A persistence lens is a hierarchy of disjoint upper and lower level sets of a continuous luminance image's Reeb graph, providing a contrast-invariant topological representation of image contrast variation. Pulled back to the image, the boundary components of a persistence lens's interior components are Jordan curves that serve as a hierarchical segmentation of the image, and may be rendered as vector graphics. A persistence lens determines a varilet basis [10] for the luminance image, in which image simplification is a realized by subspace projection. Image scale space, and image fractal analysis, result from applying a scale measure to each basis function.