Character legibility: which details are important, and how might it be measured? John Hayes, Jim Sheedy, Yu-Chi Tai, Vinsunt Donato, David Glabe

Objective Determine the features of letters that are most associated with individual letter legibility Measure features in several ways: –Individual letter features –Statistical characteristics of individual components in the singular value decomposition of the letter image

Method Reanalysis of previous dataset Letter legibility was measured using 40 subjects who performed a distance threshold legibility task Using regression analysis we determined the characteristics of letters that were predictive of legibility In a second method of analysis, we reviewed the statistical characteristics of the eigenvalues from the singular value decomposition of each letter.

Stimulus Set 10 letters (a, c, e, m, n, o, r, s, v, and w) 11 fonts (Baskerville, Bodoni, Centaur, Consolas, DIN, Futura, Garamond, Georgia, Helvetica, Rockwell, and Verdana)

Method 1: Letter features Common features among all letters: letter height, letter width, max width of main stroke, min width of main stroke, serifs Many letters had additional unique features

Main stroke minimum width Opening size Maximum height of letter Maximum vertical dimension of main stroke Main stroke maximum width Maximum width of letter

Analysis Stepwise regression of the same letter across different fonts. Identified those features that contributed the most unique variance with respect to legibility. Both linear and quadratic components were considered as legibility can increase with a particular feature up to a point and then decrease Exclusion from the model did not necessarily mean lack of importance, as it may just be correlated with other variables that accounted for slightly more variability.

Main stroke minimum width Opening size Maximum height of letter Maximum vertical dimension of main stroke Main stroke maximum width Maximum width of letter Max height of letter, MS minimum width, MS width ratio (max/min), Max vertical dim of stroke, Serif

Cap opening size Maximum bowl height Maximum bowl width Significant factors: Max height of letter, MS minimum width, Max bowl width

Cross stroke angle Cap opening width Cap opening height Cross stroke width Max height of letter, Max width of letter, MS minimum width, MS width ratio (Ma./min), Max vertical dim of stroke, Bottom to cross-stroke/total letter height, Cap opening width, cross stroke width, cross-stroke angle (degrees), Serif

Maximum lower opening size

Opening size Max height of letter, MS minimum width, MS width ratio (max/min), Opening size, Serif

Maximum bowl width Maximum bowl height Max height of letter, Max width of letter, MS minimum width, MS width ratio (Max/min)

Maximum width of horizontal stroke Horizontal length of horizontal stroke Minimum width of horizontal stroke Width of horizontal stroke at attachment to main stroke Max height of letter, Min width of horizontal stroke, Width ratio (max/min), Width of horizontal stroke at attachment to main stroke, Serif

Backslash angle Opening size, upper curve Vertical dimension of stroke, lower curve Max horizontal width of stroke, lower curve Max horizontal width of stroke, upper curve Vertical dimension of stroke, upper curve Opening size, lower curve Vertical distance between S curves Max height of letter, Max width of letter, MS minimum width, MS width ratio (Max/Min), Max width of stroke perpendicular to point of tangency of vertical dimension- upper curve, Max vertical dimension of upper stroke, Ratio of previous two parms, Max width of stroke perpendicular to point of tangency of vertical dimension, Max vertical dimension of stroke – lower curve, Ratio of previous two parms, Serif

Opening size Max height of letter, Max width of letter, MS minimum width, MS width ratio (Max/Min), Opening size, Serif

Left upper opening size Right upper opening size Lower opening size Max height of letter, Max width of letter, MS minimum width, MS width ratio (Max/Min)

Summary statistics for each of the stepwise models. The predicted relative legibility for each letter is determined by applying the mean attribute value to the stepwise regression models. The observed relative legibility was the average legibility across fonts and subjects. The model R 2 includes both subjects and letter attributes. The attribute R 2 considers only the effect of the letter characteristic. Letter Observed Relative Legibility Predicted Relative Legibility Between S Variance Model R 2 Within S Variance Letter Attributes Variance Attribute R 2 a c e m n o r s v w

Conclusions for individual letter characteristics Demonstrated significant relationships between individual letter attributes and relative legibility. We need the advice of the font designers to inform us on whether this information is helpful in the design process. Furthermore, we need to test some of the relationships in fonts with poor legibility and modify them with suggested improvements to determine a causal relationship between attributes and legibility. Replication with other measures of legibility and fonts will help determine if these findings are robust.

Singular Value Decomposition SVD separates a single matrix into a set of ordered independent matrices that completely define the original matrix. The order is based on the amount of variance that is accounted for by each component. A letter can be transformed into a numerical matrix of 0’s and 1’s based on the on or off state of sub-pixels

SVD model A mn = U mm S mn V T nn –A is the original array based on the picture –U is the orthonormal eigenvector of AA T –V is the orthonormal eigenvector of A T A –S is the diagonal array of eigenvalues which weight the contribution of the elements of the eigenvectors. Multiplying USV for each element of S provides the separate components for the singular value decomposition

Hypothesis The simpler the structure the more legible the letter The statistical properties of the eigenvalues from SVD provide us with information on the simplicity of the structure The summary statistics used included the first eigenvalue, sum of first 2, 5, 10, or 20 eigenvalues, and the slope of the first 5 or 10 eigenvalues. Rationale: the more variance accounted for in the first few eigenvalues, the simpler the structure.

Identify the following letter

First eigenvalue converted back to an image

Eigenvalue 1 + 2

Eigenvalues 1, 2, 3

Eigenvalues 1,2,3,4

Eigenvalues 1,2,3,4,5

Eigenvalues 1,2,3,4,5,6

Eigenvalues 1,2,3,4,5,6,7

Eigenvalues 1,2,3,4,5,6,7,8

Complete matrix, Verdana m

What is this letter?

Eigenvalue 1

Eigenvalue 1,2

Eigenvalue 1,2,3

Eigenvalue 1,2,3,4

Eigenvalue 1,2,3,4,5

Eigenvalue 1,2,3,4,5,6

Eigenvalue 1,2,3,4,5,6,7

Eigenvalue 1,2,3,4,5,6,7,8

Complete Centaur e

Method of Analysis Stepwise regression of statistical eigenvalue properties on legibility. Same dataset as individual letter characteristics. Pixel density was added into the model though it is not a part of SVD Jackknife procedure employed to determine predictive ability of the model. –Analysis was run eleven times, each time excluding a different font. –The legibility of the missing font was predicted by the other fonts. –The r 2 of the predicted legibility with the actual legibility was significant at.42.

First 20 eigenvalues Values range from 0 -> 1 Sum of all eigenvalues = 1.0

Excluded Font VariablesR2R2 Baskerville Density 2, Sum5, E1.52 Bodoni Density 2, Sum5, E1.49 Centaur Density 2, Sum5, E1.50 Consolas Density 2, Sum5.53 DIN Density 2, Sum5.48 Futura Density 2, Sum5, E1.54 Garamond Density 2, Sum5, E1.50 Density 2, Sum5, E1.50 Helvetica Density 2, Sum5, E1.50 Rockwell Density 2, Sum5, E1.50 Verdana Density 2, Sum20.46 All Fonts Density 2, Sum5, E1.51 Summary for SVD Density squared, Sum of the first five eigenvalues, and the value of the first eigenvalue are the most frequent predictors of legibility About 50% of the variability of legibility is accounted for by SVD + density models. The more information represented in the first few eigenvalues, the higher the legibility.

Future Directions In this study legibility was measured by the identification of a single letter in the middle of two other letters. We plan to test legibility of letters based on the similarity of the first eigenvalue of the letters on both the right and the left as well in combination with the target to determine if we can identify a confusion index. We wish to explore this methodology on paragraphs of different fonts to determine if a simpler structure is easier to read.