Discrete Sibson interpolation

IEEE Trans Vis Comput Graph. Mar-Apr 2006;12(2):243-53. doi: 10.1109/TVCG.2006.27.

Abstract

Natural-neighbor interpolation methods, such as Sibson's method, are well-known schemes for multivariate data fitting and reconstruction. Despite its many desirable properties, Sibson's method is computationally expensive and difficult to implement, especially when applied to higher-dimensional data. The main reason for both problems is the method's implementation based on a Voronoi diagram of all data points. We describe a discrete approach to evaluating Sibson's interpolant on a regular grid, based solely on finding nearest neighbors and rendering and blending d-dimensional spheres. Our approach does not require us to construct an explicit Voronoi diagram, is easily implemented using commodity three-dimensional graphics hardware, leads to a significant speed increase compared to traditional approaches, and generalizes easily to higher dimensions. For large scattered data sets, we achieve two-dimensional (2D) interpolation at interactive rates and 3D interpolation (3D) with computation times of a few seconds.

Publication types

  • Evaluation Study
  • Research Support, N.I.H., Extramural
  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Algorithms*
  • Computer Graphics
  • Image Enhancement / methods*
  • Image Interpretation, Computer-Assisted / methods*
  • Imaging, Three-Dimensional / methods*
  • Information Storage and Retrieval / methods*
  • Numerical Analysis, Computer-Assisted
  • Signal Processing, Computer-Assisted*
  • User-Computer Interface