The 10 distinct letters appearing (in Roman font) in the chart below are used in the assessment of visual acuity. The actual charts are set in Sloan fonts and are referred to as Snellen Charts.
The letters composing each line were selected [1] to balance the between-line overall difficulty in correctly identifying the five letters.
The table below lists the Sloan letters (in Roman font), their estimated probability (p) of being correctly identified by normal-acuity subjects, their corresponding entropy, and their -log contrast sensitivity:
We now refer to the subgroups introduced earlier on here and obtain the follow classification of the fonts according to the (largest) subgroup of symmetries afforded by each font:
Each font in each class is the symmetry orbit of that subgroup. Shortly, we may say that the font has the symmetry of that subgroup.
Moreover, now we may associate to each subgroup a number, such as the maximum entropy of the fonts with the symmetry of that subgroup. From the above table where the entropies are listed we then obtain:
The letters composing each line were selected [1] to balance the between-line overall difficulty in correctly identifying the five letters.
The table below lists the Sloan letters (in Roman font), their estimated probability (p) of being correctly identified by normal-acuity subjects, their corresponding entropy, and their -log contrast sensitivity:
We now refer to the subgroups introduced earlier on here and obtain the follow classification of the fonts according to the (largest) subgroup of symmetries afforded by each font:
- K, R -------> { 1 },
- Z, N, S -------> { 1, o },
- V -------> { 1, v },
- D, C -------> { 1, h },
- H, O --------> { 1, v, h, o }.
Each font in each class is the symmetry orbit of that subgroup. Shortly, we may say that the font has the symmetry of that subgroup.
Moreover, now we may associate to each subgroup a number, such as the maximum entropy of the fonts with the symmetry of that subgroup. From the above table where the entropies are listed we then obtain:
- K, R -------> { 1 } -----> 0.669,
- Z, N, S -------> { 1, o } -----> 0.693,
- V -------> { 1, v } -----> 0.656,
- D, C -------> { 1, h } -----> 0.687,
- H, O --------> { 1, v, h, o } -----> 0.692.
This is then our first example of subgroups indexed by numerical evaluations. Later on we will remark that this experimental situation can be treated in analogy with the previous case, where the elements of a given group were indexed by numerical evaluations.
===== Reference Cited =====
[1] Ferris FL 3rd, Freidlin V, Kassoff A, Green SB, Milton RC. Relative letter and position difficulty on visual acuity charts from the Early Treatment Diabetic Retinopathy Study. Am J Ophthalmol. 1993 Dec 15;116(6):735-40.
Last revised on 03/01/2011
These postings are based on "Symmetry Studies" An Introduction to the Analysis of Structured Data in Applications" Cambridge Press (2008)
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