Reduced inverse distance weighting interpolation for painterly rendering

Abstract

The interpolation problem of irregularly distributed data in a multidimensional domain is considered. A modification of the inverse distance weighting interpolation formula is proposed, making computation time independent of the number of data points. Only the first K neighbors of a given point are considered, instead of the entire dataset. Additional factors are introduced, preventing discontinuities on points where the set of local neighbors changes. Theoretical analysis provides conditions which guarantee continuity. The proposed approach is efficient and free from magic numbers. Unlike many existing algorithms based on the k-nearest neighbors, the number of neighbors is derived from theoretical principles. The method has been applied to the problem of vector field generation in the context of artistic imaging. Experimental results show its ability to produce brush strokes oriented along object contours and to effectively render meaningful texture details. © 2009 Springer Berlin Heidelberg.