## Experimental evaluation of fingerprint verification system based on double random phase encoding

Optics Express, Vol. 14, Issue 5, pp. 1755-1766 (2006)

http://dx.doi.org/10.1364/OE.14.001755

Acrobat PDF (1311 KB)

### Abstract

We proposed a smart card holder authentication system that combines fingerprint verification with PIN verification by applying a double random phase encoding scheme. In this system, the probability of accurate verification of an authorized individual reduces when the fingerprint is shifted significantly. In this paper, a review of the proposed system is presented and preprocessing for improving the false rejection rate is proposed. In the proposed method, the position difference between two fingerprint images is estimated by using an optimized template for core detection. When the estimated difference exceeds the permissible level, the user inputs the fingerprint again. The effectiveness of the proposed method is confirmed by a computational experiment; its results show that the false rejection rate is improved.

© 2006 Optical Society of America

## 1. Introduction

2. E. Watanabe and K. Kodate, “Implementation of a high-speed face recognition system that uses an optical parallel correlator,” Appl. Opt. **44**, 666–676 (2005). [CrossRef] [PubMed]

4. P. Refregier and B. Javidi, “Optical encryption based on input plane Fourier plane random encoding,” Opt. Lett. **20**, 767–769 (1995). [CrossRef] [PubMed]

6. H. Suzuki, T. Yamaya, T. Obi, M. Yamaguchi, and N. Ohyama, “Fingerprint verification for smart-card holders based on optical image encryption scheme,” in *Optical Information Systems*,
Bahram Javidi and Demetri Psaltis, eds., Proc. SPIE **5202**, 88–96 (2003). [CrossRef]

## 2. Review of hybrid authentication system that combines fingerprint verification with PIN verification

### 2.1 Smart card holder authentication method

### 2.2 Optical image encryption and pattern matching

*f*(

*x*,

*y*). Then,

*f*(

*x*,

*y*) is multiplied by a phase mask with a random image of

*R*(

*x*,

*y*), and the phase modulated image

*f*

_{m}(

*x*,

*y*) is expressed as follows:

*F*

_{m}(

*u*,

*v*) is multiplied by another random phase mask that corresponds to an encryption key image exp[

*jK*

_{E}(

*u*,

*v*)]. This image is generated from a fingerprint image. Subsequently, the encryption image

*F*

_{m}(

*u*,

*v*)exp[

*jK*

_{E}(

*u*,

*v*)] is obtained, and it is recorded as enrollment information. During decryption, the complex conjugate of the encrypted image

*u*,

*v*)exp[-

*jK*

_{E}(

*u*,

*v*)] is multiplied by a phase mask that corresponds to a decryption key image exp[

*jK*

_{D}(

*u*,

*v*)] . Therefore, a complex amplitude image

*u*,

*v*)exp[

*j*{-

*K*

_{E}(

*u*,

*v*)+

*K*

_{D}(

*u*,

*v*)}] is obtained. Its Fourier transform produces the decrypted image

*f*

_{r}(

*x*

_{d},

*y*

_{d}) as follows:

*N*(

*u*,

*v*)=exp[

*j*{-

*K*

_{E}(

*u*,

*v*)+

*K*

_{D}(

*u*,

*v*)}] ,

*n*(

*x*

_{d},

*y*

_{d})= ℑ[

*N*(

*u*,

*v*)] , and ℑ[] denotes the Fourier transform operator. Let us consider the following two images:

*n*(

*x*

_{d},

*y*

_{d}) represents the correlation between

*g*

_{1}(

*x*′,

*y*′) and

*g*

_{2}(

*x*′,

*y*′). This implies that the decrypted image in double random phase encoding is the convolution of the plane image and the correlation between two images.

8. J.L. Horner and P.D. Gianino, “Phase-only matched filtering,” Appl. Opt. **23**, 812–816 (1984) [CrossRef] [PubMed]

*n*(

*x*

_{d},

*y*

_{d}) be the POC of the two fingerprint images. In other words, the phase components of the Fourier-transformed fingerprint images are used as keys in double random phase encoding; the two fingerprint images

*g*

_{E}(

*x*′,

*y*′) and

*g*

_{D}(

*x*′,

*y*′) are Fourier transformed as follows:

*A*

_{E}(

*u*,

*v*) and

*A*

_{D}(

*u*,

*v*) are the amplitude components and exp[

*jP*

_{E}(

*u*,

*v*)] and exp[

*jP*

_{D}(

*u*,

*v*)] are the phase components. Then, the phase components are used as keys as follows:

*n*(

*x*

_{d},

*y*

_{d}) approximately satisfies the following relation:

*δ*() denotes the Dirac delta function and

*α*and

*β*represent the shift of the fingerprint. When a correct fingerprint is used, the restored image

*f*

_{r}(

*x*

_{d},

*y*

_{d}) is expressed as

*x*

_{d}-

*α*,

*y*

_{d}-

*β*) with the same intensity pattern as that of

*f*(

*x*,

*y*). When an incorrect fingerprint is used,

*f*

_{r}(

*x*

_{d},

*y*

_{d}) produces a random image, which is the convolution of

*f*

_{m}(

*x*,

*y*) and a random sequence.

10. Shoude Chang, Simon Boothroyd, Paparao Palacharla, and Sethuraman Pachanathan, “Rotation-invariant pattern recognition using a joint transform correlator,” Opt. Commun. **127**, 107–116 (1984). [CrossRef]

11. Vahid R. Riasati, Partha P. Banerjee, Mustafa A. G. Abushagur, and Kenneth B. Howell, “Rotation-invariant synthetic discriminant function filter for pattern recognition,” Opt.Eng. **39**, 1156–1161 (2000). [CrossRef]

### 2.3 PIN encoding into 2D image

12. Official website, “QR code.com,” http://www.denso-wave.com/qrcode/index-e.html.

13. J. Tanida and Y. Ichioka, “Optical logic array processor using shadowgrams,” J. Opt. Soc. Am. **73**, 800–809 (1983). [CrossRef]

## 3. Improvement in the proposed system

### 3.1 Preprocessing for fingerprints that are shifted significantly

### 3.2 Estimation of distance between two fingerprints

### 3.3. Generation of template for core detection

*x*

_{e},

*y*

_{e}) is expressed as follows:

*x*

_{1},

*y*

_{1}) denote the coordinates of the correlation peak between the enrollment fingerprint and the template and (

*x*

_{2},

*y*

_{2}) denote the coordinates of the correlation peak between the verification fingerprint and the template.

*a*, minor axis

*b*, angular range of arc

*θ*, and line thickness

*w*. These parameters are obtained by using some training fingerprint images. In order to determine the best parameter configuration, an evaluation function ∆

*E*is defined as the average error between the actual position difference and the estimated position difference of two fingerprint images. It is expressed as follows:

*x*

_{a},

*y*

_{a}) denote the actual position difference of two fingerprint images. The training sequence is summarized as follows:

- Set the parameters.
- Generate a pair of training fingerprint images captured from the same fingerprint and calculate their actual position difference (
*x*_{a},*y*_{a}) by correlation. - Calculate the core positions of two training fingerprint images (
*x*_{1},*y*_{1}) and (*x*_{2},*y*_{2}) by the correlation between each training image and the template image; subsequently, determine their estimated difference (*x*_{e},*y*_{e}). - Repeat steps 2 and 3 for all fingerprint image pairs of the same individual.
- Calculate the energy function ∆
*E*. - Update ∆
*E*if its current value is less than its previous value; memorize the parameter configuration. - Repeat steps 1 to 6 until all parameter configurations are tested.
- Finally, select the best parameter configuration with the smallest value of ∆
*E*.

## 4. Experiments

### 4.1 Template generation

*a*= 82,

*b*= 86,

*θ*= 57 [degree], and

*w*= 3, and an image exhibiting the core is shown in Fig. 8(b). It is demonstrated that this template can determine the approximate position of the core even when the fingerprint image is shifted significantly. We evaluated the performance of the generated template image by applying it to another 50 test images of the eight individuals. The result revealed an average estimation error of 7.7 pixels.

### 4.2 Verification

*N*

_{PIN}is the bit number of the PIN (in this case, 64 bits);

*N*

_{Error}, average value of the error bit number of the decoded PIN;

*N*

_{FP}, number of false positive trials;

*N*

_{FN}, number of false negative trials; and

*N*

_{s}, total number of trials in the experiment. When the BER is equal to zero, the verification is considered to be a “success”; otherwise, it is considered to be a “failure.”

### 4.3 Discussion

## 5. Conclusion

## Acknowledgments

## References and links

1. | S. Ishida, M. Mimura, and Y. Seto, “Development of Personal Authentication Techniques Using Fingerprint Matching Embedded in Smart Cards,” IEICE Trans. Inf. & Syst. |

2. | E. Watanabe and K. Kodate, “Implementation of a high-speed face recognition system that uses an optical parallel correlator,” Appl. Opt. |

3. | B. Javidi and J.L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. |

4. | P. Refregier and B. Javidi, “Optical encryption based on input plane Fourier plane random encoding,” Opt. Lett. |

5. | Bor Wang, Ching-Cherng Sun, Wei-Chia Su, and Arthur E. T. Chiou, “Shift-Tolerance Property of an Optical Double-Random Phase-Encoding Encryption System,” Appl. Opt. |

6. | H. Suzuki, T. Yamaya, T. Obi, M. Yamaguchi, and N. Ohyama, “Fingerprint verification for smart-card holders based on optical image encryption scheme,” in |

7. | H. Suzuki, T. Yamaya, T. Obi, M. Yamaguchi, and N. Ohyama, “Fingerprint verification for smart card holders identification based on optical image encryption,” Jpn. J. Opt. |

8. | J.L. Horner and P.D. Gianino, “Phase-only matched filtering,” Appl. Opt. |

9. | K. Ito, et al., “A fingerprint matching algorithm using phaseonly correlation,” IEICE Trans. Fundam. Electron. Commun. Comut. Sci. |

10. | Shoude Chang, Simon Boothroyd, Paparao Palacharla, and Sethuraman Pachanathan, “Rotation-invariant pattern recognition using a joint transform correlator,” Opt. Commun. |

11. | Vahid R. Riasati, Partha P. Banerjee, Mustafa A. G. Abushagur, and Kenneth B. Howell, “Rotation-invariant synthetic discriminant function filter for pattern recognition,” Opt.Eng. |

12. | Official website, “QR code.com,” http://www.denso-wave.com/qrcode/index-e.html. |

13. | J. Tanida and Y. Ichioka, “Optical logic array processor using shadowgrams,” J. Opt. Soc. Am. |

14. | S. Ito, T. Kanaoka, Y. Hamamoto, and S. Tomita, “An Algorithm for Classification of Fingerprints Based on the Core,” IECE , D-ll |

**OCIS Codes**

(070.4560) Fourier optics and signal processing : Data processing by optical means

(100.1160) Image processing : Analog optical image processing

**ToC Category:**

Fourier Optics and Optical Signal Processing

**History**

Original Manuscript: November 21, 2005

Revised Manuscript: February 28, 2006

Manuscript Accepted: February 28, 2006

Published: March 6, 2006

**Citation**

Hiroyuki Suzuki, Masahiro Yamaguchi, Masuyoshi Yachida, Nagaaki Ohyama, Hideaki Tashima, and Takashi Obi, "Experimental evaluation of fingerprint verification system based on double random phase encoding," Opt. Express **14**, 1755-1766 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-5-1755

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### References

- S. Ishida, M. Mimura, and Y. Seto, "Development of Personal Authentication Techniques Using Fingerprint Matching Embedded in Smart Cards," IEICE Trans. Inf. & Syst. 84,812-818 (2001).
- E. Watanabe and K. Kodate, "Implementation of a high-speed face recognition system that uses an optical parallel correlator," Appl. Opt. 44,666-676 (2005). [CrossRef] [PubMed]
- B. Javidi and J.L. Horner, "Optical pattern recognition for validation and security verification," Opt. Eng. 33,1752-1756 (1994). [CrossRef]
- P. Refregier and B. Javidi, "Optical encryption based on input plane Fourier plane random encoding," Opt. Lett. 20,767-769 (1995). [CrossRef] [PubMed]
- Bor Wang, Ching-Cherng Sun, Wei-Chia Su, and Arthur E. T. Chiou, "Shift-Tolerance Property of an Optical Double-Random Phase-Encoding Encryption System," Appl. Opt. 39,4788-4793 (2000). [CrossRef]
- H. Suzuki, T. Yamaya, T. Obi, M. Yamaguchi and N. Ohyama, "Fingerprint verification for smart-card holders based on optical image encryption scheme," in Optical Information Systems, Bahram Javidi, Demetri Psaltis, eds., Proc. SPIE 5202, 88-96 (2003). [CrossRef]
- H. Suzuki, T. Yamaya, T. Obi, M. Yamaguchi and N. Ohyama, "Fingerprint verification for smart card holders identification based on optical image encryption," Jpn. J. Opt. 33,37-44 (2004).
- J.L. Horner and P.D. Gianino, "Phase-only matched filtering," Appl. Opt. 23,812-816 (1984) [CrossRef] [PubMed]
- K. Ito, et al., "A fingerprint matching algorithm using phaseonly correlation," IEICE Trans. Fundam. Electron. Commun. Comut. Sci. 87,682-691 (2004).
- Shoude Chang, Simon Boothroyd, Paparao Palacharla, and Sethuraman Pachanathan, "Rotation-invariant pattern recognition using a joint transform correlator," Opt. Commun. 127,107-116 (1984). [CrossRef]
- V. R. Riasati, ParthaP. Banerjee, M. A. G. Abushagur, and K. B. Howell, "Rotation-invariant synthetic discriminant function filter for pattern recognition," Opt.Eng. 39,1156-1161 (2000). [CrossRef]
- Official website, "QR code.com," http://www.denso-wave.com/qrcode/index-e.html.
- J. Tanida and Y. Ichioka, "Optical logic array processor using shadowgrams," J. Opt. Soc. Am. 73,800-809 (1983). [CrossRef]
- S. Ito, T. Kanaoka, Y. Hamamoto and S. Tomita, "An Algorithm for Classification of Fingerprints Based on the Core," IECE, D-Ⅱ73 1733-1741 (1990)

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