Natural Neighbour Interpolation

#1
My problem concerns the application of Natural Neighbour Interpolation (NNI) to point data in the creation of a surface. The algorithm was first described in this book chapter:

Sibson, R. 1982. A brief description of natural neighbour interpolation. Pp. 21-36 in V. Barnett (Editor). Interpreting Multivariate Data. John Wiley & Sons.

The NNI has been implemented in a Geographic Information System to analyze spatial datasets defined as a X,Y location and an attribute value at that location. We would like to learn about the applicability of this algorithm to generate a 2D surface from a set of random points when the surface to be interpolated is heterogeneous with respect to the landscape being modeled. My basic concern is that one should not generate a 2D surface from random points when interpolation would likely create false tiles or Thiessen polygons at x,y locations where interpolation should not be valid.

More specifically, we are attempting to map dead forest stand biomass based on field estimates at a number of field plots (point locations). The problem is that our landscape is extremely fragmented because forested areas are interspersed among agricultural areas. What we did was to run the Natural Neighbour Interpolation from the set of field points using standing dead biomass as the response variable for the interpolation, and then imposed a spatial mask generated from a satellite land cover map to isolate forested areas of interest. Otherwise, our fundamental question is how to generate a 2-D surface that will map out the spatial distribution of dead tree biomass on a fragmented landscape? One possible solution is to apply a k-Nearest Neighbour algorithm that would base the interpolation using a multivariate feature vector defined using an independent dataset such as a select set of satellite image bands. The interpolation of the attribute of interest would then be by multispectral space and areas where the interpolation should not be undertaken could be masked out.

I was looking for any papers that might address this topic even in the broadest of terms or whether the application we took was in fact valid.

Any advice appreciated.