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TECHNICAL N

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Matching Fingerprints

by Computer

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U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards
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NBS TECHNICAL NOTE 466

ISSUED JULY 1968

Matching Fingerprints by Computer

J. H. Wegstein and J. F. Rafferty

Center for Computer Sciences and Technology

Institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

and

Walter J. Pencak

Federal Bureau of Investigation

Washington, D. C. 20535

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, Government Printing Office

Washington, D.C., 20402 - Price 20 cents

Matching Fingerprints by Computer

by J.H. Wegstein, J.F. Rafferty, and W.J. Pencak

A procedure is described for determining whether

two fingerprint impressions were made by the same finger.

The procedure uses the X and Y coordinates and the

individual directions of the minutiae (ridge endings

and bifurcations). The identity of two impressions is

established by matching a constellation or group of

minutiae in one impression with a corresponding con- stellation in the other impression in terms of the

relative distances and relative angles of the minutiae.

Key words: Computerized-fingerprint-identification,

fingerprints, pat tern- recognition.

1. Introduction

Several approaches have been made to automatic fingerprint identification including holographic techniques. 1*2. The techniques that use details of a fingerprint such as cores, deltas, ridge counts, ridge

endings, and ridge bifurcations tend to be specialized according to the

method by which the information is taken from the fingerprint.

Thiebault3. has described a technique using the directions of minutiae

(ridge endings and bifurcations) where the data are obtained by a special

camera that photographs the finger. Where a human operator identifies

the core and delta as a reference axis, a matching technique has been

developed that utilizes only the positions of minutiae.^* The technique

described in this paper is intended primarily for use with an automatic

reader that reads minutiae directly from a fingerprint card without

identifying cores and deltas.

This paper describes a procedure for matching fingerprint impressions by computer using only two types of minutiae: ridge endings and

bifurcations . While it is anticipated that minutiae data may soon be

read automatically by machine, the work reported in this paper utilizes

data read manually. Each fingerprint impression used is photographed

and enlarged by a factor of 10. The minutiae on each of these enlargements are then marked with a pencil on a piece of transparent plastic

laid over the enlargement.

Since a ridge ending in one print may appear as a bifurcation in

another print from the same finger, no distinction is made between ridge

endings and bifurcations in recording data. For each of these minutiae,

both a location and direction are defined as shown in Figure 1. If the areas marked B are considered as ridges, then point P is the location of

a ridge ending and the line GP defines the direction of this minutia.

If the areas marked A are considered as ridges, then point P is the

location of a bifurcation, and the line GP defines the direction
associated with this minutia. Minutiae for two fingerprint impressions

identified as IIP2 and IIP4 are shown in Figures 2 and 3.

The transparency is next taped to a drawing board so that all

minutiae markings fall in the first quadrant of an X-Y coordinate system.

The X axis is set parallel to the horizontal lines on the standard

fingerprint card from which the print was photographed. The X and Y

coordinates of each minutia, as shown in Figure 1, are then read in

millimeters and recorded. The angle 9 which the minutia direction makes

with the X axis is recorded in degrees. The value of 9 may range from

to 360 degrees. Each minutia is also given an identification number P.

A table of data is thus prepared consisting of four columns of numbers P,

X, Y, and 9 for each fingerprint impression to be studied.

2. The Technique for Matching Fingerprints

This matching procedure is based on matching a constellation or group of minutiae formed about a particular minutia called the nucleus

from one impression with a corresponding constellation from another

impression. Figure 4 shows such a constellation using a minutia labeled

a as a nucleus. Although a particular constellation flexes and stretches,

it retains a certain pattern identity in impressions taken from the same

finger over a period of years. 5« Matching just one constellation from

one impression with a corresponding constellation from another impression

appears to be sufficient for concluding that both impressions were made

by the same finger.

Both relative distances and relative angles are used to match a constellation in one fingerprint impression with a similar constellation

from another impression. The computer works with two minutiae at a time,

such as a and b in Figure 4, from each of two different sets of impression data. As shown in Figure 5, it attempts to relate the pair of

minutiae a and b from Impression 1 with a pair of minutiae _e and _f from

Impression 2„ Starting with minutiae a and b_, the computer computes AS

the distance between the minutiae, A9 the difference between the angles

of these minutiae, and Ay. the angle between the direction of minutia a and the direction of the distance vector to minutia b. Similarly, values

for ASS

, A93

, and Ay are computed with respect to minutiae e and _f in

Impression 2. Next, the differences

AS = AS2

- ASX A9 = A93

- A9T Ay = Ay3

- Ay1 are computed. If AS is less than KS, A9 is less than K.9, and Ay is less

than Ky then a score S is set equal to one and pair jib is considered

matched with ^f . KS, K9, and Ky are parameters that must be adjusted for

optimum performance. The computer next relates minutia a. to another

minutia such as £ in Figure 4. If the pair a_c can be matched with e and

some other minutia in the second impression, the score is increased by

one. This process is repeated until the score S reaches a predetermined

2-
value SM at which time Impression 1 is considered to be matched with

Impression 2, and the computer prints "MAKE". If the score S fails to

reach SM after S3 tries , the score S is reset to zero and the computer

tries to find new pairs ah and _ef that will establish a and e as nuclei

for constellations that match. SM and S3 are also adjustable parameters.

3. Filing Minutia Data

Prior to attempting to match fingerprints the computer pre-processes

each set of data by reading in the table of values of P, X, Y, and 9 for

each fingerprint impression. A typical impression will provide about 75

minutiae. For each minutia point, the computer computes an auxiliary

variable cp where co = 9 if 6 is less than or equal to 180° and cp = 9

- 180

if 9 is greater than 180°. The minutia data are next sorted so that the

corresponding values of cp are in ascending order. Thus a minutia whose 9

is 1° or 181° will be near the beginning of the table and a minutia with

a 9 value of 179° or 359° will be near the end of the table. The table

of values of P, X, Y, and 9 ordered according to cp is next written on magnetic tape along with an identification number (Ident) for the impression and a number (IMX) which is the total number of points taken from

the impression. Minutia data for numerous fingerprint impressions have

thus been stored on magnetic tape for matching studies.

4. Sequencing the Search for a Match

The complete logical details of the computer program for matching

fingerprint impression data are given in the flow diagrams in the

Appendix. In the following text, numbers in parentheses refer to box

numbers in the flow diagrams. Text in parentheses elaborates details of

the flow diagrams and can be safely ignored by the non- programmer.

The operator first identifies two impressions that are know to be in

the magnetic tape file (0), for example, Ident 1 = IIP2 and Ident 2 = IIP4.

IIP2 and IIP4 are two impressions from the same finger taken about three

years apart and the data from these will be used here in illustrating the

procedure. Their minutiae tracings are shown in Figures 2 and 3.

The computer next reads from magnetic tape a table of data for each

of the two impressions (1). The values of cp as explained earlier are re-computed and entered as a fifth column in each table (2-13). Figure 6

shows the middle portion of each table. The leftmost column in each table,

I, is the line number and is not part of the table itself. (For conve- nience in programming, the numbers in these tables are identified as elements in a three dimensional array Axnk. Thus A 44 3 3 is the same as the 44th value of Y in IIP4 and is equal to 202.)
The search for a match begins by finding the first minutia in IIP2

with a cp greater than or equal to 90°. This minutia, P=8, becomes the a referred to in Figure 5 and the next minutia, P=42, would become the b.

Similarly, in table IIP4, minutia 40 becomes e and minutia 44 would

become _f. (Boxes 2-13 locate the line numbers corresponding to a and e and also determine the center of gravity of the area covered by the

minutiae from each of the impressions.)

Before attempting the match illustrated in Figure 5, the computer

first checks to see if minutiae a and _e are pointing in approximately

the same direction by computing T 9 = 9 (a) - 9 (e) . If T © is less

than M9, an adjustable parameter, the computer goes on to check whether

minutiae a and e are in the same neighborhood in the fingerprint. This

is accomplished by comparing differences in X andY with parameters KX

and KY respectively (22-22.1). These measures of X and Y are referred

to the center of gravity of the area covered by the minutiae of each

impression to compensate for the arbitrary location of the minutiae

tracings with respect to the X-Y coordinate axes.

In the illustrative data, minutiae 8 and 40 point in the same direction, but their values of X differ by an excessive amount. As

referenced to the center of the pattern, the maximum difference allowed

in this example is KX = 30 mm. Therefore minutia 40 is rejected (22.3)

and the computer begins to step through the IIP4 data in a zig-zag

pattern looking for an acceptable minutia e_. (Subroutine "Zip-Zap"

performs this index stepping.) The first steps of the path taken in

searching for _e are shown at the upper right of Figure 6. The computer

will give up the search when | cp (a) - cp (e) | becomes greater than

M9 = 30° (40), or when the IIP4 data have been exhausted. In this

example an _e corresponding to minutia point 22 is found to be satisfactory. The computer therefore takes minutia 42 in IIP2 as _b and begins

a zig-zag search of the IIP4 data for a satisfactory _f. This path is

illustrated at the lower right of Figure 6.

When the possible values for _f are exhausted, e is advanced

another step along its zig-zag path and i begins a new zig-zag search.

When the possible values for e are exhausted, _b is advanced another

step along its zig-zag path and both _e and _f are reset and restarted in

their search. Similarly, when necessary, a also takes steps along a zig-zag path and each of the other points are restarted in succession.

In this example a score is achieved when a is 42 and b is 24 in

IIP2 while e is 42 and £ is 24 in IIP4. This changes the search pattern.

a and e are now held stationary while b and _f execute zig-zag search

patterns (q = 2 in the flow charts). In the example, the score S quickly advances to SM = 4 and the computer prints "MAKE" followed by

the table:
IIP2 IIP4

a b e f

42 24 42 24

42 41 42 41

42 22 42 22

42 79 42 79

The resulting matching constellations are shown in Figure 7.

5. Conclusion

The various parameters used in this procedure are listed below

along with typical values and brief explanations of their functions.

K0=8

KS=6

K7=6

Scoring parameters.

K0 also terminates the range of

_f if differences between certain

cp values exceed K0.

Skips steps of e by noting if a and je are not in the same direction.

mQ-oc; Skips steps of _f by noting if b and i axe. not in the same direction.

Sets stops on range of e if cp angle between a and e exceeds M0.

Sets stops on range of _f if cp angle between b and _f exceeds M0.

SM=4 Score required to "MAKE".

Kl=5 Maximum number of steps a can take.

K2=10 Maximum number of steps _b can take for a given a.

„__1 _ Maximum number of steps b can take while looking for another score after score accumulation has begun and a and jc are held stationary.

Maximum allowed difference in X values for a and e or _b and jE

KX=35 where each X is measured from the center of gravity of the

rectangular area covered by minutiae.

Maximum allowed difference in Y values for a. and e or b and f

KY=41 where each Y is measured from the center of gravity of the

rectangular area covered by minutiae.

Numerous computer runs must be made with fingerprint data from a given reader to determine optimum values for these parameters. Ideally,

impressions from the same finger should always give a "MAKE" when

compared and impressions from different fingers should always give a "NO" when compared. From experiments performed to date it appears

feasible to find a set of parameters that will always give a "MAKE"

when two impressions from the same finger are compared. However, these

same parameters may on rare occasions also give a "MAKE" when two

impressions from different fingers are compared. This flaw may be

tolerated in a working system because human beings, who must always

confirm identifications, can readily detect these false matches.
Computations to date indicate that this matching technique is

much more reliable than a previously reported technique that emphasized

compression of fingerprint data for filing. •

The authors are indebted to the Identification Division of the

Federal Bureau of Investigation for its assistance and support in the

preparation of this paper.

References

1. Yefsky, S.A., Editor, Proceedings of the First

National Symposium on Law Enforcement Science

and Technology , 1967, Thompson Book Company.

2. Trauring, M. , Automatic Comparison of FingerRidge Patterns. Nature 197 , 4871 (March 1963),

938-940.

3. Thiebault, R. , "Automatic Process for the

Identification of Fingerprints," Proceedings , International Symposium on Automation of

Population Register Systems , Vol. 1, Jerusalem,

Israel, 1967, 207-226.

4. Kingston, C.R. and Rudie, D.D., NYSIIS

Fingerprint Classification Methods Study Status

Report , October 1966 , The New York State

Identification and Intelligence System, Albany,

N.Y., 1966.

5. Wegstein, J.H. and Rafferty, J.F. , "Machine

Oriented Fingerprint Classification System,"

Proceedings of the First National Symposium on Law Enforcement Science and Technology , 1967,

Thompson Book Company.

6. Wegstein, J.H. , A Computer Oriented Single- Fingerprint Identification System , National

Bureau of Standards Technical Note 443, U.S.

Government Printing Office, Washington, D.C.,

1968.
Location and Direction of a Minutia

Figure I.
o

Figure Z

Impression UPS

1
V\

A

tf

s».

<n

Figure 3

Impress/on UPH-
Constellation

of Minut/ae

Fiaure H-.

10
Min u fia e Pair -from

Impression /.

A6, - 6k- B*

Minutiae Pair from

Impression 2.

A9z*di-9e

Matching

pairs of

Minutiae

AS =&6Z -AB,

AS = ASX - 45,

^y = A?* -AY,

Fi 3 ure S.

11
K=l

Impression IIP2

IMX = 91

i p x y e <p 40 29 208 222 233 53

41 47 296 157 233 53

42 38 223 178 235 55

43 37 222 181 236 56

44 36 230 193 58 58

45 35 220 199 239 59

46 40 328 181 75 75

47 33 318 217 81 81

48 61 333 153 83 83

49 44 337 168 85 85

50 79 328 224 87 87

51 41 344 189 89 89

52 8 385 245 90 90 a

53 42 348 174 91 91

54 7 397 229 91 91

55 24 349 217 92 92

56 22 372 201 93 93

57 5 388 247 274 94

58 107 441 242 274 94

K=2

Impression IIP4

IMX = 74

IP X Y cp 40 31 225 229 249 69

41 46 258 193 70 70

42 39 195 181 254 74

43 37 183 186 256 76

44 36 186 202 77 77

45 40 281 215 90 90 e

46 44 297 204 100 100

47 61 298 188 100 100

48 33 258 244 110 110

49 24 291 255 111 111

50 138 230 122 111 111

51 41 297 227 114 114

52 79 264 252 114 114

53 42 307 215 116 116

54 22 319 254 116 116 e

55 23 316 230 300 120

56 82 360 228 121 121

57 43 353 226 303 123

58 67 344 180 305 125

A Portion of the Minutia Data from Two Fingerprint Impressions

Figure 6.

12
Fingerprint

Impression 1LP2

Fingerprint

Impression HP¥

Constellations

of Minutiae

Figure 7

13
APPENDIX

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1.

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Part I.

t TJevf I Idenf %

Kh KS KV H9 Si K to. & fa Kf

i_±

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///.. =o TM^XMX, T,^o

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H, =o JM-, =rwt t/= yyt - yy>

/<=!

3. ]>

i =/

3.1

Jl. * = £+!

Ill II.

XH = _ W = o « E

/o.

j:

i = i+/

yy^JL±M

\< =-U

MsA'Ain

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t

fas£=Aiv 4-/80

j=L±l

g,/ V

£.3 g.v

-£ '1

r.5" x^

G

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£.7 I g.g

I5T. %

I0% =1, 7^ = U-l, T?=0

HH^~q e = To3

y Aqsi * neszj

l[ /f.3 \<

<

e=c-/

is.s 7

yW/ : /Wy"~*

/^z_i

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e-e+i

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T03 = e

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frwi 'Wo"

K h'.ti yr+A

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si !' ZZ(')

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Minutiae Matcher

Pari z. 36 2|

31

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T2

5^_

T£~TZ + \

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b=U

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Q Me : Irol

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^'V M <

1A.

Kxilrxl *J? y*£

>©

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P&= Aav -Aevx

rX =A*v-Aetx.+T)(

H =A*3,-Ae3x+TY

JL. 1\

^JH^u

HH,"0

H5

JZL

<^( m jJr&T)

71

<E> —%

1(oDels (z)

iS.i >

T T.5.5 >

KYiTJryi)

%SM

KX TJFxl)

15-

rx^Abi, -Atxx+TX

57? zz(v)

ZZ(3)

t=3

12,

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15
Minutiae Matcher

M

Part 3.

-> AS = AS^~ AS,

4V = AV>»- A?,

2.

T* 3. y = f?

Function

^A

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#>

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30 t 31 3Z

55.

IF

33.

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d^ y-#-iZ£l

V = o("Ip/> J x+/

->*»(4x:o^

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r

H^TH%

AV,=TAyi

AS, -=TA5I

AO,~TA0I

Afi = TA<j>}

®"

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AAs-Atui

10. v

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?<y >3to-y

Subroutine "j>eis" &

33J

3i

THLi^HLf

THWtrffffy

THt- = tf*

74 a/ - 66,

Til'- U

THUl-HU

THHZ^HH% TUZ * Hj. TA<?I -A(f, r = 2

'jh*K 5 : 5M >^—*«

(p0Hii>^n»0

A y -Ai35 -Ae3J A93 = AffJ -A evj

?=&»-'$ Af5 =Afs3 -Aesy

AVs^-Aeis

Subroutine

x "li P -lap"

@ 3.

35 //Lt=<

<

_tt

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Print MAKE" iL(*=£ ^c^zz>

^=_

^*— - ~

"

/*.

*! r*

//.

/x. £ = 10* * //«

16

HU=HLt-l
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