The fundamental premise of visualization is that a useful correspondence between pixels and data can be built. However, visualization programs rarely operate at the pixel level. Instead of the discrete, finite space of pixels, the most common visualization models work with canvases of floating-point coordinates and geometric shapes. Preserving some source data link all the way down to the pixel level provides many opportunities for improving visualization. This paper describes Abstract Rendering (AR), a framework that preserves the data-to-pixel link. Using this pixel-level link, AR is used to provide a unique control over the final visual representation of data sets at all scales and from a variety of visualization technique families.