# Binary Biometric Representation through Pairwise Adaptive Phase Quantization

- Chun Chen
^{1}Email author and - Raymond Veldhuis
^{1}

**2011**:543106

**DOI: **10.1155/2011/543106

© Chun Chen and Raymond Veldhuis. 2011

**Received: **18 October 2010

**Accepted: **24 January 2011

**Published: **20 February 2011

## Abstract

Extracting binary strings from real-valued biometric templates is a fundamental step in template compression and protection systems, such as fuzzy commitment, fuzzy extractor, secure sketch, and helper data systems. Quantization and coding is the straightforward way to extract binary representations from arbitrary real-valued biometric modalities. In this paper, we propose a pairwise adaptive phase quantization (APQ) method, together with a long-short (LS) pairing strategy, which aims to maximize the overall detection rate. Experimental results on the FVC2000 fingerprint and the FRGC face database show reasonably good verification performances.

## 1. Introduction

Extracting binary biometric strings is a fundamental step in template compression and protection [1]. It is well known that biometric information is unique, yet inevitably noisy, leading to intraclass variations. Therefore, the binary strings are desired not only to be discriminative, but also have to low intraclass variations. Such requirements translate to both low false acceptance rate (FAR) and low false rejection rate (FRR). Additionally, from the template protection perspective, we know that general biometric information is always public, thus any person has some knowledge of the distribution of biometric features. Furthermore, the biometric bits in the binary string should be independent and identically distributed (*i.i.d.*), in order to maximize the attacker's efforts in guessing the target template.

Several biometric template protection concepts have been published. Cancelable biometrics [2, 3] distort the image of a face or a fingerprint by using a one-way geometric distortion function. The fuzzy vault method [4, 5] is a cryptographic construction allowing to store a secret in a vault that can be locked using a possibly unordered set of features, for example, fingerprint minutiae. A third group of techniques, containing fuzzy commitment [6], fuzzy extractor [7], secure sketch [8], and helper data system [9–13], derive a binary string from a biometric measurement and store an irreversibly hashed version of the string with or without binding a crypto key. In this paper, we adopt the third group of techniques.

*i.i.d.*bits.

The categorized one-dimensional quantizers.

User independent | User specific |
---|---|

Linnartz and Tuyls [9] | Vielhauer et al. [14] |

Tuyls et al. [10] | Feng and Wah [15] |

Kevenaar et al. [11] | Chang et al. [16] |

Chen et al. [17] | |

Equal width | Equal probability |

Linnartz and Tuyls [9] | Tuyls et al. [10] |

Vielhauer et al. [14] | Kevenaar et al. [11] |

Feng and Wah [15] | Chen et al. [17] |

Chang et al. [16] |

Apart from the one-dimensional quantizer design, some papers focus on assigning a varying number of quantization bits to each feature. So far, several bit allocation principles have been proposed: fixed bit allocation (FBA) [10, 11, 17] simply assigns a fixed number of bits to each feature. On the contrary, the detection rate optimized bit allocation (DROBA) [19] and the area under the FRR curve optimized bit allocation (AUF-OBA) [20], assign a variable number of bits to each feature, according to the features' distinctiveness. Generally, AUF-OBA and DROBA outperform FBA.

Since the phase quantization has shown in [21] to yield a good performance, in this paper, we propose a user-specific adaptive phase quantizer (APQ). Furthermore, we introduce a Mahalanobis distance-based long-short (LS) pairing strategy that by good approximation maximizes the theoretical overall detection rate at zero Hamming distance threshold.

In Section 2 we introduce the adaptive phase quantizer (APQ), with simulations in a particular case with independent Gaussian densities. In Section 3 the long-short (LS) pairing strategy is introduced to compose pairwise features. In Section 4, we give some experimental results on the FVC2000 fingerprint database and the FRGC face database. In Section 5 the results are discussed and conclusions are drawn in Section 6.

## 2. Adaptive Phase Quantizer (APQ)

In this section, we first introduce the APQ. Afterwards, we discuss its performance in a particular case where the feature pairs have independent Gaussian densities.

### 2.1. Adaptive Phase Quantizer (APQ)

Essentially, APQ has both equal-width and equal-probability intervals, with rotation offset that maximizes the detection rate.

### 2.2. Simulations on Independent Gaussian Densities

## 3. Biometric Binary String Extraction

The APQ can be directly applied to two-dimensional features, such as Iris [22], while for arbitrary features, we have the freedom to pair the features. In this section, we first formulate the pairing problem, which in practice is difficult to solve. Therefore, we simplify this problem and then propose a long-short pairing strategy (LS) with low computational complexity.

### 3.1. Problem Formulation

The aim for extracting biometric binary string is for a genuine user who has features, we need to determine a strategy to pair these features into pairs, in such way that the entire -bit binary string ( ) obtains optimal classification performance, when every feature pair is quantized by a -bit APQ. Assuming that the feature pairs are statistically independent, we know from [19] that when applying a Hamming distance classifier, zero Hamming distance threshold gives a lower bound for both the detection rate and the FAR. Therefore, we decide to optimize this lower bound classification performance.

The detection rate given a feature pair is computed from (8). Considering that the performance at zero Hamming distance threshold indeed pinpoints the minimum FAR and detection rate value on the receiver operating characteristic curve (ROC), optimizing such point in (15) essentially provides a maximum lower bound for the ROC curve.

### 3.2. Long-Short Pairing

There are two problems in solving (15): first, it is often not possible to compute in (8), due to the difficulties in estimating the genuine user PDF . Additionally, even if the can be accurately estimated, a brute-force search would involve evaluations of the overall detection rate, which renders a brute-force search unfeasible for realistic values of . Therefore, we propose to simplify the problem definition in (15) as well as the optimization searching approach.

Simplified Problem Definition

with defined in (11). Furthermore, instead of brute force searching, we propose a simplified optimization searching approach: the long-short (LS) pairing strategy.

Long-Short (LS) Pairing

The computational complexity of the LS pairing is only . Additionally, it is applicable to arbitrary feature types and independent of the number of quantization bits . Note that this LS pairing is similar to the pairing strategy proposed in [21], where Euclidean distances are used. In fact, there are other alternative pairing strategies, for instance greedy or long-long pairing [21]. However, in terms of the entire binary string performance, these methods are not as good as the approach presented in this paper, especially when is large. Therefore, in this paper, we choose the long-short pairing strategy, providing a compromise between the classification performance and computational complexity.

## 4. Experiments

In this section we test the pairwise phase quantization (LS + APQ) on real data. First we present a simplified APQ, which is employed in all the experiments. Afterwards, we verify the relation between and for real data. We also show some examples of LS pairing results. Then we investigate the verification performances while varying the input feature dimensions ( ) and the number of quantization bits per feature pair ( ). The results are further compared to the one-dimensional fixed quantization (1D FQ) [17] as well as the the FQ in combined with the DROBA bit allocation principle (FQ + DROBA).

### 4.1. Experimental Setup

We tested the pairwise phase quantization on two real data sets: the FVC2000(DB2) fingerprint database [23] and the FRGC(version 1) face database [24].

(i)*FVC2000*: The FVC2000(DB2) fingerprint data set contains 8 images of 110 users. The features were extracted in a fingerprint recognition system that was used in [10]. As illustrated in Figure 8, the raw features contain two types of information: the squared directional field in both
and
directions and the Gabor response in 4 orientations (0,
,
,
). Determined by a regular grid of 16 by 16 points with spacing of 8 pixels, measurements are taken at 256 positions, leading to a total of 1536 elements.

(ii)*FRGC*: The FRGC(version 1) face data set contains 275 users with a different number of images per user, taken under both controlled and uncontrolled conditions. The number of samples
per user ranges from 4 to 36. The image size was
. From that a region of interest (ROI) with 8762 pixels was taken as illustrated in Figure 9.

A limitation of biometric compression or protection is that it is not possible to conduct the user-specific image alignment, because the image or other alignment information cannot be stored. Therefore, in this paper, we applied basic absolute alignment methods: the fingerprint images are aligned according to a standard core point position; the face images are aligned according to a set of four standard landmarks, that is, eyes, nose and mouth.

Our experiments involved three steps: training, enrollment, and verification. (1) In the training step, we first applied a combined PCA/LDA method [25] on a training set. The obtained transformation was then applied to both the enrollment and verification sets. We assume that the measurements have a Gaussian density, thus after the PCA transformation, the extracted features are assumed to be statistically independent. The goal of applying PCA/LDA in the training step is to extract independent features so that by pairing them we could subsequently obtain independent feature pairs, which meet our problem requirements. Note that for FVC2000, since we have only 80 users in the training set, applying LDA results in very limited number of features (e.g., ). Therefore, we relax the independency requirement for the genuine user by applying only the PCA transformation. (2) In the enrollment step, for every genuine user , the LS pairing was first applied, resulting in the user-specific pairing configuration . The pairwise features were further quantized through a -bit APQ with the adaptive angle , and assigned with a Gray code [26]. The concatenation of the codes from feature pairs formed the -bit target binary string . Both and the quantization information ( ) were stored for each genuine user. (3) In the verification step, the features of the query user were quantized and coded according to the quantization information ( ) of the claimed identity, leading to a query binary string . Finally, the decision was made by comparing the Hamming distance between the query and the target string.

### 4.2. Simplified APQ

### 4.3. APQ - Property

In this section we test the relation between the APQ detection rate and the pairwise feature's distance on both data sets. The goal is to see whether the real data exhibit the same property as we found with synthetic data in Section 2.2: the feature pairs with higher obtains higher detection rate .

### 4.4. LS Pairing Performance

### 4.5. Verification Performance

We test the performances of LS + APQ at various numbers of input features as well as various numbers of quantization bits . The performances are further compared with the one-dimensional fixed quantization (1D FQ) [17]. The EER results for FVC2000 and FRGC are shown in Table 3 and Figure 15.

In [19], it was shown that FQ in combination with the DROBA adaptive bit allocation principle (FQ + DROBA) provides considerably good performances. Therefore, we compare the LS + APQ with the FQ + DROBA. In order to compare both methods at the same - setting, for LS + APQ, we extract only features from the features, thus pairs from the LS pairing. Afterwards, we apply the 2-bit APQ for every feature pair (see Figure 3). In this case, . Table 6 shows the EER performances of LS + APQ and FQ + DROBA at several different - settings. Results show that LS + APQ obtains slightly better performances than FQ + DROBA.

## 5. Discussion

## 6. Conclusion

Extracting binary biometric strings is a fundamental step in biometric compression and template protection. Unlike many previous work which quantize features individually, in this paper, we propose a pairwise adaptive phase quantization (APQ), together with a long-short (LS) pairing strategy, which aims to maximize the overall detection rate. Experimental results on the FVC2000 and the FRGC database show reasonably good verification performances.

## Declarations

### Acknowledgment

This research is supported by the research program Sentinels (http://www.sentinels.nl/). Sentinels is being financed by Technology Foundation STW, the Netherlands Organization for Scientific Research (NWO), and the Dutch Ministry of Economic Affairs.

## Authors’ Affiliations

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