Psychophysical Evaluation of Congenital Colour Vision Deficiency: Discrimination between Protans and Deutans Using Mollon-Reffin's Ellipses and the Farnsworth-Munsell 100-Hue Test

Abstract

We have used the Farnsworth-Munsell 100-hue (FM 100) test and Mollon-Reffin (MR) test to evaluate the colour vision of 93 subjects, 30.4 ± 9.7 years old, who had red-green congenital colour vision deficiencies. All subjects lived in Belém (State of Pará, Brazil) and were selected by the State of Pará Traffic Department. Selection criteria comprised the absence of visual dysfunctions other than Daltonism and no history of systemic diseases that could impair the visual system performance. Results from colour vision deficient were compared with those from 127 normal trichromats, 29.3 ± 10.3 years old. For the MR test, measurements were taken around five points of the CIE 1976 colour space, along 20 directions irradiating from each point, in order to determine with high-resolution the corresponding colour discrimination ellipses (MacAdam ellipses). Three parameters were used to compare results obtained from different subjects: diameter of circle with same ellipse area, ratio between ellipse's long and short axes, and ellipse long axis angle. For the FM 100 test, the parameters were: logarithm of the total number of mistakes and positions of mistakes in the FM diagram. Data were also simultaneously analysed in two or three dimensions as well as by using multidimensional cluster analysis. For the MR test, Mollon-Reffin Ellipse #3 (u' = 0.225, v' = 0.415) discriminated more efficiently than the other four ellipses between protans and deutans once it provided larger angular difference in the colour space between protan and deutan confusion lines. The MR test was more sensitive than the FM 100 test. It separated individuals by dysfunctional groups with greater precision, provided a more sophisticated quantitative analysis, and its use is appropriate for a more refined evaluation of different phenotypes of red-green colour vision deficiencies.

Fig 1. FM 100 results compared with MR results. The three phenotypes studied in this work are illustrated with results obtained from a single subject from each group.

(A,D) Protan subject P005. (B,E) Deutan subject D073. (C,F) Normal trichromat subject C178. (A-C) FM 100 results. The red and blue contours represent means and standard deviations, respectively, for the Score_i (n = 4 trials). The colour vision deficient subjects made more mistakes than the control subject. In addition, the mistakes made by the protan and deutan subjects had specific orientations in the FM diagram. (D-F) MR results were plotted in the u’v’ coordinates of the CIE 1976 colour space. Data points were fitted with ellipses to generate the Mollon-Reffin colour discrimination ellipses. Both the protan and deutan had larger colour discrimination ellipses than the normal trichromat. In addition, protan and deutan thresholds were elongated along their respective colour confusion lines, making their ellipses more elongated than the ellipses of the normal trichromat.

Fig 2. FM 100 results compared with MR results. The phenotypes studied in this work are illustrated with average results for the three groups.

Subjects were classified as (A,D) protans, (B,E) deutans, and (C,F) controls according to their performance in the FM 100 test or the MR tests.

Fig 3. Statistical comparisons of the FM 100 results: total number of mistakes.

Comparisons between the number of mistakes made by protans (n = 44), deutans (n = 47), and controls (n = 91). The number of mistakes was taken as the logarithm of the Total Error. The columns and error bars represent, respectively, means and standard deviations for the three groups. There were statistical significant differences between the number of mistakes made by protans or deutans versus controls, as well as between protans and deutans. Significant differences: *p < 0.05; ***p < 0.0001; Kruskal-Wallis.

Fig 4. FM 100 results visualized in three dimensional Cartesian plots.

The values of log (Total Error), Left Central Point, and Right Central Point were plotted for all subjects that performed the FM 100 test. The values for Total Error completely separated congenital colour vision deficient subjects from controls. Introduction of central points in this analysis separated protans from deutans mostly due to distinct higher values of Right Central Point and slightly lower values of Left Central Point for protans in relation to deutans. A few deutans intruded in the protan region of the plot (see text for further discussion of this issue).

Fig 5. Statistical comparisons of results obtained with the MR test: sizes of the Mollon-Reffin ellipses.

Comparisons between the sizes of colour discrimination ellipses for protans, deutans, and controls. Both protans and deutans had ellipses significantly larger than controls. There were no statistical differences between protans and deutans. Significant differences: ***p < 0.0001; Kruskal-Wallis.

Fig 6. Statistical comparisons of results obtained in the MR test: elongations of the Mollon-Reffin ellipses.

Comparisons between the elongations of colour discrimination ellipses for protans, deutans, and controls. Both protans and deutans had ellipses significantly more elongated than controls. There were no statistical differences between protans and deutans, except for Ellipse #3. Significant differences: *p = 0.05; ***p < 0.0001; Kruskal-Wallis.

Fig 7. Statistical comparisons of results obtained with the MR test: orientations of the Mollon-Reffin ellipses.

Comparisons between the orientations of colour discrimination ellipses for protans, deutans, and controls. There were significant statistical differences between protans and deutans for α of Ellipses 2–5. The largest difference for α between protans and deutans occurred in the Mollon-Reffin Ellipse #3 (see text for the explanation). Significant differences: *p < 0.05; **p < 0.01; Kruskal-Wallis. Differences between protans and controls as well as deutans and controls were not illustrated.

Fig 8. Results of the MR test visualized in three dimensional Cartesian plots.

For this plot, only the results for the Mollon-Reffin Ellipse #3 were used. The values of angle α (orientation in degrees), diameter d (diameter of the circle with equal area in 10⁻³ √u’v’ unities, and ratio a/b (inclination) were plotted for all subjects that performed the MR test: protans (red bars), deutans (green bars), and controls (black bars). Ellipse #3 data completely separated colour vision deficient subjects from controls: protans and deutans had larger, more elongated, and less inclinated Ellipses #3 than controls. In addition, Ellipse #3 data separated protans for deutans almost completely, mostly due to the large difference in the ellipse orientation: protans had α between -1.1° and +18°, while the majority of deutans had α between -4.5° and -22.9°. Two subjects classified as deutans using data from all MR ellipses were plotted in the protan region of the figure (see text for more details).

Fig 9. Dendrogram for MR test results.

For this plot, only the results for the Mollon-Reffin Ellipse #3 were used. The dendrogram was generated using the Method of Ward and d, a/b, and α as parameters. The linkage distances were expressed as Euclidean distances. Ellipse #3 data split the subjects in 3 major groups and 11 subgroups which completely separated colour vision deficient subjects from controls: subgroups 1–4 comprised all controls; subgroups 5–7 and 9 comprised only deutans; subgroups 8, 10, and 11 comprised all protans plus two deutans, D006 and D044 (see text for more details about these two subjects).