Pair Correlation Functions with Free-Form Boundaries for Distribution Inpainting and Decomposition

Pair Correlation Functions (PCF) have been recently spreading as a reliable representation for distributions, enabling the efficient synthesis of point-sets, vector textures and object placement from examples. In this work we introduce a triangulation-based local filtering method to extend PCF-based analysis to exemplars with free-form boundaries. This makes PCF applicable to new problems such as the inpainting of missing parts in an input distribution, or the decomposition of complex, non-homogeneous distributions into a set of coherent classes, in which each category of points can be studied together with their intra and inter-class correlations.