Geometry of isophote curves

TL;DR

This paper investigates the evolution of symmetry sets and medial axes of isophote curves in 2D images, extending prior work to include singular members and proposing a combined object and appearance modeling approach.

Contribution

It extends the analysis of symmetry sets to include singular isophote curves from surface sections, integrating object skeletons with image appearance modeling.

Findings

Analyzed the evolution of symmetry sets for singular isophote curves.

Proposed a combined object and appearance representation method.

Extended prior smooth curve analysis to include singular members.

Abstract

In this paper, we consider the intensity surface of a 2D image, we study the evolution of the symmetry sets (and medial axes) of 1-parameter families of iso-intensity curves. This extends the investigation done on 1-parameter families of smooth plane curves (Bruce and Giblin, Giblin and Kimia, etc.) to the general case when the family of curves includes a singular member, as will happen if the curves are obtained by taking plane sections of a smooth surface, at the moment when the plane becomes tangent to the surface. Looking at those surface sections as isophote curves, of the pixel values of an image embedded in the real plane, this allows us to propose to combine object representation using a skeleton or symmetry set representation and the appearance modelling by representing image information as a collection of medial representations for the level-sets of an image.