Fingerprint Image Enhancement via Raised Cosine Filtering

Fingerprint Image Enhancement via Raised Cosine Filtering Shing Chyi Chua 1a, Eng Kiong Wong 2, Alan Wee Chiat Tan 3 1,2,3 Faculty of Engineering and Technology, Multimedia University, Melaka, Malaysia. a E-mail: scchua@mmu.edu.my Abstract This paper aims to present fingerprint image enhancement by using directional circular raised cosine filters which are implemented using a radial component and an angular component. It has been compared with the common filters used for bandpass filtering, i.e. circular Gabor filters and Log-Gabor filters at the same bandwidth. The experimental results have found that the circular raised cosine filters perform at par with the Gabor filters at bandwidth of three octaves for fingerprint image enhancement. The circular raised cosine filters have the advantages of: i) the frequency tail has gradual frequency response that drops towards zero, and ii) its residual can be implemented as a lowpass filter in tandem with a narrow bandpass filter. The Log-Gabor filter did not perform as well due to its design of null DC and thus the results have also shown that the DC component is necessary for fingerprint image enhancement. Keywords: Fingerprint enhancement, raised cosine filter, Gabor filter, Log-Gabor filter Introduction Fingerprint enhancement is a process whereby the raw fingerprint images are improved so that feature extraction such as minutiae detection (for matching) can improve the overall performance. The need for such enhancement is due to quality of the fingerprint images, some regions in the fingerprint are not well-defined, or the condition of the fingerprint when it is acquired such as wet or dry (which may cause excessive blotching or blurring), or noise that may be accidentally introduced such as smearing of inkrolled fingerprint, etc. The image that is enhanced shall improve visual perception based on the human viewers (i.e. to make it clearer ) and thus is assumed to be a better image than it previously was. In fingerprint image, enhancement is aimed at increasing the contrast between the ridges and valleys; and for connecting broken ridges due to insufficient amount of ink, etc. [1]. Fingerprint image enhancement can either be carried out in the spatial domain or the frequency domain. Observation of frequency response of the image to be enhanced is crucial as it provides the cue of how filters are to be designed. Fingerprint enhancement can be done on binary ridge images or grey level images. However the binary images, which are obtained through extraction of the grey level images, suffered from lost of information of the true ridge structures. Grey level images can be modelled locally as a sinusoidal plane wave which has well defined frequency and orientation and thus can be exploited for the enhancement. However, enhancement cannot be applied to poor quality regions [2]. Localized linear filters are commonly used as feature or texture extractors especially in classification and segmentation. Such filters have characteristics of bandpass filters with certain optimal joint localized properties in the spatial and frequency domain. One such filter is the Gabor filters, motivated by the studies by Daugman (1985) [3] on visual modelling of simple cells which found out the orientation selectivity of visual cortical neurons. Daugman has shown that Gabor filters provide optimal joint resolution in space and spatial-frequency and that Gabor filters exhibit spatial responses similar to receptive field profiles in mammalian vision. Gabor filters are employed in wide range of applications such as texture segmentation, retina identification, edge detection, image representation, etc. Gabor filters represent time varying signals that are localized in spatial and frequency domain by the product of a Gaussian function and a sinusoid. However, Gabor filters suffer a drawback due to having nonzero DC component which can significantly affect low frequency bands in the frequency domain. According to Kovesi (2015) [4], the maximum bandwidth of a Gabor fiter is about one octave and it will not be optimal if one is seeking broad spectral information. An alternative is the Log-Gabor filters proposed by Field (1987) [5]. The filter can only be analytically defined in frequency domain as Gaussian functions with a null DC component at the origin due to the singularity of the log function (it is a Gaussian function when one views it in the logarithmic frequency scale). The filter is a product of a radial component and an angular component. Field suggested that natural images are better coded in the logarithmic frequency so as not to over represent the low frequency components and under represent the high frequency components which seems to align with measurements on mammalian visual system that humans have cell response that are symmetric on the logarithmic frequency scale. Various researches in fingerprint enhancement using Gabor filters includes [2], [6]; on circular Gabor filters [7], [8]; and improved or enhanced Gabor filters [9], [10], and other types of filters such as anisotropic filters [11], [12], and frequency domain filtering [13], [14]. A comparative study on most major filtering approaches to texture feature extraction can be found in [15]. In this paper, a circular raised cosine filtering is proposed and implemented for fingerprint enhancement. Comparison has been made with circular Gabor filter and Log-Gabor filter. It has been found that raised cosine filtering produces similar filtered output as that of the Gabor filtering approach while having advantages of i) the frequency end drops gradually towards zero, ii) a residue which can perform lowpass filtering while maintaining narrow bandpass filtering. The 698

investigation is strictly performed based on fingerprint image enhancement. Circular Raised Cosine Filtering For fingerprint images the ridge information are all clustered in a circular spectrum at a distance proportional equal to the frequency of the ridge. In a local window, this feature is even more striking as shown in Fig.1. A simple circular raised cosine filtering can be used as the spectra information is not broad. Figure 1: Frequency spectra of fingerprint in a localized window The raised cosine filter has the advantage that the frequency tail drops gradually to zero, a feature both Gabor filters and Log- Gabor filters lack of. As the frequency tail tends towards infinity, the response of these two types of filters drops towards infinitesimal value. Fig. 2 shows the frequency response plot with normalized radius of Gabor filter, Log-Gabor filter and raised cosine filter at bandwidth of one octave and wavelength of 10 pixels. Fig. 2 is a close-up view of the frequency response plot towards higher frequency end. As can be seen, the raised cosine filter response end drops gradual to zero, while Gabor filter and Log-Gabor filter tends towards an infinitesimal value which is often thresholded to cut down unnecessary computation time. The choice of the threshold value (such as below 1% of amplitude or below 1% of the power spectrum) is often arbitrary and by employing raised cosine filtering with the same bandwidth, it eliminates one from thresholding arbitrarily. Fig. 3 shows the half-magnitude response plot. As observed, the raised cosine and Gabor filters exhibit an almost exact response and thus the filtered image should be very close or hard to discern from one another. Figure 2: Frequency response of circular Gabor filter, Log- Gabor filter and raised cosine filter Close-up view of the frequency tail In this paper, a six directional raised circular cosine filter is implemented. Fig. 4 shows the half-magnitude response plot of the six directional raised cosine filters at wavelengths (or ridge distances) of five, 10 and 20 pixels (the larger the wavelength, the smaller the concentric bands). The circular implementation of the various filters depends on two components, i.e. the radial component f(r) and the angular component f( ) as described by Eq. (1) below. f(r, )=f(r)f( ) (1) The angular component is given by 2 ( ) / ] f ( ) exp[ 2, (B / 2) 1/ 2log2 (2) o where o is the orientation angle and B is the angular bandwidth which is set to 2 /k, and k is the number of direction/orientation needed. The radial component for Gabor, Log-Gabor and raised cosine filters is as given in Table 1. 699

Filter International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 1 (2016) pp 698-705 Table 1: Radial component of different filters Radial component Gabor 2 f ( r) exp[ ( r f ) / 2 ] where / f 1/ 2log2[( 2 1) ( 2 1)] r Log-Gabor 2 f ( r) exp[ log( r / f ) / 2] where r BW r (BW / 2 ) log2 / 2 Raised cosine f ( r) 0. 5cos( ( r f )/ 2kf ) 0. 5 for ( 1 2k ) f r ( 1 2k) f where k ( 2 1) ( 2 1) Note: BW is the radial bandwidth BW BW r BW All design parameters assumed that the overlapping of the response occurred at half magnitude as can be seen from Fig. 3 and Fig. 4. Fig. 5 shows the parameters used to derive the raised cosine filter s radial component. The parameter k is 1/3 when the radial bandwidth BW required is one octave. Fig. 6 shows the representation of the radial component, angular component and raised cosine filter oriented at 0 o, 60 o, and 120 o at wavelength of 10 pixels. Fig. 7 shows the raised cosine filter s frequency spectrum (left) and its corresponding spatial domain. Note that both responses have been enlarged for ease of visual inspection. The spatial domain plot shows sinusoidal-like waveform with equally spaced wavelengths and thus proves that raised cosine filter can be used to enhanced fingerprint image which exhibit sinusoidal likeness of the same wavelength. Figure 4: Raised cosine response at half magnitude for six directions with bandwidth of one octave and wavelength of five, 10 and 20 pixels Figure 5: Raised cosine filter design parameters Figure 3: Filter response at four directions with one octave bandwidth and wavelength of 10 pixels (c) Figure 6: The radial component (left), angular component (middle) and filter representation (right) in the direction of 0 o 60 o (c) 120 o at ridge distance of 10 pixels 700

image in Fig. 8 while the quantized image in Fig. 8. As can be seen, the regions of the quantized image are in proportion to the number of directions used in the filtering process and are thus used in the selection of regions to obtain the final enhanced image. ˆ ~ I merged ( m, n) I n( m, n) where n (6) Ienhanced( m, n) H[ I merged ( m, n)] (7) (c) Figure 7: The filter s frequency spectrum (left) and its corresponding spatial domain (right) in the direction of 0 o 60 o (c) 120 o at ridge distance of 10 pixels Filtering Process The raised cosine frequency domain filtering process is as follows. First the input fingerprint image is transformed into the frequency domain via Fast Fourier Transform (FFT). That is M 1N 1 mu nv F( u, I( m, n) exp 2 i (3) M N m 0 n 0 where I(m,n) is the input image of size MxN. The radial component is designed at the same ridge distance r of the fingerprint image (the estimation of ridge distance is not discussed in this paper). The FFT image is then multiplied with each directional filter (six direction has been chosen) to obtain the directional filtered images. I ( u, F( u, f ( r, ), : 0 I ( u, F( u, f ( r, ), 1 I ( u, F( u, f ( r, ) 5 1 0 5 where f(r, ) is the nth-directional filter with n=n /6, n=0,1,,5. The magnitude of inverse FFT images are then obtained. 1 1 1 M N mu nv I ˆ n ( m, n) I n ( u, exp 2 i MN M N (5) u 0 v 0 Each region is block selected based on the direction of quantized image of the orientation field ~. It is then histogram equalized H[.] to produce the enhanced fingerprint image. An example of the orientation field is as shown superimposed on an original (4) Figure 8: Orientation image Quantized orientation image Results and Discussion Fig. 9 shows an original fingerprint image and Fig. 9 the enhanced fingerprint image. Fig. 10 shows binary images of original fingerprint and enhanced fingerprint (both images have also been segmented) obtained using Otsu threshold. The binary image of the enhanced fingerprint also shows that many ridgelines are now connected and more well-defined as compared to the original image. For regions that are of poor quality, the enhancement process is unable to recover much visibility. Such poor quality regions are usually masked out and not considered. Fig. 11 shows the thinned images of the binary enhanced fingerprint images. Fig. 11 is the thinned image with short ridgelines of less than 30 pixels removed. Some postprocessing needs to be carried out to connect short 701

segments which are in alignment within certain tolerance and to remove false features such as the false minutiae structures of holes, spurs, spikes, and triangles if fingerprint matching is involved [16]. The enhanced fingerprint image as depicted in Fig. 9 are produced by using six directional raised cosine filters at bandwidth of three octaves which has been found optimum. Fig. 12 shows the results of each filtered image for each of the six orientations: 0 o, 30 o, 60 o, 90 o, 120 o, and 150 o. It is clearly revealed that regions that are aligned with the directions of the directional filters are more striking. The author has also discovered that, if the raised cosine function is bounded only at the high frequency tail while maintaining a residue at the low frequency end, raised cosine filter not only performs as a bandpass filter but also acts as a lowpass filter. For comparison, the frequency response plots with residue at one octave and without residue at three octaves are as depicted in Fig. 13. By inspecting the filter s response plots, one can notice a similarity and a difference. The difference is that the bandwidth is differed by three octaves and one octave. On the similarity, both the responses have a DC value at the origin. Clearly, the present of the DC value must have an influence on the filtered image. It has also been found that by using the residue as a lowpass filter, an enhanced image can be produced at bandwidth of just one octave as depicted in Fig. 14. The corresponding thinned image is shown in Fig. 14. Figure 10: Binary image of the original fingerprint enhanced fingerprint Figure 9: Original fingerprint Enhanced fingerprint image The enhanced image by raised cosine filtering is as good as those produced by with Gabor filter at the same bandwidth. This is as shown in Fig. 15. On the other hand, the Log- Gabor filter did not produce the expected enhancement. This is as depicted in Fig. 15. A careful comparison of raised cosine, Gabor and Log-Gabor filters response plots at bandwidth of three octaves as illustrated in Fig. 16 revealed that both raised cosine and Gabor filters have DC components while Log-Gabor is locked at null DC due to its design. As all filters are tested using the same bandwidth of three octaves, performance should be at par with each other. Due to the existence of the DC components for raised cosine and Gabor filters, the authors have again performed another experiment on Log-Gabor filter to see if the fingerprint image is rightly enhanced. Now, a DC component of 0.5 is experimentally added at the original of zero frequency of Log-Gabor filters. This is to confirm whether the DC component plays a role in fingerprint enhancement. Alas, Fig. 17 shows the enhanced fingerprint image of the Log- Gabor filters, which clearly shows that the fingerprint image is now enhanced. On the computation requirement, by averaging the time taken to perform the enhancement of 100 images of the NIST 702

Special Database 4 [17], the time is 4.16s, 4.09s and 4.07s for Log-Gabor, Gabor, and raised cosine filters. The test is carried out on Windows Vista, 32-bit OS using Intel Core Dual 1.5GHz and 2038 MB of RAM. All the source codes are written and tested using Matlab R2007a. while having advantage of i) the high frequency end drops gradually towards zero and thus eliminates one from thresholding, ii) a residue which can perform lowpass filtering while maintaining small bandpass filtering which is often more desirable than wide bandpass filtering. (c) (d) Figure 11: Thinned enhanced image enhanced image with short ridgelines removed Conclusion A fingerprint enhancement approach using raised circular cosine filter has been proposed. The frequency response characteristic is similar to that of the Gabor filters. The filter s response towards the higher frequency tail drops gradual to zero and thus eliminate the need for thresholding, which is usually carried out for Gabor filters and Log-Gabor filters as their response towards higher frequency tail tend towards infinitesimal value. It has been found that the raised cosine filtering performed at par with Gabor filtering at bandwidth of three octaves for the image investigated while the raised cosine filtering with residue at one octave bandwidth has also been found to produce the enhanced fingerprint image. Investigation has also shown that the raised DC component in the bandpass design is necessary to obtain the desired enhanced fingerprint image. This is clearly demonstrated by comparing Log-Gabor filter and the Log-Gabor filter with added DC value. On the timing requirement, it is found that raised cosine filtering is faster. In conclusion, the raised cosine filtering produces similar output to that of the Gabor filtering approach (e) Figure 12: Filtered images at 0 o 30 o (c) 60 o (d) 90 o (e) 120 o (f) 150 o (f) 703

Figure 13: Response plot Half magnitude plot Figure 15: Enhanced fingerprint image by Gabor filter Log-Gabor filter Figure 14: Enhanced image Thinned enhanced image of one octave raised cosine filtering with residue Figure 16: Response plots of raised cosine, Gabor, and Log- Gabor filters at three octaves of bandwidth 704

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