Machine learning has progressed rapidly in the field of image analysis in recent years, particularly with larger datasets and more computational power becoming readily available. However, the applications that machine learning has been slower to make progress in are typically those in which data or labels are more difficult or expensive to obtain, such as medical imaging. In situations such as these, methods that can robustly enable machine learning techniques have the potential to allow for automated workflows or more sophisticated analysis in applications that have not been explored before. Additionally, many aspects of medical images can cause increased complexity in analysis, such as high resolution, 3-dimensional nature, or detailed anatomy across many size scales. This work attempts to address these problems through several methods designed to apply machine learning to small, medical imaging datasets. One method that can be used to enable deep learning with small datasets is transfer learning, in which features learned on a task from a separate, larger dataset are used as the initial baseline for learning on the smaller target dataset, in order to improve algorithm initialization. In this work, a method of transfer learning using a convolutional autoencoder is applied to the classification of 3D shoulder labral tear magnetic resonance images (MRIs). This application is investigated because clinical diagnosis based on unenhanced MRI is difficult, and often requires the use of costly and invasive contrast-enhancing procedures. In other fields of medical imaging, such as histopathology, images can be extremely high-resolution, far too large to apply typical deep learning algorithms for analysis. Often, important clinical features in these images will be much smaller than the relative size of the image. For example, in placenta histopathology, identification of maternal blood vessel lesions called decidual vasculopathy is important for the characterization of mothers at risk for hypertensive disorders in pregnancy such as preeclampsia, however these lesions are small and sparse throughout the whole-slide histological image. This work proposes the use of a multiresolution hierarchical deep learning framework in order to minimize the number of false positives when searching a high-resolution image for sparse features. This framework is applied to the search of blood vessel lesions in placenta histopathology, as well as a second application of object detection in high-resolution satellite imagery to demonstrate generalizability. Because the majority of placentas in large hospitals are currently being thrown out without pathological examination, this automated method of hierarchically analyzing tissue slides has the potential to provide an assessment of the risk of preeclampsia for the majority of mothers who do not currently have access to this service.