Persistence Lenses: Segmentation, Simplification, Vectorization, Scale Space and Fractal Analysis of Images
This provides a novel mathematical framework for image processing tasks like segmentation and simplification, potentially benefiting computer vision and graphics researchers, though it appears incremental in applying topological methods to images.
The paper introduces persistence lenses as a hierarchy of level sets from an image's Reeb graph to achieve hierarchical segmentation, vectorization, simplification, scale space, and fractal analysis of images, with results including Jordan curves for segmentation and varilet basis for simplification.
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 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.