Publication Abstract
Rough Interface Reconstruction Using the Level Set Method
Kim, Y., Machiraju, R., & Thompson, D. (2004). Rough Interface Reconstruction Using the Level Set Method. Proceedings of IEEE Visualization 2004. Austin, TX. 251-258. DOI:10.1109/VISUAL.2004.94.
Abstract
We present a new level set method for reconstructing interfaces
from point aggregations. Although level-set-based methods are advantageous because they can handle complicated topologies and
noisy data, most tend to smooth the inherent roughness of the original
data. Our objective is to enhance the quality of a reconstructed
surface by preserving certain roughness-related characteristics of
the original dataset. Our formulation employs the total variation
of the surface as a roughness measure. The algorithm consists of
two steps: a roughness-capturing flow and a roughness-preserving
flow. The roughness capturing step attempts to construct a surface
for which the original roughness is captured – distance flow
is well suited for roughness capturing. Surface reconstruction is
enhanced by using a total variation preserving (TVP) scheme for
the roughness-preserving flow. The shock filter formulation of Osher
and Rudin is exploited to achieve this goal. In practice, we have
found that better results are obtained by balancing the TVP term
with a smoothing term based on curvature. The algorithm is applied
to both fractal surface growth simulations and scanned data
sets to demonstrate the efficacy of our approach.