Fourier and Variational Based Approaches for Fingerprint Segmentation

Abstract

Fingerprint recognition plays an important role in many commercial applications and is used by millions of people every day, e.g. for unlocking mobile phones. Fingerprint image segmentation is typically the first processing step of most fingerprint algorithms and it divides an image into foreground, the region of interest (ROI), and background. Two types of error can occur during this step and both have a negative impact on the recognition performance: 'true' foreground can be labelled as background and features like minutiae can be lost, or conversely 'true' background can be misclassified as foreground and spurious features can be introduced. The contribution of this study is threefold: We propose the feature extractors for fingerprint images with Fourier and variational based approaches (see Chapter 2 and Chapter 3). In the Fourier domain (cf. [1]), we assume that fingerprint patterns mostly stay in a specific range of frequencies. We introduce a novel factorized directional bandpass (FDB) segmentation method based on the directional Hilbert transform of a Butterworth bandpass (DHBB) filter interwoven with soft-thresholding for feature extraction. Then, a morphological operator is applied on these extracted features to obtain the ROI. In the variational approach (cf. [2]), fingerprint images are characterized by a smooth, curved and oriented pattern which has a sparse representation in certain transform domains. Based on this assumption, we propose a model for global three-part decomposition (G3PD) which takes the nature of the texture occurring in real fingerprint images into account. The G3PD method decomposes the original fingerprint image into a piecewise constant image, ``texture image'' and noise image. The decomposition is obtained by finding the minimizer of the convex minimization $\text{TV}-G^{3/4}_{1,1}-\ell_1-G^{-3/4}_{\infty,\infty}$. After texture extraction by the G3PD method, the ROI is attained by morphological operators. We provide a manually marked ground truth segmentation for 10560 images of the FVC database as an evaluation benchmark which is made publicly available. We conduct a systematic performance comparison between our proposed methods and four of the most often cited fingerprint segmentation algorithms. The evaluation shows that our approaches clearly outperform these four widely used methods, especially the $\text{TV}-G^{3/4}_{1,1}-\ell_1-G^{-3/4}_{\infty,\infty}$ model.