School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore.
IEEE Trans Image Process. 2012 Apr;21(4):1537-47. doi: 10.1109/TIP.2011.2172805. Epub 2011 Oct 19.
The arithmetic mean and the order statistical median are two fundamental operations in signal and image processing. They have their own merits and limitations in noise attenuation and image structure preservation. This paper proposes an iterative algorithm that truncates the extreme values of samples in the filter window to a dynamic threshold. The resulting nonlinear filter shows some merits of both the fundamental operations. Some dynamic truncation thresholds are proposed that guarantee the filter output, starting from the mean, to approach the median of the input samples. As a by-product, this paper unveils some statistics of a finite data set as the upper bounds of the deviation of the median from the mean. Some stopping criteria are suggested to facilitate edge preservation and noise attenuation for both the long- and short-tailed distributions. Although the proposed iterative truncated mean (ITM) algorithm is not aimed at the median, it offers a way to estimate the median by simple arithmetic computing. Some properties of the ITM filters are analyzed and experimentally verified on synthetic data and real images.
算术平均值和顺序统计中位数是信号和图像处理中的两个基本操作。它们在噪声衰减和图像结构保持方面各有优缺点。本文提出了一种迭代算法，通过将滤波器窗口中的样本极值截断到动态阈值来实现。所得到的非线性滤波器具有这两种基本操作的一些优点。提出了一些动态截断阈值，保证滤波器的输出从平均值开始逐渐接近输入样本的中位数。作为副产品，本文揭示了有限数据集的一些统计信息，作为中位数与平均值偏差的上限。提出了一些停止准则，以方便长尾巴和短尾巴分布的边缘保持和噪声衰减。虽然所提出的迭代截断平均值（ITM）算法不是针对中位数的，但它提供了一种通过简单的算术计算来估计中位数的方法。对 ITM 滤波器的一些特性进行了分析，并在合成数据和真实图像上进行了实验验证。
