Median based approaches for noise suppression and interest point detection.
Zhenwei Miao · 2013
Mean and median are two basic operations in signal/image processing.They are widely used for their easy implementation and soundly mathematical analysis tools.The mean filter achieves the best performance in attenuating Gaussian noise.However, it cannot effectively suppress the long-tailed noise and it blurs image structures.On the contrary, the median filter has the advantages in suppressing the long-tailed noise and preserving image structures.These advantages motivate us to develop the median based approaches in both noise suppression and interest point detection.Noise suppression is a fundamental and important research topic in signal/image processing.The recently proposed iterative truncated arithmetic mean (ITM) filter provided an effective way to suppress the long-and short-tailed noise.By iteratively truncating the extreme samples, the ITM filter's output starts from the mean and approaches the median.The termination condition enables the ITM filter owning merits of these two operations.The filter's output can be used as an approximation of the sample median without using the time consuming data sorting algorithm.The merits of the ITM filter inspire part of the work in this thesis.We firstly analyze the ITM filter and verify that the ITM filter is more effective than the median filter in suppressing both Gaussian and Laplacian noise.Furthermore, we propose a fast implementation named fast ITM (FITM) filter.Mathematical analysis of the computational complexity is given.The ITM and FITM filters are of order O(n √ n) and O(n log n), respectively.It is seen that the FITM filter has a lower computational complexity than the ITM filter.iv