Department of Electrical Engineering, Indian Institute of Technology, Kanpur, UP 208016, India.
IEEE Trans Image Process. 2010 Mar;19(3):561-72. doi: 10.1109/TIP.2009.2036685. Epub 2009 Nov 20.
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.
本文提出了一种新的快速核密度估计（FKDE）算法，该算法基于数据空间的主方向划分（PDDP）。还开发了一个新的框架，以便在基于非参数非因果马尔可夫随机场（NNMRF）的纹理合成算法中应用 FKDE 算法（包括提出的和现有的算法）。所提出的 FKDE 算法的目标是利用核的有限支撑特性进行快速密度估计。已经表明，用于划分数据空间的超平面边界和数据空间的主分量向量是有效 FKDE 的两个要求。将所提出的算法与早期的算法进行了比较，并使用了多个高维数据集。误差和时间复杂度分析证明了与早期算法相比，所提出的 FKDE 算法的效率。由于局部模拟退火，直接将 FKDE 算法合并到基于 NNMRF 的纹理合成算法中是不可能的。这项工作提出了一种新的方法，将局部模拟退火的效果纳入 FKDE 框架中。之后，使用来自标准数据库的多种不同自然纹理对所开发的纹理合成算法进行了测试。在所提出的基于 FKDE 的纹理合成算法与早期算法之间，从视觉相似性和时间复杂度方面进行了比较，显示了其效率。
