Multi-Scale Reconstruction of Implicit Surfaces with Attributes from Large Unorganized Point Sets

  • Authors:
  • Affiliations:
  • Venue:
  • SMI '04 Proceedings of the Shape Modeling International 2004
  • Year:
  • 2004

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Abstract

We present a new method for the multi-scale reconstructionof implicit surfaces with attributes from large unorganizedpoint sets. The implicit surface is reconstructed bysubdividing the global domain into overlapping local subdomainsusing a perfectly balanced binary tree, reconstructingthe surface parts in the local subdomains from non-disjunctsubsets of the points by variational techniques using radialbasis functions, and hierarchically blending togetherthe surface parts of the local subdomains by using a familyof functions called partition of unity. The subsets of thepoints in the inner nodes of the tree for intermediate resolutionsare obtained by thinning algorithms. The reconstructionis particularly robust since the number of data points inthe partition of unity blending zones can be specified explicitly.Furthermore, the new reconstructionmethod is valid fordiscrete datasets in any dimension, so we can use it also toreconstruct continuous functions for the surfaceýs attributes.In a short discussion, we evaluate the advantages and drawbacksof our reconstruction method compared to existing reconstructionmethods for implicit surfaces.