2 research outputs found
Geometry of isophote curves
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.Comment: 15 pages, 7 figure
Level sets of functions and symmetry sets of surface sections
We prove that the level sets of a real C s function of two variables near a non-degenerate critical point are of class C [s/2] and apply this to the study of planar sections of surfaces close to the singular section by the tangent plane at an elliptic or hyperbolic point, and in particular at an umbilic point. We go on to use the results to study symmetry sets of the planar sections. We also analyse one of the cases coming from a degenerate critical point, corresponding to an elliptic cusp of Gauss on a surface, where the differentiability is reduced to C [s/4]. However in all our applications we assume C  ∞  smoothness