Verifying an identity claim by fingerprint recognition is a commonplace experience for millions of people in their daily life, e.g. for unlocking a tablet computer or smartphone. The first processing step after fingerprint image acquisition is segmentation, i.e. dividing a fingerprint image into a foreground region which contains the relevant features for the comparison algorithm, and a background region. We propose a novel segmentation method by global three-part decomposition (G3PD). Based on global variational analysis, the G3PD method decomposes a fingerprint image into cartoon, texture and noise parts. After decomposition, the foreground region is obtained from the non-zero coefficients in the texture image using morphological processing. The segmentation performance of the G3PD method is compared to five state-of-the-art methods on a benchmark which comprises manually marked ground truth segmentation for 10560 images. Performance evaluations show that the G3PD method consistently outperforms existing methods in terms of segmentation accuracy.