Character legibility; which details are important, and how might it be measured? John Hayes, Jim Sheedy, Yu-Chi Tai, Vinsunt Donato, David Glabe, Objective Summary of individual letter characteristic regression models Letter characteristics are regressed on legibility. The different fonts provide the variability in the models Singular Value Decomposition Ventura m Centaur e Baskerville a Bodoni c Calibri n Consolas o DIN r Frutiger s Garamond v Helvetica w 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 Full Model Stepwise Model Max height of letter, MS minimum width, MS width ratio (max/min), Max vertical dim of stroke, serif a R2 Intercept a2 p a1 Max Height of Letter 0.339 0.665 0.000 0.060 a2 Max Width of Letter 0.239 0.674 0.127 a3 MS Max Width 0.230 0.738 0.001 0.135 a4 MS minimum width 0.437 0.805 0.002 0.027 a5 MS Width Ratio (Max/Min) 0.096 0.979 -0.017 0.353 a6 Opening size 0.005 0.925 0.849 a7 max bowl width 0.436 0.664 a8 max bowl height 0.018 0.864 0.691 Serif .127 0.969 -0.074 0.282 c 0.880 2.612 -0.005 0.000003 0.010 0.879 0.774 0.017 0.699 0.452 0.791 0.023 0.728 1.211 -0.171 0.015837 .005b 0.067 0.845 0.442 0.004 0.968 0.858 a10 Max vertical dim. of stroke 0.696 2.285 0.000004 .676 1.052 -0.215 e 0.900 2.096 -0.004 0.000002 0.620 1.656 -0.003 0.021 0.055 0.489 0.744 0.513 0.006 -0.000022 0.425 0.920 -0.035 0.030 0.087 0.902 0.379 0.672 1.887 0.012 a11 (Max vertical dimension of stroke)/(max width of stroke) 0.092 0.466 0.080 0.364 a12 Distance, bottom of letter to cross-stroke 0.015 0.960 a13 Bottom to cross-stroke/total letter height 0.480 1.380 -1.073 a14 Cap opening height 0.169 0.209 a15 Cap opening width 0.376 0.555 0.045 a16 Cross-stroke width 0.763 0.355 -0.000038 0.003 a17 Cross-stroke angle (degrees) 0.335 0.661 0.062 .407 0.908 -0.154 0.035 m 0.007 1.273 0.811 0.161 1.070 0.221 0.061 1.260 1.359 -0.007 0.857 0.151 1.221 0.238 .005 1.326 0.026 0.841 n 0.784 2.189 0.115 1.086 0.308 0.829 0.326 0.851 0.066 1.066 -0.041 0.050 0.680 0.814 .577 1.043 -0.161 o 0.693 1.941 0.009 0.899 2.452 0.059 0.470 0.651 -0.000020 0.426 1.005 -0.025 0.029 .803b 2.402 0.000007 .016b 0.046 1.011 0.525 0.417 1.588 -0.002 .258 0.984 -0.085 0.111 r 0.860 2.866 1.032 0.954 0.094 0.359 0.098 0.349 0.132 8.122 -7.063 0.271 a18 length of horizontal stroke 0.150 a22 max width of horizontalstroke 0.038 0.565 a23 min width of horizontal stroke 0.509 0.861 0.014 a24 Width ratio (max/min) 0.637 1.210 -0.057 a25 width of horizontal stroke at attachment to main stroke, measured by a perpendicular line from the horizontal stroke to where it meets main stroke 0.491 0.850 0.016 .625 1.167 -0.229 s 2.404 0.648 1.699 0.047 0.524 0.583 0.671 0.681 1.166 -0.211 0.021476 .010b a26 Max width of stroke perpendicular to point of tangency of vertical dimension, upper curve 0.420 0.604 0.031 a27 Max vertical dimension of stroke, upper curve 0.695 0.145 0.064 0.209000 a28 Ratio of previous two parameters 0.373 1.271 -0.129 a29 Max width of stroke perpendicular to point of tangency of vertical dimension, lower curve 0.444 0.605 0.025 a30 Max vertical dimension of stroke, lower curve 0.670 2.118 -.007 0.000009 a31 Ratio of previous two parameters 0.459 1.196 -0.101 0.022 a32 Opening size, upper curve (line from corner of end stroke to closest location of center stroke) 0.235 0.131 a33 Opening size, lower curve (line from corner of end stroke to closest location of center stroke) 0.200 0.168 a34 Vertical distance between s "curves" 0.156 a35 Backslash angle 0.184 0.189 .679 -0.228 v 0.856 3.045 -0.006 0.570 2.617 0.034 0.722 0.750 0.599 -0.000035 0.587 1.254 -0.077 0.456 0.923 .434 1.187 -0.188 0.028 w 0.650 3.378 0.796 3.573 0.971 0.430 0.928 0.468 1.316 0.020 a36 L upper opening size 0.225 0.140 a37 R upper opening size 0.182 0.190 a38 lower opening size 0.991 .247 1.213 0.120 Letter Attributes Linear Component Quadratic Component Descriptive Statistics B beta Beta Mean Min Max a Intercept 2.20 1 a1 Max Height of Letter 884.55 496 1175 a2 Max Width of Letter -.004 -2.775 .000003 2.998 782.55 494 967 a3 MS Max Width 164.09 82 209 a4 MS minimum width 73.18 23 132 a5 MS Width Ratio (Max/Min) .001636 .148 3.03 1.41 7.52 a6 Opening size 211.00 100 279 a7 max bowl width 361.91 257 568 a8 max bowl height 312.55 174 411 Serif -.143 -.389 .55 c 1.068 1.00 885.00 1168 .000001 .896 726.91 396 945 -.002 -.459 170.73 217 -.000006 -.349 96.91 22 206 2.69 1.02 7.91 388.18 162 621 668.27 347 854 a10 Max vertical dim. of stroke 724.91 374 950 -.309 -.722 e 1.38 .000000 .771 884.45 1173 -1.905 1.890 759.64 451 1022 165.45 222 -.000007 -.488 93.55 21 196 -.000847 -.092 2.76 1.05 8.43 -.000001 -.212 220.27 60 731.18 393 937 a11 (Max vertical dimension of stroke)/(max width of stroke) 4.50 3.40 4.94 a12 Distance, bottom of letter to cross-stroke 456.82 231 565 a13 Bottom to cross-stroke/total letter height .518 .426 .651 a14 Cap opening height 243.18 123 331 a15 Cap opening width 430.64 281 640 a16 Cross-stroke width 89.18 39 172 a17 Cross-stroke angle (degrees) 74.95 2 90 -.146 -.391 m 1.871 -.001 -.894 866.45 483 1148 1.447 1346.82 616 1707 163.82 83 241 75.73 157 -.002396 -.103 2.89 1.42 7.14 216.18 79 533 -.525 -.797 n -0.211 864.55 865.64 376 1112 .001 .314 162.82 84 236 .012 2.811 -.000079 -3.380 79.82 26 158 .005997 .326 2.67 1.39 5.81 .004 2.566 -.000004 -1.627 247.45 78 558 o 2.053 885.36 1179 .000002 841.27 486 1031 -.007 -1.574 169.27 80 225 98.18 -.013 -.144 2.72 8.27 -.003 -1.834 503.73 304 643 688.55 348 892 725.36 367 970 r 1.024 1117 627.18 255 825 .000005 .224 155.64 155.36 1.03 a18 length of horizontal stroke 388.91 661 a22 max width of horizontalstroke 167.27 a23 min width of horizontal stroke 74.18 24 148 a24 Width ratio (max/min) 2.93 5.79 a25 width of horizontal stroke at attachment to main stroke, measured by a perpendicular line from the horizontal stroke to where it meets main stroke 76.36 34 -.241 -.421 1.256 -1.553 1.837 882.18 1171 639.36 325 883 162.45 212 94.00 197 2.53 1.08 7.23 a26 Max width of stroke perpendicular to point of tangency of vertical dimension, upper curve 130.64 71 a27 Max vertical dimension of stroke, upper curve 410.64 230 567 a28 Ratio of previous two parameters .072 .223 3.29 2.71 4.93 a29 Max width of stroke perpendicular to point of tangency of vertical dimension, lower curve 133.18 a30 Max vertical dimension of stroke, lower curve 429.45 576 a31 Ratio of previous two parameters -.007579 -.287 3.46 5.98 a32 Opening size, upper curve (line from corner of end stroke to closest location of center stroke) 172.36 85 336 a33 Opening size, lower curve (line from corner of end stroke to closest location of center stroke) 188.36 88 360 a34 Vertical distance between s "curves" 392.18 660 a35 Backslash angle 162.27 152 175 -.154 -.367 v 2.802 .557 858.36 499 -.005 -4.590 4.219 890.73 458 154.55 81 101.73 31 195 .003206 .100 2.18 4.81 307.64 112 682 -.090 -.180 w 3.011 860.73 523 -3.637 3.706 1262.27 692 1582 157.00 89.91 30 -.192 -.916 .027067 .781 2.25 5.17 a36 L upper opening size .000 .152 260.18 475 a37 R upper opening size 264.27 477 a38 lower opening size 414.64 208 569 SVD is based on a theorem from linear algebra which says that a rectangular matrix A can be broken down into the product of three matrices - an orthogonal matrix U, a diagonal matrix S, and the transpose of an orthogonal matrix V . Amn = UmmSmnV Tnn where UTU = I; V TV = I; the columns of U are orthonormal eigenvectors of AAT , the columns of V are orthonormal eigenvectors of ATA, and S is a diagonal matrix containing the square roots of eigenvalues from U or V in descending order. Main stroke minimum width Opening size Maximum height of letter Maximum vertical dimension of main stroke Main stroke maximum width Maximum width of letter Method Letter Observed Relative Legibility Predicted Relative Legibility Between S Variance Model R2 Within S Variance Letter Attributes Variance Attribute R2 a 0.93 0.946 0.414 0.664 0.586 0.250 0.427 c 0.926 0.425 0.793 0.575 0.368 0.640 e 0.82 0.815 0.346 0.762 0.654 0.416 0.636 m 1.34 1.333 0.464 0.766 0.536 0.302 0.563 n 0.96 0.971 0.479 0.689 0.521 0.210 0.403 o 0.94 0.924 0.579 0.757 0.421 0.178 0.423 r 1.04 1.027 0.491 0.702 0.509 0.211 0.415 s 0.84 0.837 0.379 0.799 0.621 0.420 0.676 v 1.08 1.079 0.473 0.792 0.527 0.319 0.605 w 1.13 1.114 0.467 0.810 0.533 0.343 0.644 Hypothesis 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. 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. Conclusions for individual letter characteristics Font Letter Observed Relative Legibility Font Excluded Complete Dataset Predicted Legibility Residual Baskerville a 0.93 0.77 0.16 0.80 0.13 c 0.85 0.84 0.02 0.01 e 0.69 0.86 -0.16 -0.17 m 1.33 0.96 0.36 0.99 0.34 n 0.89 0.04 o 0.00 0.87 -0.01 r 0.88 0.05 s -0.10 v 0.83 0.10 w 0.97 0.12 0.11 Bodoni 0.03 0.73 -0.14 -0.13 0.75 1.29 1.11 0.18 0.98 -0.15 0.81 0.90 -0.09 -0.08 0.95 1.00 -0.05 -0.04 0.66 -0.19 0.92 0.07 Centaur -0.12 0.64 -0.25 -0.23 0.40 0.39 -0.03 -0.02 -0.18 Consolas 1.02 1.05 0.94 1.01 1.17 -0.36 -0.29 1.06 0.19 1.03 0.14 1.14 0.21 0.17 1.08 -0.06 DIN 1.12 -0.07 1.10 -0.20 1.50 1.49 1.45 1.13 1.09 -0.22 1.18 0.20 1.25 1.27 Font Letter Observed Relative Legibility Font Excluded Complete Dataset Predicted Legibility Residual Futura a 0.75 1.06 -0.30 -0.31 c 1.02 0.98 0.04 0.99 e 0.82 1.01 -0.19 1.00 m 1.30 1.17 0.13 n 0.94 -0.05 o 1.08 -0.07 r 0.14 s 0.85 0.89 -0.04 v 1.14 0.92 0.23 0.22 w 1.27 0.21 1.07 Garamond 0.79 -0.01 0.80 0.90 -0.06 0.70 0.88 -0.18 0.87 -0.17 1.31 0.33 0.84 0.91 0.00 -0.09 0.68 -0.20 0.07 0.83 0.97 0.08 Georgia 0.95 0.03 0.93 -0.02 1.44 1.33 0.12 0.11 -0.11 1.10 -0.08 0.24 1.21 1.05 0.16 0.15 Helvetica 1.03 -0.03 0.86 1.11 -0.25 1.43 1.32 1.09 0.09 1.20 1.23 1.22 0.01 Rockwell 1.04 1.41 1.61 1.54 -0.12 1.29 -0.35 -0.29 1.12 1.19 1.13 -0.14 0.81 1.18 1.36 Verdana 0.17 1.59 1.42 1.45 1.15 0.32 0.27 0.10 1.34 0.40 0.34 1.25 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. Further we need to test some of the relationships in fonts with poor legibility and modify them with the suggested improvements to determine a causal relationship between the attributes and legibility. Replication with other measures of legibility and fonts will help determine if these findings are robust. 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 r2 of the predicted legibility with the actual legibility was significant at .42. Stimulus Set 10 letters (a, c, e, m, n, o, r, s, v, and w) 11 fonts (Baskerville, Bodoni, Centaur, Consolas, DIN, Futura, Garamon, Georgia, Helvetica, Rockwell, and Verdana) 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. Summary 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.