Fingerprint image enhancement using multiple filters

Fingerprint

The skin covering the surface of a human hand and foot is patterned with ridges which are curved protruding single segments. Two parallel ridges are separated by a gap called a valley. Ridges and valleys form curved, complicated, and unique patterns that help in the exudation of perspiration, allow for gripping as well as allow for a sense of touch (Datta et al., 2001; Noor et al., 2018). Ridges have small pores that extrude perspiration, when an item is picked or touched, the perspiration leaves an exact impression i.e., latent print, of the ridges on the object. The latent print depends on the object’s surface as well as environmental factors such as humidity and heat. Ridges run smoothly, at certain regions they form distinctive shapes characterized by ridge terminations and high curvature. Those regions are known as singularities or singular regions. Ridge physical characteristics exhibit minute patterns, with few examples as such: the ridge becomes discontinuous (ridge-ending), ridge splits into two (bi-furcation), and short ridge. These physical characteristics are common; however, they are in unique combinations for every fingerprint and are known as minutiae (see Fig. 1). The features can be classified between i.e., high or low level (Tahmasebi & Kasaei, 2002; Jan et al., 2016), the former singular region and latter minutiae (Maio & Maltoni, 1997).

Ridges and valleys exhibit oriented sinusoidal-shaped patterns which is a fundamental property in the thorough analysis of fingerprint images. The local ridge orientation of each ridge pixel denoted by [x, y], is the angle ridge forms crossing through an arbitrarily small neighbourhood of non-overlapping blocks, centered at [x, y] with the horizontal axis. The dominant direction to which the ridges are oriented is taken as the orientation of the block. Another useful property is ridge frequency which is, at a point [x, y], the number of ridges per unit length along a non-overlapping block centered at [x, y] and orthogonal to orientation. In short, it is the distance between ridges at each point in a local non-overlapping window neighbourhood in fingerprint processing.

An individual can have one type of pattern or a mix of the patterns, however, the patterns are unique and they do not change over time. No two individuals have been found to have the same finger pattern (Treisman, 1985). Hence of individuality, the ease of studying, and its non-invasive and inexpensive methods of capturing, fingerprints are the go-to metric for biometric identification in the past century. Optical sensors and solid sensors capture fingerprint images, each with its own merits. In optical sensors, a finger is placed onto a surface and visible light is directed at it. The valleys reflect back the light while the ridges absorb the light, hence enabling one to differentiate between ridges, appearing dark, and valleys appearing bright. Solid state sensors, by applying pressure onto the sensor with a finger, measure and digitizes the physical shape. For a digital fingerprint image, the input is a matrix, containing values representing the pixel’s brightness intensity, and hence a representation of the original data captured by sensors. Additional image processing techniques are carried out to remove any sensor noise.

In fingerprint identification, minutiae from the fingerprint image are vital for the verification of an individual. The system identification performance is dependent on the accuracy and reliability of the features extracted. The fingerprint minutiae ridge pattern is matched with the corresponding minutiae via alignment and pairing for identification. Key features of a fingerprint from the fingerprint’s image may not be always easy to pick as identification depends on the image’s quality or a finger’s quality. In a good image ridges and valleys are patterned in a smooth manner, with the ease of distinguishing between the two. However, in a real scenario, image quality depends on the finger’s condition and the scanner’s ability to record a fingerprint. A finger’s skin affected by cuts bruises or if the skin’s surface is too wet/dry are a few factors that determine the quality of a fingerprint image. Natural abrasion of ridges via aging or manual labor results in difficulty in identifying ridge patterns. Apart from the physical condition of fingers, incorrect finger pressure technique and sensor noise are also factors a fingerprint image may be of poor quality. These issues may cause ridges to appear discontinuous making it look as if there are extra minutiae when there are not. Other issues include parallel ridges seeming as one, genuine minutiae features being corrupted or incorrect location recorded of minutiae i.e., orientation and position.

Related work

The goal of image enhancement algorithms or filters is to recover the recoverable regions, as well as clarify the ridge details, improve the contrast between ridges and valleys, mitigate/eliminate any unnecessary noise elements, isolating the area of interest in the greyscale images. It is crucial in all images involving feature detection, as indicated by the current work done in this area for easy identification of minutiae that are not properly visible.

Low-level systematic abstract operation on fingerprint images is image pre-processing. For a given pixel value of a fingerprint image, pre-processing transforms it to a newer value, while taking into account the nearby surroundings. They can be easily picked out and restored with respect to the neighboring pixels with pre-processing operations (Khalil et al., 2019). During fingerprint image analysis, a process called segmentation is carried out. Segmentation involves separating the fingerprint region from the image to ensure areas of the background do not interfere with the fingerprint’s features. It ensures no features are extracted from a noisy area within the background. The background of a fingerprint image is an isotropic pattern while the foreground consists of oriented stripes. Using a simple local intensity scheme, foreground and background can be distinguished from one another, provided the background is consistent and lighter than the foreground area. However, the introduction of noise from fingerprint scanners, dust specks, and grease require more robust techniques for segmentation. Foreground and background areas are distinguished from one another by using local histograms of ridge orientations, computing images into blocks, and estimating the orientation and histogram for each pixel (Mehtre et al., 1987; Chaudhary, Singh & Dimri, 2020). High peaks of a histogram indicate foreground area, while flat or near flat indicates isotropic region i.e., the background region. On encountering a perfectly uniform area where local ridge orientation cannot be found, block variance can be used to differentiate the background/foreground of fingerprint images (Das, 2018). For each block, variance is calculated from greyscale values. Low variance values of blocks are denoted as the background of a fingerprint image while above a specified threshold is denoted as the foreground Fig. 2.

Smoothing reduces noise and is a standard in pre-processing digital images. Many image processing methods do not perform well in a noisy environment (see Fig. 3), which is why smoothing is used as a preprocessing module in applications. The issue with traditional smoothing-based approaches to enhance fingerprint images and remove noise is the risk of smoothing relevant information within the image. The partial differential equation approach is among the preferred methods to achieve smoothing.

The fingerprint image is taken as an initial state of a parabolic diffusion process, wherein the diffusion is controlled by the derivative of the fingerprint image pixels via diffusion tensor, hence known as the coherence diffusion process which adaptively uses smoothing-based methods (Ali et al., 2012). It is based on the Perona & Malik (1990) model, in which the diffusion tensor enhances the coherent ridge structure of fingerprint images via a nonlinear diffusion process. The diffusion tensor controls the process of diffusion i.e., smoothing at different directions (Liu et al., 2020). In other words, the algorithm treats each pixel according to the neighbouring pixels.

Gabor filters have the well-known property of being both frequency and orientation-selective with optimal combined resolution in different domains, thus achieving favorable and better performance (Xia, Lv & Sun, 2018). Gabor filters are defined by a sinusoidal plane wave, which itself is defined by its orientation and coordinates, incorporating a Gaussian envelope. Gabor filter’s parameters are tuned i.e., the Gaussian envelope standard deviations, with respect to x and y. The higher the values more robust the filter at the cost of incurring spurious ridges, lower the values less likely to remove noise but not incur spurious ridges (Hajri et al., 2020). Despite the Gabor filter’s better performance, there are two limitations. The maximum bandwidth possible is approximately one octave, and the filter is not optimal in seeking widespread frequency information alongside maximum spatial localization. Also, it is to be noted that the signal orthogonal to the local region’s orientation cannot be always represented by a sinusoidal wave hence Gabor filter performance is impaired in bandwidth-oriented areas. An alternative solution is a log-Gabor filter, the filter is optimized as it is constructed with arbitrary bandwidth (Wang et al., 2008). This also reduces the over-representation of lower-ranged frequencies. An added advantage is the visual aspect of symmetric cell responses on the logarithmic frequency axis as a function of log-Gabor.

Log-Gabor has Gaussian functions, each viewed on the frequency and logarithmic frequency scales respectively. Given the singularity at the origin of the log function hence an analytic expression in the spatial image domain cannot be constructed, and due to their properties of frequency selection and orientation selection log-Gabor filter utilizes frequency representation. Log-Gabor filter in several applications has led to promising results i.e., facial expression classification (Vatcharaphrueksadee et al., 2022), iris identification (Mukherjee et al., 2021; Jayavadivel & Prabaharan, 2021), finger knuckle enhancement (Benmalek et al., 2022). Log-Gabor filter is also used in textural feature detections for different applications such as cataract detection (Chande et al., 2022).

Normalization

Taking the greylevel values of pixel (i, j) from a fingerprint image f(i, j), within N × N window, the following steps achieve the normalization:

1. Calculate the mean of the fingerprint image (1)${\displaystyle \text{mean}=\frac{1}{N^2}\sum _{i=0}^{N-1}\sum _{j=0}^{N-1}f\left(i,j\right)}$

2. Calculate variance by (2)${\displaystyle \text{Var}=\frac{1}{N^2}\sum _{i=0}^{N-1}\sum _{j=0}^{N-1}{\left(f\left(i,j\right)-\text{mean}\left(I\right)\right)}^2}$

3. Fingerprint image pixel intensity values are normalized by the following process (3)${\displaystyle G\left(i,j\right)=\left\{\begin{array}{c}{\text{mean}}_0+\sqrt{\frac{{\text{var}}_0{\left(I\left(i,j\right)-\text{mean}\right)}^2}{\text{var}}};\text{if}f\left(i,j\right)>M\hfill \\ {\text{mean}}_0+\sqrt{\frac{{\text{var}}_0{\left(I\left(i,j\right)-\text{mean}\right)}^2}{\text{var}}};\text{otherwise}\hfill \end{array}\right.}$

where mean₀ and var₀ are desired respective mean and variance values to which the newer normalized pixel intensity i.e., G(i, j) is equally spread around. This ensures better utilization of pixel intensity values with better contrast.

Segmentation

The foreground is a pattern made up of black and white regions, representing ridges and valleys. Hence, the foreground region will show higher variance when compared to the background regions. Taking the greylevel intensity values from a fingerprint image g(i, j), defined by w × w window, at pixel (i, j), following steps achieves segmentation:

1. Divide image fingerprint image into blocks, of w × w pixels (w is taken as 16). Calculate the mean value of each block via (4)${\displaystyle \text{mean}\left(m,n\right)=\sum _{w}g\left(i,j\right)}$ where g(i, j) denotes the pixel grey value and m, n represents the image’s respective block’s row and column.

2. Calculate each of the block’s variance values (5)${\displaystyle \text{var}\left(m,n\right)=\frac{\sum _{i=1}^w\sum _{j=1}^w{\left[g\left(i,j\right)-\text{mean}\right]}^2}{w\times w}}$ where m = 1, 2, …, M and n = 1, 2, …, N.

3. Check if the variance is above a certain threshold T for each block (6)${\displaystyle \text{var}\left(m,n\right)=\left\{\begin{array}{c}\text{var}\left(m,n\right);\text{var}\left(m,n\right)>T\hfill \\ 0;\text{otherwise}\hfill \end{array}\right.}$

This leaves behind the area of interest i.e., the foreground.

Coherence diffusion filter

A coherence diffusion filter is a nonlinear diffusion enhancement algorithm consisting of partial differential equations which retain fingerprint intensity image values based on the gradient of neighbouring image intensities. The filter smooths the images adaptively to its requirements. (7)${\displaystyle {\delta }_{t}I=\text{div}\left(\text{D}.\nabla I\right)}$ and (8)${\displaystyle \text{D}=\frac{1}{1+{\left(\frac{\left|\right|\nabla \left|\right|}{k}\right)}^2}}$ where “div” is the divergence operator, “D” is diffusion tensor, “ ∇I” is image gradient and “ k” is the respective constant.

Log-Gabor filter

The log-Gabor filter is two parts, the radial filter frequency response and angular frequency response as shown below (9)${\displaystyle {\text{G}}_r\left(r\right)=exp\left(-\frac{{\left[log\left(\frac{r}{f_{\circ }}\right)\right]}^2}{2.{\sigma }_r^2}\right)}$ (10)${\displaystyle {\text{G}}_{\theta }\left(\theta \right)=exp\left(-\frac{{\left[\theta -{\theta }_0\right]}^2}{2.{\sigma }_{\theta }^2}\right)}$

Multiplying them together provides us with the log-Gabor filter through which the fingerprint is passed. (11)${\displaystyle \text{G}\left(r,\theta \right)={\text{G}}_r\left(r\right).{\text{G}}_{\theta }\left(\theta \right)}$

Polar coordinate (r, θ), the local center frequency f₀, the local orientation angle θ₀, the scale bandwidth σ_r and angular bandwidth σ_θ is used in the construction of the log-Gabor filter. These four parameters are used to control the filter’s response. The orientation angle and the frequency field are calculated by the steps mentioned below, both values are instantaneous in nature to the local region of a fingerprint image. The following steps calculate the orientation angle θ₀ and center frequency f₀ for the local region.

1. Divide image into equal blocks, each of size B × B. For a 500 dpi resolution of a fingerprint image, the average frequency of fingerprint ridges (distance between two ridges) is 8 pixels. Hence image blocks twice the frequency size (16 × 16) will contain relevant ridge structure (Stojanović et al., 2016). For block sizes lesser than w, the computation time increases while the clarity of features degrades when the block size is increased above w.

2. Calculate gradients δ_x(x, y) and δ_y(x, y) of each pixel within the block.

3. Calculate the orientation of each block at pixel (i, j) (12)${\displaystyle {\theta }_0=\frac{1}{2}{tan}^{-1}\left(\frac{\sum _{u=i-\frac{W}{2}}^{i+\frac{W}{2}}\sum _{v=j-\frac{W}{2}}^{j+\frac{W}{2}}2{\delta }_x\left(u,v\right){\delta }_y\left(u,v\right)}{\sum _{u=i-\frac{W}{2}}^{i+\frac{W}{2}}\sum _{v=j-\frac{W}{2}}^{j+\frac{W}{2}}{\delta }_x^2\left(u,v\right)-{\delta }_y^2\left(u,v\right)}\right)}$

4. The orientation is orthogonal in the frequency domain to the spatial domain, hence (13)${\displaystyle {\theta }_0={\theta }_0+\frac{\pi }{2}}$ to get the corresponding angle in the frequency domain.

5. Within each block, take pixel values that are orthogonal to the local orientation. From the resulting B × B matrix of pixel values, summing each column will result in a one-dimensional array i.e., a one-dimensional x-signature wave with extrema representing ridge and valleys waveform (Orczyk & Wieclaw, 2011).

The extrema correspond to the pattern of the fingerprint image. The frequency f₀ is calculated from the one-dimensional wave via (14)${\displaystyle f_0=\frac{1}{T\left(i,j\right)}}$ where T(i, j) is the total number of pixels given between consecutive ridges i.e., peaks (see Fig. 5). Hence θ₀ and f₀ corresponds to equations (9) and (10), respectively.

Binarization

The resulting fingerprint image is composed of different greyscale pixel intensity values. For better contrast enabling more clarity of ridges and valleys binarization is recommended to improve contrast via Otsu thresholding. A local threshold T is calculated, and any pixel value of a fingerprint image above T is fixed to a value of one while below the threshold is set as zero. Finding the threshold T involves the minimization of intra-class variances (15)${\displaystyle {\sigma }_w^2\left(t\right)=w_0\left(t\right){\sigma }_0^2\left(t\right)+w_1\left(t\right){\sigma }_1^2\left(t\right)}$ where w₀ and w₁ are the probabilities of two classes, with threshold t separating them apart. Variances of the two classes are denoted by ${\sigma }_0^2$ and ${\sigma }_1^2$. (16)${\displaystyle w_0\left(t\right)=\sum _{i=0}^{t-1}p\left(i\right)w_1\left(t\right)=\sum _{i=t}^{L-1}p\left(i\right)}$

Between intra-class variance and inter-class variance, reducing the former increases the latter and is denoted via the class’s probabilities w and mean µ. (17)${\displaystyle {\sigma }_b^2\left(t\right)=w_0\left(t\right)w_1\left(t\right){\left[{\mu }_0\left(t\right)-{\mu }_1\left(t\right)\right]}^2.}$ A greyscale image has 256 depth of pixel intensities, the threshold T value is selected that corresponds to the lowest class variance. Hence for a fingerprint image f(i, j) (18)${\displaystyle f\left(i,j\right)=\left\{\begin{array}{c}1;f\left(i,j\right)>T\hfill \\ 0;\text{otherwise}.\hfill \end{array}\right.}$