR Electronic
T1 An absolute interval scale of order for point patterns
JF Journal of The Royal Society Interface
JO J R Soc Interface
FD The Royal Society
DO 10.1098/rsif.2014.0342
VO 11
IS 99
A1 Protonotarios, Emmanouil D.
A1 Baum, Buzz
A1 Johnston, Alan
A1 Hunter, Ginger L.
A1 Griffin, Lewis D.
YR 2014
UL http://rsif.royalsocietypublishing.org/content/11/99/20140342.abstract
AB Human observers readily make judgements about the degree of order in planar arrangements of points (point patterns). Here, based on pairwise ranking of 20 point patterns by degree of order, we have been able to show that judgements of order are highly consistent across individuals and the dimension of order has an interval scale structure spanning roughly 10 just-notable-differences (jnd) between disorder and order. We describe a geometric algorithm that estimates order to an accuracy of half a jnd by quantifying the variability of the size and shape of spaces between points. The algorithm is 70% more accurate than the best available measures. By anchoring the output of the algorithm so that Poisson point processes score on average 0, perfect lattices score 10 and unit steps correspond closely to jnds, we construct an absolute interval scale of order. We demonstrate its utility in biology by using this scale to quantify order during the development of the pattern of bristles on the dorsal thorax of the fruit fly.