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The ubiquitous ellipse

Publication ,  Journal Article
Sapiro, G; Bruckstein, AM
Published in: Acta Applicandae Mathematicae
February 1, 1995

We discuss three different affine invariant evolution processes for smoothing planar curves. The first one is derived from a geometric heat-type flow, both the initial and the smoothed curves being differentiable. The second smoothing process is obtained from a discretization of this affine heat equation. In this case, the curves are represented by planar polygons. The third process is based on B-spline approximations. For this process, the initial curve is a planar polygon, and the smoothed curves are differentiable and even analytic. We show that, in the limit, all three affine invariant smoothing processes collapse any initial curve into an elliptic point. © 1995 Kluwer Academic Publishers.

Duke Scholars

Published In

Acta Applicandae Mathematicae

DOI

EISSN

1572-9036

ISSN

0167-8019

Publication Date

February 1, 1995

Volume

38

Issue

2

Start / End Page

149 / 161

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

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MLA
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Sapiro, G., & Bruckstein, A. M. (1995). The ubiquitous ellipse. Acta Applicandae Mathematicae, 38(2), 149–161. https://doi.org/10.1007/BF00992844
Sapiro, G., and A. M. Bruckstein. “The ubiquitous ellipse.” Acta Applicandae Mathematicae 38, no. 2 (February 1, 1995): 149–61. https://doi.org/10.1007/BF00992844.
Sapiro G, Bruckstein AM. The ubiquitous ellipse. Acta Applicandae Mathematicae. 1995 Feb 1;38(2):149–61.
Sapiro, G., and A. M. Bruckstein. “The ubiquitous ellipse.” Acta Applicandae Mathematicae, vol. 38, no. 2, Feb. 1995, pp. 149–61. Scopus, doi:10.1007/BF00992844.
Sapiro G, Bruckstein AM. The ubiquitous ellipse. Acta Applicandae Mathematicae. 1995 Feb 1;38(2):149–161.
Journal cover image

Published In

Acta Applicandae Mathematicae

DOI

EISSN

1572-9036

ISSN

0167-8019

Publication Date

February 1, 1995

Volume

38

Issue

2

Start / End Page

149 / 161

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics