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Mean and median are two basic operations in signal/image pro cessing. They are widely used for their easy implementation and soundly mathematical analys is tools. The mean filter achieves the best performance in attenuating Gaussian noise. Howeve r, it cannot effectively suppress the long-tailed noise and it blurs image structures. On the cont rary, the median filter has the advantages in suppressing the long-tailed noise and preserving i ma e structures. These advantages motivate us to develop the median based approaches in both no ise suppression and interest point detection. Noise suppression is a fundamental and important research t opic in signal/image processing. The recently proposed iterative truncated arithmetic mean (ITM) filter provided an effective way to suppress the longand short-tailed noise. By iterati vely truncating the extreme samples, the ITM filter’s output starts from the mean and approaches th median. The termination condition enables the ITM filter owning merits of these two opera tions. The filter’s output can be used as an approximation of the sample median without using t he time consuming data sorting algorithm. The merits of the ITM filter inspire part of the wor k in this thesis. We firstly analyze the ITM filter and verify that the ITM filter i s more effective than the median filter in suppressing both Gaussian and Laplacian noi se. Furthermore, we propose a fast implementation named fast ITM (FITM) filter. Mathemati c l analysis of the computational complexity is given. The ITM and FITM filters are of order O(n√n) andO(n log n), respectively. It is seen that the FITM filter has a lower computation al complexity than the ITM filter.

Median based approaches for noise suppression and interest point detection.