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Area and length preserving geometric invariant scale-spaces

Publication ,  Conference
Sapiro, G; Tannenbaum, A
Published in: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
January 1, 1994

In this paper, area preserving geometric multi-scale representations of planar curves are described. This allows geometric smoothing without shrinkage at the same time preserving all the scale-space properties. The representations are obtained deforming the curve via invariant geometric heat flows while simultaneously magnifying the plane by a homethety which keeps the enclosed area constant. The flows are geometrically intrinsic to the curve, and exactly satisfy all the basic requirements of scale-space representations. In the case of the Euclidean heat flow for example, it is completely local as well. The same approach is used to define length preserving geometric flows. The geometric scalespaces are implemented using an efficient numerical algorithm.

Duke Scholars

Published In

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

DOI

EISSN

1611-3349

ISSN

0302-9743

ISBN

9783540579571

Publication Date

January 1, 1994

Volume

801 LNCS

Start / End Page

449 / 458

Related Subject Headings

  • Artificial Intelligence & Image Processing
  • 46 Information and computing sciences
 

Citation

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Sapiro, G., & Tannenbaum, A. (1994). Area and length preserving geometric invariant scale-spaces. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 801 LNCS, pp. 449–458). https://doi.org/10.1007/bfb0028376
Sapiro, G., and A. Tannenbaum. “Area and length preserving geometric invariant scale-spaces.” In Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 801 LNCS:449–58, 1994. https://doi.org/10.1007/bfb0028376.
Sapiro G, Tannenbaum A. Area and length preserving geometric invariant scale-spaces. In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). 1994. p. 449–58.
Sapiro, G., and A. Tannenbaum. “Area and length preserving geometric invariant scale-spaces.” Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 801 LNCS, 1994, pp. 449–58. Scopus, doi:10.1007/bfb0028376.
Sapiro G, Tannenbaum A. Area and length preserving geometric invariant scale-spaces. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). 1994. p. 449–458.
Journal cover image

Published In

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

DOI

EISSN

1611-3349

ISSN

0302-9743

ISBN

9783540579571

Publication Date

January 1, 1994

Volume

801 LNCS

Start / End Page

449 / 458

Related Subject Headings

  • Artificial Intelligence & Image Processing
  • 46 Information and computing sciences