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ISSN 0005-1055, Automatic Documentation and Mathematical Linguistics, 2019, Vol. 53, No. 3, pp. 143–159. © Allerton Press, Inc., 2019.
Russian Text © The Author(s), 2019, published in Nauchno-Tekhnicheskaya Informatsiya, Seriya 2: Informatsionnye Protsessy i Sistemy, 2019, No. 6, pp. 28–44.
Method of Coding for Multicomponent Objects (RHA)
and Its Application for Ordering Roman Fonts
E. T. Petrovaa, *, T. G. Petrovb, **, S. V. Chebanovc, ***, and S. V. Moshkind, ****
aGraphic artist, independent researcher, St. Petersburg, Russia
bSokolov Co Ltd, St. Petersburg, Russia
cSt. Petersburg State University, St. Petersburg, 199034 Russia
dNational Library of Russia, St. Petersburg, 191023 Russia
*e-mail: katia.petrova@gmail.com
**e-mail: tomas_petrov@rambler.ru
***e-mail: s.chebanov@gmail.com
****e-mail: svmoshkin52@gmail.com
Received December 27, 2018
Abstract—The authors propose to systematize the font frameworks of the ''H'' sign types of different fonts on
the base of the RHA information language, which has been developed for different types of objects, by assign-
ing a code to the framework by placing the H font in the standardized window (FontWindow), with the sub-
sequent calculation of quantity characteristics (characterizations). The codes are rendered in a diagram. The
sorting of codes is carried out using the SBCO special alphabet, where S, B, C, O are, on one hand, code ele-
ments, and on the other hand, component designations of fonts frameworks. The sorting of codes is carried
out by alphabets (1) ratings of assignment of components fields in a FontWindow, (2) entropies, and (3) anen-
tropies. The codes are accompanied by the names of coded fonts. The authors propose a principle of placing
codes, which does not depend on the name, style, width, the purpose of the font, and its author. The
described method organizes H fonts by resembling of their frameworks. The created list-catalog can include
all Latin and Cyrillic H fonts of direct inscriptions. The catalog layout includes 99 codes of H font frameworks
ranged into 6 classes from 24 possible classes in the system made by authors. The proposed variant of the
applying of the method can be used as a base of creating of a common method of coding and systematization
of bicolored (in the present paper) and multicolored images on the plane, including maps and other presen-
tations, which include sets of components of different colors and forms.
Keywords: font sign, allograph, FontWindow, letter frame, alphabetical ordering of font codes, letter frame
entropy, letter frame anentropy, RHA code of the frame of sign type, RHA-system of the frames of sign types,
R-class of the frames of sign type, entropy–anentropic diagram, fonts-synonyms, font-clone, geographical
maps, geological maps, multi-color images
DOI: 10.3103/S0005105519030087
INTRODUCTION
Font diversity, which arises as a result of a special
type of artistic creativity, is represented by numerous
variants, and each year the font and design studios
release new ones. There are over 13 000 fonts. Design-
ers, authors, and printers are often faced with the need
to search for fonts of a desired pattern, while sorting the
font database on a computer or on the website of the
seller or font manufacturer. Pirated clone fonts exist
that completely copy the design of the author’s versions
under a modified name [1, 2], synonym fonts created in
the image of a basic font and similar to the base font, as
well as fonts with the same name but a different pattern.
There are several ways to classify fonts [3], from
which groupings can be distinguished by: historical
aspects [4, 5], design features (with serif and sans serif
[6, 7]), type of creation (handwritten, stencil, etc. [8,
9]), purpose (type, accidental, and character [10–
12]). All of these methods for organizing fonts require
expert judgment. Universal (today) is a simple order-
ing using a natural font alphabet, as used in programs
(for example, FontExplorer and FontExpert), and in
printed catalogs [13, 14], and on font sites [15–17].
However, the names (titles) of fonts do not have a
semantic load; therefore when using them, without
knowing the font “in person,” without having measur-
able characteristics of the fonts and their ordering sys-
tem, similar fonts can be found only with special
applications [18]. One popular application [19] recog-
nizes isolated characters of the Latin font supplied to
the program input and offers several types of font
AUTOMATION
OF TEXT PROCESSING
144
AUTOMATIC DOCUMENTATION AND MATHEMATICAL LINGUISTICS Vol. 53 No. 3 2019
PETROVA et al.
names to choose from. The site Identifont, which
offers to search for the desired font by answering ques-
tions, narrows the search to several font names [20].
These resources are available and easy to use; however,
they are fragmented and do not give an unambiguous
ordering of fonts according to their form among those
similar in shape, they have no way of tracking the vari-
ability of the form from font to font. These applica-
tions do not include unlicensed fonts [18]. From a
practical point of view, the current situation is quite
acceptable for designers engaged in fonts; however it is
impossible to see the general principles of organiza-
tion of font variety, the tendency of their appearance,
the specifics of their use, the features of the psycho-
physiology of perception, or to predict the appearance
of new fonts with certain characteristics.
In [21] it was noted that the construction of an all-
encompassing detailed classification of fonts is hardly
possible at all, since they are the product of artistic
creation. At the same time, when describing them, one
usually seeks to cover the object in detail. However, if
one does not require taking all the features of the
objects that are being described into account, perhaps
smoothly changing and not having definite boundaries
between clearly different ones, these objects can be
described, for example, by selecting some measurable
properties that are important for a given group of
objects and comparing objects via these properties, as
natural scientists do (more precisely, we are talking
about different ways of working: with idiography, that
is, revealing diversity, and nomothetic, revealing laws;
an example of their combination is [22]).
As a universal characteristic of continuously
changing compositions of objects, a dual list of the
names of the components that make up the object and
the proportions of these components in the object that
is subjected to entropy–anentropic analysis (the RHA
method by T.G. Petrov [23]) was chosen. The analysis
consists in that fact that after obtaining the rank for-
mula R, C. Shannon’s information entropy is com-
puted (Н = –Σpilnpi, where рi is the frequency of the
ith component normalized to 1 [24, p. 48]), which
characterizes the uniform distribution of components,
and anentropy (A = –[(Σlnpi)/n] – ln(n), where n is
the number of components that represent the object
[24, p. 61]), as introduced by T.G. Petrov to character-
ize the non-uniformity of the contribution of the com-
ponents to their distribution, based on the comparison
of which meaningful conclusions are drawn in the
studied objects. At the same time, H and A can be cal-
culated for complete (which makes it possible to more
fully represent their individuality) or truncated com-
positions of objects (for the purpose of their compari-
son, regardless of the nature of the objects and the
ways of studying them).
The RHA [23] information language-method was
developed for uniform description of this type of com-
position representation, which was originally pro-
posed to describe the chemical compositions of rocks,
and later manifested itself as a method of encoding
and alphabetical ordering of the compositions of
objects of any nature, the types of components of
which are either discrete, or discretized [25, 26].
A modern discussion of the RHA method was given in
[24–31]. The presentation of compositions (of miner-
als, rocks, texts, population ages, species composition
of plankton, types of correspondence, etc.) processed
by this method has two basic requirements: (1) cer-
tainty of the composition components to be specified,
i.e., the uniqueness of their distinction and (2) the
closeness of the sum of the sizes of the specified parts
to 100% (or to unity). The exact equality of the sum of
the contents of the components to 100% is more likely
to arouse suspicion in the quality of analysis than to
indicate its accuracy. For the clause given in parenthe-
ses, it should be noted that in works on computer sci-
ence, to which the RHA method belongs, percentages
are not used as a measure of the intensity of a property
or the frequency of events, but rather parts p
i of the
whole taken as a unity (∑pii = 1).
Thus, RHA is:
• a method of presenting data on composition;
• a method of primary processing of this data;
• an information retrieval language for the descrip-
tion of compositions;
• a method of coding data on the composition of a
particular object;
• a code of the composition of this object;
• a method of ordering compositions.
Bearing in mind the diversity of the capabilities of
the RHA method, it became natural to continue the
development of the method using the example of
encoding typographic fonts, which was started in [32].
The objectives of this article are to describe an
alphanumeric method of encoding characters of fonts
of a direct lettering, which allows encoding and order-
ing them by rank-and-entropy characterizations1 in
the form of a table, to present the catalog layout of the
''H'' sign types and to visualize their distribution on
entropy–anthropic diagrams.
THE "H" SIGN TYPE AND THE STANDARD
OF ITS DESCRIPTION
The frame of the "H" sign type (Fig. 1a) is under-
stood as a schematic representation of the "H" sign,
consisting of two vertical segments of comparable
length, that is, boles and a connecting horizontal or
slightly right-inclined connecting segment (with the
left-inclined connecting segment, the Cyrillic “И”
sign types begin, and with the right-inclined, “N”),
whose height is not taken into account (except for the
1In contrast to the non-quantitative characteristics of objects,
hereinafter, quantitative characteristics, in our case, entropy and
anentropy, will be called characterizations.
AUTOMATIC DOCUMENTATION AND MATHEMATICAL LINGUISTICS Vol. 53 No. 3 2019
METHOD OF CODING FOR MULTICOMPONENT OBJECTS (RHA) 145
prohibition of the occupation of the extreme upper
and lower positions). This sign type, as common for the
letter H of the Latin alphabet and H of the Cyrillic
alphabet, was chosen in [32] on this topic. This sign
type, being a work of art in a particular font, may have
numerous features that are not taken into account in a
formalized description of the font. Thus, various modi-
fications of the crossbar and boles of this type are
ignored, as well as the unevenness of the tone or thick-
ness of the components of the sign type, and we obtain
a simplified image of the "H" sign type, that is, the frame
of the "H" sign type, which is subject to coding (Fig. 1).
As a result, the "H" code of a specific font of a particular
typeface will be obtained.
For comparability of different frames, their height is
taken as a unity, and for compatibility of the width of
frames, the maximum possible width is entered, for which
the sum of the unity and the number ϕ of the golden pro-
por tio n is taken, that is , the valu e 1 + 1.618 = 2.618 . T h e
addition of the unity is due to the fact that there are
variants of "H", whose width exceeds 1.618 with a height
equal to unity. For the visual presentation and compa-
rability of the "H" frames of different fonts, a special
window was built, that is, the FontWindow (F), with a
fixed height, taken as a unity, and a width equal to 2.618.
The resulting "H" frame of the Braggadoci font is placed
in the FontWindow as an example (Fig. 2).
A FontWindow with an area of FS with the frame
placed in it has components for which we set the fol-
lowing notation:
(1) two main vertical bars of the frame, having a
total area of SS (Stem);
(2) a connecting horizontal bar of the frame with
an area of BS (Bar);
(3) an internal space of the frame with an area of CS
(Counter);
(4) a residual free space with an area of OS (Outdoor).
The sum of the areas of the specified components
is FS = SS + BS + CS + OS = 2.618, w hich is taken as
100%, and in further calculations as 1.
We consider the idealized cases of the shape of the
font character as the specified parameters approach
the 100% of the area SF of the FontWindow F (Fig. 3).
Therefore, we obtain a set of areas of the compo-
nents of the frame of the letter and the area of free
space in the FontWindow. This set will be converted to
code by the RHA method.
REPRESENTATION
OF THE FONTWINDOW WITH THE "H" FRAME
IN THE RHA LANGUAGE
The Rank formula R
The description of sign types in the RHA language
includes a semi-quantitative characteristic of the sign
type by the composition of its components using the
rank formula R [23] (the first symbol in the name of
the method) and a quantitative description of the area
composition of the sign type. The ranking of signifi-
cances in describing sets of parts is a very common
Fig. 1. Transitions from the sign type (a) to the H allograph
of the Braggadocio (b) font and the "H" frame of the Brag-
gadocio font (c).
(b) (с)(a)
Fig. 2. The FontWindow with the "H" frame inscribed in it,
where: S—boles; B—connecting bar; C—internal
space of the allograph; O—residual space of the
FontWindow.
2.618
1
Fig. 3. Extreme–idealized forms of the H font sign:
(а) the form of H with the total area of boles SS close to 100%. The greater the value of SS is, the smaller the area of the internal
space is and the wider the allograph is, the richer the font is;
(b) if the BS area (connecting bar area) approaches 100%, a crossbar remains in the FontWindow with the disappearing partici-
pation of all other components of the allograph;
(c) approaching 100% of the internal space of the allograph (CS) results in an approach to the zero areas of the remaining com-
ponents in the FontWindow, which affects the lightness of the letter;
(d) with free area OS approaching 100%, an allograph occurs with the disappearance of all other parts. The allograph is super-
narrow.
(b) (с) (d)(a)
146
AUTOMATIC DOCUMENTATION AND MATHEMATICAL LINGUISTICS Vol. 53 No. 3 2019
PETROVA et al.
procedure; however, such sequences have not been
considered in science thus far, since they have not
been understood as a particular object. However, rank
formulas are a fundamentally new object of interest to
informatics. The rank formula R of the component
composition of the "H" sign type as the first part of the
code is a sequence of names of the components of the
frame for reducing the shares of their areas in the
FontWindow. Thus, the rank formula contains two
types of data about the frame: (1) qualitative charac-
teristic about it, since it reports on a set of specific
components of the frame located in the FontWindow
and (2) ordinal characterizations, as the relative values
of the components are reported in the rank formula:
importance, significance, and the size of the frame
parts in the FontWindow.
We construct the rank formula for the "H" frame of the
Braggadocio font (see. Fig. 1 and Appendix2, No. 32).
The "H" frame of this font has the following areas of
parts (in %): SS = 42.77, BS = 0.30, CS = 3.20, OS =
53.73. By writing the areas with their abbreviations on
reducing the values and using inequality signs, we
obtain the sequence O > S > C > B. After this, by elim-
inating inequality signs and values of areas, we obtain
the rank formula OSSSCSBS. Another example is the
frame of the Distill font (see Appendix, No. 66): SS =
7.8 4, BS = 4.39, CS = 36.50, OS = 51.27; it cor resp ond s
to the rank formula OSCSSSBS.
Thus, the proposed area ranking divides the possi-
ble variety of straight fonts into groups that have the
same rank formulas. This is the first step in ordering
the variety of fonts. An indefinitely large number of
specific combinations of areas may correspond to the
same rank formula. Among them are formulas that
have neighboring components that practically do not
differ in content. Equal signs are used to highlight such
components.
There are no definite boundaries between the
degrees of similarity from the “very” similar (two books
of one edition) to “almost nothing in common” (two
legs of a person and the cry of a gull). On the other
hand, in some areas of knowledge (crystal chemistry
and mineralogy) it turns out to be justified to consider
values that differ by no more than 15 rel %3 as equal.
In order not to look for other rationales and not
stray from this topic, let us take this boundary in our
case. Accordingly, we will put an equal sign between
neighboring symbols in the rank formula of the frame
areas if the result of dividing the previous (in the rank
formula) area share by the next one does not exceed
1.15. In this case, the order of the components, that is,
2Hereinafter, in order to demonstrate examples of "H" sign types
of different fonts, references to Appendix will be given before the
principles of its construction are described.
3Relative percentages are understood as the ratio of two quanti-
ties, expressed as a percentage when dividing the greater one by
the lesser one.
the frame parts, is preserved in the rank formula, and
the order of these characters is given by the alphabet (S
B C O) only if they are exactly equal.
The second part of the composition code, entered
after the rank formula, the integral characterization of
the frame, entropy (H), is mainly responsible for
medium–large areas, the third, anentropy (A), is
mainly responsible for small ones.
Entropy and anentropy allow one to more fully take
the diversity of the set of sizes of areas into account.
Let us turn to these concepts.
Entropy H
Let us consider the FontWindow with the H frame
inscribed in it from the point of view of the degree of
equi-dimensionality of the areas of its components: SS,
BS, CS, OS. An extremely equi-dimensional complex is
represented by a frame inscribed in the FontWindow,
in which the areas of all components of the window
contents are equal to each other.
An extremely different-sized content of the window
is filled with a single, that is, any, part (Fig. 3).
Accordingly, the number of extremely different-sized
complexes will be equal to the number of components
of the complex (i.e., four); the extremely equi-dimen-
sional complex will be the only one that can be useful.
As a measure of uniformity, we take C. Shannon’s
information entropy, which is used in many branches
of knowledge [33]. At the inception stage of the RHA
method, it was proposed for geochemistry as a measure
of the complexity of the chemical composition4 [34]. It
is determined by the formula:
where pi is the frequency of an event, in this case, it is
equal to the shares of the areas of the components of the
content of the FontWindow, whereby ∑pi =1. In the
considered case, pi is the share of the area occupied by
the ith part of the content of the FontWindow. The
value “–pilnpi” is the contribution of a single part of the
FontWindow content to the entropy (Fig. 4). If pi = 0,
then the contribution of this component to the entropy
is not calculated. At pi = 1, the component contribu-
tion is 0.
As we see in Fig. 4, the dependences of the active5
contribution to entropy and anentropy on the contents
4The use of informational entropy as a measure of complexity is,
in principle, not the only option for estimating complexity (for
example, solving a complex task is not evaluated by entropy).
5Investments are qualified as active that directly depend on the
presence of the considered components and do not contain
explicit parameters related to the calculation procedure (accord-
ing to the number of components). They are opposed to passive
contributions, for which the calculation of the value explicitly
depends on the parameters of the calculation. In our case, the
parameter of the passive contribution in the formulas is equal to
the number of components, four.
ln ,
ii
Нpp
=−
AUTOMATIC DOCUMENTATION AND MATHEMATICAL LINGUISTICS Vol. 53 No. 3 2019
METHOD OF CODING FOR MULTICOMPONENT OBJECTS (RHA) 147
until the maximum contribution to the entropy is
reached at p = 0.368… behave symbatically, after reach-
ing the specified maximum, in the opposite manner.
At uniform distribution of p, i.e., at p1 = p2 =
p3=… = pn = 1/n the entropy of the composition of
the object, which can be interpreted as its complexity,
is maximum and equal to lnn (natural logarithms),
where n is the number of counted FontWindow com-
ponents. Therefore, a filled FontWindow will be called
equi-dimensional. In our example, the entropy is max-
imal and is equal to ln4 = 1.386… We built such a
frame of the "H" sign type (Fig. 5). The font developed
on the basis of such a sample could have the name
*SuperCompl6, that is, extremely equi-dimensional.
An object consisting of a single part (p = 1) has a
minimum equi-dimensionality equal to 0. For frame
analysis, when equi-dimensionality is minimal, this
corresponds to an empty FontWindow or one that is
uniformly filled with one part (component) (exam-
ples, Figs. 3a, 3b, 3c, 3d). In our case, if a free field is
occupied by a single part, then, like many other ideals,
this ideal of simplicity makes the use of such a sign type
senseless. The "H" frame of the Super C font (Appen-
dix, No. 64), which is almost completely represented
by free space, is the closest to it. On the verge of such
a situation there are the so-called “conceptual fonts”
that use the rejection of some letter elements, for
example, "H" of the Gropius Display font (Appendix,
No. 10), whose "H" frame does not have a crossbar
and free space between the boles, and GHSans (Appen-
dix No. 22), whose "H" is devoid of a crossbar. The first
one has the rank formula OSSSBS = CS and entropy H =
0.665; for the second one, OSSSCSBS and H = 0.866.
Anentropy А
The third integral characterization of the composi-
tion, that is, anentropy, was proposed by T.G. Petrov
[23] to reduce the degree of uncertainty in the descrip-
tion of the composition of a multicomponent system
when it is mapped by two characterizations, that is, the
rank formula and entropy. It is clear that the more
components in the system and the fewer its character-
izations, the greater the undetermined information
about a particular object, system, organism, etc., is.
Anentropy is calculated by the formula
where the designations are the same as in the entropy
formula. The active contribution of the pi component
to the anentropy is “–lnpi.”
Anentropy, determined by the arithmetic mean of
the active contribution taken with a negative sign, is
relatively weakly dependent on large pi and strongly
dependent on small pi. It changes from 0, with a uni-
6The “*” sign is placed before a linguistic (semiotic) object that is
non-existent, but was invented as a mental experiment.
– 1/ ln – ln ,
i
Anpn
=
form distribution, i.e., when the entropy is maximal,
up to an indefinitely large quantity, when at least one
pi approaches zero. For fonts, the latter situation is
very rare, but, in order not to deny their ordering, all
characterizations of their character types are given in
the Appendix. For the diagrams, they can be placed in
them above the entropy value, close to the upper edge
of the diagram, breaking the frame line somewhat, to
mark the anomaly of the point and focus on the fact
that as pi tends to zero, the entropy tends to +∞. As an
example, this refers to the anomalous sign types of the
fonts Gropius Display No. 10 and GHSans No. 22,
which almost cease to be letters, or to the figures
shown in Fig. 3, where (a) the shares of parts of B, C
and O areas approach 0; (b) the SS, BS, OS areas are
disappearing; (c) the SS, CS, OS areas approach zero;
(d) the SS, BS, CS areas tend to zero.
Thus, anentropy is calculated for the same areas in
the FontWindow as entropy, but, unlike it, the nega-
tive logarithm of the area share is used as an contribu-
tion, i.e., “–lnpi.” This value approaches 0 when pi
approaches 1 (this is for all foundations of logarithms),
i.e., to the area of the entire FontWindow, and
increases monotonically with decreasing pi.
THE METHOD OF ORDERING
RHA CODE-WORDS OF H SIGN TYPES
The combination of the rank formula, entropy, and
anentropy is considered as the FontWindow code with
Fig. 4. The dependencies of active contribution to
entropy “–piln pi”, (lower curve) and to anentropy
“‒lnpi” (upper curve) from shares of the areas рi.
0
0.1
0.01
0.001
0.0001
0.00001
0.000001
Inverstment
0.00001
0.0001
0.001
0.01
0.1
1
10
100
pi
Fig. 5. H components under the condition of equality of all
areas in the FontWindow.
2.618
148
AUTOMATIC DOCUMENTATION AND MATHEMATICAL LINGUISTICS Vol. 53 No. 3 2019
PETROVA et al.
its contents and, at the same time, as a word in the
information RHA language. Three alphabets are used
to build this word.
The first alphabet is the order of the characters of
the components given by the authors of the article:
S C B O given in the notation of Fig. 2. We adopted
this sequence as the alphabet for the ordering of the
rank formulas for the frames of letters. First, the entire
set of specific RHA code-words of the FontWindow
(accompanied by font names) is divided into groups
with identical first members of rank formulas, after
which the groups are arranged according to the alpha-
bet (SBCO), as when using alphabets of existing
scripts. Then, within each group, the operation is
repeated with the second member of the rank formula,
and so on. As a result, for the four-letter (rating) part
of the codes, we have a complete set of possible rank
formulas, which are arranged in the table as words in
the alphabetical sequence by SBCO, where rank for-
mulas for which there are examples, are in bold.
The second alphabet is continual, that is, the
entropy values. Within a group of identical rank for-
mulas for the alphabetical ordering of sign types,
entropy is used, which is expressed as a real number.
However, the direction of ordering descriptions of
objects within a group with the same rank formulas, in
principle, may be different. Thus, in the article on
alphabets [32], the arrangement of codes by non-
decreasing of H was used, as in the case of streamlining
the codes of the age distribution of the population [26].
In [32], the direction of ordering was taken without
any justification, in [26] the direction was justified
using historical and demographic reasons. With the
accumulation of material on H, and the analysis of the
HA diagrams, it became clear that the variant of order-
ing fonts used in [32] makes it difficult to interpret the
results. Therefore, it was decided to alphabetically
order the H values by their lack of an increase7, which
we explain below.
The third alphabet is also continual, that is, the
anentropy values. To order codes with similar R and H,
the A values are used according to their lack of decrease,
which was chosen due to the fact that the inverse rela-
tionship between H and A dominates statistically.
7This means that different fonts may have equal entropy values.
RHA-ORDERING OF H SIGN TYPES
Codes of 99 arbitrarily selected Latin fonts from the
ParaType, MyFonts, FontShop collections are pre-
sented in the Appendix. Rank formulas are ordered by
the SBCO alphabet. Entropies within the same rank
formula, that is, the R-class of the font, are ordered by
the lack of an increase. In the “Frame in F” column,
the frames are inserted into the FontWindow so that the
left border of the FontWindow coincides with their left
border. This allows us to draw a number of conclusions.
(1) Out of the total number, 24, of possible R-classes
of H (see Table 1), 6 classes are presented (including the
first one, proposed only in this article).
(2) Approximately 90% of all the H sign types consid-
ered by the authors in this article belong to two R-classes:
OsSsCsBs (Nos. 11–64) external space, boles, con-
necting bar, internal space,
OsCsSsBs (Nos. 65–99) external space, internal
space, boles, connecting bar.
The first class are predominant, in which there are
54 fonts with relatively thick boles, and the second, in
which there are 35 “leaner” ones.
(3) The theoretical construction of the H frame,
which we called *SuperCompl, with the rank formula
SsBsCsOs, with a sequence of characters matching the
sequence of characters in the alphabet, the maximum
possible (for four components) entropy and the mini-
mum possible anentropy, defines the role of this frame
as the beginning for ordering fonts according to rank
formulas (see Table 1), entropy (see the Appendix),
and anentropy. The sequences of characters at the
beginning of words in alphabetic dictionaries are most
similar to sequences of characters at the beginning of
the alphabet, ideally they should be the alphabet itself.
Accordingly, the last R-component of the RHA word
(rank formula) will represent the sequence of charac-
ters inverse to the alphabet.
(4) The location of the theoretical H frame of
*SuperCompl as the first in the ordering is determined
by the method of ordering the rows of the table and
within the R-classes. Its exclusivity follows from the
fact that: (a) this sign contains all components that are
clearly visually distinguishable and (b) this image,
which has the maximum entropy, with any changes in
proportions between the four components, will be
transformed into any different sign, which will have
Table 1. All possible rank formulas–R-classes of "H" sign types ordered according to the SBCO alphabet
1SsBsCsOs7B
sSsCsOs13 CsSsBsOs19 OsSsBsCs
2S
sBsOsCs8B
sSsOsCs14 CsSsOsBs20 OsSsCsBs
3S
sCsBsOs9B
sCsSsOs15 CsBsSsOs21 OsBsSsCs
4S
sCsOsBs10 BsCsOsSs16 CsBsOsSs22 OsBsCsSs
5S
sOsBsCs11 BsOsSsCs17 CsOsSsBs23 OsCsSsBs
6SsOsCsBs12 BsOsCsSs18 CsOsBsSs24 OsCsBsSs
AUTOMATIC DOCUMENTATION AND MATHEMATICAL LINGUISTICS Vol. 53 No. 3 2019
METHOD OF CODING FOR MULTICOMPONENT OBJECTS (RHA) 149
less entropy, as in the OsSsBsC class, to which it is
assigned in the catalog layout, and in all others, arising
from the initial equality of the areas of the FontWin-
dow components.
Let us again note that when the share of the area of
any component tends to 1, the frame will experience
the same effect as when filling the FontWindow with
one tone, i.e., the entropy will decrease to zero and the
anentropy will grow indefinitely. The same will hap-
pen when the areas of any (one or more) components
tend to 0.
(5) in sequences of the most widely represented
classes of frameworks OsSsCsBs and OsCsSsBs by the
lack of an increasing of entropy (against the back-
ground of a general decrease in the visually perceptible
width of the frame, up to the frame of the fonts Super
C No. 64 and FR Pasta Mono No. 99, which are prac-
tically indistinguishable visually), the frames of the
first class have a much greater variety of entropy
parameters than those of the second class. This follows
from both the Appendix and the representation of the
distribution of the corresponding points in Fig. 6.
(6) Fonts that are identical or most similar in
appearance mostly have the same rank formulas and
the same or similar entropic characterizations. In the
Appendix, they are located adjacently, such as:
PT_PTS75 Bold No. 25 and PT_PTS65 Demi No. 26
(with codes: R, OsSsCsBs, Н = 0.860, А = 0.664 and
Н= 0.858, А = 0.671, re spectively ), Taho m a No. 78
and Kabel No. 79 (OsCsSsBs, 0.837, 0.702 and
OsCsSsBs, 0.835, 0.704), or close, for example, Regata
No. 21 and PT_PTS95 Black No. 30 (OsSsCsBs, 0.866,
0.667 and 0.848, 0.713).
Exceptions, for example, the greatest closeness of
letter forms in the fonts 49 and 86, or 52 and 89, are due
to the fact that when the areas of different components
of the frame are similar, small changes in one of the
areas can lead to a rearrangement in the rank formula.
(7) Visually, the sequence of codes for the change
in H in the two most represented R-groups in the table
reveal some general tendencies in changing the shape
of the frame. This commonality is due to the fact that
in the FontWindows of these groups the share of free
space prevails and increases; therefore in both cases
the frames become increasingly narrow by the end of
these groups. In cases where other components of the
FontWindow are in the first place in the rank formula,
an increase in their share of the area leads to the for-
mation of monstrous frames, such as those shown in
Figs. 3a, 3b, 3c.
(8) Against the background of these trends the
frames stand out that are sharply different from those
belonging to general trends to one degree or another.
This is a consequence of the fact that the framework
has three characterizations (R, H, A,) provided that
∑pi = 1, and under linear ordering of descriptions, only
one is used. Deviations from the tendency in changing
the forms of frames in the Appendix, especially pro-
nounced in the OsSsCsBs block, are a reflection of the
inadequacy of the representation of frame structures
that have more than two components, with a single
information entropy. As examples of frames whose
entropy does not differ or differs by no more than
0.001 while the entropy differs significantly we give
Nos. 17–18, 31–32, 34–35, 43–44, 46–47, and 48–49.
When the values of entropy and anentropy are similar,
the differences between the frames become insignifi-
Fig. 6. Entropy–anentropic characterization of the frameworks given in the Appendix.
1 Font SBCO
H
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4
A
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2 Font SOCB
3 Font COSB
4 Font OSBC
5 Font OSCB
6 Font OCSB
150
AUTOMATIC DOCUMENTATION AND MATHEMATICAL LINGUISTICS Vol. 53 No. 3 2019
PETROVA et al.
cant and almost disappears: Nos. 24–25, 58–59, 74–
75, and 92–93. In this case, we have a vivid visual illus-
tration that a boundless breadth of diversity that is esti-
mated by a single number may occur when the variety
of values is very significant.
The question of deviations from the tendencies of
changes in the frames at the linear ordering of their
entropy is largely eliminated by using the entropy–
anentropic diagrams given below.
FONT FRAMEWORKS
IN THE ENTROPY–ANENTROPY
HA-DIAGRAM
For a general review of the entropy–anentropic
characterization of the font collection, we present
Fig. 6.
As we can see, the points on the diagram are dis-
tributed unevenly, with a relatively small area in the
intervals of H 0.6–1.0 and A 0.6–1.2.
The *SuperCompl frame, which was built theoreti-
cally on the principle of maximizing H and minimizing
A and which is still the only representative of the R-class
SsBsCsO, is in the lower right corner of the diagram.
Fonts whose entropy–anentropic characterizations are
located to the right and below it in the proposed dia-
gram do not exist and cannot exist for a frame with four
components. At the same time, another no less import-
ant feature of this frame is that insignificant changes in
the areas of its components lead to the generation of all
5 existing and 18 under-represented classes in the
Appendix. No other class has been found.
Since the transition to *SuperCompl from any exist-
ing frame class can occur due to small changes in any
component, deviations from *SuperCompl can continue
in an undefined direction, generating new frames. A
similar situation occurs in the case of strange attractors
[35] or bifurcations [36, 37] as described in functional
analysis. The *SuperCompl frame acts as a pure ideal;
loss of completeness of it leads to the appearance of all the
other 23 classes of frames, each of which has some devi-
ation from the ideal *SuperCompl due to kenosis (a
decrease) of at least one of the components and the ele-
vation of the others. Thus, all possible frames are in one
ideal variant and are its emanations [38]. The same rela-
tionship exists between a vector with module 0, which is
not directed anywhere, and an arbitrarily small vector
that has one and only one directionality, while all other
directionalities are excluded, the same as a geometric
point with respect to any other shape.
The maximum values of entropy and at the same
time the closest to the theoretical value of the
*SuperCompl font are the frames of the two R-class
fonts SsOsCsBs and one each of the classes OsSsCsBs
and OsCsSsBs. The ratios of the areas of the four
FontWindow components of such fonts are closest to
each other and to the ratio of the theoretical *Super-
Compl.
The minimum entropy values have frames with the
OsSsCsBs and OsCsSsBs rank formulas, they are the
narrowest and most recent ones in the font lists of the
corresponding R-classes. The free space sharply dom-
inates in these fonts in the FontWindow.
The "H" frames of conceptual fonts have the highest
anentropy values (A = +∞): Gropius Display (No. 10)
has only two components of font coding (boles and
free space of the FontWindow) and GHSans (No. 22),
has three components. These are missing from the
diagram.
The R-classes OsSsCsBs and OsCsSsBs are the most
represented in the system, while the fields of their
entropy–anentropic characterizations overlap to a
large extent, they have differences. With equal values
of entropy, the "H" frames of OsSsCsBs in most cases
have higher values of anentropy (Fig. 6).
The high density of points on the diagram did not
allow showing the position of the points with images of
allographs and their frames to make the picture more
visual without significantly reducing the number of
points on the diagram. Figure 7 shows HA and images
of allographs of R-class OsSsCsB; Fig. 8 shows images
of frames of the same R-class.
When comparing the characteristics of H and A of
the "H" frames in Fig. 8, it is possible to observe gen-
eral trends in the shape of frames and their grouping.
Frames whose components are commensurate in
area in the FontWindow occupy the area of high entropy
values. Accordingly, frames whose components have
very small shares among other components have large
anentropy values. Two of the variants found in the liter-
ature: GHSans (No. 22), which is devoid of the crossbar
and Gropius Display (No. 10), which is devoid of two
components, have the maximum anentropy value of
+∞. Therefore, they are not placed on the diagram.
Along the bottom edge of the dotted area (Fig. 7,
Fig. 8) from right to left, from the bottom up, a ten-
dency is clearly observed from the widest to the nar-
rowest fonts, which correlates with an increase in the
area of free space in the FontWindow.
In the case of equality or closeness of R, H, and A,
the compositions and images of the H sign types are
either similar or close in terms of the ratio of the frame
areas, although they differ aesthetically.
The codes of the clone fonts have the same values
as the “honest” fonts; therefore the clones in the dia-
gram will be at the same point or almost coincide with
the previous “honest” ones.
Thus, during the transition from the allograph to its
frame, there is a change in the salience of sign types: in
the case of allographs, letter forms that have features
(Nos. 28, 36, 44, 69, 89, 92, and 95) and missing com-
ponents (Nos. 10 and 22) stand out, and in the case of
frames, they have extreme entropy characterizations
(No. 1 MaxHminA and No. 64, min HMax A)
AUTOMATIC DOCUMENTATION AND MATHEMATICAL LINGUISTICS Vol. 53 No. 3 2019
METHOD OF CODING FOR MULTICOMPONENT OBJECTS (RHA) 151
Fig. 7. H allographs with the rank formula OsSsCsBs and Ss=Bs=Cs=Os (No. 1, in the lower right corner) on the entropy–anen-
tropic diagram (the numbers at the points correspond to the numbers in the Appendix).
1
H
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1. 3 1.4
A
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
41
42
43
44
45
46
47
48
49
50
52
53
54
55
56
57
58
59
60
61
62
63
64
11
12
13
14
15
16
17
18
19
20
25
27
28
29
31
32
33
34
36
37
40
The schematization of the coding of the compo-
nent composition of the frames leads to a sharp reduc-
tion in the qualitative diversity; in particular, this is
due to the exclusion of the extreme (sharply standing
out or “pathological”) variants of allographs.
DISCUSSION OF RESULTS
The presented collection (“collection” in the sense
of Foucault [39]) has 99 fonts, that is, it is a represen-
tative of a universum with an unknown structure and
Fig. 8. H frames with the rank formula OsSsCsBs and Ss=Bs=Cs=Os (No. 1) the entropy–anentropic diagram.
1
H
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4
A
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
41
42
43
44
45
46
47
48
49
50
52
53
54
55
56
57
58
59
60
61
62
63
64
11
12
13
14
15
16
17
18
19
20
25
27
28
29
31
32
33
34
36
37
40
152
AUTOMATIC DOCUMENTATION AND MATHEMATICAL LINGUISTICS Vol. 53 No. 3 2019
PETROVA et al.
limits of variation. It is still small for general conclu-
sions; thus, for now, only some preliminary consider-
ations can be made.
The rank formulas we present in the table exhaust
their variety with 24 classes, of which with an arbitrary
choice of 99 fonts presented in the Appendix, only
5 classes are implemented (the 6th one we designed),
while the overwhelming number of them are in only two
classes. Therefore, we see that only a small part of the
logically admissible variety of roman fonts is used.
The large problem was choosing the direction of
ordering entropy and anentropy due to the lack of obvi-
ous indisputable reasons for determining the sign of
changes, to decrease or to increase (for rocks this direc-
tion was determined by the fact that crystallization of
magmas occurs when the temperature decreases, and
this, in turn, directs the composition of the magmatic
solution to its separation and a statistically significant
decrease in the entropy of the new systems that are min-
erals compared with the initial silicate solution).
Fonts as works of art are generally not related to
each other and their authors apparently did not know
how their design evolved over time; thus, until the the-
oretical form of the letter and the accumulation of a
“sufficiently” complete collection of sign types was
created, the problem of their ordering was not even
formulated. Initially borrowed from other cases, as
data was accumulated the ordering by increasing
entropy (as in [32]) yielded to a more heuristic type
under the pressure of another and higher coherence of
the whole when a new reference point was detected.
The ''H'' frame of *SuperCompl was a starting point,
occupying the lowest and extreme right position in the
diagram (Fig. 6). This frame acts as basic string of gen-
erative grammer [40], which is initial point for gener-
ating of all of the other frames
The small variety of rank formulas (it seems to
increase slightly with the intended accumulation of
materials) indicates the rather narrow information-
aesthetic requirements for fonts of consumers and
designers who provide services.
When varying the ratio of the frame areas, it
becomes possible to predict and build the shape of the
H frames that are located between adjacent points on
the HA diagram or on any line tied to this diagram,
which can be considered a frame family line.
Thus, even the available material shows that the
RHA method provides an alternative method for mak-
ing new judgments about existing and potential fonts.
CONCLUSIONS
The question arises of why all this is necessary if
there are already ways to search for similar font pat-
terns. This can be given a general answer.
The conversion of science to art is a means to under-
stand “how IT is done,” “why SUCH a letter form is
better,” “why THIS WAY is more convincing, more
beautiful, more emotional, more appropriate ….” Is it
possible to understand, and it is interesting, why less
than one-third of the 24 classes of fonts are used? What
will happen if one composes layouts of letters and
frames for classes that are still empty? Perhaps these
layouts will give an impulse to the artist’s imagination to
create something acceptable and new?
As an example of this, the frame of the Arial font
(see the Appendix, No. 73) was chosen and, by adopt-
ing a constant set of its metric characterizations (17.56,
2.33, 10.09, 70.02), we permuted their values for the
components of the new frames. Thus, two frames with
new rank formulas, were built, namely,
COBS and SBOC , as well as
one with the same rank formula as the only still theo-
retical (*SuperCompl) SBCO . If the first
two seem to be of little promise, then the last variant,
as we believe, can be considered quite decent for use in
some significant texts of headings–inscriptions.
There are no clear correspondences between char-
acterizations of letters, complete “words” in the RHA
language, and usually distinguished properties of let-
ters; however, islands of local correspondences
between the images of letters and codes exist; this is
the advantage of a meaningful code. This also applies
to cases when one needs to find a font with quantita-
tively defined properties, for example, when perceiv-
ing a moving text, or a fixed text from a vehicle moving
with a known characteristic speed; when perceiving
texts that have to be read at an angle that is signifi-
cantly different from direct, written on non-planar
surfaces, observed with curved mirrors when inspect-
ing hard-to-reach parts of structures, etc. In connec-
tion with this, we can mention the problem of studying
the semiotics of moving inscriptions, which turned out
to be one of the essential problems in the study of the
linguistic landscape of a city8 (the observer’s position,
perspective point, including being on a moving vehi-
cle, as one of the four main images, principal imaging
systems, in cognitive linguistics [41, p. 254–255]).
The proposed system for encoding H of direct let-
tering when organizing a single data bank will allow
one to:
(1) find the frames that are similar or analogous in
lettering;
(2) purposefully obtain monotonously varying series
of frames, thereby expanding the variety of fonts;
(3) begin the study of the psychology of text per-
ception at a quantitative level in the following areas:
(a) gathering statistics and identifying visual-the-
matic connections, for which types of texts with letter
forms are used more often;
8See, for example, a series of articles in a special issue of the
International Journal Bilingualism, 2014, Vol. 18 (5).
AUTOMATIC DOCUMENTATION AND MATHEMATICAL LINGUISTICS Vol. 53 No. 3 2019
METHOD OF CODING FOR MULTICOMPONENT OBJECTS (RHA) 153
(b) tracking trends and the development of fashion
for certain letter forms;
(c) highlighting the zones of the most readable let-
ter forms for predicting the creation of new fonts for
specific purposes;
(d) identifying letter forms that are not used in
design at all and trying to determine the reasons for this.
The integrality of font characterizations used in
RHA codes certainly requires some skill to work suc-
cessfully with them, as with all new tools.
The method considered in this article can be used
in coding geographic maps, where the rank formula
is built, for example, according to the ratio of the
areas of the intervals between the contours of the
map, according to the ratio of the areas of different
landscapes on the terrain, or geological maps, for
which the ratio of areas of images of rocks of different
compositions, ages, or varying degrees of mineraliza-
tion is significant. It is possible to transfer to coding
volumes or mass ratios in an object, for example, a
particle size analysis of rocks. This method is also
suitable for describing the coloring of stones [42],
animal skins, interiors, the leaf mosaic of trees, the
structure of a rash in dermatology, etc.
Most of the work on the RHA method was carried
out using the Petros3.2 program compiled by
S.V. Moshkin.
APPENDIX
The RHA-systematics of H frames
No. R-class HA Font Allograph Frame in F SS %B
S %C
S %O
S %
1Ss=Bs=Cs=Os1.386 0.000 *SuperCompl l 25.00 25.00 25.00 25.00
|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*
2Ss=OsCsBs1.187 0.303 King Tut Black 39.42 4.01 20.25 36.32
3SsOsCsBs1.134 0.340 Blackoak Std 52.01 4.01 20.24 23.74
4SsOsCsBs0.980 0.787 Guinness Extra
Stout NF 50.7 0.88 9.73 38.7
|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*
5CsOsSsBs0.900 0.678 Vienna
Extended LET 4.56 3.07 62.8 29.6
|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*
6OsSsBsCs0.908 0.759 Cuadrifonte 38.31 4.03 2.19 55.47
7OsSsBs=Cs0.896 0.729 Tonal 33.60 3.47 3.03 59.89
8OsSsBsCs0.796 1.373 YWFT Pudge 44.77 2.06 0.33 52.85
9OsSsBs=Cs0.747 1.378 Sinaloa 36.87 0.85 0.82 61.46
10 OsSs=BsCs0.665 +∞ Gropius Display 38.20 0.00 0.00 61.80
|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*
11 OsSsCsBs1.103 0.341 Aksent 27.47 5.22 12.80 54.51
154
AUTOMATIC DOCUMENTATION AND MATHEMATICAL LINGUISTICS Vol. 53 No. 3 2019
PETROVA et al.
12 OsSsCsBs1.020 0.571 Egyptienne
Extd D Bold 34.19 2.09 10.47 53.26
13 OsSsCsBs0.970 0.808 Quadrata 21.63 0.69 17.00 60.68
14 OsSsCsBs0.966 0.491 Glaser Stencil 16.34 3.63 14.00 66.03
15 OsSsCsBs0.937 0.713 Georgia 19.16 1.21 15.05 64.58
16 OsSsCsBs0.911 0.582 PT_PTC75
Caption Bold 16.31 2.76 12.31 68.62
17 OS=CB 0.909 0.704 Book Antiqua 15.86 1.41 15.59 67.14
18 OsSsCsBs0.908 1.169 Falstaff 33.66 0.22 8.54 57.58
19 OsSsCsBs0.884 0.773 School-
Book_Bold 16.74 1.12 13.88 68.25
20 OsSsCsBs0.878 0.660 Project Fairfax 18.84 2.21 9.65 69.31
21 OsSsCsBs0.866 0.667 Regata 19.61 2.40 8.25 69.74
22 OsSsCsBs0.866 +∞ GHSans 18.20 0.00 15.16 66.65
23 OsSsCsBs0.864 0.669 Thickset 23.33 3.42 4.94 68.32
24 OsSsCsBs0.861 0.677 PT_PTS85
Extra Bold 17.75 2.31 9.35 70.58
25 OsSsCsBs0.860 0.664 PT_PTS75
Bold 15.07 2. 24 11.43 71.27
26 OsSsCsBs0.858 0.671 PT_PTS65
Demi 15.0 6 2 .17 11.46 71. 31
27 OsSsCsBs0.857 0.993 BodoniBold 18.16 0.46 12.85 68.53
28 OsSsCsBs0.856 0.736 Yess_Bold 24.35 2.15 5.81 67.69
29 OsSsCsBs0.848 0.713 PT_PTS95
Black 20.67 2.18 7.16 69.99
30 OsSsCsBs0.839 0.677 Century Gothic 14.80 2.35 10.34 72.51
No. R-class HA Font Allograph Frame in F SS %B
S %C
S %O
S %
AUTOMATIC DOCUMENTATION AND MATHEMATICAL LINGUISTICS Vol. 53 No. 3 2019
METHOD OF CODING FOR MULTICOMPONENT OBJECTS (RHA) 155
31 OsSsCsBs0.825 0.845 YWFT Black
Slabbath 27.25 1.80 4.05 66.89
32 OsSsCsBs0.825 1.294 Braggadocio 42.77 0.30 3.20 53.73
33 OsSsCsBs0.822 0.935 Acsioma_Shock 31.78 1.50 3.06 63.65
34 OsSsCsBs0.810 0.734 FF Archian
Stencil Pro 16.54 2.13 8.0 4 73.29
35 OsSsCsBs0.809 0.947 Acsioma_Next
Rough 30.52 1.53 2.91 65.05
36 OsSsCsBs0.806 0.975 Acsioma_Me-
dium 31.47 1.44 2.71 64.38
37 OsSsCsBs0.800 1.007 Acsioma_Super
Shock 31.75 1.29 2.64 64.33
38 OsSsCsBs0.797 0.980
School-
Book_Cond
Bold
31.78 1.33 2.50 64.38
39 OsSsCsBs0.797 1.012 Acsioma_Next 16.94 0.63 10.04 72.39
40 OsSsCsBs0.777 0.793
PT_PTN87
Narrow Extra
Bold
15.92 1.84 7.48 74.76
41 OsSsCsBs0.758 0.876 PT_PTN97
Narrow Black 19.07 1.59 5.22 74.12
42 OsSsCsBs0.756 1.008 Adamant 23.24 1.01 4.13 71.62
43 OsSsCsBs0.753 0.828 PT_PTN77
Narrow Bold 13.57 1.63 8.44 76.36
44 OsSsCsBs0.752 1.289 Avatar 34.82 0.80 1.28 63.10
45 OsSsCsBs0.726 1.558 Fatta 36.97 0.46 0.73 61.84
46 OsSsCsBs0.724 0.991 Diamonds 19.03 1.10 4.71 75.16
47 OsSsCsBs0.723 1.657 Gaslon 31.29 0.12 2.07 66.52
48 OsSsCsBs0.694 0.970
PT_PTS87
Cond Extra
Bold
15.10 1.22 5.62 78.07
49 OsSsCsBs0.693 1.227 BodoniCondC 12.69 0.32 9.11 77.88
No. R-class HA Font Allograph Frame in F SS %B
S %C
S %O
S %
156
AUTOMATIC DOCUMENTATION AND MATHEMATICAL LINGUISTICS Vol. 53 No. 3 2019
PETROVA et al.
50 OsSsCsBs0.691 0.935 PT_PTS77
Cond Bold 12.34 1.31 7.26 79.10
51 OsSsCsBs0.689 1.249 Garbage 17.65 0.36 5.42 76.56
52 OsSsCsBs0.675 1.074 PT_PTS97
Cond Black 17.76 1.03 3.75 77.46
53 OsSsCsBs0.657 0.983 PT_PTS67
Cond Demi 9.68 1.18 8.30 80.84
54 OsSsCsBs0.642 2.333 Loudine 27.98 0.02 0.87 71.12
55 OsSsCsBs0.640 1.291 Impact 19.94 0.64 2.27 77.14
56 OsSsCsBs0.614 1.082 Hill 11.08 0.99 5.72 82.21
57 OsSsCsBs0.591 1.144
PT_PTS79
Extra Cond
Bold
10.91 0.85 5.22 83.02
58 OsSsCsBs0.582 1.235
PT_PTS89
Extra Cond
Extra Bold
13.51 0.74 3.40 82.35
59 OsSsCsBs0.581 1.352
PT_PTS99
Extra Cond
Black
16.26 0.61 2.18 80.96
60 OsSsCsBs0.570 1.165
PT_PTS69
Extra Cond
Demi
8.31 0.79 6.68 84.22
61 OsSsCsBs0.544 1.585 CompactBold 15.33 0.26 2.10 82.31
62 OsSsCsBs0.389 1.895 Radar 5.82 0.10 3.79 90.29
63 OsSsCsBs0.344 1.938 Titanic Con-
densed 6.22 0.14 2.11 91.52
64 OsSsCsBs0.177 2.613 Super C 1.96 0.04 1.49 96.51
|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*|*
65 OsCsSsBs1.118 0.382 Flat10 ArtDeco 19.20 3.34 25.40 52.05
66 OsCsSsBs1.0 47 0.451 Distill 7.8 4 4.39 36 .50 51. 27
67 OsCsSsBs0.998 0.476 Ecyr 10.46 3.77 23.83 61.94
No. R-class HA Font Allograph Frame in F SS %B
S %C
S %O
S %
AUTOMATIC DOCUMENTATION AND MATHEMATICAL LINGUISTICS Vol. 53 No. 3 2019
METHOD OF CODING FOR MULTICOMPONENT OBJECTS (RHA) 157
68 OsCsSsBs0.955 0.713 Ustav 16.08 1.13 19.70 63.09
69 OsCsSsBs0.947 0.520 YWFT LED 13.26 3.34 16.45 66.94
70 OsCsSsBs0.903 0.600 Yess_Regular 11.86 2.61 16.64 68.89
71 OsCsSsBs0.899 0.593 Lodge 6.40 3.79 22.26 67.54
72 OsCsSsBs0.893 0.618 PT_PTC55
Caption Regular 11.04 2.50 17.25 69.20
73 OsCsSsBs0.874 0.651 Arial 10.09 2.33 17.56 70.02
74 OsCsSsBs0.864 0.661 Verdana 10.16 2.30 16.82 70.72
75 OsCsSsBs0.863 0.768 SchoolBook_-
Book 12.45 1.26 16.51 69.77
76 OsCsSsBs0.862 0.765 Bengaly 12.82 1.28 15.97 69.93
77 OsCsSsBs0.848 0.908 Bodoni 13.17 0.69 16.32 69.82
78 OsCsSsBs0.837 0.702 Tahoma 10.18 2.07 15.49 72.26
79 OsCsSsBs0.835 0.704 Kabel 9.28 2.12 16.50 72.10
80 OsCsSsBs0.826 0.898 Pacioli 8.20 0.89 21.09 69.82
81 OsCsSsBs0.824 0.864 Times New
Roman 10.81 0.95 16.77 71.46
82 OsCsSsBs0.822 0.732 PT_PTS55
Regular 9.34 1.92 16.01 72.73
83 OsCsSsBs0.814 0.766 PT_PTS45
Light 8.31 1.74 17.36 72.59
84 OsCsSsBs0.795 0.841 Calipso 6.16 1.50 20.29 72.05
85 OsCsSsBs0.781 0.876 School-
Book_Cond 11.33 1.06 13.15 74.46
86 OsCs=SsBs0.748 0.825 PT_PTN67
Narrow Demi 10.61 1.62 10.88 76.89
No. R-class HA Font Allograph Frame in F SS %B
S %C
S %O
S %
158
AUTOMATIC DOCUMENTATION AND MATHEMATICAL LINGUISTICS Vol. 53 No. 3 2019
PETROVA et al.
ACKNOWLEDGMENTS
The authors thank K.M. Kirichenko for compiling a
program for analyzing images of letters; N.A. Pavlova,
T.M. Zhuravskaya, and K.A. Manukyan for help with ter-
minology.
CONFLICT OF INTEREST
The authors declare that they have no conflict of interest.
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87 OsCsSsBs0.726 0.883 PT_PTN57
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Translated by S. Avodkova