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

Martin Brooks

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arXiv · 1604.07361

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

Martin Brooks

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Abstract

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.

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Martin Brooks. 2016-04-25. Persistence Lenses: Segmentation, Simplification, Vectorization, Scale Space and Fractal Analysis of Images. https://arxiv.org/abs/1604.07361

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