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Visibility and its dynamics in a PDE based implicit framework

Publication ,  Journal Article
Tsai, YHR; Cheng, LT; Osher, S; Burchard, P; Sapiro, G
Published in: Journal of Computational Physics
September 1, 2004

We investigate the problem of determining visible regions given a set of (moving) obstacles and a (moving) vantage point. Our approach to this problem is through an implicit framework, where the obstacles are represented by a level set function. The visibility problem is formally formulated as a boundary value problem (BVP) of a first order partial differential equation. It is based on the continuation of values along the given ray field. We propose a one-pass, multi-level algorithm for the construction of the solution on a grid. Furthermore, we study the dynamics of shadow boundaries on the surfaces of the obstacles when the vantage point moves along a given trajectory. In all of these situations, topological changes such as merging and breaking occur in the regions of interest. These are automatically handled by the level set framework proposed here. Finally, we obtain additional useful information through simple operations in the level set framework. © 2004 Elsevier Inc. All rights reserved.

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Published In

Journal of Computational Physics

DOI

ISSN

0021-9991

Publication Date

September 1, 2004

Volume

199

Issue

1

Start / End Page

260 / 290

Related Subject Headings

  • Applied Mathematics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

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Tsai, Y. H. R., Cheng, L. T., Osher, S., Burchard, P., & Sapiro, G. (2004). Visibility and its dynamics in a PDE based implicit framework. Journal of Computational Physics, 199(1), 260–290. https://doi.org/10.1016/j.jcp.2004.02.015
Tsai, Y. H. R., L. T. Cheng, S. Osher, P. Burchard, and G. Sapiro. “Visibility and its dynamics in a PDE based implicit framework.” Journal of Computational Physics 199, no. 1 (September 1, 2004): 260–90. https://doi.org/10.1016/j.jcp.2004.02.015.
Tsai YHR, Cheng LT, Osher S, Burchard P, Sapiro G. Visibility and its dynamics in a PDE based implicit framework. Journal of Computational Physics. 2004 Sep 1;199(1):260–90.
Tsai, Y. H. R., et al. “Visibility and its dynamics in a PDE based implicit framework.” Journal of Computational Physics, vol. 199, no. 1, Sept. 2004, pp. 260–90. Scopus, doi:10.1016/j.jcp.2004.02.015.
Tsai YHR, Cheng LT, Osher S, Burchard P, Sapiro G. Visibility and its dynamics in a PDE based implicit framework. Journal of Computational Physics. 2004 Sep 1;199(1):260–290.
Journal cover image

Published In

Journal of Computational Physics

DOI

ISSN

0021-9991

Publication Date

September 1, 2004

Volume

199

Issue

1

Start / End Page

260 / 290

Related Subject Headings

  • Applied Mathematics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences