Fingerprint image enhancement and reconstruction using the orientation and phase reconstruction

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Information Sciences 530 (2020) 201–218

Contents lists available at ScienceDirect

Information Sciences journal homepage: www.elsevier.com/locate/ins

Fingerprint image enhancement and reconstruction using the orientation and phase reconstruction Rashmi Gupta a, Manju Khari a, Deepti Gupta a, Rubén González Crespo b,∗ a b

Ambedkar Institute of Advanced Communication Technologies & Research, Delhi, India Universidad Internacional de La Rioja, Logroño, Spain

a r t i c l e

i n f o

Article history: Received 21 February 2019 Revised 12 January 2020 Accepted 16 January 2020 Available online 11 February 2020 Keywords: Fingerprint identiﬁcation Minutiae Orientation ﬁeld Ridge frequency Fingerprint enhancement Fingerprint reconstruction

a b s t r a c t Fingerprints are the one of the most important means in the forensics as a means of identiﬁcation of the criminals owning to the uniqueness and the distinct features in them. Fingerprint identiﬁcation is considered as an important means for the identiﬁcation of the people around the globe. Minutiae are the details present in the human ﬁngerprints which are used as a means of identiﬁcation and veriﬁcation. Minutiae are the distinctive points which can be used for the effective reconstruction of the ﬁngerprint image. However, there was a limitation that was considered. The minutiae points are completely not enough for reconstruction of the image. Many spurious minutiae are not included and the results for the latent ﬁngerprints are not as accurate as they are for the normal data sets. In this paper, a novel technique has been proposed which considers the minutiae density and the orientation ﬁeld direction for the reconstruction of the ﬁngerprint. Two public domain databases Fingerprint veriﬁcation competition 2002 (FVC2002) and ﬁngerprint veriﬁcation competition 20 04 (FVC20 04) have been used for the experimental results and to validate the suggested methods for the ﬁngerprint reconstruction and enhancement. © 2020 Elsevier Inc. All rights reserved.

1. Introduction Fingerprint recognition is one of the most widespread and effective method for the identiﬁcation of an individual. This is used to conﬁrm the identity of a person by comparing the ﬁngerprint impression of two ﬁngerprints. Even with new emerging techniques in the ﬁeld of biometrics, ﬁngerprint holds the tag of being most reliable among other physiological traits of a human body due to their uniqueness, permanence, acceptability and collectability. Thus, it ﬁnds it use in several applications today in the ﬁeld of criminology, banking etc. Fingerprints are considered genetically unique; no two individuals can have same ﬁngerprint, even the twins birthed at the same time are proven to have different ﬁngerprints. Fingerprints are the patterns on a ﬁnger known as the ridges which are resulted from the friction between surrounding and the fetus. These lines and curves are formed on the base of the skin due to the pressure developed on the skin. They remain same throughout the lifetime. Fingerprints do not tend to change however they grew as the individual grow. Hence ﬁngerprint identiﬁcation and its applications is the base of today’s research in biometrics.

∗

Corresponding author. E-mail addresses: [email protected] (M. Khari), [email protected] (R.G. Crespo).

https://doi.org/10.1016/j.ins.2020.01.031 0020-0255/© 2020 Elsevier Inc. All rights reserved.

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Automatic ﬁngerprint recognition has been an essential part of the widely spread technological innovations in terms of both forensic and biometric applications. Even after having a history of almost thousand years during which ﬁngerprints have been used as the identity proof of an individual and almost a decade on research on automated system, fully automatic ﬁngerprint identiﬁcation system is still a problem. Moreover, most of the research today is focused on matching the template of the ﬁngerprint to an approximate area covering the shape and size of an exact ﬁngerprint. The miniaturization of the sensors used in ﬁngerprints only leads to the usage of the small area where the previous technique cannot be used. Partial and latent ﬁngerprints are also common in the ﬁngerprint applications and especially in forensic department, where small useable portions of latent ﬁngerprints must be matched to the previously enrolled database. Fingerprint contains features which are usually the combination of the ridges and the valleys in the ﬁngerprint. In 1912, it was found that the study of 30–40 pores (poroscopy) [1] alone cannot be used in the creation and identiﬁcation of the ﬁngerprint. From then on, ﬁngerprint identiﬁcation has been relied upon the features which are divided into three different levels. The structures are generally deﬁned in three categories or levels namely level 1 features, level 2 features and level 3 features. The difference in the features lies in the occurrence of these features. Level 1 features are considered to have the details at the macro level such as ridge stream and the pattern type in the ﬁngerprint. Level 2 type of features contains the local features such as the ridge endings and bifurcations also known as Galton characteristics. These two constitute the two types of minutiae in the ﬁngerprint. Lastly level 3 features are the dimensional attributes such as shape, size, pores, and deviation in the ridge ﬂow, breaks and many other permanent details in the ﬁngerprint. Fig. 1 describes different types of ﬁngerprint patterns namely whorl, loop and arch. Arches constitute about 5–6% of the ﬁngerprint while whorl and loop comprise of 24–26% and 60–65% respectively. Fingerprints are described using the two levels which are deﬁned as topological or global features formed where a ridge line outlines a pattern. Loop also called as the singular points and the delta acts as a wrapper around the ridge lines [4]. The coarse ridge line and the singular points are somewhat useful for the ﬁngerprint classiﬁcation but cannot be used to an accurate and effective matching. A second level which is constituted by the presence of local ridge details known as minutiae is the local level of classiﬁcation as identiﬁed in [5] consisting of around 150 local details called minutiae details. Minutiae are deﬁned by the ridge endings and the bifurcations. A ridge ending is nothing but the point where the ridge ends abruptly and the point where a ridge divides into two is known as ridge bifurcation. Minutiae are generally the prominent detail in a ﬁngerprint that is stable and robust. It can be used to get the consistent results when minutiae extraction is considered. However, when the ﬁngerprint is of low quality generally in the case of latent ﬁngerprint or rolled ﬁngerprint identiﬁcation process can be challenging due the number of minutiae not enough to get the desired ridge structure as given in [6]. The last level is every ﬁne level which consists of features having the speciﬁc ridge details like the dots, pores etc. [6]. These traits are now receiving the due attention as they are related to the increased accuracy when compared to the results obtained by using only level 1 and level 2 features. In some cases, the ridges are lost or broken as in case of latent ﬁngerprint so, ﬁngerprint reconstruction is necessary for the generation of the orientation ﬁeld and the ridge structures.

Fig. 1. Types of ﬁngerprint patterns (a) plain whorl (b) central pocket whorl (c) double loop whorl (d) accidental whorl (e) plain arch (f) tented arch (g) radial loop (h) ulnar loop.

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Fingerprint reconstruction can only be said to have been successful when the reconstructed image will match the original ﬁngerprint image based on the minutiae points. The main aim of the ﬁngerprint reconstruction is at make the original ﬁngerprint image resemble the reconstructed image. Fingerprint reconstruction can be carried out in two major steps by reconstructing the orientation ﬁeld i.e. the phase and the gradient of the ﬁngerprint image and then calculating the frequency of the minutiae points present in the ﬁngerprint image. 2. Related work 2.1. Literature survey Fingerprints are the impressions or mark made on the surface by a person’s ﬁngertip which is used for the identiﬁcation of the individuals from the unique patterns of whorls and ridges on the ﬁngertips. Fingerprint identiﬁcation method includes obtaining a ﬁngerprint image then extracting the characteristic features to be identiﬁed in a ﬁngerprint image. The authors proposed eﬃcient technique in [33,34] to discard unimportant coeﬃcients. The identiﬁed features are then matched with a preset threshold for the identiﬁcation. The ﬁngerprint templates are used to ﬁnd a valid region of coincidence between the ﬁngerprint template and the ﬁngerprint to be identiﬁed. According to the valid region of coincidence ﬁngerprint matching is done. This method can be stated as the direct recognition method. However, if a ﬁngerprint is reconstructed based on the orientation and phase as the ﬁngerprint features, the regenerated ﬁngerprint can be used for the recognition purpose. Reconstruction of a ﬁngerprint is advantageous when the ﬁngerprints alone cannot be used for the recognition that is when they are unclear or are of poor quality. These kinds of ﬁngerprints are known as latent ﬁngerprints which are merely the skin impressions found at the crime scene by the criminals left accidently. Generally, those are not directly visible to our eyes. Some physical or chemical methods were used to capture and process such images. Latent ﬁngerprints are used as important proof for to detect the criminals in security systems such as law enforcement agencies. Latent ﬁngerprints are the ﬁnger impressions with the poor quality images with unclear ridge structure. Fingerprint reconstruction can give a better result for this type of research and investigation if the reconstruction is done accurately. There are various methods for the reconstruction of the orientation ﬁeld as discussed below. The orientation ﬁeld can be calculated using two models gradient based methods and model-based methods. Model based method is a complex method as it relies on the global regularity of the orientation values around the singular points. This work was ﬁrst given in [2], it showed that the local ridge orientation of ﬁngerprint can be described using the direction ﬁled concept of the differential geometry. It was presented in the terms of deltas and cores also known as singular points as shown in Fig. 2. This method is popularly known as zero pole method in the literature. The ﬁngerprint orientation reconstruction that the former used still doesn’t used the knowledge of the orientation ﬁled and is solely based on the minutiae points which resulted in a distorted ﬁngerprint image based on the orientation. The next step in the reconstruction is the ridge patterns which are reconstructed based on the orientation ﬁeld. There are number of algorithms which only generate either the partial skeleton or the wide ridges. The method proposed in [3] was able to reconstruct the full ﬁngerprint image using the minutiae set but it had a disadvantage that it contained many spurious minutiae points. Several methods for the automatic ﬁngerprint recognition are there based on the global ﬂow of patterns which are popular and reliable but due to the increasing usage of the ﬁngerprint as an identity tool the whole attention has been increased on this ﬁeld of the biometrics making ﬁngerprint as an important topic of the research over the last few decades. The values of the phase of the orientation image are an important aspect for all the processes in an automatic ﬁngerprint identiﬁcation system. Orientation ﬁeld thus is widely used and acknowledged in the singular point detection, classiﬁcation and ﬁngerprint enhancement. The directional ﬁeld of ﬁngerprints is estimated in [9] using the principle component analysis. The method given here computes the direction in any pixel location as well as its coherence. Also, in this paper detection the singular points from high resolution directional ﬁeld are discussed. The method given in [9] is compared to the averaging method. Further. In

Fig. 2. Singular points.

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[12] the authors develop an effective algorithm to locate a reference point and compute the corresponding reference orientation consistently and accurately for all types of ﬁngerprints. To compute the reliable orientation ﬁeld, an improved orientation smoothing method is proposed based on adaptive neighborhood. It shows better performance in ﬁltering noise while maintaining the orientation localization than the conventional averaging method. The authors presented the classiﬁcation of ﬁngerprints into ﬁve categories: arch, tented arch, left loop, right loop and whorl in [15]. The algorithm is presented in [17] which extracts singular points (cores and deltas) in a ﬁngerprint image and performs classiﬁcation based on the number and locations of the detected singular points. The program was developed in C++ language, using statistical techniques. The strategy allows to extract attributes of an image and to increase the quality of the process due to the reduction of noise, compared with results obtained by other methods. The author in [11] proposed an algorithm to ensure that the performance of an automatic ﬁngerprint identiﬁcation/veriﬁcation system will be robust with respect to the quality of input ﬁngerprint images, it is essential to incorporate a ﬁngerprint enhancement algorithm in the minutiae extraction module. They presented a fast ﬁngerprint enhancement algorithm, which can adaptively improve the clarity of ridge and valley structures of input ﬁngerprint images based on the estimated local ridge orientation and frequency. They had evaluated the performance of the image enhancement algorithm using the goodness index of the extracted minutiae and the accuracy of an online ﬁngerprint veriﬁcation system. There are various methods for orientation ﬁeld estimation namely ﬁlter-bank based methods [15,16] gradient based methods [9,10] and model-based methods [19–21]. The ﬁlter- bank based method is more noise resistant than gradient based methods, but the accuracy is less than the former. Also, they have a limitation of number of ﬁlters to be used and computationally expensive. In [27] the author presented the reconstruction of orientation ﬁeld. It was done from the form the singular points (core and delta) using the zero-pole model. However, the orientation ﬁeld in ﬁngerprints cannot simply be accounted for by singular points only. The author proposed ridge pattern reconstruction only generates a partial skeleton of the ﬁngerprint, which is obtained by drawing a sequence of splints passing through the minutiae. The author [29] has proposed a novel ﬁngerprint reconstruction algorithm to reconstruct the phase image, which was then converted into the grayscale image. They proposed a reconstruction technique due utilizes which the ﬁngerprints orientation from the minutiae, and it in the matching stage for the improvement of the systems performance to add some virtual minutiae and use Delaunay triangulation. In [23] According to the author Latent ﬁngerprint matching has played a critical role in identifying suspects and criminals. The author compared to rolled and plain ﬁngerprint matching, latent identiﬁcation accuracy is signiﬁcantly lower due to complex background noise, poor ride quality and overlapping structured noise in latent images. However, the gradient based approach is thus being a common approach, used to estimate the orientation in a ﬁngerprint image introduced by Kass and Wilkin [18]. Recently, [30] a different approach for data acquisition, post processing and visualization has been introduced called MR ﬁngerprinting. It uses a repeated, serial acquisition of data for the characterization of individual parameters of interest; MRF uses a pseudo randomized acquisition that causes the signals from different ﬁngerprints to have a unique signal evolution. The processing after acquisition involves a pattern recognition algorithm to match the ﬁngerprints to a predeﬁned dictionary of predicted signal evolutions. These can then be translated into quantitative maps of the magnetic parameters of interest. There has been some improvement [31] in the above said method to reconstruct high-quality time-series images and accurate tissue parameter maps like spin density maps. With this improved technique to capture the ﬁngerprint the probability to get the accurate results is fairly high. However, sometimes physical factors like the presence of dirt on the ﬁnger or some wound can ruin the quality of ﬁngerprint image. Also, there are some medical issues like cancer and age factor causes the removal of ﬁngerprint impression hence they are diﬃcult to be captured using the biometric means. With these constraints, even with the high-quality sensor there is no guarantee that the ﬁngerprint image will be of good quality making it necessary to employ some advance techniques for the ﬁngerprint enhancement and reconstruction which can further contribute to the better results when identiﬁcation will be carried out.

2.2. Contribution of the paper In this paper a novel approach for the ﬁngerprint enhancement and reconstruction has been proposed. First, preprocessing is done on the ﬁngerprint image obtained from the dataset FVC 2002 and FVC 2004. Then, the orientation ﬁeld and phase are estimated from the minutia marked imaged, following the former, ridge structures are obtained, and enhancement is done on the ridge structure to get the reconstructed image. This reconstructed image is used for the identiﬁcation and veriﬁcation purpose. The obtained reconstructed image is obtained by using the reconstruction using the higher order polynomial for the continuous phase. Also, the spurious minutiae obtained in the background are detected and reduced; which was a disadvantage in [25,28]. The matching of the reconstructed ﬁngerprints is done against the original ﬁngerprint used for the reconstruction getting the recognition rate as 98.05% for FVC 2002 dataset and 97.72% on FVC 2004 dataset respectively. Also, the ﬁngerprint (reconstructed) is matched against the different impressions of the same ﬁngerprint and the recognition is 49.25% for FVC 2002 and 50.02% on dataset FVC2004 respectively. The low value of the recognition rate for the different impressions of the same ﬁnger due to the factors like partial ﬁngerprint obtained, low visibility etc. The block diagram given in Fig. 3 describes different stages involved in the reconstruction of a ﬁngerprint. It is divided into two stages, the ﬁrst stage describes the stages involved in minutiae marking in Fig. 3(a) the steps include enhancement of ﬁngerprint

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Fig. 3. (a): Steps invoved in minutiae marking. (b): Steps invoved in Figerprint reconstruction.

followed by binarization, thinning and minutiae marking. When the minutiae marked image is obtained orientation ﬁeld and phase are estimated to generate the ridge structure and ridge map which are further used to reconstruct the image. Fig. 3(b) represents the stages of ﬁngerprint image reconstruction. The minutiae marked image is used for obtaining the orientation ﬁeld, phase and ridge structure which are enhanced and added to get the reconstructed image. So, improving the ﬁngerprint quality has proved an effective method to get the better results. In this paper the study has been carried out for the general ﬁngerprint representation given in Section 3, ﬁngerprint enhancement in Section 4, reconstruction of ﬁngerprint in Section 5. The proposed method is discussed in Section 6 followed by result and conclusion in Sections 7 and 8 respectively. 3. Fingerprint representation Fingerprints are the distinctive structures due to the presence of ridges and the minutiae points. These irregularities in a ﬁngerprint form the base of similarity measure of a ﬁngerprint. The ﬁngerprint identiﬁcation system uses the databases which matches the enquiry against the large database consisting of millions of ﬁngerprints. The detection of similarity is

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based on the ridge pattern formed in the ﬁngerprint. The minutiae point in a ﬁngerprint is used to carry out the narrow search in the database. As proposed [7] a ﬁngerprint I(x, y) can be represented in the form of frequency and amplitude modulated signal represented as given in Eq. (1).

I (x, y ) = a(x, y ) + b(x, y ) cos(ψ (x, y )) + n(x, y )

(1)

where four components can be found namely the amplitude b (x, y), intensity offset a(x, y), noise n(x, y) and phase cos ψ (x, y)). For the formation of ridges and minutiae only the phase components ψ (x, y) is considered and the rest of the three components are just for the ﬁngerprint to appear more realistic when reconstruction is considered. Therefore, a perfect ﬁngerprint model can only be composed of two-dimensional FM signal as given in Eq. (2).

I (x, y ) = cos(ψ (x, y ))

(2)

The instantaneous frequency is nothing, but the gradient of the phase and its direction is considered normal to the local ridge frequency. Its magnitude is equal to the magnitude of the local ridge frequency. According to [8] phase can be decomposed in two units namely the continuous phase and the spiral phase as described in Eq. (3).

ψ (x, y ) = ψc (x, y ) + ψs (x, y )

(3)

So, the phase can also be termed as the composite phase having spiral phase ψ s (x, y) and continuous phase ψ c (x, y) as given in above equation. The continuous phase does not contain any rotational component and its integral is zero around any closed path. The spiral path is composed of the ‘n’ spirals which are having xn and yn as coordinates. The polarity of the spiral phase is given by pn ∈ {1, −1}. A minutia is formed when a spiral is added to a continuous phase. Due to the decrease of the ridge frequency from left to right a minutia is formed in the direction of 0°. Similarly, when a spiral is added of negative polarity the minutiae in the direction of 180° is formed. The presence of the spiral phase is merely responsible for the presence of the ending or bifurcation in a ﬁngerprint. 4. Fingerprint enhancement A ﬁngerprint is resulted due to the friction caused on the outer skin of thumb or ﬁngers which leads to the formation of impression called ridges. While the general in-depth is not to be considered in this paper but in the biometric circle it is assumed that no two people can have same ﬁngerprint even the twins birthed at the same time are believed to have two different ﬁngerprint impressions. An outcome to this assumption leads to the fact that the information contained within a single ﬁngerprint is quite enough for the identiﬁcation purpose. Fingerprint is a combination of the all the three level details mentioned in section I, the image quality is considered as an important factor in the performance index of the minutiae extraction and matching algorithms. A good quality ﬁngerprint is considered to have a good contrast between the valleys and the ridges whereas on the contrary a bad quality ﬁngerprint is generally corrupted with the noise which can be in the form of cuts, smudges, creases, bruises or different skin conditions (oily or dry). Sometimes there can be human factors like the unhelpful attitude of the subjects or unclean scanning devices or the age or work factor (manual workers and elderly people) leading to the low ﬁngerprint quality. Fig. 4 describes different ﬁngerprint images with different qualities of possible ﬁngerprint images. The main objective of the enhancement of the ﬁngerprint is to increase the contrast between the ridges and valleys in the ﬁngerprint. Due to the non-stationary nature of the ﬁngerprint image, general purpose enhancement techniques are not readily used. Gray scale or binary image is preferred for the image enhancement. A binary image is deﬁned by only two values of the pixel. In this the ﬁngerprint image is assigned the value one if they are ridges and the subsequent valleys are valued as zero. However, there is a disadvantage of losing the information during the extraction of the ridges by the ridge extraction algorithm in a gray scale image. The true ridges are often lost making the performance of the algorithm low. Similarly, the enhancement of the binary images also has the intrinsic disadvantages. Orientation estimation is one of the main steps in the ﬁngerprint enhancement. It is described by the local direction of the ridge and valley structure.

Fig. 4. Different ﬁngerprint qualities (a) good quality (b) ﬁngerprint with too much of dry skin (c) ﬁngerprint with noise component.

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Table 1 Present gradient based methods. Method

Year

Kass and wilkin [18] Hong et al. [11] Jain and Hong. L [16] Bazen and Gerez [9] Wieclaw [13] Mei et al. [22]

1987 1998 1999 2002 2011 2012

Since global feature are important when the identiﬁcation is considered, orientation in a ﬁngerprint image can precise the information content in a ﬁngerprint image. Also, values of the phase of the orientation image are an important aspect for all the processes in an automatic ﬁngerprint identiﬁcation system. Orientation ﬁeld thus is widely used and acknowledged in the singular point detection [9,12], classiﬁcation [15–17] and ﬁngerprint enhancement [10,11,13,14]. There are various methods for orientation ﬁeld estimation namely ﬁlter-bank based methods [15,16] gradient based methods [9,10] and model-based methods [19–21]. The ﬁlter- bank based method is more noise resistant than gradient based methods, but the accuracy is less than the former. Also, they have a limitation of number of ﬁlters to be used and computationally expensive. The gradient based approach is thus is a common approach, used to estimate the orientation in a ﬁngerprint image introduced by kass and wilkin in 1987 [18]. The advantage of using this method is that the values thus obtained are continuous but there were some smudges and creases which the indicators of the presence of noise were. The methods proposed by the authors emphasize the use selection of the value of the block along with the necessity of normalization. Normalization is important when large -scale noise is concerned. The authors presented the basic approach for the orientation estimation where the whole analysis was done on the selection of scale of block, computation of the gradient in the x direction and y direction and the marking of the region of maximum noise. The existing gradient based methods are given in Table 1. The most important advantage of this algorithm is the fact that the obtained values are continuous. The ﬂowchart of the ﬁngerprint enhancement is given in Fig. 5. The steps include normalization, orientation image estimation, frequency image estimation, region mask generation and ﬁltering. The steps involved in ﬁngerprint enhancement are described below: 4.1. Normalization Normalization of a ﬁngerprint image is done to a pre-speciﬁed mean and variance to standardize the intensity values in an image. The grey levels are adjusted so that it lies in the desired range of values. Let I(i, j) be the grey level at pixel (i, j) and the normalized grey level is represented by N(i, j). The normalized image is deﬁned by Eq. (4)

⎧ 2 ⎪ Vo (I (i, j ) − M ) ⎪ ⎪ i f I (i, j ) > M, ⎨MO + V N (i, j ) = ⎪ 2 ⎪ ⎪ ⎩MO − Vo (I (i, j ) − M ) otherwise V

Fig. 5. Flow diagram of ﬁngerprint enhancement.

(4)

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Fig. 6. Orientation estimation.

Here, M and V are the approximated values of mean and variance of I(i, j) and MO and VO are the desired values of mean and variance respectively. Normalization is used to standardize the dynamic levels of variation in grey-level values which changing the existing ridge structure. 4.2. Orientation estimation Orientation ﬁeld is the local orientation of the ridges contained in a ﬁngerprint. This is a fundamental step in the enhancement process. The least mean square developed by hong.et.al (LMS) estimation method is used to compute the orientation image. The Fig. 6 represents orientation estimation. The algorithm is as follows. Step 1. Divide the image in the block of size WXW in the normalized ﬁngerprint image. Step 2. The gradients are computed at each pixel ∂ x (i, j) and ∂ y (i, j) at each pixel (i, j). These are gradient magnitudes of x and y respectively. Operator can be chosen based on complexity. For simple operations, we can use Sobel operator or for some complex operations we can use Marr- Hildreth operator. Horizontal Sobel operator is used to compute ∂ x (i, j) while vertical Sobel operator is used to compute ∂ y (i, j) Step 3. The local orientation is estimated by using the following Eqs. (5)–(7)

Vx (i, j ) =

i+ w2

w

j+ 2

2∂x (u, v )∂y (i, j ),

(5)

∂x (u, v )2 − ∂y (i, j )2 ,

(6)

u=i− w2 v= j− w2

Vy (i, j ) =

i+ w2

w

j+ 2

u=i− w2 v= j− w2

1 V (i, j ) θ (i, j ) = tan−1 x 2 Vy (i, j )

(7)

where θ (i, j) is the least square estimate of the local ridge orientation of the block centered at pixel (i, j). It represents the direction which is dominant in the Fourier spectrum of the WXW window. Step 4. Modiﬁcation of the incorrect local ridge orientation. The block size taken is twice the distance between the ﬁngerprint ridges. For the correction of the ﬁeld the image is converted into the continuous vector ﬁeld which can be explained as:

φx (i, j ) = cos(2θ (i, j )), and

(8)

φy (i, j ) = sin(2θ (i, j ))

(9)

where ∂ x and ∂ y are the x and y components of the vector ﬁeld. After the computation of vector ﬁeld, the smoothening is done with the help of Gaussian ﬁlter.

φx (i, j ) =

wφ /2

wφ /2

W (u, v )φx (i − uw, j − vw )

(10)

W (u, v )φy (i − uw, j − vw )

(11)

u=−wφ /2 v=−wφ /2

φy (i, j ) =

wφ /2

wφ /2

u=−wφ /2 v=−wφ /2

where W represents a 2- dimensional gaussian low pass ﬁlter having unit integral and wφ X wφ is the size of the ﬁlter.

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Step 5: The ﬁnal smoothening operation is done at the block level which is of default size 8 × 8. The local ridge orientation is computed at (i, j) using the formula given below:

1 tan 2

O(i, j ) =

φy (i, j ) φx (i, j )

(12)

This algorithm gives a smooth orientation ﬁeld. 4.3. Ridge frequency estimation Local ridge frequency is used for the construction of the Gabor ﬁlter. The local frequency of the ridges is represented by the frequency image. The ﬁrst step for frequency estimation involves the division of the image into the blocks of size W × W. Next, the grey level values of all the pixels located inside the block are projected along a direction orthogonal to the local ridge orientation. The region where the presence of minutiae and singular points is less, the grey levels along with the ridges and the furrow are modeled into the sinusoidal shaped waveform along with the direction to the local ridge orientation. Let G be the normalized image and O be the orientation of an image, the algorithm of the frequency calculation is as follows. Step 1: The image is divided into block of size W × W Step 2: For each of the block which is centered at pixel(i, j), a window is computed of size lxw which is deﬁned in the ridge coordinate system. Step 3: For each block centered at pixel (i, j), the x signature is computed, of the ridges and furrows within the window. If there no singular point or the minutiae present, then the x signature takes the form of discrete sinusoidal wave shape having same frequency as ridges and furrows. Therefore, the frequency ridges can be estimated from x signature. Step 4: Let T(i, j)represents the average number of pixels in the two consecutive peaks. Having frequency (i, j) which is computed as 1/T(i, j). If there are no consecutive peaks detected, then the frequency value assigned is s to differentiate from different valid frequencies. s Can be any random value which does not lies in the valid frequency range. For the unrecoverable region where the minutiae points don’t appear or singular points are missing and a well-deﬁned sinusoidal shaped wave form doesn’t appear, the frequency values of these blocks are interpolated from the frequency corresponding to the neighboring block. Interpolation is done using the following formula. For each block centered at (i, j) interpolation is done using the Eq. (13). If there exist at least one block of frequency with value s, then and are interchanged.

(i, j ) =

⎧ i, j ), ⎪ ⎨(

wφ /2

u=−wφ /2

⎪ ⎩ w φ / 2

u=−wφ /2

When

w φ / 2

v=−wφ

w φ / 2

v=−wφ

i f (i, j ) = s

Wg (u, v )μ((i − uw, j − vw )) /2

Wg (u, v )δ ((i − uw, j − vw ) + 1 ) /2

otherwise

(13)

0, i f x ≤ 0 x, otherwise

(14)

0, i f x ≤ 0 1, otherwise

(15)

μ (x ) = δ (x ) =

Wg a discrete Gaussian kernel and w is the size of kernel. The low pass ﬁlter is used to remove the outliers in the image. The outliers are due to the change in the inter-ridge distance in the image. Also, the assessment of the recoverable and unrecoverable region is done based on the shape of the wave formed by the ridges and furrows. 4.4. Gabor ﬁltering Ridge orientation and ridge frequency are used to construct an even symmetric Gabor ﬁlter. A two-dimensional Gabor ﬁlter contains a sinusoidal plane wave which has an orientation and frequency adjusted by a Gaussian envelope. The advantage of using Gabor ﬁlters is there orientation and frequency selective properties. These properties help to get the maximize response in a ﬁngerprint image. Also, Gabor ﬁlter preserves the ridge structure for reducing noise. The even symmetric Gabor ﬁlter is a real part of Gabor function which is given by a cosine modulated Gaussian wave as shown in ﬁgure The even symmetric Gabor ﬁlter has a general form as given in Eq. (16)

1 G(x, y; θ , f ) = exp − 2

x2θ

σx2

−

y2θ

σy2

cos(2π f xθ )

(16)

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where θ is the orientation of the Gabor ﬁlter, f is the frequency of sinusoidal plane wave and σ x and σ y are the space constants of the gaussian envelope along x and y axes respectively. For Gabor ﬁlter to be applied the frequency, orientation is calculated ﬁrst which can be calculated using ridge frequency calculation and orientation estimation respectively as given in above steps. The Gabor ﬁlter is applied to the ﬁngerprint image by spatially convolving the image with ﬁlter. The application of the Gabor ﬁlter G to get the enhanced image is done as given in Eq. (17) wx

wy

2 2

E (i, j ) =

G(u, v; O(i, j ), F (i, j ))N (i − u, j − v ),

(17)

−yx u= −wx 2 v= 2

where F and O represents the ridge frequency image and orientation image respectively, N is the normalized ﬁngerprint image and wx and wy are the width and height of the Gabor ﬁlter mask. 5. Fingerprint reconstruction Reconstruction of the ﬁngerprint by various methods has been discussed in this section along with the comparison of result with the proposed method. An explanation is given in Table 2. Since minutiae template has become in a compact representation of a ﬁngerprint, it has been assumed that it is not possible to reconstruct the original ﬁngerprint from a minutiae template. The template, by deﬁnition, is a compact description of the biometric sample; it is not expected to reveal signiﬁcant information about the original data. Therefore, templategeneration algorithms are typically assumed to be one-way algorithms. Recently, however, this belief has been challenged by some researchers [11,14,27] who were successful in reconstructing a ﬁngerprint image from the given minutiae template. The Analysis of ﬁngerprint reconstruction from minutiae template is very important to determine if it is possible to fool an expert human placing a reconstructed ﬁngerprint image in crime scenes and to perform masquerade attacks against an automatic ﬁngerprint recognition system (for instance, injecting a reconstructed image in a communication channel or making a fake ﬁnger). Fingerprint reconstruction can be beneﬁcial in application like smart cards (where memory is critical) since the orientation map required for matching need not be stored explicitly but can be generated from the template. The minutiae information alone may be used for classifying ﬁngerprints. Fingerprint reconstruction may also be used for improving the interoperability among minutiae encoders and matchers from different vendors, which was identiﬁed as a problem in [5]. The author proposed an algorithm to ensure that the performance of an automatic ﬁngerprint identiﬁcation/veriﬁcation system will be robust with respect to the quality of input ﬁngerprint images, it is essential to incorporate a ﬁngerprint enhancement algorithm in the minutiae extraction module. We present a fast ﬁngerprint enhancement algorithm, which can adaptively improve the clarity of ridge and valley structures of input ﬁngerprint images based on the estimated local ridge orientation and frequency. We have evaluated the performance of the image enhancement algorithm using the goodness index of the extracted minutiae and the accuracy of an online ﬁngerprint veriﬁcation system. Experimental results show Table 2 Comparison of ﬁngerprint algorithms given in literature. Algorithm

Method for reconstruction (orientation and ridge)

Performance evaluation

Hill [27]

Zero-pole method, partial skeleton reconstruction

N/A

Cappelli et al. [3]

Modiﬁed zero pole method, streamlines and gabor ﬁltering Nearest minutiae in eight sectors, AM-FM model

Type-I attack 81.49% on FVC2002 identiﬁcation

Feng and Jain [29]

Ross et al. [28] Abdullah Bajahzar, Hichem Guedri [32] Proposed

a b c d

Minutiae triplets, streamlines and line integral convolution Fractal interpolation

Nearest minutiae in eight sectors, continuous phase generation, AM-FM model for correction

Type 1 attack: TARa 94.13% at 0%of FARb =0.1% on FVC2002 DBA_1 Type-II attack TARa =45.89% at FAR=0.1% on FVC2002 DBI_A Type I attack 23% MSE- 0.13–0.338 Relative error- 8.068–20.382% Type 1 attack-N/A Type I attack: TARa = 97.95% on FVC2002 and 94..09% on FVC2004 Type 2 attack: TAR =49.25% and 50.02% on FVC 2002 and FVC2004

Type I attack is referred to the matching of reconstructed image to the same dataset from it is extracted. Type II attack is referred to the matching against a different impression. TAR is the true accept rate. FAR is the false accept rate.

Comments Reconstruction of partial skeleton of the ﬁngerprint Presence of the spurious minutiae in the reconstructed image. Spurious minutiae and blocking effect

Generation of the partial ﬁngerprint Reduction rate in ﬁngerprint curves. Reduced spurious minutiae.

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that incorporating the enhancement algorithm improves both the goodness index and the veriﬁcation accuracy. They modeled ridges and valleys as a sinusoidal-shaped wave along the direction normal to the local ridge direction and extracted the amplitude, frequency, and variance of the sinusoid. Based on these parameters, they classify blocks as recoverable and unrecoverable. In [6] the orientation ﬁeld was reconstructed from the singular points (core and delta) using the zero-pole model. However, the orientation ﬁeld in ﬁngerprints cannot simply be accounted for by singular points only. The author proposed ridge pattern reconstruction only generates a partial skeleton of the ﬁngerprint, which is obtained by drawing a sequence of splints passing through the minutiae. The authors in [7] proposed to estimate the orientation ﬁeld by selecting wellstructured triangles from the minutia set and computing the orientation values within each triangle by interpolation. This method fails to estimate the orientations where minutiae are not enough. The work suggested in [8] proposes a novel approach to reconstruct ﬁngerprint images from the standard templates and investigates to what extent the reconstructed images are like the original ones (that is, those the templates were extracted from). The eﬃcacy of the reconstruction technique has been assessed by estimating the success chances of a masquerade attack against nine different ﬁngerprint recognition algorithms. The experimental results show that the reconstructed images are very realistic and that, although it is unlikely that they can fool a human expert, there is a high chance to deceive state-of-the-art commercial ﬁngerprint recognition systems. Similar works have been proposed in [9–12]. In [12] the paper proposes a Gaussian weighted method for ﬁngerprint orientation ﬁeld reconstruction from the minutia template only. In the method, prior information about ridge ﬂow characteristics is considered to more accurately model the ridge orientation. Experimental results show that the method can obtain an accurate orientation ﬁeld in terms of the accuracy of the orientation ﬁeld-based ﬁngerprint classiﬁcation and the performance of the orientation descriptor-based ﬁngerprint matching. Feng et al. proposed a dictionary of orientation patches to estimate the orientation ﬁeld in the manually marked ROI. An essential component of this lights-out capability is to develop a fully automatic latent feature extraction module. This is highly desirable when the throughput of the latent matching systems is considered. It had advantage of the increased capability between the features extracted in talent and that of extracted from the reference points by an AFIS. The algorithm developed in [12] worked for plain and rolled ﬁngerprints and the authors lead to the proposal of the use of dictionary learning for the orientation estimation of the ﬁngerprints however there was a limitation that the ridge structure information was ignored and only the patches of the orientation were taken for the reconstruction purpose making it not very successful for the segmentation and frequency estimation. In [23] the author has concluded that the latent ﬁngerprint matching is playing a crucial role in the identiﬁcation of the criminals and suspects. The author has compared the performance of the rolled and plain ﬁngerprints to the latent ﬁngerprints. Owning to the complex background and the presence of the noise the results were slightly lower than that of the former. The poor ridge structure, overlapping in the structures and low quality were the reasons for the low-quality ﬁngerprints. It was concluded that for the improved consistency and the reduced mark-up cost a fully automatic and highly accurate latent matching algorithms are required. Also, one of the major problems in a ﬁngerprint-based system is retaining ﬁngerprint images. The authors in [32] proposed a method to minimize the ﬁngerprint images size and retain the reference points. The method is divided into three parts, the ﬁrst part is about digital image preprocessing that allows eliminating the noise, improving the image, converting it into a binary image, detecting the skeleton and locating the reference point. The second part uses Douglas-Peucker method for the detection of critical points and the ﬁngerprint reconstruction is ﬁnally done in the last part using fractal interpolation curves. However, the result is not satisfactory when the number of iterations is small. 6. Proposed method The aim of the ﬁngerprint reconstruction is to is to recreate a gray scale ﬁngerprint image from the given set of minutiae points which can be deﬁned as M = {mk = (xk , yk , αk }nk=1 where (xi , yi ) indicates the location of the kth minutiae point and α i which ranges from (−π < α < +π ) and indicated the direction of the minutiae. In this method we propose a method which is based on the mechanism of dictionary-based ﬁngerprint reconstruction as per our prior knowledge 1) orientation ﬁeld reconstruction and 2) continuous phase reconstruction are being used. Orientation ﬁeld reconstruction regenerates the orientation ﬁeld of the ﬁngerprint image and the continuous phase dictionary is used for the ridge pattern structure regeneration. This algorithm works well where the ridges are broken and gives a better conﬁdence measure for the enhancement and segmentation results. The proposed algorithm works on the Gabor-like-ﬁlter [24]. The block diagram is given in Fig. 7. The block diagram consists of six phases of ﬁngerprint reconstruction namely a) original image b) minutia extracted image c) minutiae cloud d) orientation image e) phase image f) reconstructed image. 6.1. Orientation ﬁeld reconstruction The orientation ﬁeld can be reconstructed as per our prior knowledge from the methods proposed in [3,25]. The ﬁngerprint image is divided into the non-overlapping blocks.8 × 8 pixels, the image being size of 512 × 512 and each block is estimated with an orientation value O (z). There may be some block where the information is redundant, so a set of orientation patches are collected of size (6 × 6) with each block of 8 × 8 pixels. A threshold is set, and the average quality of the block is calculated (here T = 3.60). The nearest minutiae are used to predict the local ride orientation of each eight sectors. The minutiae direction α k is doubled to make it equal to αk + π . The sine and cosine components are summed as given in

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Fig. 7. Block diagram for the ﬁngerprint reconstruction.

Fig. 8. Reliability map indicating the singular points of orientation ﬁeld.

Eqs. (18) and (19) respectively.

u=

k

cos(2αk )wk

(18)

sin(2αk )wk

(19)

k=1

v=

k k=1

wk is the weighing function. The distance between the block center and the Kth minutiae is used to mark the orientation direction. In case of the singular points (core, delta), they have maximum curvature and can be located by measuring the strength of the peak using the following Eq. (20)

min _intertia(x, y ) =

((Gyy + Gxx ) − (φx Gxx − Gyy ) − (φy Gxy )) 2

(20)

The reliability is calculated using the Eq. (21). Fig. 8 shows the reliability map using the orientation points. Fig. 9.

rel iabil ity(x, y ) = 1 −

min _intertia(x, y ) max _intertia(x, y )

(21)

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213

Fig. 9. Primary and secondary singular points.

max _intertia(x, y ) = Gyy + Gxx − min _intertia(x, y )

(22)

Orientation ﬁeld reliability contains the singular points, minutiae points and the rest of the information of the original ﬁngerprint image. The presence of noise corrupted ridge structures and low gray value contrast can be adjusted using a low pass ﬁlter. To perform the low pass ﬁltering the orientation is needed to be converted into the continuous vector ﬁeld which can be written as given in Eqs. (23) and (24).

φx = cos(2θ (x, y ))

(23)

φy = sin(2θ (x, y ))

(24)

where φ x and φ y are the x and y components of the vector ﬁeld respectively and the low pass ﬁlter can be applied as given in Eqs. (25) and (26)

φx (i, j ) =

wφ /2

wφ /2

W (u, v )φx (i − uw, j − vw )

(25)

W (u, v )φy (i − uw, j − vw )

(26)

u=−wφ /2 v=−wφ /2

φy (i, j ) =

wφ /2

wφ /2

u=−wφ /2 v=−wφ /2

where W is a two-dimensional low pass ﬁlter. 6.2. Continous phase reconstruction The gradient of the continues phase can be calculated at block level as given in Eq. (27)

Gc (m, n ) = G(m, n ) − Gs (m, n )

(27)

Gc (m, n) is the gradient of the composite phase and Gs (m, n) is the gradient of the spiral phase. The gradient of the spiral phase can be normally computed but there occurs a problem in the calculation of the G(m, n) as it is normal to the local ridge orientation and cannot be computed as O(m, n ) + π /2 as there is a discontinuity in the pase gradient at range [0,π ), Also the frequency and the ridge orientation is not well deﬁned in the nearby region of the minutiae. So, the orientation unwrapping and phase unwrapping is done at the range [0,π )and [0,2π ) respectively. The wrapping is done from the topmost level until all the foreground blocks are unwrapped. Unwrapping is done in accordance to the adjacent block which can be deﬁned as (m + 1, n). Singularities are detected as described in section A. However the discontinuity due to singularity is sometimes unavoidable. For the frequency and ridge area Gc (m, n) is computed in accordance to [26] where blocks contain no minutiae. The continuous phase can be formed at each foreground block (m, n) of 8 × 8 pixels. It is calculated using the Eq. (28) and the range of x and y is given by Eq. (29)

ψc (x, y ) = Gcx (m, n )x + Gcy (m, n )y + P (m, n ),

(28)

8(m − 1 ) ≤ x < 8m, 8(n − 1 ) ≤ y < 8n,

(29)

where Gcx (m, n) and Gcy (m, n) signify the components of Gc (m, n) and the phase offset is determined at block (m, n) by P(m, n). The phase offset is initially assumed to be zero and the block is iterated to check that the block is connected to all the four neighbors are reconstructed. If the reconstruction is not done, then the phase offset is calculated and is put in the queue. The steps are performed all the blocks are reconstructed concluding that the continuous phase is reconstructed giving the ridge pattern and a secondary image of the reconstructed blocks. P(m, n) Use the mean value of the phase offsets. The phase quantities are changed into the complex quantities which are then averaged and are converted back to phase.

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After obtaining the continuous phase it is added to the spiral phase, and a reconstructed image is obtained for different impressions of the same ﬁngerprint for the matching purpose. However, there are some spurious minutiae introduced. The location of the spurious minutiae is the region of the singularity. Since the ridge frequency is assumed constant, the spurious minutiae are there which are removed using the AM-FM model. Also, by using a higher order polynomial (third order polynomials) can be used to model the continuous phase in each region with discontinuity in the ridge in the border regions. 7. Experimental results The algorithm for ﬁngerprint minutiae extraction is carried out on the FVC2002 and FVC2004 database from the ﬁngerprint veriﬁcation competition (2002) and (2004). The feature extraction is done on the image taken from the database and then it is matched with the template created. The original database contains subsets DB_1, DB_2, DB_3, DB_4 containing at least 12 samples from a single person of the total 150 ﬁngers making the total of 1600 ﬁngerprint images in each of the subset. The images are in tiff format. The resolution of each sample ﬁngerprint image is 500 dpi and optical sensor is used for the subset DB_1 and DB_2 while thermal senor is being used for the generation of DB_3 subset of the ﬁngerprint database. The proposed ﬁngerprint reconstruction algorithm is assessed on the databases FVC2002 and FVC2004 provided by the biometric systems. The databases selected of FVC2002 uses the optical sensor (TouchviewII by Idenix) for DB_1 dataset while optical sensor (FX20 0 0 by biometrika) is used for DB_2. The database FVC2004 has used the optical sensor (V300 by crossmatch) for dataset DB_1 and (U.are.U40 0 0 by digital persona) for dataset FVC2004. The total number of ﬁngerprints used as the dataset is 400 images each of 100 images from a single dataset. The ﬁngerprint image is reconstructed using the ridge frequency and the direction θ (x, y). The ﬁngerprint image is reconstruction by ﬁrst extracting the minutiae points, then ridge frequency and the minutiae directions are calculated for the reconstruction of the ﬁngerprint image. The reconstructed images are then compared to the original subset and the subset created by the different impression of the same ﬁnger images. The performance index is then calculated for both identiﬁcation and the veriﬁcation. Some sample ﬁngerprints are shown in the Figs. 10 and 11 below. 7.1. Minutiae points generation The block diagram (Fig. 3) of the ﬁngerprint reconstruction contains the stages of getting an input from the database and then image enhancement is done with the help of fast Fourier transform. The conventional method of image enhancement with histogram equalization and fast Fourier transform encounters the problem of having so many discontinuities in between the ridges, so a new method was implemented with uses a mean ﬁlter in the enhancement procedure. Next step is the conversion of the grayscale image to the binary image after comparing the intensity values with the threshold. Next is the conversion of the ridges to a pixel width called which is termed as thinning. Proceeding further we are marking the minutiae which are nothing but the ridge endings and bifurcations. The similarity index is computed with the threshold

Fig. 10. Sample database of FVC-2002 (DB_1 and DB_2).

Fig. 11. Sample database of FVC-2004 (DB_1 and DB_2).

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Fig. 12. Different stages of the ﬁngerprint recognition.

Fig. 13. (a) Corrupted image (b) orientation image (c) segmented image (d) minutiae cloud (e) frequency component (f) ﬁngerprint image after ﬁltering (g) Enhanced Fingerprint image.

set is 0.56 There are eight ﬁngerprint images of eight different ﬁngerprints taken in different angles. The matched accuracy obtained is 96%. Fig. 12 shows the different stages of the minutiae extraction. 7.2. Fingerprint enhancement A fast ﬁngerprint enhancement algorithm which can adaptively improve the clarity of ridge and valley structures based on the local ridge orientation and ridge frequency estimated from the inputted image is introduced. The performance of the algorithm was evaluated using the goodness index of the extracted minutiae and the performance of an online ﬁngerprint veriﬁcation system which incorporates our ﬁngerprint enhancement algorithm in its minutiae extraction module. For poor ﬁngerprint images especially ones which large noise component, this method was found to be better than the traditional Fast Fourier based method. Fig. 13(a) is the corrupted image taken from the database DB1 (FVC-2004), then the orientation image, segmented image, minutiae cloud, frequency component is shown from the Fig. 13(a) to (e) respectively. The image is then ﬁltered by using a mean ﬁlter and the result is shown in Fig. 13(f). The ﬁnal step in the enhancement is the enhanced ﬁngerprint image which is renormalized so that the ridge segments will have zero mean and unit standard deviation. The Fig. 13(g) is the ﬁnal enhanced image. 7.3. Reconstruction of the ﬁngerprint image The next section is the reconstruction of the ﬁngerprint image. The minutiae image as obtained from the section A is taken and the orientation image is reconstructed. The gradient of the continuous phase is reconstructed. The spiral phase of the image is taken. The continuous orientation phase and the spiral phase are then added to form a reconstructed image. The ﬁnal image is ﬁltered using the mean ﬁlter to get the reconstructed image. Some of the stages of the reconstruction are shown in Fig. 14. The different stages are a) Minutiae calculated image (b) minutiae cloud (density) (c) orientation image (d) spiral phase (e) reconstructed image. And Fig. 15(a) shows the original images from the database and the reconstructed image is shown in Fig. 15(b). Some examples of the reconstructed images are shown in Fig. 15(a) and (b)

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Fig. 14. (a) Minutiae calculated image (b) minutiae cloud (density) (c) orientation image (d) spiral phase (e) reconstructed image.

Fig. 15. (a) Original ﬁngerprint images (b) reconstructed ﬁngerprint images from the proposed algorithm.

7.4. Classiﬁcation The ﬁngerprint veriﬁcation is done on FVC2002 and FVC2004 databases. The datasets considered are DB_1 and DB_2 of both the databases. In type I attack the reconstructed ﬁngerprint is matched with the original ﬁngerprint from which it is extracted while each reconstructed ﬁngerprint image is matched with the other eight impressions of the same ﬁnger for the type II attack. There are 400 type I attacks in total for both FVC 2002 and FVC 2004. In type I attack the True acceptance rate is 97.95% and 94.09% on FVC2002 and FVC2004 database respectively. While in type II attack the matched accuracy is 49.25% and 50.02% on database FVC2002 and FVC2004 respectively. Moreover, the spurious minutiae are reduced. Classiﬁcation stage, the FNN and the RBFNN is used to evaluate the accuracy and performance in detection of an individual’s ﬁngerprint. The algorithm for the training of the neural network is trainlm; logsig transfer function is used for the hidden layer which contains 10 neurons while output layer uses purelin transfer function which has one neuron as shown in the Fig. 16 of the selected architecture of neural network. Mean square error (MSE) denotes the mean square error difference between the targets and the outputs. Better performance is obtained with lower value of MSE. When compared to the measured, the performance graph of the neural network is shown in Figure which signiﬁes that the accuracy is satisfactory. Over ﬁtting occurs when the model is comprehensively complex like as compared to the number of observations there are many parameters. There are 3 plots of regression representing training, validation and testing. The perfect result-output is equal to target. If the value of R is near to zero, and then there is no linear relationship between the targets but incase R is equal to one then there is an exact correlation between the target and the outputs. The training data of our result directs a good ﬁt. When the

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Fig. 16. Selected Neural Network Architecture.

Fig. 17. Recognition rate for type 1 attack.

value of R is grander than 0.9, our succeeding stage would be to inspect whether there is a condition of extrapolation then the training set should be included in the dataset or the extrapolation then the superﬂuous data should be collected to be included in the test set. The accuracy achieved with FVC 2002 is acceptable with an R value of 0.97954 which is very close to the ideal value of unity. The recognition rate for type 1 attack is given in Fig. 17. 7.5. Time complexity and computational requirements The algorithm is tested on a system with 4 GB RAM and Intel (R) core (TM) i3-4005U CPU @1.70 GHZ. The reconstruction of the ﬁngerprint image for the database FVC 2002 takes 1.30 s per image and for the FVC 2004 it is 4.02 s per image. The time complexity can be further improved once the system is optimized. 8. Conclusion and future work Fingerprint reconstruction is used to obtain the ﬁngerprint image from the minutiae template. Fingerprint image reconstruction is basically done for the following three reasons namely (a) to secure the minutiae template (b) to improve the ﬁngerprint synthesis (c) for the improvement of the interoperability of ﬁngerprint template generated by different algorithm and sensors. Even though there is advancement in the technology in the recent years, even though there is a level of discrepancy between the reconstructed image and the original ﬁngerprint image in terms of the performance basis. In this report, an improved methodology is discussed which can be used to obtain the ﬁngerprint reconstructed image. The prior knowledge regarding the ridge structure is used in the algorithm for the improvement of the ridge structure. The two kinds of dictionaries are used in this paper which is known as orientation based and continuous phase-based dictionaries. These dictionaries are used to obtain the orientation ﬁeld from the obtained minutiae set. The continuous phase-based dictionary is used for the reconstruction of the ridge pattern. The reconstructed ﬁngerprint mage as shown in Fig. 15(a) and (b), are close to the original ﬁngerprint image. Future work will investigate to make the reconstructed ﬁngerprints more realistic. The suggested method for orientation ﬁeld reconstruction only considers the local orientation pattern. The role of global orientation prior knowledge as well as singular points may further improve the ridge orientation reconstruction. The ridge

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frequency ﬁeld used in this paper can be either ﬁxed priori or reconstructed from the ridge frequency around minutiae. Future studies will investigate frequency ﬁeld reconstruction directly from the minutiae position and management. Declaration of Competing Interest None. CRediT authorship contribution statement Rashmi Gupta: Conceptualization, Data curation, Writing - original draft. Manju Khari: Methodology, Data curation, Formal analysis. Deepti Gupta: Software, Investigation, Writing - original draft. Rubén González Crespo: Formal analysis, Supervision, Writing - review & editing. References [1] D.R. Ashbaugh, Quantitative-Qualitative Friction Ridge Analysis: an Introduction to Basic and Advanced Ridgeology, CRC press, 1999. [2] B. Sherlock, D. Monro, A model for interpreting ﬁngerprint topology, Pattern Recognit. 26 (7) (1993) 1047–1055. [3] R. Cappelli, D. Maio, A. Lumini, D. Maltoni, Fingerprint image reconstruction from standard templates, IEEE Trans. Pattern Anal. Mach. 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