Nonlinear hyperbolic smoothing at a focal point.

Hyperbolic Smoothing at a Focal

FOCAL POINT AND FOCAL K-PLANE

This paper deals with the basic notions of k-tautimmersions . These notions come from two special cases; that is, tight and taut immersions. Tight and taut based on high and distance functions respectively and their basic notions are normal bundle, endpoint map, focal point, critical normal. We generalize hight and distance functions to cylindrical function and define basic notions of k-taut ...

Hyperbolic "Smoothing" of Shapes

We have been developing a theory of generic 2-D shape based on a reaction-diffusion model from mathematical physics. The description of a shape is derived from the singularities of a curve evolution process driven b y the reaction (hgperbolic) term. The diffusion (parabolic) term is related to smoothing and shape simplification. However, the unification of the two is problematic, because the sl...

Clustering by Hyperbolic Smoothing

This paper addresses the minimum sum-of-squares clustering problem. The mathematical modeling of this problem leads to a min-sum-min formulation which, in addition to its intrinsic bi-level nature, has the significant characteristic of being strongly nondifferentiable. To overcome these difficulties, the solution method proposed adopts a smoothing strategy using a special C ∞ differentiable cla...

Solutions of Nonlinear Hyperbolic Equations at Resonance