The vulnerabilities of face-based biometric systems to presentation attacks have been finally recognized but yet we lack generalized software-based face presentation attack detection (PAD) methods performing robustly in practical mobile authentication scenarios. This is mainly due to the fact that the existing public face PAD datasets are beginning to cover a variety of attack scenarios and acquisition conditions but their standard evaluation protocols do not encourage researchers to assess the generalization capabilities of their methods across these variations. In this present work, we introduce a new public face PAD database, OULU-NPU, aiming at evaluating the generalization of PAD methods in more realistic mobile authentication scenarios across three covariates: unknown environmental conditions (namely illumination and background scene), acquisition devices and presentation attack instruments (PAI). This publicly available database consists of 5940 videos corresponding to 55 subjects recorded in three different environments using high-resolution frontal cameras of six different smartphones. The high-quality print and videoreplay attacks were created using two different printers and two different display devices. Each of the four unambiguously defined evaluation protocols introduces at least one previously unseen condition to the test set, which enables a fair comparison on the generalization capabilities between new and existing approaches. The baseline results using color texture analysis based face PAD method demonstrate the challenging nature of the database.