Persistence Lenses: Segmentation, Simplification, Vectorization, Scale Space and Fractal Analysis of Images

A persistence lens is a hierarchy of disjoint upper and lower level sets of a continuous luminance image’s Reeb graph. 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. c ©2016 Martin Brooks 1 ar X iv :1 60 4. 07 36 1v 1 [ cs .C V ] 2 5 A pr 2 01 6