Surface Evolution Under Curvature Flows
| Title: | Surface Evolution Under Curvature Flows |
| Author: |
Lu, Conglin; Cao, Yan; Mumford, David Bryant
Note: Order does not necessarily reflect citation order of authors. |
| Citation: | Lu, Conglin, Yan Cao, and David B. Mumford. 2002. Surface evolution under curvature flows. Journal of Visual Communication and Image Representation 13(1-2): 65-81. |
| Full Text & Related Files: |
Mumford_SurfaceEvolution.pdf (547.0Kb; PDF) 
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| Abstract: | In many areas of computer vision, such as multiscale analysis and shape description, an image or surface is smoothed by a nonlinear parabolic partial differential equation to eliminate noise and to reveal the large global features. An ideal flow, or smoothing process, should not create new features. In this paper we describe in detail the effect of a number of flows on surfaces on the parabolic curves, the ridge curves, and umbilic points. In particular we look at the mean curvature flow and the two principal curvature flows. Our calculations show that two principal curvature flows never create parabolic and ridge curves of the same type as the flow, but no flow is found capable of simultaneously smoothing out all features. In fact, we find that the principal curvature flows in some cases create a highly degenerate type of umbilic. We illustrate the effect of these flows by an example of a 3-D face evolving under principal curvature flows. |
| Published Version: | doi:10.1006/jvci.2001.0476 |
| Terms of Use: | This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA |
| Citable link to this page: | http://nrs.harvard.edu/urn-3:HUL.InstRepos:4726298 |
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Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University
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