In this paper, we study the classification problem in the situation where large volumes of training data become available sequentially (online learning). In medical imaging, this is typical, e.g., a 3D brain MRI dataset may be gradually collected from a patient population, and not all of the data is available when the analysis begins. First, we describe two common ensemble learning algorithms, AdaBoost and bagging, and their corresponding online learning versions. We then show why each is ineffective for segmenting a gradually increasing set of medical images. Instead, we introduce a new ensemble learning algorithm, termed Lossless Online Ensemble Learning (LOEL). This algorithm is lossless in the online case, compared to its batch mode. LOEL outperformed online-AdaBoost and online-bagging when validated on a standardized dataset; it also performed better when used to segment the hippocampus from brain MRI scans of patients with Alzheimer's Disease and matched healthy subjects. Among those tested, LOEL largely outperformed the alternative online learning algorithms and gave excellent error metrics that were consistent between the online and offline case; it also accurately distinguished AD subjects from healthy controls based on automated measures of hippocampal volume.