1. 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
0.010
0.879
0.774
0.017
0.699
0.452
0.791
0.023
0.728
1.211
-0.171
.005b
0.067
0.845
0.442
0.004
0.968
0.858
a10 Max vertical dim. of stroke
0.696
2.285
.676
1.052
-0.215 e
0.900
2.096
-0.004
0.620
1.656
-0.003
0.021
0.055
0.489
0.744
0.513
0.006
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
0.003
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
0.426
1.005
-0.025
0.029
.803b
2.402
.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
.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
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
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
0.587
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
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)
.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
.896
726.91
396
945
-.002
-.459
170.73
217
-.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
.771
884.45
1173
-1.905
1.890
759.64
451
1022
165.45
222
-.488
93.55 21
196
-.092
2.76
1.05
8.43
-.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
616
1707
163.82 83
241
75.73
157
-.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
-3.380
79.82 26
158
.326
2.67
1.39
5.81
.004
2.566
-1.627
247.45 78
558 o
2.053
885.36
1179
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
.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
-.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
.100
2.18
4.81
307.64
112
682
-.090
-.180 w
3.011
860.73
523
-3.637
3.706
692
1582
157.00
89.91 30
-.192
-.916
.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.