
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
APA
Chicago
ICMJE
MLA
NLM
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.

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