title: Multivariate methods to visualise colour-space and colour discrimination data.
abstract: OBJECTIVE
  Despite most modern colour spaces treating colour as three-dimensional (3-D), colour data is usually not visualised in 3-D (and two-dimensional (2-D) projection-plane segments and multiple 2-D perspective views are used instead). The objectives of this article are firstly, to introduce a truly 3-D percept of colour space using stereo-pairs, secondly to view colour discrimination data using that platform, and thirdly to apply formal statistics and multivariate methods to analyse the data in 3-D. This is the first demonstration of the software that generated stereo-pairs of RGB colour space, as well as of a new computerised procedure that investigated colour discrimination by measuring colour just noticeable differences (JND).
  
  
  METHODS
  An initial pilot study and thorough investigation of instrument repeatability were performed. Thereafter, to demonstrate the capabilities of the software, five colour-normal and one colour-deficient subject were examined using the JND procedure and multivariate methods of data analysis.
  
  
  RESULTS
  Scatter plots of responses were meaningfully examined in 3-D and were useful in evaluating multivariate normality as well as identifying outliers. The extent and direction of the difference between each JND response and the stimulus colour point was calculated and appreciated in 3-D. Ellipsoidal surfaces of constant probability density (distribution ellipsoids) were fitted to response data; the volumes of these ellipsoids appeared useful in differentiating the colour-deficient subject from the colour-normals. Hypothesis tests of variances and covariances showed many statistically significant differences between the results of the colour-deficient subject and those of the colour-normals, while far fewer differences were found when comparing within colour-normals.
  
  
  CONCLUSIONS
  The 3-D visualisation of colour data using stereo-pairs, as well as the statistics and multivariate methods of analysis employed, were found to be unique and useful tools in the representation and study of colour. Many additional studies using these methods along with the JND and other procedures have been identified and will be reported in future publications.
authors.affiliation: Department of Optometry, University of Johannesburg, Gauteng, South Africa.
authors.forename: Gareth D
authors.initials: GD
authors.lastname: Hastings
authors.forename: Alan
authors.initials: A
authors.lastname: Rubin
mesh_terms: D000328:Adult; D003118:Color Perception / Q000502:physiology*; D003867:Depth Perception / Q000502:physiology; D004192:Discrimination, Psychological / Q000502:physiology*; D005260:Female; D006801:Humans; D008297:Male; D015999:Multivariate Analysis; D010865:Pilot Projects; D012984:Software; D013028:Space Perception / Q000502:physiology*; D055815:Young Adult
keywords: colour discrimination; colour space; just noticeable differences; multivariate analyses; stereo-pairs