A Multichannel Approach to Fingerprint Classification

JAIN ET AL.: A MULTICHANNEL APPROACH TO FINGERPRINT CLASSIFICATION 353Fig. 6. Fingerprints have well defined local frequency and orientation.(a) Ridges in a local region. (b) Fourier spectrum.furrow details in the fingerprint are lost. On the other hand,if they are too small, the filter is not effective in removingnoise. In our algorithm, the values of d x and d y were empiricallydetermined and both were set to 4.0.A fingerprint image is decomposed into four componentimages corresponding to four different values of q (0 o , 45 o ,90 o , and 135 o ) with respect to the x-axis (Fig. 5). A fingerprintimage is convolved with each of the four Gabor filtersto produce the four component images. Convolution with a0 o -oriented filter accentuates ridges parallel to the x-axis,and it smoothes ridges which are not parallel to the x-axis.Filters tuned to other directions work in a similar way. Accordingto our experimental results, the four componentimages capture most of the ridge directionality informationpresent in a fingerprint image and thus form a valid representation.We illustrate this by reconstructing a fingerprintimage by adding together all the four filtered images. Thereconstructed image is similar to the original image but theridges have been enhanced (Fig. 7).Before decomposing the fingerprint image, we normalizethe region of interest in each sector separately to a constantmean and variance. Normalization is done to remove theeffects of sensor noise and finger pressure differences. LetI(x, y) denote the gray value at pixel (x, y), M i and V i , theestimated mean and variance of sector S i , respectively, andN i (x, y), the normalized gray-level value at pixel (x, y). Forall the pixels in sector S i , the normalized image is defined as:N x,yi1 6=%& K' K2V73I1x,y6-M80iM0+V, if I x,y > Mii(13)22V073I1 x,y6-Mi8M -, otherwise,0Vi21 6where M 0 and V 0 are the desired mean and variance values,respectively. Normalization is a pixel-wise operation whichdoes not change the clarity of the ridge and furrow structures.If normalization is done on the entire image, then itcannot compensate for the intensity variations in the differentparts of the finger due to finger pressure differences.Normalization of each sector separately alleviates this problem.For our experiments, we set both M 0 and V 0 to a valueof 100. Normalized, filtered, and reconstructed images for thefingerprint shown in Fig. 4 are shown in Fig. 7.2.3 Feature VectorIn each component image, a local neighborhood withridges and furrows that are parallel to the correspondingFig. 7. Normalized, filtered, and reconstructed fingerprint images. (a)Normalized image. (b) Component image 0°. (c) Component image45°. (d) Component image 90°. (e) Component image 135°. (f) Reconstructedimage.filter direction exhibits a higher variation, whereas a localneighborhood with ridges and furrows that are not parallelto the corresponding filter tends to be diminished bythe filter which results in a lower variation. The spatialdistribution of the variations in local neighborhoods of thecomponent images thus constitutes a characterization ofthe global ridge structures and is well captured by thestandard deviation of grayscale values. In our algorithm,the standard deviation within the sectors defines the featurevector.Let C iq (x, y) be the component image corresponding to qfor sector S i . For "i, i = 0, 1, ¡, 47 and q ³ [0 o , 45 o , 90 o , 135 o ],a feature is the standard deviation F iq , defined as:3 1 6 8 2 , (14)Fi = Ê Ci x,y - Miq q qK iwhere K i is the number of pixels in S i and M iq is the mean ofthe pixel values in C iq (x, y). The 192-dimensional featurevectors, also called FingerCodes (similar to the IrisCode