Multi-scale reconstruction of implicit surfaces with attributes from large unorganized point sets

We present a new method for the multi-scale reconstruction of implicit surfaces with attributes from large unorganized point sets. The implicit surface is reconstructed by subdividing the global domain into overlapping local subdomains using a perfectly balanced binary tree, reconstructing the surface parts in the local subdomains from non-disjunct subsets of the points by variational techniques using radial basis functions, and hierarchically blending together the surface parts of the local subdomains by using a family of functions called partition of unity. The subsets of the points in the inner nodes of the tree for intermediate resolutions are obtained by thinning algorithms. The reconstruction is particularly robust since the number of data points in the partition of unity blending zones can be specified explicitly. Furthermore, the new reconstruction method is valid for discrete datasets in any dimension, so we can use it also to reconstruct continuous functions for the surface´s attributes. In a short discussion, we evaluate the advantages and drawbacks of our reconstruction method compared to existing reconstruction methods for implicit surfaces.