Fast Estimation of Nonparametric Kernel Density Through PDDP, and its Application in Texture Synthesis

Abstract

In this work, a new algorithm is proposed for fast estimation of nonparametric multivariate kernel density, based on principal direction divisive partitioning (PDDP) of the data space.The goal of the proposed algorithm is to use the finite support property of kernels for fast estimation of density. Compared to earlier approaches, this work explains the need of using boundaries (for partitioning the space) instead of centroids (used in earlier approaches), for better unsupervised nature (less user incorporation), and lesser (or atleast same) computational complexity. In earlier approaches, the finite support of a fixed kernel varies within the space due to the use of cluster centroids. It has been argued that if one uses boundaries (for partitioning) rather than centroids, the finite support of a fixed kernel does not change for a constant precision error. This fact introduces better unsupervision within the estimation framework. The main contribution of this work is the insight gained in the kernel density estimation with the incorporation of clustering algortihm and its application in texture synthesis. Texture synthesis through nonparametric, noncausal, Markov random field (MRF), has been implemented earlier through estimation of and sampling from nonparametric conditional density. The incorporation of the proposed kernel density estimation algorithm within the earlier texture synthesis algorithm reduces the computational complexity with perceptually same results. These results provide the efficacy of the proposed algorithm within the context of natural texture synthesis.

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