F. Cazals, J. Giesen, M. Pauly, A. Zomorodian, Conformal Alpha Shapes, Symposium on Point-Based Graphics (2005), pp. 55-61.
We define a new filtration of the Delaunay triangulation of a
finite set of points in Rd, similar to the alpha shape
filtration. The new filtration is parameterized by a local scale
parameter instead of the global scale parameter in
alpha shapes. Since our approach shares many properties with the
alpha shape filtration and the local scale parameter conforms to
the local geometry we call it conformal alpha shape filtration.
The local scale parameter is motivated from applications and previous
algorithms in surface reconstruction. We show how conformal alpha
shapes can be used for surface reconstruction of non-uniformly sampled
surfaces, which is not possible with alpha shapes.
title = "Conformal Alpha Shapes",
author = "Cazals, F. and Giesen, J. and Pauly, M. and Zomorodian, A.",
booktitle = "Proc. Symp. Point-Based Graph.",
year = 2005,
pages = "55---61",