Math @ Duke

Publications [#264980] of Guillermo Sapiro
Papers Published
 Tsai, YHR; Cheng, LT; Osher, S; Burchard, P; Sapiro, G, Visibility and its dynamics in a PDE based implicit framework,
Journal of Computational Physics, vol. 199 no. 1
(2004),
pp. 260290 [doi]
(last updated on 2018/10/16)
Abstract: 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 onepass, multilevel 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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