New developments in median filters

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The median filter is a nonlinear filter that outputs the median of the data inside a moving window of predetermined length and has been traditionally used to remove impulse noise from images. The filter is known for its ability to preserve edges while smoothing a noisy signal. One of the major drawbacks of the median filter is that it tends to alter pixels undisturbed by noise and disturb features like thin lines, because it is implemented invariantly across the image. One way to circumvent this problem is to detect impulse noise prior to the filtering operation. In this work, two new types of median filters that employ impulse detection mechanisms prior to filtering operations are proposed. These are the rank-conditioning and thresholding (RCT) median filters and the noncausal linear prediction error based median filters. The rank-conditioned and threshold median filters are based on simultaneous application of rank-conditioning and the thresholding of the deviation of the center pixel from healthy pixels in the window. Simultaneous application of these conditions is aimed at reducing the probability of a healthy pixel being detected as noisy. Rank-conditioning is kept fixed as one of the conditions - the rank of the centre pixel inside the sliding window does not lie in the trimming range if it is an impulse. Three different thresholding conditions are investigated. In RCT-I filter, the absolute difference of the centre pixel from the median is compared against a pre-defined threshold. The RCT-II filter employs the thresholding scheme of Chen and Wu's adaptive centre-weighted median filter. The thresholding scheme of signal-dependent rank-ordered mean filter is used in RCT-III filter. The corrupted pixel is replaced by the rank-ordered mean. ..
Supervisor: Prabin Kr. Bora