title: An absolute interval scale of order for point patterns.
abstract: 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.
authors: CoMPLEX, University College London, London, UK Department of Computer Science, University College London, London, UK emmanouil.protonotarios.10@ucl.ac.uk.
authors: Emmanouil D
authors: http://orcid.org/0000-0003-0386-160X
authors: ED
authors: Protonotarios
authors: Laboratory for Molecular Cell Biology, University College London, London, UK.
authors: Buzz
authors: B
authors: Baum
authors: CoMPLEX, University College London, London, UK Experimental Psychology, Psychology and Language Sciences, University College London, London, UK.
authors: Alan
authors: A
authors: Johnston
authors: Laboratory for Molecular Cell Biology, University College London, London, UK.
authors: Ginger L
authors: GL
authors: Hunter
authors: CoMPLEX, University College London, London, UK Department of Computer Science, University College London, London, UK.
authors: Lewis D
authors: http://orcid.org/0000-0001-6286-2018
authors: LD
authors: Griffin
mesh_terms: D000465:Algorithms; D000818:Animals; D004331:Drosophila melanogaster / Q000254:growth & development; D006801:Humans; D008954:Models, Biological; D010364:Pattern Recognition, Visual / Q000502:physiology*; D010775:Photic Stimulation; D058618:Sensilla / Q000648:ultrastructure
keywords: order; point pattern; psychophysical scaling