Analytical Study on Typeface Visual Identiﬁcation

Xavier Molinero

1,∗ a

, Josep Freixas

1 b

and Montserrat T

apias

2 c

Department of Mathematics, Universitat Polit

ecnica de Catalunya · BarcelonaTECH, Spain

Department of Optics and Optometry, Universitat Polit

ecnica de Catalunya · BarcelonaTECH, Spain

Keywords:

Visual Identiﬁcation, Measure of Topographies, Power Indices.

Abstract:

In this study, our objective is to explore methodologies for the identiﬁcation of diverse typefaces. Utilizing

the gathered data, we conducted a thorough analysis of the outcomes, distinguishing between successes and

failures for both uppercase and lowercase letters within each typeface. The analytical framework is anchored

in three distinct recognition measures. The initial measure draws upon the relative frequency of accurate re-

sponses, providing insights into the overall performance of each typeface. The second measure is constructed

around the F-score derived from confusion matrices, offering a comprehensive evaluation of recognition pre-

cision and recall. Lastly, the third measure is formulated on the well-established Shapley-Shubik index, exten-

sively scrutinized and endorsed within the realm of classical game theory. This multifaceted approach allows

us to comprehensively assess the distinct aspects of typeface recognition, contributing to a nuanced under-

standing of their effectiveness and characteristics.

1 INTRODUCTION

Low vision is a common visual impairment, espe-

cially among older adults, which makes it difﬁcult for

individuals to read printed materials due to reduced

clarity and sharpness of vision. Typographers have

developed speciﬁc typographies to enhance identiﬁ-

cation for low vision readers, by increasing contrast,

reducing glare, and optimizing letter size and spac-

ing. Serif fonts such as Times New Roman and Gara-

mond are considered more legible as serifs guide the

eye along the text. Sans-serif fonts such as Arial and

Verdana provide a clearer and simpler design, improv-

ing readability. However, designers must test their

typographies with low vision users, as identiﬁcation

or readability is subjective and can vary depending

on the individual’s vision impairment. By optimiz-

ing typographies for low vision readers, we can make

printed materials more inclusive and improve acces-

sibility for all.

In this research, we introduce and discuss three

distinct measures for typographic identiﬁcation. The

initial measure is described in Subsection 2.1. Fol-

lowing that, the second measure is introduced and

https://orcid.org/0000-0002-5203-4347

https://orcid.org/0000-0002-9033-9432

https://orcid.org/0000-0003-2421-0718

∗

Corresponding author.

detailed in Subsection 2.2. Lastly, Subsection 2.3

presents a novel measure, which is founded on the

Shapley-Shubik index derived from game theory. This

section provides a comprehensive deﬁnition and ex-

ploration of the application of the Shapley-Shubik in-

dex in the context of typographic recognition.

2 TYPOGRAPHIC

RECOGNITION

From now on, we assume that each letter of a given

typography T is presented n times. Let be µ

T × T → N, where µ

(X,Y ) = k is the number of

times that observers said Y when X is shown. For in-

stance, µ

(X,Y ) = 5 means that 5 times the observers

have said Y when X has been shown. Thus, the most

identiﬁcable tipography should verify

(X,Y ) =



n if X = Y

0 if X 6= Y

(1)

for all X,Y ∈ T . Next, we analyze those dataset in

three different ways, i.e., applied to three visual iden-

tiﬁcations of topographies.

124

Molinero, X., Freixas, J. and Tàpias, M.

Analytical Study on Typeface Visual Identiﬁcation.

DOI: 10.5220/0012719300003708

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 9th International Conference on Complexity, Future Information Systems and Risk (COMPLEXIS 2024), pages 124-127

ISBN: 978-989-758-698-9; ISSN: 2184-5034

2.1 Identiﬁcation from Relative

Frequency

In the initial phase, we examine the foundational sta-

tistical concept of relative frequency, as outlined by

Spiegelhalter in 2019 (Spiegelhalter, 2019).

Given a typography T , for each character X ∈ T

that we show to observers, we determine the relative

frequency of X, i.e., the number of times that we said

X divided by n. This value can be computed as fol-

lows:

(X) =

(X,X)

∑

Y ∈T

(X,Y )

(X,X)

In addition, we also deﬁne a general identiﬁable value

for the given typography T , based on the relative fre-

quency:

(T ) =

∑

X∈T

(X) .

2.2 Identiﬁcation from Confusion

Matrix

In the subsequent step of our analysis, we employ

confusion matrices (Blog at WordPress.com., 2024)

as a fundamental analytical tool to assess a key met-

ric associated with each typography T , namely the F-

score. Widely acknowledged in classiﬁcation tasks,

the F-score offers a nuanced evaluation by striking

a balance between precision and recall, making it

particularly pertinent to the nuances of typographic

recognition. By leveraging confusion matrices, we

scrutinize the performance of each typeface in terms

of true positives, false positives, and false nega-

tives, offering a comprehensive understanding of their

recognition capabilities.

For a detailed exploration of the computational

aspects and theoretical underpinnings of the F-score

within the scope of our study, interested readers are

directed to (Brabec et al., 2020; Wikipedia, 2024).

These references delve into the intricacies of F-score

calculations, elucidating the nuances of its application

and interpretation in the context of our research. In

particular, we consider µ

(X) = µ

F−score

(X) deﬁned

2TruePositive

2TruePositive + FalsePositive + 2FalseNegative

where TruePositive is a test result which correctly

indicates that a condition hold, FalsePositive is a

result that indicates a given condition exists when it

does not, and FalseNegative is a test result which

wrongly indicates that a condition does not hold.

As we have done for the relative frequency, we

deﬁne a general identiﬁable value for the given tipog-

raphy T as follows

(T ) =

∑

X∈T

(X) .

Example. Let T be a typography where

{a,b, p, q} ∈ T . Suppose that, after doing the experi-

ments with 10 presentations for each letter, we obtain

the following results:

From this table we are able to compute µ

(a) as fol-

lows

(a) =

2 · 7

2 · 7 + 2 + 2 · 2

where the red values are TruePositive, the blue

ones are FalsePositive, the green ones are

FalseNegative, and yellow numbers are the re-

maining values.

2.3 Identiﬁcation from Shapley-Shubik

Index

Thirdly, we deﬁne a speciﬁc weighted voting

game (Taylor and Zwicker, 1999). In general, given

n characters (or players) we assign a weight (non-

negative integer) for each character and a quota q (a

positive integer). We say that a coalition of characters

S is winning or successful if and only if the sum of the

corresponding weights is more or equal to q.

Subsequent to the consideration of a typogra-

phy denoted as T , we proceed to allocate a unique

weighted voting game, denoted as Γ

(X), for each

distinct typographic element X ∈ T . This allocation

is carried out in accordance with a speciﬁc method-

ology designed to systematically capture the nuances

of typographic recognition within the framework of

weighted voting games. By tailoring the approach for

each individual typeface element, this methodolog-

ical precision allows for a detailed examination of

the intricate dynamics governing typographic recog-

nition. Consequently, this structured assignment en-

Analytical Study on Typeface Visual Identiﬁcation

125

ables a profound exploration of the interrelations be-

tween typographic elements and their correspond-

ing recognition measures, offering insightful observa-

tions grounded in the principles of game theory.

Next, to the consideration of a typography denoted

as T , we proceed to allocate a unique weighted voting

game for each distinct typographic element X ∈ T ,

denoted as Γ

(X). This allocation is carried out

in accordance with a speciﬁc methodology designed

to systematically capture the nuances of typographic

identiﬁcation within the framework of weighted vot-

ing games. In particular, Γ

(X) is described as fol-

lows:

(X) := [q

(X); µ

(X,Y

),... ,

(X,Y

)]

where Y

, for i ∈ {1,. .. ,k}, are all characters of T .

Considering the 80% success rate, for each weighted

voting game Γ

(X), we stated the quota q

(X) as

the 80% of the total n presentations considered, i.e.,

(X) = 0.8 · n. From these weighted voting game

(X), we are able to compute the corresponding

Shapley-Shubik value of X with respect to Γ

(X),

denoted by µ

(X) (Shapley and Shubik, 1954). In

essence, µ

(X) is the number of times that X is pivot

(it makes that a coalition of characters will be success-

fully) divided by all possible permutations. Finally,

we consider a general identiﬁable value for the given

tipography T based in those values as follows

(T ) =

∑

X∈T

(X) .

Example. Let T be a typography where

{a,b, p, q} ∈ T . Suppose that, after doing the exper-

iments with 10 presentations for each carhacter, we

obtain the following results:

(a) = [8;8,1,0,1] → µ

(a) = 1

(b) = [8;2,8,0,0] → µ

(b) = 1

(p) = [8;0,1,7, 2] → µ

(p) = 2/3

(q) = [8;0,0,4,6] → µ

(q) = 1/5

Thus,

(T ) = 1 + 1 +

Note that this last method is the main novelty of

this work. It gives us a new point of view to determine

whether a typography is indistinguishable or not. In

fact, it let us to see how relevant is a character to make

a coalition of characters a successfully coalition.

3 CONCLUSION AND FUTURE

WORK

In this work, we deﬁne three different values or mea-

sure to identify how good is a given typeface or ty-

pography. Subsequently, it is necessary to apply these

measures to speciﬁc typefaces and systematically as-

sess their effectiveness. This comprehensive evalu-

ation will not only provide insights into the perfor-

mance of individual typefaces but will also contribute

to a nuanced understanding of the applicability and

robustness of each measurement method in the con-

text of our study.

A prospective avenue for further research involves

the exploration of alternative power indices, such as

Banzhaf, Deegan-Packel, Holler, among others. This

expansion should allow a more comprehensive under-

standing of the typographic recognition. Additionally,

our future effors will also focus on an examination

of typography recognition within the realm of social

networks, where we intend to investigate the inter-

play and relationships among characters as a social

network.

The ﬁnal results help us to choose the best typog-

raphy and improve the design of speciﬁc characters

in the considered typography, in terms of visual iden-

tiﬁcation tasks and readability (Braida et al., 2018).

It let us to rank optotypes in order to classify them

according to the visual identiﬁcation.

ACKNOWLEDGEMENTS

J. Freixas and X. Molinero has been partially sup-

ported by funds from the Ministry of Science and In-

novation grant PID2019-104987GB-I00 (JUVOCO)

and the Catalan government [2021 SGR 01419 AL-

BCOM].

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