Universal approach for DCT-based constant-time Gaussian filter with moment preservation
Universal approach for DCT-based constant-time Gaussian filter with moment preservation
复制标题
基于 DCT 的具有矩保持的恒定时间高斯滤波器的通用方法
DOI：
10.1109/icassp.2018.8461679
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
S. Kyochi and S. Kamata
中科院分区：
文献类型：
--
作者：
K. Sugimoto;S. Kyochi and S. Kamata
本文提出了一种基于离散余弦变换（DCT）的恒时高斯滤波器（O(1) GF）的通用方法。众所周知，DCT有八种类型的定义。现有的O(1) GF方法根据其原始概念使用不同的DCT类型。然而，对所有类型的DCT尚未进行全面和定量的研究。与现有方法不同，本文提出的方法涵盖了所有类型的DCT和任意阶矩保持，这使我们能够通过综合分析来阐明每个DCT得出的O(1) GF的差异。在通用方法的基础上，提出了一种基于简单凸分析的权系数优化的封闭解。实验发现DCT-7的近似精度最高，这是一个不同于现有方法的新结论。
This paper presents a universal approach for constant-time Gaussian filters (O(1) GF) based on the Discrete Cosine Transform (DCT). It is well known that DCT has the eight types of definitions. Existing methods of O(1) GF use difference DCT type according to their original concepts. However, all types of DCT have not been studied comprehensively and quantitatively. Unlike existing methods, the proposed approach covers all types of DCT and moment preservation for arbitrary orders, which enables us to clarify differences of O(1) GF derived from each DCT through a comprehensive analysis. Based on the universal approach, a closed-form solution to optimize weight coefficients is also proposed based on a simple convex analysis. Experiments found that DCT-7 shows the highest approximate accuracy, which is a new conclusion different from existing methods.