A Fast Nonparametric Noncausal MRF-Based Texture Synthesis Scheme Using a Novel FKDE Algorithm

In this paper, a new algorithm is proposed for fast kernel density estimation (FKDE), based on principal direction divisive partitioning (PDDP) of the data space. A new framework is also developed to apply FKDE algorithms (both proposed and existing), within nonparametric noncausal Markov random field (NNMRF) based texture synthesis algorithm. The goal of the proposed FKDE algorithm is to use the finite support property of kernels for fast estimation of density. It has been shown that hyperplane boundaries for partitioning the data space and principal component vectors of the data space are two requirements for efficient FKDE. The proposed algorithm is compared with the earlier algorithms, with a number of high-dimensional data sets. The error and time complexity analysis, proves the efficiency of the proposed FKDE algorithm compared to the earlier algorithms. Due to the local simulated annealing, direct incorporation of the FKDE algorithms within the NNMRF-based texture synthesis algorithm, is not possible. This work proposes a new methodology to incorporate the effect of local simulated annealing within the FKDE framework. Afterward, the developed texture synthesis algorithms have been tested with a number of different natural textures, taken from a standard database. The comparison in terms of visual similarity and time complexity, between the proposed FKDE based texture synthesis algorithm with the earlier algorithms, show the efficiency.