Fingerprint recognition with phase-only correlation.

Teusdea, Alin Cristian ; Gabor, Gianina

1. INTRODUCTION

Nowadays security systems are a generic issue. Biometrics is a popular security criterion to restrict access to some systems and preserve their security. A part of biometrics is fingerprint recognition or matching. From the several methods developed in the past years, the phase-only correlation (POC) (Chien, 2004; Ito et al., 2005; Ito et al., 2004; Miyazawa et al., 2005; Takita, 2003) is important because its sub-pixel image translation capability. The past experiments developed a modified POC by rectangular band filtering the cross-spectrum of the POC function (BPOC) (Ito et al., 2005; Ito et al., 2004) in order to improve the genuine-impostor rejection.

This paper presents a theoretical introduction and some experiments for evaluating recognition performances of the proposed method and the dedicated ones.

2. METHODS AND SAMPLES

2.1 Phase only cross-correlation

The recognition process is used for object registration which means that one object is "compared" with several objects. Comparison criteria concludes if the compared objects are or not similar with other objects. The comparison process basically works with two objects. In our case the comparison method is the cross-correlation while the objects are the fingerprints.

In a single cross-correlation process the two objects are denoted as reference and non-reference. That means that from the cross-correlation process we obtain the information if the reference is similar or not with the non-reference object.

The cross-correlation considers two (NxM) images, ref (x,y) as reference image and nref (x,y) as non-reference image. The 2D discrete Fourier transforms of these images, denoted as Ref (u,v) and NRef (u,v), are given by (Ito et al., 2005; Ito et al., 2004)

Ref(u,v) = REF(u,v) x exp[i x [[phi].sub.ref](u,v)], (1)

NRef(u,v) = NREF(u,v) x exp[i x [[phi].sub.nref] (u,v)], (2)

where REF(u,v) and NREF(u,v) are the amplitude parts and [[phi].sub.ref] (u,v) and [[phi].sub.nref] (u,v) are the phase parts of the 2D discrete

Fourier transforms.

The phase-only cross-spectrum (Ito et al., 2005; Ito et al., 2004; Takita, 2003) is defined by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

and thus the phase-only cross-correlation is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (4)

If ref(x,y) = nref(x,y) then [DELTA][[phi].sub.rn](u,v) [equivalent to] 0 and the phase-only correlation is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (5)

This means that if the two images are identical then the POC gives a highly sharp peak so the matching accuracy is higher than in the classical method.

2.2 Band limited phase-only cross-correlation

The cross-correlation process on a database is basically characterized by two quantities: the autocorrelation peak intensity (API) and the cross-correlation peak intensity (CPI). The API value is obtained from all "autocorrelations" between the new fingerprint and the genuine class fingerprints as witness fingerprints. More precisely the minimum value from this set of "autocorrelations" peaks is denoted as API . In the same manner the CPI value is the maximum value of all the other cross-correlation peaks generated with the impostor classes fingerprints.

Phase-only correlation is a very precise matching method and effective for the verification process. This is done by fine "comparing" of the high frequencies in the Fourier transforms of the fingerprints.

When one has to register a new fingerprint then the correlation process must match it with some deformed representations of it. The deformations alter exactly the high frequencies. The reference-witness correlation can have a lower API value than the reference-nonreference correlation CPI value. This means that the involved matching process fails (figure 1 a, b, c; figure 2 a, b).

Fingerprint database registration matching process has to correlate only frequencies that are common to all fingerprints from the same class. This is the reason why the band limited phase only correlation (BPOC) (Ito et al., 2005; Ito et al., 2004) was introduced. This correlation uses a 2D band filter on the phase-only cross-correlation spectrum. The band filter is defined with two sub-unitary valued coefficients: over the rows direction, cL , and over the columns direction, cC .

The BPOC results as in figure 3 a, b, show that the matching process is successful as the API value (figure 3 a) is greater than the CPI value (figure 3b).

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

2.3 Elliptic band limited phase-only cross-correlation

In this paper the authors proposes an elliptic band phase-only correlation, (EPOC). In this method, there is used an elliptic band filter with the same cL and cC parameters instead of a rectangle band filter with cL and cC parameters. The reason of this choice is that the power spectrum of the fingerprints usually presents the highest density of the information in a centered elliptic form. As mentioned before, this centered ellipse contains that kind of spatial frequencies that can accommodate the database fingerprint registration.

The POC, BPOC and EPOC, phase-only correlations comparative results are presented in the next section.

3. RESULTS AND DISCUSSIONS

In this paper, a fingerprint database was used which was scanned with Cross Match Verifier 300 Classic (USB) at 500dpi in 30.5 x 30.5 mm image size (http://www.neuro technologija.com/download/CrossMatch_Sample_DB.zip).

The database contains fingerprint classes with 6 fingertips x 8 different scanned fingerprints for each of the 76 persons. The fingerprint index denotes "pppjf_s.tif", as ppp is the person number, ff is the fingertip number and s is the number of the fingerprint version.

The experimental results from the BPOC and EPOC are presented in figure 4, person with index 12 and fingertip index 3, 4, 5, 6, 7, 8, over the same set of fingertips of persons with indexes 13, 14, 17, 22, 27, 45, 47, 76. The band limited POC parameters were selected with the values: cL = 0.80 and cC = 0.45 . There are presented the Genuine Acceptance Rate, GAR, and the False Rejection Rate, FRR. The GAR is calculated when the False Acceptance Rate is FRR = 0. This means that there was selected a threshold value ([Th.sub.C]), which is the highest value from all the maximum intensity of the cross-correlation peaks (CPI). Genuine class POC values higher than [Th.sub.C] were considered in GAR calculation while the smaller ones were considered in FRR calculation.

[FIGURE 4 OMITTED]

The EPOC technique has the highest GAR value for all six fingertips of the person with index 12, in an experiment with 336x48= 16,128 POC correlations. In this experiment the differences of GAR coefficients performed with EPOC and BPOC techniques for the same fingertip lies between 3.44% and 15.38%.

4. CONCLUSIONS

In this paper, there are presented two modified phase-only correlation methods: the rectangle band limited, BPOC, and the proposed elliptic band limited, EPOC. These matching methods are very efficient for fingerprint recognition (single correlation experiment).

The results in figure 4 emphasize that elliptic band limited phase-only correlation, EPOC, has better performances (higher GAR values) than the rectangle band limited phase-only correlation, BPOC. Thus, for fingerprint database registration, the EPOC method is more efficient than the BPOC method.

Our future research will develop a more robust EPOC method to geometrical deformations of the fingerprints, with a Log-Polar transform. Another future plan is to work with a much larger fingerprint database to ensure statistical significance so as to be able to use it in biometrics technology.

5. REFERENCES

Chien, L. H. & Aoki T. (2004). Robust motion estimation for video sequences based on phase-only correlation, Proceedings of the 6th IASTED SIP 2004, Hamza M.H. (Ed), pp. 441-446, ISBN 0-88986-434-9, Honolulu, USA, Aug. 2004, ACTA Press, Canada.

Ito ,K.; Nakajima H.; Kobayashi K. & Aoki T., Higuchi T. (2004) . A fingerprint matching algorithm using phase-only correlation, IEICE Transactions. Fundamentals, E87-A, No. 3, March 2004, pp. 682-691, ISSN 1745-1337.

Ito K.; Morita A.; Aoki T.; Higuchi T.; Nakajima H. & Kobayashi K. (2005). A fingerprint recognition algorithm using phase-based image matching for low-quality Fingerprints, Proceedings of IEEE Int. Conf. on Image Processing, pp. II-33 - II-36, ISBN: 0-7803-9134-9, September 2005, Genova, Italy, IEEE, NJ USA.

Miyazawa, K.; Ito K.; Aoki T.; Kobayashi K. & Nakajima H. (2005) . An efficient iris recognition algorithm using phase-based image matching, Proceedings of IEEE Int. Conf. on Image Processing, pp. II-33--II-36, ISBN: 0-7803-9134-9, September 2005, Genova, Italy, IEEE, NJ USA.

Takita, K.; Aoki T.; Sasaki Y.; Higuchi T. & Kobayashi K. (2003). High-accuracy subpixel image registration based on phase-only correlation, IEICE Transactions. Fundamentals, E86-A, No. 8, August 2003, pp. 1925-1934, ISSN 1745-1337.