Now showing items 1-11 of 11

• #### Affine properties of convex equal-area polygons ﻿

2012-10
In this paper we discuss some affine properties of convex equal-area polygons, which are convex polygons such that all triangles formed by three consecutive vertices have the same area. Besides being able to approximate ...
• #### Affine skeletons and monge-ampere equations ﻿

2009
An important question about a. ne skeletons is the existence of differential equations that are related to the 'affine distance' and the 'area distance' (hence to a. ne skeletons) in the same way the Eikonal equation is ...
• #### Area distances of convex plane curves and improper affine spheres ﻿

2008
The area distance to a convex plane curve is an important concept in computer vision. In this paper we describe a strong link between area distances and improper affine spheres. Based on this link, we propose an extremely ...
• #### Evolution of an extremum by curvature motion ﻿

2004
In this paper we consider the evolution of an isolated extremum of a function under the curvature motion in the plane. We define different notions of circular extrema and show that, immediately after the motion begins, the ...
• #### A fast marching method for the area based affine distance ﻿

2008-01
In a previous paper, it was proved that the area based affine distance of a convex region in the plane satisfies a non-homogeneous Monge-Ampere differential equation. Based on this equation, in this paper we propose a fast ...
• #### A geometric representation of improper indefinite affine spheres with singularities ﻿

2011
Given a pair of planar curves, one can define its generalized area distance, a concept that generalizes the area distance of a single curve. In this paper, we show that the generalized area distance of a pair of planar ...

2009

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• #### A numerical scheme for the curvature equation near the singularities ﻿

2005
In this paper we propose a modification in the usual numerical method for computing the solutions of the curvature equation in the plane . This modification takes place near the singularities of the image. We propose to ...
• #### Polygons with parallel opposite sides ﻿

2013-09
In this paper we consider convex planar polygons with parallel opposite sides. These polygons can be regarded as discretizations of closed convex planar curves by taking tangent lines at samples with pairwise parallel ...