Image recognition problems of fingerprint identification

Image recognition problems of fingerprint identification i va NikodEmusz-SzEkely* and Vladimir SzEkely t

The paper describes an efficient algorithm for locating some fingerprint features as minutiae. Both software and hardware realizations are treated. Emphasis is placed on fastening the algorithm in order to facilitate quasi real-time applications for personal identification. fingerprints

pattern recognition

searching minutiae

wHont+

The use of fingerprints for personal identification is not a new invention, but the possibility of automated recognition and identification offered by the recent computational power of microcomputer systems opens new perspectives for their use. The well-known forensic use is not the only possibility. Secure personal identification is needed in many other areas such as security systems, banking systems, replacing PIN codes, etc. These areas demand secure and at the same time extremely fast algorithms for fingerprint identification. This paper deals with some algorithmic solutions concerning this matter. First we will review some elements of fingerprint analysis. The classification of fingerprint images is usually carried out on the basis of some global features of the pattern. Four such features are commonly investigated: the whorl, the core, the loop and the delta (see Figure 1). The number and relative position of these features are very characteristic and extremely useful for a rough classification and for searching a database. There are other features which are not deterministic for the global pattern but could be very characteristic for local details. They are the minutiae, which are essentially branching points of fingerprint ridge lines. Figure 2 shows some examples of such features. On a typical fingerprint we find some 50 to 80 such minutiae. These are the basis of fine identification. The probability that two fingerprints originating from different fingers have the same minutiae pattern is practically zero. Moreover, a subset of the *HTSZ, Hungary *Department of Electron Devices, Technical University of Budapest, Budapest, Hungary

Nil ~"..

Figure 7.

Loop

DELTA

Global fingerprint features

minutiae pattern is usually enough for a reliable decision. These facts show that algorithms for localizing minutiae are of great importance. This is the main goal of our work.

M I N U T I A E

Figure 2.

Local fingerprint features (minutiae)

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NOISE CONSIDERATIONS

,

The problem of fingerprint recognition is characterized by the fact that the images are rather noisy. The classical recording technique with inked fingers often suffers from blurring caused by ink wiping. A new hardware solution is the fingerprint-grabber camera. This requires only one touch of the finger on the surface of a glass prism, and using the phenomenon of total reflection a reasonably good picture is obtained. However, in this case on the peripheral area of the picture the fingerprint ridges are broken, dotted, instead of being continuous lines. Because of this, many problems arise if we try to follow (pixel by pixel) the fingerprint ridges in order to find feature points. A more reliable way (in our opinion) is to base the algorithms on pixel number counting in rectangular sub-areas of some derived pseudo-images. In this case the effect of the noise is significantly reduced. Moreover, these kinds of algorithms can be easily mapped either into effective software segments or into special hardware. SEARCHING MINUTIAE

The fingerprint image looks familiar to people who deal with field calculation problems. It looks like a field-line map of an electrostatic field or current-flow lines of some stream phenomenon. This similarity might be the basis for a type of minutiae locating algorithm. A two-dimensional electrostatic field can be associated with the fingerprint image, where the field lines correspond to the fingerprint ridges. But how to handle the fact that some fingerprint ridge lines disappear at a point? This can also occur with electrostatic field lines if some amount of charge is present. In terms of the analysis of vector functions, the field shows divergence at that point. The conclusion is: we have to calculate the divergence of some two-dimensional pseudo-field associated with the fingerprint image. In regions not containing minutiae (and other feature points) this divergence will be zero (disregarding some random components originating from the noisy character of the image). In the neighborhood of a minutia the divergence must showa maximum. Thus we have to calculate this two-dimensional divergence function and search its local maxima. The divergence of an E(x, y) vector field can be calculated as

aEx aEy

div E = ~ x + 8y

(1)

We can calculate its approximate value by the finite difference method

AEx

/kEy

div E ~ ~ x - + -Ay

(2)

h

ET

,/ /

~ay "I,./

r

~_L~E B~

rely

rectx

a

b

c

Figure 3. Calculating the divergence fingerprint ridge lines. The field strength is determined by two quantities. The first is the intensity, which might be related to the density D of the field strength lines. The second is the direction angle a, which is the tangential direction of the field lines. Using these quantities E~ = const D cos a

(4)

Let us consider a regular region of field lines with line distance d (that is, D = 1/d line density) and with direction angle a. We image a rectangular sub area (a x b) from the picture (Figure 3b). On this area we carry out the following steps. • Shift the image in the y direction with ~y • Perform an EXOR operation on the shifted image with the original • Calculate the area of the black regions of the EXOR image in the rectangle. The result is 1

AREA = a. b. a y ~ cos a + ERR

(5)

where the maximum of the error is

ERRmax-

d J (1 -- af)bf cos a [ (1 bf)af

if bf < af if af < bf

(6)

where a

af = fract(~sina) bf = fract(bcosa) and fract() means the fractional part of a real number. The value of ERR is usually fairly small except in the case when the field lines are parallel with the sides of the a x b rectangle and their density is small. This means that Equation (5) is a good approximation for the x component of the field strength given by Equation (4). Let us to introduce symbolic notation for some image operations.

• SHIFT(image, dx, dy) means a lateral shift of the binary or grey-scale image by the amount of dx, dy • EXOR(imageA, imageB) means exclusive-or operation

or, using the notation of Figure 3a

ERx-ELx+ET-E ~

......

(3)

on two binary images • SUMM(image, rectx, recty) gives a grey,scale image from a binary one by adding the pixel values in a rectangular window defined by rectx and recty (see also Figure 3c)

However, a new problem arises: how to calculate the Ex, Ey field strength components associated with the

With this notation, the two field strength components can be approximately calculated:

div E ~

h

where h = Ax = Ay

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Microprocessors and Microsystems

XSEbitimage = EXOR(FPbitimage, SH I FT(FPbitimage, A, 0)) YSEbitimage = EXOR(FPbitimage, SHIFT(FPbitimage, 0, A)) EXgrayimage = SUMM(YSEbitimage, RXx, RXy) EYgrayimage = SUMM(XSEbitimage, RYx, RYy)

(7)

where FPbitimage is the original fingerprint image, XSEbitimage means a pseudoimage with x-direction shift and EXOR, RXx etc are the parameters of the summation rectangles, A is the 'elementary shift' and the field components are written into two grey-level pseudoimages. Referring to Equation (3) the divergence is easily calculated by

DlVgrayimage = SHIFT(EXgrayimage, h/2, O) - SHIFT(EXgrayimage, h/2, O) + (SHIFT(EYgrayimage, 0, h/2) - SHIFT(EYgrayimage, 0, h/2))

(8)

One only point remains open: the + sign in the above expression. This depends on the local direction of the fingerprint ridges. T h e / / / d i r e c t i o n means a + sign whilst the///direction corresponds to a - sign. To decide about this we can again use the above defined image operations. The relation between a +45 ° shifted and a - 4 5 ° shifted pseudo image gives us the direction information.

P4 5SEbitimage = EXOR(FPbitimage, SHIFT(FPbitimage, A, A)) M4 5SEbitimage = EXOR(FPbitimage, SHIFT(FPbitimage, A, - A ) ) DIRbitimage = SUMM(P45SEbitimage, RDx, RDy) > SUMM(M45SEbitimage, RDx, RDy)

(9) where DIRbitimage is the direction pseudo-image, and the RDs are the summation parameters. CERTAINTY OF DIRECTION A number of recorded fingerprint images show a characteristic Wpe of imperfection: some well-bounded subareas are roughly blurred. A typical case of this is shown in Figure 4a (encircled area). This error is caused by an unintentional lateral slip of the finger during the ink

recording. A similar problem arises if the contact between the finger and the target is not strong enough in some regions. In such cases we have only amorphous spots instead of fingerprint lines (Figure 4b). These sub-areas are unsuitable for the analysis and must be excluded from the investigation. The problem arises: how we can recognize these regions of the image? The basis of our solution is the fact that in the 'good' parts of the image any subregion shows quasi-parallel lines, with a characteristic direction of the lines, whilst in 'poor' regions we cannot recognize a definite direction. By associating a given figure of 'direction certain W' to each subregion, the subregions of the image can be classified and the validi W of localized fingerprint features can be checked. Let us investigate a 'perfect' subregion: parallel lines with clean, noiseless contours. Let the angular direction of the lines be given by the angle a related to the x axis (Figure 5). Using the four EXOR-image defined earlier, and following some simple trigonometrical considerations, we can write

Y= = P= = X= = M = =

SUMM(YSEbitimage, RCx, ROy) L. A. I sin(a - 90°)1 k. SUMM(P45SEbitimage, Rex, RCy) L- A. I sin(a - 45°)1 SUMM(XSEbitimage, RCx, RCy) L. A. [sin(a) l k. SUMM(M45SEbitimage, RCx, RCy) L . A - I sin(a + 45°)]

(10)

where SUMM is the function introduced earlier, L is the contour length falling into the investigated square, RCs are the summation parameters, k = l / x 2 and A is the elementary image-shift, considered to be infinitesimal. It is obvious that the four values X, Y, P, M hold information on the angular position of lines. These values are not equal but show characteristic differences depending on the angle a. In the case of the 'perfect' image the angle can be easily calculated, but any noise in the image also appears in these four values. With increasing noise the relative difference between these values diminishes and the information holding the angular direction disappears. Image parts with two or more dominant line directions

d

figure 4.

Blurred images

Vol 77 No 4 7993

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RUN-TIME CONSIDERATIONS

Contours

Figure 5.

Calculation

of d i r e c t i o n certainty

show the same effect. The more blurred is the image, the smaller is the difference between X, Y, P and M. In an extremely noisy region the four values are nearly the same. We rank order the four values according to their magnitudes M1 > M2 > M3 > M4

and thereafter the direction certainty Cd is calculated as Cd -

The algorithm is realized in software, but the fact that it is based on the regular use of some very elementary image processing steps offers the possibility to map it into special purpose hardware. Such hardware will be constructed in the near future. The authors hope that using the hardware, calculation of the divergence image will require only a fraction of a second.

ACKNOWLEDGEMENT

M3 + M4

The work is supported by the NAWA 4 DIMENZIO Kft.

.e,

218

HARDWARE MAPPING

M1 + M2

In the case of the perfect image this quotient is fairly independent of angle: the value is exactly 1 + v ~ ~ 2.4142. For a strongly blurred image Cd falls to 1. In a practical realization we calculate the Cd values for the neighbourhood of all the fingerprint features found. Cd > 1.7 means that the local pattern is clean, and the real presence of the given feature is confirmed. Between 1.3 and 1.7 the acceptance is questionable (we modify the weight value of that feature). Below 1.3 the feature is always rejected (because it is usually not a true detection of a real feature but the effect of noise). A typical result of the identification is shown on the screen print of Figure 6. The small circles are the minutiae found. This screen is only for demonstration; in practical use the coordinates and direction parameters of the localized features are forwarded for comparison with a database, instead of displaying.

Figure 6.

The algorithm is written in C language for the 80286 processor. For an image size of 512 X 300 pixels the program generates the divergence pseudo field in 7-8 s. This means only 45 ps per divergence value, which can be reached only with a very sophisticated programming technique. Calculation of the direction pseudo-image requires 4 s. With the overhead of sorting and qualifying the feature points the whole identification requires only 20-28 s on a 20 MHz clock-rate machine. Some experiments were undertaken in order to improve speed by using assembler level programming 3. The results show that there is no significant speed gain compared to the C version.

Typical r e s u l t

of i d e n t i f i c a t i o n

REFERENCES 1 Kawagoe, M and Tojo , A 'Fingerprint pattern classification' Pattern Recogn. Vol 17 No 3 (1984) pp 295-303 2 Xuening, S, Nlinde, C, Quingyun, S and Guisheng, Q 'A new automated fingerprint identification system' J. C o m p u t . Sci. T e c h n o L Vol 4 No 4 (1989) pp 289294 3 Kartali, B Private communication Eva Nikoddmusz-SzdkeJy received an electrical l engineering degree from the Technical University Budapest, in the branch of Telecommunication. in 1977.She first joined the development team of BEAG (an electroacoustics manufactured and her first area of interest was the digital realization of analogue electroacoustic tasks e.g. sound delay. In 1983 she ioined HTSZ (Cooperative for Telecommunication). She has been dealing with the development of image processing systems for remote (sate#ire) sensing of Earthimages.Her main activity is the development of hardware units for image processing.

I

Szdkety rece/ved a n electrical ring degree from the Technical ty of Budapest, Hungary, in 1964. He he Department of Electron Devices ol lnical University of Budapest in 1964. y he is a full-time professor and head of artment of Electron Devices of TUB. His earch area was the theory of Gunn His later researchinterests have been n the area of computer aided designof ~cular emphasis on circuit simulation, nodelling and computer graphics. He of several CAD programs in the field of integrated circuit desi~'~and simulation. He has been engagedin the investigation of thermal propertJ'esof semiconductor devices and integrated circuits for the last 15 cears. His newest fields of activity are computer graphics and image processing.

Microprocessors and Microsystems