The use of biometrics to authenticate users and control access to secure areas has become extremely popular in recent years, and biometric access control systems are frequently used by both governments and private corporations. However, these systems may represent risks to security when deployed without considering the possibility of biometric presentation attacks (also known as spoofing). Presentation attacks are a serious threat because they do not require significant time, expense, or skill to carry out while remaining effective against many biometric systems in use today. This research compares three different software-based methods for facial and iris presentation attack detection in images. The first method uses Inception-v3, a pre-trained deep Convolutional Neural Network (CNN) made by Google for the ImageNet challenge, which is retrained for this problem. The second uses a shallow CNN based on a modified Spoofnet architecture, which is trained normally. The third is a texture-based method using Local Binary Patterns (LBP). The datasets used are the ATVS-FIr dataset, which contains real and fake iris images, and the CASIA Face Anti-Spoofing Dataset, which contains real images as well as warped photos, cut photos, and video replay presentation attacks. We also present a third set of results, based on cropped versions of the CASIA images.