Area and length preserving geometric invariant scale-spaces

Conference Paper

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.

Full Text

Duke Authors

Cited Authors

  • Sapiro, G; Tannenbaum, A

Published Date

  • January 1, 1994

Published In

Volume / Issue

  • 801 LNCS /

Start / End Page

  • 449 - 458

Electronic International Standard Serial Number (EISSN)

  • 1611-3349

International Standard Serial Number (ISSN)

  • 0302-9743

International Standard Book Number 13 (ISBN-13)

  • 9783540579571

Digital Object Identifier (DOI)

  • 10.1007/bfb0028376

Citation Source

  • Scopus