Abdelouahab Attia
email: attia.abdelouahab@gmail.com

Mourad Chaa

Zahid Akhtar

Youssef Chahir
email: youssef.chahir@unicaen.fr

Finger kunckcle patterns based person recognition via bank of multiscale binarized statistical texture features

Keywords: Biometric, Image local descriptor, BSIF, Dimensionality reduction, Classification

This paper proposes a novel finger knuckle patterns (FKP) based biometric recognition system that utilizes multi-scale bank of binarized statistical image features (B-BSIF) due to their improved expressive power. The proposed system learns a set of convolution filters to form different BSIF feature representations. Later, the learnt filters are applied on each FKP traits to determine the top performing BSIF features and respective filters are used to create a bank of features named B-BSIF. In particular, the presented framework, in the first step, extracts the region of interest (ROI) from FKP images. In the second step, the B-BSIF coding method is applied on ROIs to obtain enhanced multi-scale BSIF features characterized by top performing convolution filters. The extracted feature histograms are concatenated in the third step to produce a large feature vector. Then, a dimensionality reduction procedure, based on principal component analysis and linear discriminant analysis techniques (PCA + LDA), is carried out to attain compact feature representation. Finally, nearest neighbor classifier based on the cosine Mahalanobis distance is used to ascertain the identity of the person. Experiments with the publicly available PolyU FKP dataset show that the presented framework outperforms previously-proposed methods and is also able to attain very high accuracy both in identification and verification modes.

Introduction

In today's highly interconnected society, automated personal identification techniques have become vital of security systems, which require high classification schemes [START_REF] Angelov | Deep rule-based classifier with human-level performance and characteristics[END_REF][START_REF] Bao | Correntropy-based evolving fuzzy neural system[END_REF]). One such person recognition technique is biometrics, that is identifying a person based on their physiological and behavioral characteristics [START_REF] Adeoye | A survey of emerging biometric technologies[END_REF]. Biometrics have several advantages compared to conventional methods such as passwords or ID cards, e.g., it can be forgotten or lost [START_REF] Adeoye | A survey of emerging biometric technologies[END_REF][START_REF] Rani | Finger knuckle print recognition techniques-a survey[END_REF][START_REF] Akhtar | Secure learning algorithm for multimodal biometric systems against spoof attacks[END_REF]. In fact, many biometric traits have been proposed and widely being accpeted as well as used in diverse applications ranging from ranging from border crossing to mobile authentication (Zhang et al. 2018b;Akhtar et al. 2011). Recently, FKP characteristics is one of the hand based biometrics that is prominent emerging trait owing to advantages: (1) the acquisition of fingerknuckle surfaces is relatively easy with low cost and lowresolution simple cameras, (2) FKP based access systems can be used under various environmental conditions such as indoor and outdoor, (3) FKP features are stable and remain unchanged over time, i.e., FKP patterns are age-invariant, (4) FKP based biometric recognition systems are very reliable that gives high performances [START_REF] Rani | Finger knuckle print recognition techniques-a survey[END_REF].

In the literature, few methods for FKP based biometric recognition systems have been proposed. For instance, [START_REF] Zhang | Ensemble of local and global information for finger-knuckle-print recognition[END_REF] have presented an algorithm that integrated local orientations via ensemble of Gabor filters and global orientations via Fourier coefficients features for FKP person authentication. While, [START_REF] Zhang | Encoding local image patterns using Riesz transforms: With applications to palmprint and finger-knuckle-print recognition[END_REF] enhanced the FKP recognition accuracy using two Riesz-transformbased coding schemes (i.e., RCode1 and RCode2). [START_REF] Shariatmadar | Finger-knuckle-print recognition via encoding local-binary-pattern[END_REF] have proposed a FKP recognition scheme usable both in personal identification and verification modes. Specifically, the scheme divides the ROI of captured image into a set of blocks and Gabor filters are applied on each block, which is followed by binary patterns extraction as feature histograms. Lastly, Bio hashing method is employed for matching process between the template and query histograms. [START_REF] Zeinali | A novel method of applying directional filter bank (DFB) for finger-knuckle-print (FKP) recognition[END_REF] proposed to use Directional Filter Bank (DFB) feature extraction with dimensionality reduction by LDA method for FKP recognition. Authors in [START_REF] Shariatmadar | Finger-Knuckle-Print recognition performance improvement via multi-instance fusion at the score level[END_REF] devised a competent method based on multi-instance FKP fusion, which integrates the information from diverse fingers [i.e., he left index/middle fingers (LIF, LMF) and right index/ middle fingers (RIF, RMF)]. The information are fused at different level, i.e., feature-, matching scores-and decisionlevels. [START_REF] Nigam | Multiple texture information fusion for finger-knuckle-print authentication system[END_REF]) introduced a FKP based authentication system that depends on multiple textures with score level fusion. Firstly, FKP images are preprocessed by Gabor filters. Secondly, quality parameters are extracted to be later made use of in recognition procedure. Tao et al. [START_REF] Kong | A hierarchical classification method for finger knuckle print recognition[END_REF]) designed a hierarchical classification method for FKP recognition. The system consists of two stages. In the first stage, recognition is conducted using basic Gabor feature and a novel decision rule with the fixed threshold. Whereas, in the second stage, speeded-up robust feature is used only when the basic feature is not able to perform recognition successfully. In turn, Chaa et al. [START_REF] Chaa | Features-level fusion of reflectance and illumination images in finger-knuckle-print identification system[END_REF]) introduced a novel method that combines two types of the histograms of oriented gradients (HOG) extracted from reflectance and illumination FKP trait by Adaptive Single Scale Retinex (ASSR) algorithm. While, a novel reconstruction-based finger-knuckle-print (FKP) verification method to decrease the false rejections caused by finger pose variations in data capturing process is devised by Zhang et al. (2018a, b). Recently, [START_REF] Chlaoua | Deep learning for finger-knuckle-print identification system based on PCANet and SVM classifier[END_REF] have employed a simple deep learning method known as principal component analysis Network (PCANet). In the proposed model, PCA has been employed to learn two-stages of filter banks then a simple binary hashing and block histograms for clustering of feature vectors are used. The resultant features are finally fed to classification step, i.e., linear multiclass Support Vector Machine (SVM). The authors also studied a multimodal biometric system based on matching score level fusion. [START_REF] Zhai | A novel finger-knuckle-print recognition based on batch-normalized CNN[END_REF] designed a FKP recognition system using batch normalized convolution neural network with random histogram equalization as data augmentation scheme.

All in all, despite FKP being easy to use trait for person recognition, comparatively very limited researches have been conducted on FKP biometrics. Moreover, majority of existing FKP methods are not able to attain very high accuracy due to use of features that have lower power of discrimination. Similarly, they are very sensitive to image orientations and scales. Therefore, in this paper, we propose an automated method for finger knuckle pattern recognition that can attain excellent accuracy. The presented framework extracts ROIs from the capture finger knuckle images, which is followed by application of BSIF image descriptor on each ROI. BSIF is very robust to rotation and illumination variations. Then, the best features (corresponding to BSIF convolution filters) that achieve higher performances are selected to construct a bank of BSIF image representations. Next, a PCA + LDA based dimensionality reduction scheme is employed to obtain compact representation of the FKP trait. Lastly, nearest neighbor classifier is utilized to authenticate the user.

The remainder of this paper is organized as follows: In Sect. 2, the proposed system is described including feature extraction and matching process used in the system. Experimental protocol, dataset, and figures of merit are presented, and experimental results are given in Sect. 3. Finally, the conclusion and further works are drawn in Sect. 4.

Proposed FKP biometric system

Figure 1 depicts the schematic diagram of the proposed finger knuckle pattern (FKP) based person recognition system. The framework consists of two phases: enrollment and identification. During enrollment phase, each user presents their finger knuckle to the sensor. The FKP image of the user is captured and processed to produce regions of interest described in Sect. 2.1. Then, the features are extracted using B-BSIF method, which is detailed in Sect. 2.2. The top performing extracted features from ROI are concatenated to form raw histogram (long feature vector) on which a PCA + LDA dimensionality reduction technique discussed in Sect. 2.3 is applied to obtain concise feature representation. The compact feature representation is stored in the database as template. All templates of enrolled users are used as training data for decision making classifier explained in Sect. 2.4. During verification phase, the captured FKP image from the user undergoes the above-mentioned process, and this time the extracted features are fed to the decision-making classifier to determine the identity of the person.

Extractionof the region of interest (ROI)

The procedure of extrcating the region of interest from FKP images are similar to the method presented in [START_REF] Zhang | Online finger-knuckleprint verification for personal authentication[END_REF].The ROI extraction technique is composed of four steps, which are explanied as follows:

Step 1: A Gaussian smoothing process is applied on the original FKP image, which is then down-sampled as the smoothed image to150 dpi (Dots Per Inch).

Step 2: The X-axis of the coordinate system is fixed so that the bottom boundary of the finger can be easily extracted. The bottom boundary of the finger is determined by a canny edge detector.

Step 3: The Y-axis of the coordinate system is determined by applying a Canny edge detector on the cropped sub-image extracted from the original FKP image based on X-axis. This process helps finding the convex direction coding scheme.

Step 4: The ROI regions indicated by the rectangle are extracted.

Figure 2 illustrates the global steps the of ROI extraction.

Binarized statistical image features extraction

Binarized Statistical Image Features (BSIF) is a local image descriptor constructed by binarizing the responses to linear filters (Kannala and Rahtu 2012). BSIF learns a set of convolution filters from natural images using ICA (Independent Component Analysis) based on unsupervised scheme. These learned filters are used to represent each pixel of the capture FKP image as a binary string by computing its response to learned convolution filters. The binary string for each pixel can be considered as a local descriptor of the image intensity pattern in the neighborhood of that pixel. Finally, the histogram of the pixels binary string values allows one to characterize the texture properties within the image sub-regions.

In this paper, we have used the open-source filters (Kannala and Rahtu 2012), which were trained using 50,000 image patches randomly sampled from 13 different natural scenic images. Three main steps build the BSIF filters: mean subtraction of each patches, dimensionality reduction using PCA (Principle Component Analysis), and estimation of statistically independent filters (or basis) using ICA. Give a FKP image sample I of size n × m and a filter F i of same size, filter response is attained as follows (Kannala and Rahtu 2012):

where F i stands for the convolution filters i = {1, 2, … , m} that represent statistically independent filters whose responses can be calculated simultaneously and then binarized in order to obtain the binary string as follow(Kannala and Rahtu 2012):

Finally, the BSIF features are obtained as a histogram of pixel's binary codes that can efficiently describe the texture components of the FKP image. There are two essential factors into BSIF descriptor explicitly: the filter sizeand the length of the filter (i). Single filters with a fixed length may not be capable of generalizing well the finger knuckle patterns with varying intensities, scale and orientations. Therefore, we propose to utilize high performing multiple filters (1) with different scales in order to capture eminent features, thus the name bank of binarized statistical image features (B-BSIF), which are further detailed in experimental section. Figure 3 shows an example of an FKP image and the BSIF filters processing. Figure 3a presents the input ROI FKP image. Figure 3b illustrates the learned BSIF filter with a size 11 × 11 and of length 12 bits. While, Fig. 3c depicts the results of the individual convolution of the ROI FKP image with respective BSIF filters. Figure 3d presents the final BSIF encoded feature/image.

r i = ∑ n,m I(n, m)F i (n, m) (2) b i = 1 if r i > 0 0 otherwise

Dimensionality reduction

The histograms extracted from the encoded FKP image using B-BSIF descriptor are merged into one big feature vector. These vectors are big with high dimensions. Thus, it becomes difficult to process and evaluate them. Therefore, we perform dimensionality reduction before matching. The Principal Component Analysis (PCA) is a widely and simple method for dimensionality reduction, but in PCA separability between classes is ignored [START_REF] Turk | Eigenfaces for recognition[END_REF]. To avoide PCA's issue and to achieve more improved separability of feature subspace, Linear Discriminative Analaysis (LDA) [START_REF] Belhumeur | Eigenfaces vs. fisherfaces: recognition using class specific linear projection[END_REF]) may be deployed that may lead to attractive performances for recognition tasks. Though LDA still assumes a common covariance matrix among the classes that violates the normality principle. To supress these limitations of PCA and LDA and utilizing their strengths, in this paper, PCA + LDA has been adopted, where PCA algorithm is applied to reduce the dimensionality of large features while LDA algorithm is applied on PCA weights to increase the separability between the classes.

Matching module and normalization score

In the matching module of the proposed system, the Nearest Neighbor Classifier that uses the cosine Mahalanobis distance has been used.The criterion for similarity or dissimilarity is to minimize the distance (score) between the input query sample and the stored template. Assume that two vectors Vi and Vj stands for the feature vectors of query and template in the database images, respectively. Then the distance between V i and Vj is calculated by the following equation:

where C refers to the covariance matrix. Prior to finding the decision, a method named Min-Maxnormalization scheme is employed to transform the matching score into [0 1]. Given a set of matching scores X k , where K = 1, 2, … , n.The nor- malization scores are given as:

where X ′ K represents the normalized scores. The final decision is made using normalized score.

Experiments

In this section, we present an experimental evaluation of the proposed FKP person authentication system based on Bank BSIF descriptor.

(3)

d Ma V i , V j = V i -V j T C -1 V i -V j (4) X � K = X K -min max -min

Database

The proposed system has been tested on the publicly available FKP dataset that provided by Hong Kong Polytechnic University (PolyU) (PolyU 2010). This database has 7920 images collected from 165 persons with 125 males and 40 females, their age is in the range of years old. The images were captured in two sessions, with 48 different FKP images ofeach individual. Four finger types of every person have been collected that are: left index (LIF), left middle (LMF), right index (RIF) and right middle (RMF). Every finger type has 6 images in each session. There are total 1980 number of images for each finger type.

Experimental protocol

The evaluation of biometric recognition systems can be done in two modes: identification and verification. For the identification mode, the results have been presented in the form of the recognition rate. Rank-1 that is given by: where N i denotes the number of images successfully assigned to the right identity and N stands for the overall number of images attempts to be identified. The cumulative match curves (CMC) is used in closed-set identification task. The CMC present the accuracy performance of a biometric system and shows how frequently the individual's template appears in the ranks based on the match rates [START_REF] Jain | Bsif: binarized statistical image features[END_REF]). Thus, we have also adopted CMC curve in the experimental results. For the verification mode, we present the results in the form of the error equal rate (EER), when FAR (false accept rate) equal FRR (false reject rate). Moreover, to visually depict the performance of the biometric system, Receiver Operating Characteristics (ROC) curves have also been reported. A ROC curve explains how the FAR values are changed compared to the values of the Genuine Acceptance Rate (GAR) values.In addition in the mode of verification the measures VR@1%FAR (i.e., verification rate at operating point of 1% FAR), VR@0.1%FAR and VR@0.01%FAR have been used. Namely, VR@0.1% FAR refers to the verification rate that is equivalent to 1% FRR, is calculated for a FAR equal to 0.1%. This operating point is widely adopted in the biometric research community specially when the number of comparisons for "inter-class" tests (or "imposter tests") is more than 1000. The verification rate is significant for studying the behavior of systems with low FAR using a large database or for simulating large scale application in order to improve system's security and performance.

(5)

Rank -1 = N i N × 100(% )

Experiment results

Here, we report three different experiments: Experiment I-construction of bank of BSIF filters, Experiment IIcomparaisons between BSIF and B-BSIF and with the existing FKP recognition systems, and Experiment IIImultibiometric FKP recognition system.

Experiment I: construction of bank of BSIF filters

The goal of this experiment is to construct a bank of filters BSIF. For comprehensive analysis, each individual BSIF filter with different parameter combination is applied on each individual FKP modality (LIF, LMF, RIF and RMF) in order to select the best BSIF parameters and respective filters. Since, the filter parameters (filter size (k) and filter length (n)) have a great influence on the performance of the proposed system, several sub-experiments were performed in both FKP identification and verification modes.

The results are reported in Table 1. In Table 1, it is easy to see that the performance increases with the increase of the length (n) of the BSIF descriptor. The parameters (k, n) combinations that achieve high ranking performance on single modality has been selected and used to build the bank of BSIF (B-BSIF). These parameters are presented in Table 2, which are at this stage been fixed and used as estimated parameters for subsequent experiments. The model of the B-BSIF descriptor is illustrated in Fig. 4. As can be notice, the bank is composed of different BSIF descriptor sizes, which are (17 × 17), (15 × 15), (13 × 13), (11 × 11), (9 × 9) and (7 × 7) with the length of 12 bits. This bank of filters is applied to the each input FKP trait, as Fig. 4 also representates an example of using B-BSIF.

Experiment II: comparisons between BSIF and B-BSIF and with the existing FKP recognition systems

Here, we present two sets of experiments. First, experimental analysis to show efficacy of B-BSIF in comparsion with BSIF image texture descriptors for FKP based person recognition. The second experimentsproviding a comparison of the proposed system with prior works in the literatures. In this sets of experiments, the best BSIF parameters estimated in experiment I is utilized to built B-BSIF descriptor. The results of BSIF and B-BSIF on individual FKP traits are presented in Table 3. We can observe in Tables 1 and3 that B-BSIF performs better than BSIF. The proposed method using B-BSIF achieves higher accuracy on the LMF,RMF,and LIF, modalities, e.g., on RMF modality the system achieved EER = 0.03% and Rank-1 accuracy = 99.70% in verification and identification modes, respectively. The BSIF and B-BSIF comparsion results are also presented in term of CMC and ROC curves, which can be seen in Figs. 5,6,7,8. These graphs also reports comparison study between the (BSIF + PCA + LDA) and the proposed method (B-BSIF + PCA + LDA) using FKP modality. The results clearly show that the performance is higher when the system uses the features of the B-BSIF descriptor.

To further demonstrate the efficacy of the proposed system, the comparison of the proposed system with prior works in the literatures on individual FKP modalities is given in Table 4. The proposed scheme outperforms the existing FKP person recognition system. For instance, the proposed method on RMF modality is able to attain 99.70% and 0.03% accuracy and error rate in identification and verification scenario, respectively. While, FKP based person recognition systems proposed in [START_REF] Shariatmadar | Finger-knuckle-print recognition via encoding local-binary-pattern[END_REF] achieved 96.72% and 0.354% accuracy and error rate in identification and verification scenario, respectively.

Experiment III: Multibiometric FKP recognition system

The aim of this experiment is to study performance of the system in the case of information fusion, since multimodal systems fusing information from different sources are able to alleviate limitations (e.g., accuracy, noise, etc.) of the unimodal biometric systems. Thus, we studied different scenarios when the information presented by different finger The information were fused at score level using sum and min fusion rules. Four distinct experimental investigation were conducted by fusing only two types of fingers (Table 5), three types fingers (Table 6), all types of fingers (Table 7) and comparsion with existing FKP multimodal methods (Table 8). In Tables 5, 6 and 7, we can see that the multimodal FKP systems that fuse information from more than one source improves the accuracy of unimodal systems. For example, using only LIF modality features for person authentication (Table 4) resulted into 0.11% (EER) and 99.70% (rank-1 accuracy), while sum fusion of LIF and RMF (Table 5) yielded 0.00% (EER) and 100% (rank-1 accuracy). The comparison of proposed multimodal system with existing systems in the literature is presented in Table 8. We can notice in Table 8 that the proposed system under verification mode attained lowest EER% compared to EER%by systems in [START_REF] Shariatmadar | Finger-Knuckle-Print recognition performance improvement via multi-instance fusion at the score level[END_REF] and [START_REF] Morales | Improved finger-knuckle-print authentication based on orientation enhancement[END_REF]. In identification mode, the proposed system achieved highest recognition rate compared to schemes designed in [START_REF] Shariatmadar | Finger-knuckle-print recognition via encoding local-binary-pattern[END_REF] and [START_REF] Zeinali | A novel method of applying directional filter bank (DFB) for finger-knuckle-print (FKP) recognition[END_REF].

Conclusion

This paper presents a new method for recognizing individuals based on their finger knuckle patterns (FKP). Specifically, the proposed method uses bank of mutli-scale show that use of multiple finger types (i.e., multimodal system) improved the performance of systems using only single finger FKP information. In the future, to improve the security and robustness of the system against spoofing we aim to fuse FKP modality with other modalities (e.g., iris or voice) on mobile devices.

Fig. 1

 1 Fig. 1 Proposed framework for person recognition using FKP (finger knuckle print)

Fig. 3 a

 3 Fig. 3 a Sample of the FKP ROI image b BSIF filter with a size 11 × 11 and of length 12 c BSIF features d final BSIF

Fig. 4

 4 Fig. 4 The model of the B-BSIF descriptor: a the input ROI FKP trait, b the results of applying the different BSIF descriptor (BSIF code images), and c the histograms of the BSIF code images

Fig. 5

 5 Fig. 5 Comparison between BSIFand B-BSIF features for LMF modality a CMC curves b ROC curves

Fig. 6 Fig. 7 Fig. 8

 678 Fig. 6 Comparison between BSIF and B-BSIF features for LIF modality a CMC curves b ROC curves

Table 1

 1 The all parameters BSIF applied on the single finger

	Parameters		LMF		LIF		RIF		RMF
	k	n	Rank-1 (%)	EER (%)	Rank-1 (%)	EER (%)	Rank-1 (%)	EER (%)	Rank-1 (%)	EER (%)
	17 × 17	12	98.08	0.30	97.88	0.30	96.57	0.51	98.08	0.20
	17 × 17	11	95.56	0.89	95.66	0.91	95.05	0.91	95.96	0.51
	17 × 17	10	87.98	2.02	87.68	2.22	87.27	3.03	89.60	2.21
	17 × 17	9	83.54	2.93	83.94	3.23	81.11	4.76	84.04	3.64
	17 × 17	8	79.49	4.27	81.41	4.04	77.27	5.13	77.88	5.13
	15 × 15	12	98.28	0.22	98.38	0.30	97.58	0.61	98.89	0.10
	15 × 15	11	96.36	0.81	96.97	0.59	95.35	0.79	96.57	0.38
	15 × 15	10	89.80	2.02	89.29	2.02	88.79	2.22	89.70	1.54
	15 × 15	9	84.65	3.12	81.72	3.13	81.62	4.14	85.15	2.53
	15 × 15	8	80.81	3.74	81.82	4.15	82.12	3.52	80.81	3.64
	13 × 13	12	98.08	0.20	98.48	0.30	97.27	0.40	98.59	0.20
	13 × 13	11	96.46	0.41	97.07	0.51	96.16	0.61	97.37	0.51
	13 × 13	10	91.62	1.21	90.61	1.62	87.88	2.41	90.40	2.12
	13 × 13	9	84.95	2.44	86.16	2.52	84.14	3.84	85.45	2.83
	13 × 13	8	82.63	3.85	83.94	3.13	82.93	3.54	84.14	3.44
	11 × 11	12	98.79	0.20	98.89	0.20	97.68	0.40	98.89	0.10
	11 × 11	11	96.46	0.30	97.37	0.40	96.06	0.81	97.17	0.30
	11 × 11	10	90.51	1.92	91.52	1.72	87.68	2.42	92.53	1.62
	11 × 11	9	85.96	2.63	86.97	2.83	83.74	3.94	86.06	2.92
	11 × 11	8	85.35	2.93	85.45	2.91	83.84	3.33	88.79	2.31
	9 × 9	12	98.48	0.30	98.89	0.18	97.68	0.40	98.79	0.40
	9 × 9	11	96.97	0.69	97.68	0.38	94.44	0.99	97.07	0.51
	9 × 9	10	89.70	1.70	87.58	1.92	86.06	2.85	89.49	1.92
	9 × 9	9	85.76	2.22	85.66	2.10	81.72	3.94	87.98	2.61
	9 × 9	8	86.26	3.02	87.78	2.51	83.33	3.85	88.38	2.53
	7 × 7	12	96.46	0.51	97.37	0.38	95.86	0.62	97.17	0.61
	7 × 7	11	94.85	0.81	96.16	0.71	92.93	1.01	95.15	1.01
	7 × 7	10	84.14	3.34	83.13	2.83	80.91	3.33	84.14	84.14
	7 × 7	9	81.82	3.93	77.37	4.05	78.08	4.75	79.60	4.34
	7 × 7	8	85.25	3.33	81.21	3.52	79.19	3.94	84.95	3.74
	5 × 5	12	88.18	2.32	89.39	1.41	87.47	2.63	89.90	1.90
	5 × 5	11	82.12	3.21	80.81	3.23	80.30	3.45	83.94	3.33
	5 × 5	10	58.69	8.48	57.17	8.44	59.29	8.38	64.24	7.78
	5 × 5	9	60.91	8.92	55.35	8.36	58.79	9.07	60.51	8.49
	5 × 5	8	69.09	7.27	65.86	7.07	66.57	7.98	67.78	6.66
	Table 2 The best BSIF parameters of the bank BSIF	Parameters
				k	n
				17 × 17	12
				15 × 15	12
				13 × 13	12
				11 × 11	12
				9 × 9	12
				7 × 7

Table 3

 3 The results B-BSIF on

	single modalities	Modality	Identification	Verification
			Rank-1 (%)	EER (%)	VR@1%FAR (%)	VR@0.1%FAR	VR@0.01%FAR
						(%)	(%)
		LMF	99.70	0.10	100.00	99.90	99.19
		LIF	99.70	0.11	99.90	99.80	99.29
		RIF	98.69	0.40	99.80	99.29	98.18
		RMF	99.70	0.03	100.00	100.00	99.49

Table 4

 4 statistical image features (B-BSIF). The system first extracts features using different best performing convolution filters to encode FKP trait. Then, histograms extracted from the encoded FKP images are concatenated into a big feature vector. A PCA + LDA technique is used to reduce the dimensionality of the feature vector. Finally, the nearest neighbor classifier, based on cosine Mahalanobis distance is used to recognition the user. The experimental results on a publicly available FKP PolyU database shows not only that the FKP modality is quite useful in biometric systems, presented B-BSIF scheme is very powerful and effective in FKP recognition but also the proposed mechanism outperform other existing state-ofthe-art techniques. Furthermore, reported experiments also

	Comparative of proposed personal recognition	Identification (rank-1)
	method with the existing	Reference			Year	LMF (%)		LIF (%)	RIF (%)	RMF (%)
	approaches for FKP using PolyU dataset	El-Tarhouni et al. (2014)		2014	94.70		93.80	92.20	94.80
			Shariatmadar and Faez (2013)	2013	95.54		94.33	95.93	96.72
			Zeinali et al. (2014)		2014	90.30		88.68	89.79	89.79
			Our paper			-	99.70		99.70	98.69	99.70
			Verification (EER)
			Kong et al. (2014)		2014	0.15		0.26	0.20	0.24
			Shariatmadar and Faez (2013)	2013	0.384		0.54	0.781	0.354
			Shariatmadar and Faez (2014)	2014	0.29		0.267	0.284	0.25
			Nigam et al. (2016)		2016	1.009		1.077	0.740	1.0615
			Morales et al. (2011)		2011	0.43		1.02	0.95	0.91
			Our paper			-	0.10		0.11	0.40	0.03
	Table 5 EER/ROR (%) obtained by the fusion of two types of fingers
	EER/ROR (%) Auth/	Fusion of two types of fingers
	Ident	LIF-LMF			LMF-RMF			LMF-RIF
		EER (%)	ROR (%)	EER (%)	ROR (%)		EER (%)	ROR (%)
	Sum rule	0.00	100.00		0.00		99.90		0.08	99.90
	Min rule	0.02	99.90		0.09		99.90		0.10	99.90
	EER/ROR (%) Auth/	RIF-RMF			LIF-RIF			RMF-LIF
	Ident	EER (%)	ROR (%)	EER (%)	ROR (%)		EER (%)	ROR (%)
	Sum rule	0.09	99.80		0.00		100.00		0.00	100.00
	Min rule	0.10	99.80		0.00		100.00		0.00	100.00
	Table 6 EER/ROR (%) obtained by the fusion of three types of fingers	EER/ROR (%) Auth/ Ident	Fusion of three types of fingers LMF-LIF-RIF LMF-LIF-RMF	RMF-RIF-LMF	RMF-RIF-LIF
				EER (%) ROR (%) EER (%) ROR (%) EER (%) ROR (%) EER (%) ROR (%)
			Sum rule	0.00	100.00	0.00	100.00	0.01	99.90	0.00	100.00
			Min rule	0.00	100.00	0.00	100.00	0.10	99.90	0.00	100.00
						Table 7 EER/ROR (%) obtained by the fusion of all fingers
						EER/ROR (%) Auth/Ident	All fingers
									EER (%)	ROR (%)
						Sum rule			0.00	100.00
						Min rule			0.00	100.00

binarized


Jihong Lee
email: jihong@cnu.ac.kr1

Jo Kyounghwan

Choulsoo Jang
email: jangcs@etri.re.kr

Cooperative Localization for Multi-Robot Incorporat ing Proprioceptive/Exteroceptive Position Sensors 1

. In addition, we present a practical solution to accumulated position error in traveling long distance.

Introduction

Mobile robots require capability to estimate their position in order to navi gate autonomously in their work space. Consequently, localization by sen sor-based method has been researched as one of the most essential prob lems in mobile robotics. In previous researches, a number of works on lo calization of single robot have been reported [START_REF] Gourley | Sensor based obstacle avoidance and mapping for fast mobile robots[END_REF][START_REF] Borenstein | Measurement and correction of systematic odometry errors in mobile robots[END_REF]. However recently, many robotic applications require that robots work in collaboration in common workspace to perform a task. In such tasks as multiple robots op erate in close, we need more precise absolute localization or relative local ization of multiple robots in order to avoid collisions with each other. The multiple robot system, in comparison with the single robot system, has the advantages of collecting and integrating multiple sensor data from dif ferent robots. Accordingly, the system can obtain better localization per formance and increase the robustness of the localization accuracy for each robot by fusing collected multiple sensor data. In addition, if each robot is equipped with heterogeneous sensor, the system can improve the overall localization accuracy. Despite of above-mentioned advantages, most existing localization re searches for multiple robots have not utilized such advantages [START_REF] Ferrari | Multirobot motion coordination in space and time[END_REF][START_REF] Borenstein | Gyrodometer: A New Method for Combining Data from Gyros and Odometry in Mobile Robots[END_REF]. Even in multiple robot systems each robot estimates its position by its own sen sor data. Recently, some research works start to focus on integrating the sensor data from multiple sources in order to remove the uncertainty of the absolute or relative position of mobile robot. Most of research commonly used meth ods include triangulation [START_REF] Rekleitis | Experiments in free space triangulation using cooperative localization[END_REF], Kalman filter [START_REF] Roumeliotis | Collective localization: a distributed Kalman filter approach to localization of groups of mobile robots[END_REF], and MCL (Monte Carlo Localization) [START_REF] Liu | Monte calro multi-robot localization based on grid cells and characteristic particles[END_REF]. These approaches have improved position accuracy as contrast with the methods utilizing information from single robot. On the other hand, these approaches are relatively complex because they deal with statistic parameters. In addition, they are usually applicable to robots in in door.

In our previous research, we presented an approach for cooperative multi ple robot localization utilizing correlation between GPS errors of robots [START_REF] Lee | Cooperative Multi-Robot Localization using Differential Position Data[END_REF]. The proposed method was relatively simple compared with previously methods (include triangulation, Kalman filter, and MCL) and provided bet ter localization accuracy compared with relying on the resource of each ro bot. In this paper, we propose a practical solution to accumulated position error of cooperative multiple robot localization in traveling long distance. We define two operational parameters. One is the ratio of standard deviation between proprioceptive and exteroceptive position sensors. The other is a refresh interval to replace accumulated DR data with GPS data providing fixed standard deviation of position error. Determining the two operational parameters, we can improve the cooperative localization accuracy of mul tiple robots.

Cooperative Localization

Assumptions

In order to deal with localization problem for multiple robots, we assume the followings: 1) Each robot has GPS receiver, odometer, and gyro sensor in order to lo calize absolute position and relative position by model-based deadreckoning.

2) The closer robots have the stronger correlation between GPS data er rors. 3) All robots are equipped with communication devices that allow other robots or remote control station to receive position data measured from each robot.

Cooperative Localization Algorithm

Based on above-mentioned assumptions, we describe mathematical details of the proposed cooperative localization algorithm with the nomenclature shown in Table 1.

t e V P P i i k i k i δ ) ( ˆ1 1 1 + + + + + = (1) for k = 1,…,m. And GPS data k i P 1 ~+ are sampled at time i+1.
Then, the key idea of proposed cooperative localization algorithm is described as follows:

∑ = + + + + ∆ - = m j k i kj i k i k i P W P P 1 1 1 1 1 ) ( ~(2) k i kj i kj i L l W 1 1 1 ) 1 /( 1 + + + + = (3)
∑ = + + + = m j kj i k i l L 1 1 1 ) 1 /( 1 (4) | | 1 1 1 j i k i kj i P P l + + + - = (5) k i k i k i P P P 1 1 1 ˆ+ + + - = ∆ (6) for k = 1,…,m.
The main idea is motivated from the concept of DGPS which compensates error by comparing true data and noisy sensed data. In this approach we adopt the quasi true value as

k i L 1 + , include ) 1 /( 1 1 + + kj i l term.
When compensate GPS errors, we fuse the compensation quantity according to the distance between the robots,

) 1 /( 1 1 + + kj i l
. Note that the closer robots contribute more than the farther robots in the fusion.

Refresh Interval

Most mobile robot applications employ two basic position estimation methods: absolute/relative positioning or proprioceptive/exteroceptive position. Absolute positioning methods usually rely on landmark, map matching, satellite-based GPS data, or navigation beacons. In this paper, we assume that robots can receive the GPS data for absolute positioning, but it doesn't care the other proprioceptive sensors. Relative positioning method is usually Dead Reckoning (DR) based on odometer and gyro. Odometer and gyro are inexpensive, simple, and easy to accomplish in real time. On the other hand, odometer has its unbounded accumulation of errors, and also gyro has relatively large drift rates which cause unbounded growth in orientation errors. Therefore, it is necessary to update absolute position periodically in order to reduce potential for unbounded growth of errors. In proposed method, we have found the proper period called refresh interval to update GPS position data. The localization performance of the proposed method can be improved by replacing

Simulation Results

In this section, we simulate the proposed cooperative localization algorithm according to the virtual position. The traveling space for multiple robots is a square 40 meter on a side. We limited the maximum gap between robots to 1 meter in order to avoid collisions between the robots. The robots for simulation were assumed to cylindrical shape with a radius of 50 centimeter. The maximum velocity of robots limits 1 meter per second. There are 10 mobile robots traveling randomly on a 2D-flat platform.

We compare the proposed cooperative localization (CL) method for multiple robots with the single robot localization (SL) method by fusing dead reckoning data and the GPS data relying on the resource of each robot. In addition, we present examples to prevent position data estimated by proposed method from accumulating errors.

Virtual Position Error

In order to simulate the proposed cooperative localization method, it is necessary to construct simulation environment of a piece assumptions mentioned in section 2. We have to make two kinds of errors. One is the GPS errors of all robots respectively according to probability distribution of proper standard deviation. The other is the model errors of all robots generated by cause such as slip between the wheels of robot and the ground. First, we assume that the GPS data of individual robot are correlated strongly as the distance between robots are close. In other words, we as sume that the GPS data error of individual is correlated linearly as the dis tance between robots. It is described how to make GPS data error in previ ous research [START_REF] Lee | Cooperative Multi-Robot Localization using Differential Position Data[END_REF]. Seconds, we assume that robot model error is generated as maximum 0.1m and minimum 0m per 1m in traveling distance. It means that the model er rors between 0 and 0.1m are the same probability. It is possible to calculate standard deviation from continuous probability distribution. The calculated standard deviation is about 0.02887m per 1 second. In this paper, we simu late the cooperative localization method using this standard deviation value for model error.

The Ratio of Standard Deviation between Sensors

In previous case studies [START_REF] Lee | Cooperative Multi-Robot Localization using Differential Position Data[END_REF], we have found that the proposed method is valid in the proper ratio. The valid ratio ranges of standard deviation be tween the DR error and GPS error per unit time are about 1:2 ~ 1:5 in Fig. 1. In this case, there are robots' operating time of 300 seconds and com pensating period of 100 second. Fig. 2 and Fig. 4 show the real trajectory and position errors for robot 6 during 300s respectively. Fig. 3 shows the comparison of the accumulated distance errors for 10 robots obtained by three different localization methods. From the results of this case, we know that it doesn't suitable for most robots to replace accumulated DR data with simultaneous GPS data per 100 Seconds. In this case, there are robots' operating time of 300 seconds and refresh in terval of 50 second. Fig. 5 and Fig. 7 show the real trajectory and position errors for robot 9 respectively. Fig. 6 shows the comparison of the accu mulated distance errors for 10 robots obtained by three different localiza tion methods. From the results of this case, we present the effect of replac ing DR data accumulated with simultaneous GPS data per 50 Seconds. In this case, refresh interval is 10 second. Fig. 8 and Fig. 10 show the real trajectory and position errors for robot 3 during 300s respectively. Fig. 9 shows the accumulated distance errors for 10 robots. In this case, Fig. 9 shows that the errors of all robots aren't reduced. In this case, refresh interval of 50 seconds is more suitable than that of 10 seconds. As a result, we know that proposed method was able to improve localization accuracy in proper refresh interval (about 30s ~ 80s).

Conclusion and the Future Study

In this paper, the proposed method is motivated from the concept of DGPS which utilizes correlation between errors in common mode, and summarized in simple mathematical formula compared with existing methods. Simulation results show that the proposed method can achieve better localization performance in such cases as replacing the accumulated DR data with the GPS data providing fixed standard deviation for position error by proper refresh interval. In the future study, we will apply proposed cooperative localization algorithm to real multiple robot system.

PVWlL

  Position of kth robot estimated by cooperative localization algorithm at time i k i P ˆPosition of kth robot estimated by robot model at time i k i P ~Position of kth robot estimated by GPS data at time i i True velocity of robot between of time i-1 and time i i e Velocity error caused by slip between robot wheels and ground between of time i-1 and time i t δ Sampling period kj i Weight factor for compensation between kth robot and jth robots at time i k i P ∆ GPS data error of kth robot estimated by difference between GPS data and robot model at time i kj i Differential position data between kth robot and jth robot at time i k iParameter determined from total distance between robots at time i If m robots work in common space, the position of kth robot estimated by robot model at time i+1 as:

P 1 +

 1 ˆ and noisy data as k i P ~. And we find the cases where our algorithm can be applied in view point of statistic parameters of the sensors. Both the weight term, kj i W , and the reciprocal term of total distance between robots,

P

  ˆ are bigger than errors of the k i P 3

Fig. 1 .

 1 Fig.1. the localization performance of proposed method according to the standard deviation of GPS when the standard deviation of DR is 0.02887m. The range below dot is valid.

Fig. 2 .

 2 Fig. 2. Trajectory of a robot 10 in case 1.

Fig. 3 .Fig. 4 .

 34 Fig. 3. Accumulated position errors of 10 robots in case 1.

Fig. 5 .

 5 Fig. 5. Trajectory of a robot 5 in case 2.

Fig. 6 .Fig. 7 .

 67 Fig. 6. Accumulated position errors of 10 robots in case 2.

Fig. 8 .

 8 Fig. 8. Trajectory of a robot 5 in case 3.

Fig. 9 .Fig. 10 .

 910 Fig. 9. Accumulated position errors of 10 robots in case 3.

Table 1 .

 1 Nomenclature for Cooperative Localization Algorithm

	Symbol	Description

1This work was partly supported by the IT R&D program of MIC/IITA [2005-S-033-03, Embedded Component Technology and Standardization for URC]