We investigate an approach to the artistic stylization of photographic images and videos that uses an understanding of the role of abstract representations in art and perception. We first learn a database of representations from a corpus of images or image sequences. Using this database, our approach synthesizes a target image or video by matching geometric representations in the target to the closest matches in the database based on their shape and color similarity. We show how changing a few parameters of the synthesis process can result in stylizations that represent aesthetics associated with Impressionist, Cubist, and Abstract Expressionist paintings. As the stylization process is fast enough to work in real-time, our approach can also be used to learn and synthesize the same camera image, even aggregating the database with each new video frame in real-time, a process we call "Memory Mosaicing". Finally, we report the user feedback of 21 participants using an augmented reality version of "Memory Mosaicing" in an installation called Augmented Reality Hallucinations, where the target scene and database came from a camera mounted on augmented reality goggles. This information was collected during an exhibition of 15,000 participants at the Digital Design Weekend at the Victoria and Albert Museum (co-located during the London Design Festival).