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Theses

1967

The determination of a set of alphanumeric characters of equal The determination of a set of alphanumeric characters of equal

recognizability recognizability

Keith C. Donaldson

Harry O. Gough

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Recommended Citation Recommended Citation Donaldson, Keith C. and Gough, Harry O., "The determination of a set of alphanumeric characters of equal recognizability" (1967). Thesis. Rochester Institute of Technology. Accessed from

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The De,ter::rinat ion of A set:

ReG(jgnizability ,l

,Keith C • . ,

'·r

": i

'"

A thes i..s ,' ~s ent(2d ir_ par \..: requirem2n~s of the Bach~ Rochester Institute oiTe

. ' . • ! ..

Harry O.

Donaldson '

Go(3h o

o r c.: :~e

~"3 6r€:€ .. "., ccr, ~ : ~'{ •

. , .. J.. •

\" .

bart~rget, i.e., 5:1~ dfld ,th~t ~ney and the surrc~~d

,have g. 10,\'; density difference. Such a set is ~.;:sc.r:...bed) .. ,,' ,', ',. ," , " -' ;:,:::;?<:':':";~-,:,>"~':/,,~,

.tbg~th~r 'wit h the experimental technique and da'ca :, -,' ,'.;.:'." '".-",

:\.~f{~lysis used by the present authors, to evaluate , - ,,-, ( ;F:~t< "

'iviH~j~jset:"'Atan alpha risk of 0.10 the set of char-~;~:,~j);;¥~.~~/:"{'_;:', 'Yi~;~'·:::,:,·

a'c:~~rs~\S 23 8 9 was found to have equal recog-"

'nizability under, two,varied viewing conditions.

·.~

INTRO DUCTION

.' f.o"1"'_· e"/;~,:., .. ,." 19' o· J, :'''''a'l -n(l ;..,1-,0'-0 ... ",,' ...... ' ~·"""'ru~:,..·..;ts " " .... ~ _L ["~':'~' ""- ." ill. '- ~"J i~ ~ ~ ... a... .;. •. ,~~. ".'\;: tl

one method i 'i.vi~~ ~;'3E:ist~t employing ::he ftimilia:c .. ',:ri-

bar target ;:;-:.

I""'E----. :3 V/ Ii

!

Figure.l. tv. ...r­~\/rW1 Tri~Bar Target

(AIR 5:1)

The t~sttarget consists of·an array of tri-bars, grouped

. in threes, d~creasing'in,s~ze in a systematic pattern. The

figure of merit using thisnlcthod depends on the smaL.est

tri~har pattern imaged by, t:he instrument and recognizable

1:>Y an obse::v;.::r 0 ':'here is s0:netimes disagreement among

ohservers aboDe vinether or not a giVer: set of bars is

available. 1

It has been suggested-by McCamy, and ot~~~£ th~c .Co

alphanumeric characters be subse ituted for .: c.".; -:..:.::.:- :, ... :.

targe:: ~ I f this could' be done, much 0 f t~1e i.~J.. -Ef:i.cul'.:y

a/~soc ... 6.;::ed with the definition of rec~J:!~~:" ~5.;J:'lity wou-:..d

. dJsappear, S ii\ce. the observer could b € Cl"sk:.d :0 iderJ·\. fy

..

1

a 6haracter rather than make a judgement whether three bars

are distinguishable as suet:. This is a genuine problem in

recognition, and the o~se=V2r can b~ s~ored as right or

wrong, a pr0c~du~a no~ ?os$~.hle wi~.h ~~~ ~:~2cnt target.

char",c} er ·carg'"t is that alL

herenlly equal recognizab~i~ty. Constderable wo~k has been

done in the past Ivith this aim in vie\v in the fiel.d 0: 2-6 ophthalmology, where visual acuity is most often teste~

using the familiar. letter c;,art. The usefulness of t:·.e

previ·ous. \Vork to the presen;: research is doubtful; th"y

invariably employed high contrast characters; i.e., black

letters on a white surround; character geometry frequently

varied from worker to worker; curved and oblique contours

Ivere included, for the purpose of detecting errors in

visual refraction. Additiona11y, there are serious diff-

erences of opinion abou:: what constitutes a set of "equally

legible" or "equally difficult" characters. For example,

Hartric.ge and Owen2 claim ·:::1.e set: :. F H N P T .U X Z to

be of;::-.e 4 "sG:me difficulty"; Sloan says the set: C' J H 1<

NOR S V Z is "nearly equal in legibility".

A second consideration is that the characters selected

bear, to som" '::egree, a resemblance to the three-bar array,

since c~arE ~s some desirability in relating information

from the ch~=acter target to data based on the tri-bar target.

Figure 2 sho',;-$ such", set of characters.

2

Since most interest in optical sYHtem evaluation is in

the area of low subject-co~=rnst imaging performance, the

characters should be of .:.,'\, contr~,s::., £i.':.' 0.15 - 0.20

OBJECTIVES

The objective of the present research m;s: "c" ee,s.: the

hypothesis that the characters E 3 S 2 3 6 8 9, 1n ~lock

fo:;:m I'i'ith aspect ratio 5;1, are equally recognizable. A

chi-square test was to be applied to the data to determine

equality; the alpha risk selected was 0.10.

EXPERI~ENTAL PROCEDURE

A. Apparatus: Characters were cut from Colol--Aid paper,

No.3 Gray, reflection densi.ty = .56; the same paper, No.

5A Gray, refle~tion density = .72, was used for the surround.

These p"~et"s. ·,,;(:.-::e selected <-,; having a density difference

,,':.thin ihe r{)..'().':::,~ ori~in<.l1y select.",d; No. 5A has a density

t,bse to th<,;: ,:,£ M\ l87. Gr&y Car,L Ciiaracters measured 25mm

on aside; they were afEixe; to 6-inch squares of No. 5A

paper I'i'hich ,-,areo L.vcd:ad o.bc,wt the circumfe:ce:-.ce of a disc.

Figur\:: .3 sho.ws; a dr8.-..ving of cht:; presel1tatiO~~J ,:'!evice; the i

~isc 1~ rA~~~ed to bring in~ividual characters to the 5~"

square "pCIClclre in the plate bahin" ,,;1.\ e;h t:he disc is

piaced. The front plate was covered with No. SA paper.

B. Viewing Conditions; T':w targ>2t: \,'~,? h l: by twe

Hood lamps in reflectors; illumination "BS. hei.d conSL<>-nt

12 < - .,' ."] b 1· 7,8 1'· d· . a I:: ...J rt-c.. ~ata. are ,aval. . .:1. e Wil~cn 1....-1 locate tnat

3

-----,1 5 .,

. !

at the observer). This relationship is shown in Figure 4.

With the large-group viewing the intention was: to posi-

tion the observer approximat"'::'y by use of the Snellen Chart,

present a short s2ries of ch&rnct0~s1 calcc:~~2 ~he per

·cent. corr~cc ~~sponse, and relocste =hc observer at the

distanc~ which wo~ld result ~~ 50% cor=~ct :esponse. This

prediction t2chn~~~e was ~ns&~isfactory) p~0bahly because

the observeis f~~~ whose daca it was der~ve~ ware expar~en-

eed in ~~e viewing operation and g~oups of observers w~~e

not. C;, this basis, the secc"'c1 of tlvo sets of observations

was used in the &nalysis.

Each observer was given a report form for each series

of characters presented. As each member of the rando~.11y-

o:;:dered series was shOlvn the experimenter called out the

p:;:~sentation order number (this had been found necessary

to avoid co;,::'~s~o~1 in recording), and the observer recorded

his response in ;:,le co:;:respouling space on his form. For the

data analyzed in this pape:;:, ~he presentation series to the

fi:;:st g:..-oup, 11 men, was each character six ci.~es, 48 total;

t:-:.e secon~ men, saw each character ~w~lv0

95 total. A :;:esponse was forced in all cases.

,

DATA ANAL YS IS

Data from observers \vere talm lilted .indi vioua lly showing,

for each character, ea) numbel: of t:.I,les presented, (b) number

of times reported, and (c) nUGhc:: 0;' times :.:-eported correctly.

A typical individual tabulation ;"r; shown in ?igure 5.

~~ !., ~~:: c; t:: 1.-E G :; 2 3

, 8 9 To::al 0

(a) Presented 12 12 ~2 1.2 -! 'I 12 12 12 S5 '. _. (b) Reported 10 10 ::.6 11 12 6 1 ' .0 15 96 (c) Correct 10 5 11 H ' , l.L 3 10 9 70

Per ce'0 t • correct: 72.97,

Figure 5. Tabulation of Data of Typical Obse:.:-vcr

In the data analysis an experimental chi-square value

was calcu1~~cd from the test statistic,

)(' 2 _""24 (O-E) 2 I _ -.~­

, .-oG- ~ 1

(1)

v;'":le:ce. 0 l.~ ;:;',e :;'u,'ilber of 'c:Lrnes ti1e event happened - in this

cas~ ~~~ ~~~~er of times 3 chnr~cter was reported - and E

~s .ch~ ~U~Der of times· the event Ivould be expected if the

The arith .. ,etic .is quite ,

strcu.ghl:fo:;:-wc..:d; using the above data to calculate response

'h' . ..,,~o • "-~ ~-;;,qu.;...- ....... .. 2 [,. ~ . ",2 'r-- == ... .Ll)~_L) ~ (2 )

2 2-, <:"0-12) -:- ••• +(15 .. 120112 ='7 .. 1665

Simi~~~ly, c~~~cct response chi sqU&r8: _ 2 ,2 2 ' .

'X2 = ~lO-E) + (5-E) + ••. + (9-E)]/E :, 7,4861, (3)

where the expected va:Llc, E, is the, product of the (total)

per cc:::nt. corrc:ct and the numbo=r. of presentations of a,

6

-

character, 'i.e., E = (12)(.729). In these examnles the

experimentRl values of chi-square are less than the critical

value of chi-square for a sample of eight and an alpha risk

of 0.10, ,i.e., 12.0170. T~us th~ da~a indicate Lhat there

is no difference Ivithin the set of ;:,,12 respeJ-:1ses or the

correct responses.

T\'1O criteria \>le:ce US2C to l:'..:!j2,";:': da'Ca f:corrl individuals.

Those from observers showi~~ lJl12q~a]. respons2 w~~e =ejected;

the reasoning was 'Chnt ariY bias in ~eSrGr.3E; "". v ... h.o..tc·ver the

sponse. Oata were also discarded from observers scoring 100%

correct responses for more than "one character.

A tabulation was made of the; sunmed responses of obser-

vers meeting the above criteria and chi-sc;.uare calcu1E.ted

for response and correct response. Response chi-square was

less than the critical value, indicating that responses were

equal; correct-response chi-square was greater,than the

critical value, which indicated that the responses - and

therefore the set of chariicters - \.;e1:e not equal.

It was noticed that the summed correct responses for

the characters G and 6 were lower than similar val~€s for

the other characters. Individual tabulat~ons were recon-

sidered, eliminating from the calculations all responses

for the suspec~ed characters. Four observers previously '-,

rejected for ucequal responses became accepteble; three

Ivere not helped by this operation, since the inequality of

their responses was due to apparent biases for other char-

acters in which no pattern was noticeable. Also, with the

7

elim'ination of G and 6 re!;pOllSes, the correct-response chi-

square based on thG ten ncc('l''cnble observers, taken indivi-

dually and collect!.vely, W;),; :'esf.. 1:h"n the critical value,

9.23635 for the same 0.10 <: ... 1.'1 :::isk a.nd sar'"r:>le s1.,e of. 6.

shO\vn in Figure 6.

: ; .. '. . , ..

Ca) Presented (b) Reported (c) Correct

Per cent.

E 90 87 70

r,i, 'Ira,'~r-er •. ::!.':":-~~-

" .:> 2 ~

.)

90 90 90 10;~ 89 85 65 74 68'

CO:;:"7LQct: 10.2

8 90 87 51

Chi-square: ?..:.es:)O~"',:,2: 2.LJ.888 6.9531 Co:c::ec~: :

9 Total 90 540 84 534 53 381

Figur~ 6~ Tabula=:Lon of SUffir:.lec1 Data; of" :.';:. ~ ~b ,.~......, ... en u scr\}.::rs i.li3.V~ng .t!.C,ua.L

l{e S ;)011 S(~

A check of internal co;-.3ist,wcy was made Dy considering

eX'Jeri':.lental chi-square \'las lesS ~han the critical V6:~ .. :..:e.

Of the ten observers five i~?rov~d in performance between

the fi:st and second halves of the preseritation series; two

scored che same on both halves, and three scored worse on the

second halE.

It was decicLd to confirm the conclusions drawn from

the preceeding &~~~ysis) that the six-member set of char~

acterswas e~~ally recognizable. It was thought that this

should done so that the character viewed would be degraded

8

• - ---<;I -

imag~-wise, in a manner similar to thac which might be found

in a practical situation. Several schemes were considered;

the one finally adopted was tho: o~ defocusing the projected

image of the charactcro Acccirdingly, ench ch~~=nctcr was

phot o,[;r aphed and the rc s III t :.;~ "E: ga t i VeS werE. S l.:ccle-mounted.

0.15 - 0.16; screen illuminat~on was 210 ft-C. with no slide

in the light path; and 5.3 ft-C with a slide in place

(proj ected background).

'rvlelve slides of each d;m:acter, 72 total, were randomly

presented to six observers, four of whom were replicated.

Tabulaciol1 and sorting were acconplished according to the

previous ly i'.lent i0l'12G. cri teric-.. ..

D .. \TA A:-TALYSIS

The data f:com three obsc:rvers \,,:tere acceptable; t\"O of

these were replicated. Only one of the rejected observers

\'las rejected by reason of unequal response; the others

\·;ererejected for 100/'0 correct r,!sponses for more than one

characte::- ...

Correct-response chi-squares ';'Jere ca lculated from the

i;-,Givicual data and the summed responses; all were less

than the critic~.l. value. Of the tl\'O observers who \.;ere repli-

cated one scored :,e:ter in the secOl1c" series., the other worse.

Figure 7. Ta bt:l. c:~~ ion of Sumrr.ed Data

'" S 2 3 8 ~

:resented 60 60 60 60 60 ;;2;>ortecl 56 62 72 If 7 70 Correct 40 40 51 33 46 Per cent. correct: 67.2%

Chi-square: Respo~lse : Coi:rect:

8.0330 6.6779

of Three Observers

9 Total 60 360 53 360 32 242

.. , I

, '

CONCLUSIONS

The data indicate that, unde~ two widely varied view­

ing conditions, there is no diEf:erence i;-, cr.e correct

responses to members of the six-character Bet when they

are presented each an equal number of times.

We therefore conclude Lli1t the original objective

of the experiment has been satisfied; this is a set

of characters of the requi::ed geo .. ,etry which are, inter .§£.,

equally recognizable.

10

ACKN(1'.~LE DGEXENTS

The authors express tki.r thanks to the photographic

Science Faculty for much helpEul consultation and advice;

in particular to Professors Hollis Todd and Albert

Rickmcrs, \-lhose counsel \Vf.iE· illvc:luahlc.

To the students I"ho sex'veo <lS observers goes m.;.

undying gratitude, especi<:J.1y those -"ho served during

the early part of the project. Without their patient

cooperation the research \Vould have been literally

impossible.

11

,\,,,,, ___ .... _ .•. , 01.,. r· ... "l".~, ....

I I I

. I

x

x

x

10 -';...cO ~o

><

~ ~ ~o

..:- t[)

: 10

i·-,---J,~---1-1 -'·-'l-"-+-·-·-·I·---+~-l--;-:-.J o Q

. N lJ3't:l'dOJ

o lq

'C13c 90l

Q N

FIGURE ~ 4

r-'--I

CHARAC TE RS

USED

r~~-;-"'-"" '--"'-'-'-'-;' . i .. ,,,~--,,,,,-,,,,,~

l'· L_ .. ~ .. ~ ~-..... --.~ .. ~ i

i .

[~--! ,

:: .;.. __ Nt= .. ~..: ..... ,..,.. ......... j

,,-,-. ~-.. l L,., __ ._ .. ·1

n---.-.~--.,-j j L ' ........ _._._... I

i I :~.-~-'- 1 L ..... "'''' ......... ~ .... .hWOJ

B

FIGURE -2

APF'AFtATUS

, , , I .

I. I I

~ -f-..:::.... - -,., .....

/ " , '/

I I,

5~11 E I T:;~ 5.5'~

\

I

~

._ ... --.~-------------l . I • : ' 4/------~. 7:

FIGURE-3

,-..

I I 'I

30

FOOTNOTES

1. HcCamy, C. C.; On the Information in a l~licrophoto­graph, Appl. Optics, ~:405 (April)1965

2. Hartridge, H. and Owen, H. 8.: Test Types, Brit. J. Ophth., fi:543, 1922

3. Banister, H.: Block Capital Let~ers as Tests of Visual ACdity,. Brit. J. Ophth., 1l:lf9 (Fo.b.) 1927

4. Sloan, L. L. ~ ComparinG;') of Three Types of Test r-;arget for the ~:casur0ment of Visual Acui;;y, Qua;:t. RE:V. Ophth., 12.:4, 1952

5. Hay)? J.: (no ticla)~ Tra~~ Ophth. Soc. U.K. Vol.39) 1919.

cited i:l~ Hartridge and O\vcn, Q12 cit . .

6. Sheard: (n.::. title), (,me;:. J. Phys. Opt., 1:168, 1921 cited ~:~; Baniscer., OD cit.

~--

7. :Sythgoe,~. J,,: The ;''lensurcmen"c of Visual Acuity, S?2cial Repo::::t t\o. l73, London, H~ Sta:ionery Offica"

8. Hecht, S: ::ZclatioTi oet:t:·.1eG:n Visual Acuity and Illum­inac ior,. J. Gen. 1'11ysio1., ll: 255, ( • \" ·'28 .JU:-Io) I •. ';1

7 and 8 a;:c cited in: Sloan, L.L.: Meas"c:re:r:ent of Visual .\cuity, a Critical Review, Arch. (',?:~'.:h., 4·5:70l, (June) 1951.

9. ' Craile, K. J. W.: The E~fect of Adaptation U?O~ Visual Acuity, :Orit. J. 1'sychol., 29:252, 1939 Vi sio11 ~;,rl. Yj~SUEl1. Percent ion, Grc:.,~Qm, C. (ed) , John \-IUey & Sons, Ne\>l York, 1965, p. 340

12

BIBLIOGRAPHY

1. Banister, H.: Block Capital Letters as Tests of Visual Acuity, Brit. J. Ophth., 11:49 (Feb.)1927

2. Bl ackl'le 11 , H. R.: Contrast Thresholds, JOSA, 36:624 (1946)

3;,",CoI),an, A.: Test Letters ~lhich Comply vlith the Physio­logical Requirements of a VisuAl Test Object, Amer. J. Ophth., 11:625 (1928)

4. COIVan, A.: A Visual Test Card; Amer. J. Ophth., Q:301 (1929)

5. Duntley, S. Q., et al.: Visibility, Appl. Opt., 2:563 (May)1964

6. Graham,C. H., et al, eds.: Vision and Visual Perception, New York, John iViley & Sons, 1965

7. Hartridge, H., and Owen, H. B.: Test Types, Brit. J. Ophth., 2,:543, 1922

8. Mauge, '" . / ".

R.: Etude du Pouvoir Resolvant des Emulsions Photographiques, Science et Ind. Phot., 1:297,

9. Sloan, L. L.: Measurement of Visual Acuity, a Critical Review, Arch. Ophth., 45.:704 (June) 1951

10. Sloan, L.L·., et a1.:. Comparison of Three Types of Test Target for the Measul~ement of Visual Acuity, Quart. Rev. Ophth., ~:4, 1952

11. Sloan, L. L.: New Test Charts for the Measurement of Visual Acuity at Far and ",ear Distances, Amer. J. Ophth., 48:807, (Dec.) 1959

1936

12. Sturge, J. M.: Detection and Recognition of Low-Contrast Images, PSE, 6:156 (May-June) 1962

13. Wul feck, J., and Taylor, J., eds.: .EQ.rm Discrimination as Related to Military Problems, Publication 561, Nat. Acad. of Sciences - Nat. Res. Council, l-lashington, D. C., 1957