Technological advancements have recently allowed scanning transmission electron microscopes STEMs) to directly image atomic structures with better than 1 angstrom lateral resolution. Though the images contain chemical information about the sample through the relation of atomic number and thickness to image brightness, easy quantification of sample content using STEM images has remained elusive. This has been primarily due to the image imperfections caused by microscope instabilities, damaged or overly thick samples, or noise inherent in the high-angle annular dark field HAADF) imaging technique. With recent increases in beam current, atomic resolution electron energy loss spectroscopic EELS) mapping has made quantification possible over relatively large areas. However, the areas are still quite small in comparison to STEM images and require significantly greater acquisition times. This has excluded EELS from application to atomic-resolution quantification of beam-sensitive materials and limited the already minute sample volume studied in the STEM. This thesis has aimed to develop data analysis techniques that enhance the direct quantification of data extracted from HAADF-STEM images. Multivariate data analysis provided a means of studying correlated variations in image intensities, and was explored for application to the simple mass-thickness contrast of HAADF-STEM images. In this thesis, it is shown through image simulation that multivariate data analysis derives a linear relationship between the known sample composition and image intensity changes. The linear relationship is in the form of eigenimages and scores. Eigenimages correspond to characteristic intensity variations across many images. Scores relate the extent to which a characteristic intensity variation occurs in a particular image. These relationships can be derived many different ways, including principle component analysis, correspondence analysis, and independent component analysis. The method and implementation of these analyses are demonstrated on experimental data, giving local point defect information arising only from intensity variation. Calibration using simulated images allows quantification of individual column occupations.