Fuzzy Fingerprint Classification - Research Paper | EE 5390, Papers of Electrical and Electronics Engineering

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Fuzzy Fingerprint

Classification

Anson C. James

EE 5390

Fuzzy Logic and Engineering

1. Abstract

This paper details the development of a fuzzy fingerprint classification scheme. Based on the variance of a fingerprint image’s orientation field, the fingerprint is classified into one of three groups. Membership functions and fuzzy rules are provided herein, and recommendations for improvements and refinements of the scheme have been provided.

2. Introduction

Fingerprint identification is the most popular form of biometric identification. Biometric identification is attractive because it greatly eliminates the potential for fraud. It is well-known that fingerprints are unique, and people always carry this biometric identifier with them. With fingerprint identification, there is no need to worry about stolen ID-cards. Furthermore, fingerprint identification can easily be utilized to restrict access to unauthorized personnel. For example, fingerprint identification systems are currently used at hospitals to restrict access to pharmaceuticals only to authorized personnel. It is easy to track the inventory and use of pharmaceuticals in this manner, and the identity of each individual who obtains the drugs is known. Successful fingerprint identification applications are truly paradigms of synergy; image enhancement, orientation field estimation, distortion, fingerprint matching, and feature comparison are but a handful of the image processing topics that must be addressed. Knowing the classification of a fingerprint (i.e., knowing the nature of a fingerprint) can aid in the implementation of several algorithms utilized for fingerprint identification. For example, certain fingerprint identification algorithms involve finding certain singular points (points where fingerprint ridges converge). Knowing the fingerprint classification beforehand is tantamount to knowing the quantity and general layout of singular points beforehand. This can cut down on the computation time of these algorithms, thereby improving their performance. In such a computation-intensive application as fingerprint identification, any saving in computation time is extremely desirable.

orientation field, the image is first divided into nonoverlapping blocks (of size 5x5 in this case). Hence, the ridge orientation field is represented as an array whose elements are angles that each represent the ridge direction for a 5x5 block of the original image. The orientation field θ(i,j) is calculated as follows [2]:

tan 2

' 1 V i j

V i j i j y

x (^) (4-1)

∑ ∑

=−

=−

/ 2

/ 2

/ 2

/ 2

i w

xiw

jw

y jw

Vx i j Gx x yGy x y (4-2)

∑ ∑

=−

=−

/ 2

/ 2

/ 2

/ 2

(, ) {^2 ( , )^2 ( , )}

i w

xiw

jw

y jw

V (^) y i j Gx x y Gy x y (4-3)

Vx (i,j) and Vy(i,j) are, respectively, the vertical and horizontal contributions to the

orientation field. V (^) x '^ ( i , j )and V (^) y '^ ( i , j )represent these contributions after smoothed by a

simple 5x5 block kernel W(m,n). G (^) x (x,y) and Gy(x,y) are the horizontal and vertical gradients, respectively, and may be calculated with a 3x3 Sobel edge mask or any other suitable means. The local orientation carries an ambiguity of exactly 180°, but this is really of no importance. We can always assume an angle between positive and negative 90° and adjust accordingly. Finally, the sample variance of the ridge orientation field is calculated:

∑∑ = =

× −

n

i

m

j

i j n m 1 1

where n and m are the dimensions of the orientation field. Blocks with absolutely no ridges are not included in the variance calculation. They are easy to detect because their horizontal and vertical gradients are both negligible.

5. Fuzzification

5.1 Variance-based

The variances of several fingerprint images of Group A, Group B, and Group C were calculated to determine typical variance values for each group. Simple triangle functions sufficed to represent the membership functions for variance. Functions exist for low, medium, and high variance, as depicted in Figure 5-1. A good peak for the medium function was found to be 0.65, with boundaries for the medium function at 0. and 0.9. As are the conventions, the membership function values always sum to 1 for any possible input and each membership function only overlaps with its closest neighbors. [4] Of the methods I attempted, only the variance-based functions proved useful for fingerprint classification. Membership functions other than variance-based would have been used to further classify the fingerprints into the six typical classifications.

Figure 5-1 Membership functions for variance.

5.2 Failed Approach

Another approach was conceived and actually implemented to an extent, but it proved to be ineffectual. This method assumed that there would be more positively- sloped ridges on a right loop fingerprint orientation field image such as Figure 5-1 than a left loop fingerprint. To avoid confusion, these will be called upslanted and downslanted blocks, respectively. (Note that any block with an orientation angle between 0° and 90° would be correctly described as a positively-sloped one. However, only angles between 22.5° and 67.5°, those herein named as upslanted blocks, are represented as such on the orientation field images. Angles between -22.5° and 22.5° are represented as horizontal lines and angles between 67.5° and 90° and between -90° and -67.5° are represented as vertical lines. The angles have, in effect, been quantized to four values in this approach. The entire range of angles, of course, is still utilized for the variance calculation.) An upslanted block would correspond to an orientation between 22.5° and 67.5°, and a downslanted block would correspond to an orientation between -22.5° and -67.5°.

The ratio of upslanted blocks to the sum of the upslanted and downslanted blocks was calculated and named slantbias.

upslanted downslante d

upslanted slantbias

If all slanted blocks were upslanted, the ratio would evaluate to 1. If all slanted blocks were downslanted, the ratio would evaluate to 0. If half slanted blocks were upslanted and half downslanted, the ratio would evaluate to 0.5. In this way, a membership function for left and right could be constructed. Another approach has been conceived but not implemented and so will be discussed in the appropriate section of this report (Recommendations). Consequently, only variance-based membership functions were actually implemented for this project. This is why a classification only to the three groups, Group A, Group B, and Group C, was achieved. This is the limitation of the variance-based approach alone. Further classification into all six common recognized fingerprint classifications will require the development of additional rules, which would require further study of the patterns redolent of each of the six classifications. This would require additional time that I unfortunately did not have at my disposal. Nonetheless, the variance-based approach alone actually performs quite will within these limitations; a fingerprint can be classified to its appropriate group with astonishing accuracy.

6. Rule-based System

The variance-based fuzzy rules are straightforward:

• If variance is low, then the image is in Group A.
• If variance is medium, then the image is in Group B.
• If variance is high, then the image is in Group C.

There are four fuzzy rules for the failed approach discussed in Section 5.2:

• If variance is low AND the slantbias is middle, then the image is in Group A.
• If variance is medium AND the slantbias is left, then the image is a left loop.
• If variance is medium AND the slantbias is right, then the image is a right loop.
• If variance is high AND the slantbias is middle, then the image is in Group C.

While the failed approach proved ineffectual because of bad assumptions, it is easy to see from this example that additional (well-conceived) rules can easily be adapted to the variance-based rules to further subdivide the fingerprint images into their appropriate classifications.

7. Defuzzification

The defuzzification is very simple. Based on the calculated variance and the fuzzy rules, a crisp degree-of-confidence value is determined for each of Group A, Group B, and Group C. The group with the highest corresponding degree of confidence is the most likely group.

8. Results

Table 8-1 lists the result of the algorithm on five images in each group. All these images are high-quality images (in terms of the quantity of the fingerprint that is captured, not necessarily in terms of noise). None of these images were used to determine the membership functions of Section 5.1.

Image Name Group A Group B Group C Actual 21_5 0.9891 0.0109 0 Group A 20_5 1 0 0 Group A 56_6 0.855 0.145 0 Group A 70_3 0.9094 0.0906 0 Group A 74_6 0.853 0.147 0 Group A 2_5 0 0.8115 0.1885 Group B 4_7 0 0.5572 0.4428 Group B 27_6 0.0673 0.9327 0 Group B 38_7 0 0.5862 0.4138 Group B 3_1 0 0.1462 0.8538 Group B 5_3 0 0 1 Group C 10_7 0 0.5644 0.4356 Group C 10_6 0 0.3397 0.6603 Group C 23_7 0 0 1 Group C 29_3 0 0.3352 0.6648 Group C Table 8-1 Image classifications.

Out of all fifteen results shown here, thirteen were correctly classified and two (3_1 and 10_7) were incorrectly classified. Image 3_1 was likely incorrectly classified because the top of the fingerprint is cropped, so the horizontal ridges on the bottom of the image had more of an effect on the variance. This is a limitation of this approach, but a potential remedy is proposed in Section 10 below. Note that 10_7 and 10_6 are images of the same fingerprint taken at different times (what is called a mated pair, for better or worse). This particular fingerprint was correctly classified once (10_6) and incorrectly classified once (10_7). Both are high-quality images. This just demonstrates that the approach, although often successful, could use some tweaking.

9. Conclusion

This approach performs well for what it was designed to do. Of course, to be ready for prime time, more fuzzy rules must be created and the existing rules must be slightly tweaked. A useful implementation must be able to classify a fingerprint into any

Figure 10-2 Orientation field for image 3_1.

The scheme would be similar to that of Section 5.2. A variable called verticalbias would represent the ratio of vertical lines on the left of the singular point to the total number of vertical lines. I am extremely confident that this approach would enjoy some success because these features are almost always present in the loop images. This would be a good heuristic.

11. References

[1] Jain A.K., Pankanti S., “Fingerprint Classification and Matching,” Handbook of Image and Video Processing , Elsevier Academic Press, pp. 1219-1233, 2005.

[2] Klimanee, C., Nguyen, D.T., “On the Design of 2-D Gabor Filtering of Fingerprint Images,” Proceedings of 2004 IEEE Consumer Communications and Networking Conference (CNC2004): Consumer Networking , Las Vegas, Nevada, 2004.

[3] Maltoni, Maio, Jain, and Prabhakar, Handbook of Fingerprint Recognition , Springer- Verlag New York, Inc., 2003.

[4] Yen, Langari, Fuzzy Logic: Intelligence, Control, and Information , Prentice Hall, Upper Saddle River, New Jersey, 1999.

Note: [3] Provided the database of fingerprints utilized for this project.

Fuzzy Fingerprint

Classification

Anson C. James

April 21, 2006

EE 5390: Fuzzy Logic and Engineering

Preprocessing „

Determine the orientation field [2]:

Divide the image into nonoverlapping blocks

(5X5 in this case).

Orientation field is calculated as follows:

,where

⎤ ⎥ ⎥⎦

⎡ ⎢ ⎢⎣

=

Θ

−

)

, (

)

, (

tan 1 2

)

, (

' '

1

j

i

V

j

i

V

j

i

x y

∑

∑

=

) , ( ) , ( 2 ) , (

w i

w i x

w j

w j y

y

x

x^

y x G y x G j i V

∑

∑

−

=

)} , ( ) , ( { ) , (

w i

w i x

w j

w j y

y

x

y^

y x G y x G j i V

Preprocessing „

Gx and Gy are the horizontal and verticalgradients, respectively, and may simply becalculated with the appropriate 3X3 Sobeledge mask.

„

Vx and Vy are then smoothed with a 5X5block kernel before calculating

θ

(i,j).

Orientation Field

Orientation Field

Hmm, there’s quite a bit of variance in the orientation here!

Data Acquisition „

Data acquisition, then, consists of computingthe variance of the orientation field for eachimage.

„

Fingerprint images, then, could be classifiedinto one of three groups based on variance:

Group A: Arch and Tented Arch (low)

Group B: Right and Left Loop (medium)

Group C: Whorl and Twin Loop (high)

Data Acquisition „

Variance was calculated for several imagesfrom each group to determine the range oftypical values for each group.

„

Based on these values, the membershipfunctions could be constructed.