# Optimum Geometric Transformation and Bipartite Graph-Based Approach to Sweat Pore Matching for Biometric Identification

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## Abstract

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## 1. Introduction

## 2. Technical Background

#### 2.1. Live-Scan Fingerprint Image

#### 2.2. Pore-Based Fingerprint Image

## 3. Geometric Transformation and Bipartite Graph-Based Approach to Sweat Pore Matching

#### 3.1. Problem Statement

- Local similarity: If two pores ${r}_{i}$ and ${t}_{j}$ are mated each other in the final matching state, they would have the similar distribution patterns of neighboring pores.
- Global similarity: There is a certain geometric relationship between two pore sets, consistently in the entire picture.

#### 3.2. Local Correspondence

#### 3.3. Global Correspondence

#### 3.4. Stable Pore Matching

Algorithm 1: Stable pore matching |

## 4. Experimental Results

#### 4.1. PolyU HRF Database

#### 4.2. Synthetic Database

#### 4.3. Pore-Based Fingerprint Image

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

- Maltoni, D.; Maio, D.; Jain, A.; Prabhakar, S. Handbook of Fingerprint Recognition; Springer Science & Business Media: Heidelberg/Berlin, Germany, 2009. [Google Scholar]
- Ratha, N.; Bolle, R. Automatic Fingerprint Recognition Systems; Springer Science & Business Media: Heidelberg/Berlin, Germany, 2007. [Google Scholar]
- Pankanti, S.; Prabhakar, S.; Jain, A.K. On the individuality of fingerprints. IEEE Trans. Pattern Anal. Mach. Intell.
**2002**, 24, 1010–1025. [Google Scholar] [CrossRef] - Zhang, D.; Liu, F.; Zhao, Q.; Lu, G.; Luo, N. Selecting a reference high resolution for fingerprint recognition using minutiae and pores. IEEE Trans. Instrum. Meas.
**2011**, 60, 863–871. [Google Scholar] [CrossRef] - Jain, A.K.; Chen, Y.; Demirkus, M. Pores and ridges: High-resolution fingerprint matching using Level 3 features. IEEE Trans. Pattern Anal. Mach. Intell.
**2007**, 29, 15–27. [Google Scholar] [CrossRef] [PubMed] - Ashbaugh, D. Poroscopy. Identif. News
**1982**, 32, 3–8. [Google Scholar] - Zhao, Q.; Jain, A.K. On the utility of extended fingerprint features: a study on pores. In Proceedings of the 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition-Workshops, San Francisco, CA, USA, 13–18 June 2010; pp. 9–16. [Google Scholar]
- Roddy, A.R.; Stosz, J.D. Fingerprint features-statistical analysis and system performance estimates. Proc. IEEE
**1997**, 85, 1390–1421. [Google Scholar] [CrossRef] - Lee, J.; Pyo, M.; Lee, S.H.; Kim, J.; Ra, M.; Kim, W.Y.; Park, B.J.; Lee, C.W.; Kim, J.M. Hydrochromic conjugated polymers for human sweat pore mapping. Nat. Commun.
**2014**, 5, 3736. [Google Scholar] [CrossRef] [PubMed] - Elsner, C.; Abel, B. Ultrafast High-Resolution Mass Spectrometric Finger Pore Imaging in Latent Finger Prints. Sci. Rep.
**2014**, 4, 6905. [Google Scholar] [CrossRef] [PubMed] - Stosz, J.D.; Alyea, L.A. Automatic Systems for the Identification and Inspection of Humans; International Society for Optics and Photonics: Bellingham, WA, USA, 1994; Volume 2277, pp. 210–224. [Google Scholar]
- Kryszczuk, K.; Drygajlo, A.; Morier, P. Extraction of Level 2 and Level 3 Features for Fragmentary Fingerprint Comparison; Speech Processing and Biometrics Group, Signal Pro-cessing Institute, Swiss Federal Institute of Technology Lausanne: Lausanne, Switzerland, 2004. [Google Scholar]
- Zhao, Q.; Zhang, L.; Zhang, D.; Luo, N. Direct Pore Matching for Fingerprint Recognition; Springer: Heidelberg/Berlin, Germany, 2009; pp. 597–606. [Google Scholar]
- Liu, F.; Zhao, Q.; Zhang, L.; Zhang, D. Fingerprint Pore Matching Based on Sparse Representation; Indian Council of Philosophical Research: New Delhi, India, 2010; pp. 1630–1633. [Google Scholar]
- Cui, J.; Ra, M.S.; Kim, W.Y. Fingerprint pore matching method using polar histogram. In Proceedings of the 18th IEEE International Symposium on Consumer Electronics (ISCE 2014), JeJu Island, Korea, 22–25 June 2014; pp. 1–2. [Google Scholar]
- PolyU HRF Database. Available online: http://www4.comp.polyu.edu.hk/~biometrics/ (accessed on 19 May 2018).
- Ray, M.; Meenen, P.; Adhami, R. A novel approach to fingerprint pore extraction. In Proceedings of the Thirty-Seventh Southeastern Symposium on System Theory, Tuskegee, AL, USA, 20–22 March 2005; pp. 282–286. [Google Scholar]
- Zhao, Q.; Zhang, D.; Zhang, L.; Luo, N. Adaptive fingerprint pore modeling and extraction. Pattern Recognit.
**2010**, 43, 2833–2844. [Google Scholar] [CrossRef] - Cui, J.; Ra, M.; Kim, W.Y. Fingerprint Pore Extraction Method using 1D Gaussian Model. J. Inst. Electr. Inf. Eng.
**2015**, 52, 135–144. [Google Scholar] [CrossRef] - Fischler, M.A.; Bolles, R.C. Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography. Commun. ACM
**1981**, 24, 381–395. [Google Scholar] [CrossRef] - Moré, J.J. the Levenberg-Marquardt algorithm: implementation and theory. In Numerical Analysis; Springer: Heidelberg/Berlin, Germany, 1978; pp. 105–116. [Google Scholar]
- Pujol, J. the solution of nonlinear inverse problems and the Levenberg-Marquardt method. Geophysics
**2007**, 72, W1–W16. [Google Scholar] [CrossRef] - Gusfield, D.; Irving, R.W. The Stable Marriage Problem: Structure and Algorithms; MIT Press: Cambridge, UK, 1989. [Google Scholar]
- Manlove, D.F.; Irving, R.W.; Iwama, K.; Miyazaki, S.; Morita, Y. Hard variants of stable marriage. Theor. Comput. Sci.
**2002**, 276, 261–279. [Google Scholar] [CrossRef] - Iwama, K.; Miyazaki, S. A survey of the stable marriage problem and its variants. In Proceedings of the 2008 International Conference on Informatics Education and Research for Knowledge-Circulating Society, Kyoto, Japan, 17 January 2008; pp. 131–136. [Google Scholar]

**Figure 1.**High-resolution fingerprint image in PolyU HRF database [16]. Red and yellow circles respectively mark some of the open and closed pores.

**Figure 2.**Fluorescence fingerprint image (reprinted by permission from Macmillan Publishers Ltd.: Nature Communications [9], copyrights 2014).

**Figure 4.**Example of a generated polar histogram with three distance bins and eight angular bins: (

**a**) a circle including the center point and its adjacent points; (

**b**) the number of residing points in each bin and (

**c**) the generated polar histogram.

**Figure 6.**Experimental results of the global correspondences: (

**a**) with and (

**b**) without using the LMA refinement. $10\%$ of correspondences are randomly marked as green.

**Figure 7.**Pore extraction example: (

**a**) a fingerprint image of PolyU HRF database and (

**b**) the pore extraction result.

**Figure 8.**Experimental results of the proposed pore matching algorithm for genuine match: (

**a**) results of the pore extraction using the method described in [19]; (

**b**) the local correspondences; (

**c**) the global correspondences; (

**d**) results of the final matching and (

**e**) a superimposed image of two sweat pore fingerprints based on the final matching.

**Figure 9.**Experimental results of the proposed pore matching algorithm for genuine match: (

**a**) results of the pore extraction using the method described in [19]; (

**b**) the local correspondences; (

**c**) the global correspondences; (

**d**) results of the final matching and (

**e**) a superimposed image of two sweat pore fingerprints based on the final matching.

**Figure 10.**Experimental results of the proposed pore matching algorithm for genuine match: (

**a**) results of the pore extraction using the method described in [19]; (

**b**) the local correspondences; (

**c**) the global correspondences; (

**d**) results of the final matching and (

**e**) a superimposed image of two sweat pore fingerprints based on the final matching.

**Figure 11.**Experimental results of the proposed pore matching algorithm for imposter match: (

**a**) results of the pore extraction using the method described in [19]; (

**b**) the local correspondences; (

**c**) the global correspondences; (

**d**) results of the final matching and (

**e**) a superimposed image of two sweat pore fingerprints based on the final matching.

**Figure 12.**Experimental results of the proposed pore matching algorithm for imposter match: (

**a**) results of the pore extraction using the method described in [19]; (

**b**) the local correspondences; (

**c**) the global correspondences; (

**d**) results of the final matching and (

**e**) a superimposed image of two sweat pore fingerprints based on the final matching.

**Figure 14.**EER curves for the proposed method and PMPH with respect to two types of noise: (

**a**) the pore missing noise and (

**b**) the pore location noise.

**Figure 15.**Sweat pore matching on a fluorescence fingerprint image and a latent fingerprint image of the same donor: (

**a**) a fluorescence microscopic fingerprint image; (

**b**) a latent fingerprint image using Ninhydrin and (

**c**) the superimposed result of two fingerprints based on the final matching.

**Figure 16.**Sweat pore matching on a fluorescence fingerprint image and a latent fingerprint image of the same donor: (

**a**) a fluorescence microscopic fingerprint image; (

**b**) a latent fingerprint image using Ninhydrin, and (

**c**) the superimposed result of two fingerprints based on the final matching.

**Table 1.**The projective transformation matrix, its parameter vector, the Jacobian matrix of the algebraic distance with respect to the parameter, and the degree-of-freedom.

Name | Projective Transformation |
---|---|

Matrix (M) | $\left[\begin{array}{ccc}{m}_{00}& {m}_{01}& {m}_{02}\\ {m}_{10}& {m}_{11}& {m}_{12}\\ {m}_{20}& {m}_{21}& 1\end{array}\right]$ |

Parameter (m) | ${\left[\begin{array}{cccccccc}{m}_{00}& {m}_{01}& {m}_{02}& {m}_{10}& {m}_{11}& {m}_{12}& {m}_{20}& {m}_{21}\end{array}\right]}^{T}$ |

Jacobian (J) | $\frac{1}{{m}_{20}{x}_{r}+{m}_{21}{y}_{r}+1}\left[\begin{array}{cccccccc}{x}_{r}& {y}_{r}& 1& 0& 0& 0& -{x}_{r}{x}_{t}& -{y}_{r}{x}_{t}\\ 0& 0& 0& {x}_{r}& {y}_{r}& 1& -{x}_{r}{y}_{t}& -{y}_{r}{y}_{t}\end{array}\right]$ |

Degree-of-freedom | 8 |

Method | DPM | PMPH | Proposed |
---|---|---|---|

EER | $7.16\%$ | $8.08\%$ | $4.24\%$ |

FMR1000 | $12.44\%$ | $73.11\%$ | $16.44\%$ |

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**MDPI and ACS Style**

Kim, M.-j.; Kim, W.-Y.; Paik, J.
Optimum Geometric Transformation and Bipartite Graph-Based Approach to Sweat Pore Matching for Biometric Identification. *Symmetry* **2018**, *10*, 175.
https://doi.org/10.3390/sym10050175

**AMA Style**

Kim M-j, Kim W-Y, Paik J.
Optimum Geometric Transformation and Bipartite Graph-Based Approach to Sweat Pore Matching for Biometric Identification. *Symmetry*. 2018; 10(5):175.
https://doi.org/10.3390/sym10050175

**Chicago/Turabian Style**

Kim, Min-jae, Whoi-Yul Kim, and Joonki Paik.
2018. "Optimum Geometric Transformation and Bipartite Graph-Based Approach to Sweat Pore Matching for Biometric Identification" *Symmetry* 10, no. 5: 175.
https://doi.org/10.3390/sym10050175