A Fast Marching Method for the Area Based Affine Distance

Silva, Moacyr A.; Teixeira, Ralph; Pesco, Sinesio; Craizer, Marcos

doi:10.1007/s10851-007-0038-1

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“…We also show that this exact area distance defines a discrete indefinite improper affine sphere, as defined in [5]. We remark that the method proposed in this paper differs completely from that of [9], since the latter considers curves defined in implicit form. For the outer part of the polygon, we also propose a fast evolution algorithm that computes a new distance.…”

Section: Introductionmentioning

confidence: 80%

Area Distances of Convex Plane Curves and Improper Affine Spheres

Craizer¹,

Alvim²,

Teixeira³

2008

SIAM J. Imaging Sci.

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Abstract. 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 fast algorithm to compute the inner area distance. Moreover, the concepts of the theory of affine spheres lead to a new definition of an area distance on the outer part of a convex plane curve. On the other hand, area distances provide a good geometrical understanding of improper affine spheres.

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Section: Introductionmentioning

confidence: 80%

Area Distances of Convex Plane Curves and Improper Affine Spheres

Craizer¹,

Alvim²,

Teixeira³

2008

SIAM J. Imaging Sci.

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Affine Skeletons and Monge–Ampère Equations

Silva¹,

Teixeira²,

Velho³

2009

SIAM J. Imaging Sci.

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Abstract. An important question about ane skeletons is the existence of dierential equations that are related to the Ane Distance and the Area Distance (hence to ane skeletons) in the same way the Eikonal equation is related to the Euclidean Distance (and the medial axis). We show a surprisingly simple nonlinear second order PDE of Monge-Ampère type that relates to the ane skeletons (and extends the Eikonal equation for the medial axis). We also discuss some consequences and ideas that this new PDE formulation suggests.

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A Fast Marching Method for the Area Based Affine Distance

Cited by 2 publications

References 4 publications

Area Distances of Convex Plane Curves and Improper Affine Spheres

Area Distances of Convex Plane Curves and Improper Affine Spheres

Affine Skeletons and Monge–Ampère Equations

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