Order statistics in digital image processing

Abstract

In this review paper an analysis of their properties as well as their algorithmic computation will be presented.

Vector operators for color image zooming

“…The VDAF outputs are not as sharp but provides an excellent tradeoff between sharpness and the reduction of the streaks' effect. Finally, Fig.8 allows the visual comparison of the images restored by the VMF and the scalar (componentwise) MF [13]. These results illustrate that the scalar approach produces color shifts and artifacts whereas the vector approach preserves both the spatial and spectral characteristics of the enlarged image.…”

“…Since α (i,j) and D (i,j) significantly differs in the values, (13) and (14), respectively, produce different weights and the filtering scheme (12) will result in two different outputs.…”

“…−r (13) where β is a normalizing constant and r is a parameter adjusting the weighting effect of the membership function. Based on the aggregated Minkowski metrics D (i,j) of (6), the adaptation formula (13) is redefined as follows:…”

Modified repeated median filters

“…The DWMTM behaves excellently at the first and similarly to the MRM at the second shift, but the double window regression filters do even better, and they are additionally more robust against outliers. The possibly better preservation of shifts by the DWMTM as compared to the median has been noticed before (Pitas andVenetsanopoulos 1992, Himayat andKassam 1993).…”

“…Filters based on trimmed means have been suggested as a compromise between moving averages and running medians (Lee andKassam 1985, Pitas andVenetsanopoulos 1992). Modified trimmed mean (MTM-) filters choose the amount of trimming depending on the current time window.…”