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Friday, 4 November 2016

Digital Image Processing — Filters

Restoration in The Presence of Noise Only
— Spatial Filtering


When the only degradation present in an image noise, equations:
                                                g (x, y) = f (x, y) + η (x, y)
and
                                                G (u, v) = F (u, v) + N (u, v)
The noise terms are unknown, so subtracting them from g (x, y) and G (u, v) is not a realistic option. In this case N (u, v) can be subtracted from G (u, v) to obtain an estimate N (u, v) from the spectrum of G (u, v).
Mean Filters: - The different types of noise reduction mean filters are given below: -
1.    Arithmetic Mean Filter: - This is the simplest of the mean filters. Let Sxy represent the set of coordinates in a rectangular subimage window of size m x n, centered at a point (x, y). The arithmetic mean filter computes the average value of the corrupted image     g (x, y) in the area defined by Sxy. The value of the restored image f’ at point (x, y) is simply the arithmetic mean computed using the pixels in the region defined by Sxy.

f’ (x, y) = 1/mn ∑ g (s, t)
This operation can be implemented using a spatial filter of size m x n in which all coefficient’s have value 1/mn. A mean filter smooth local variations in an image and noise is reduced as a result of blurring.
2.    Geometric Mean Filter: - An image restored using a geometric mean filter is given by the expression

f’ (x, y) = [ π(s, t) € Sxy g (s, t)]
Each restoration pixel is given by the product of the pixels in the subimage window, raised to the power 1/mn. A geometric mean filter achieves smoothing comparable to the arithmetic mean filter, but it tends to loss less image detail in the process.
3.    Harmonic Mean Filter: - Harmonic mean filter works well for salt noise, but fails for pepper noise. It does well also with other type of noise like Gaussian noise.

4.    Contraharmonic Mean Filter: - This filter is well suited for reducing or virtually eliminating the effects of salt-and-pepper noise.

5.    Median Filter: -The best known order statistic filter is median filter, which is as its name implies, replaces the value of pixel by the median of the intensity levels in the neighborhood of that pixel.

6.    Midpoint Filter: - The midpoint filter simply computes the midpoint between maximum and minimum values in the area encompassed by the filter. This filter combines order statistics and averaging. It works best for randomly distributed noise, like Gaussian or uniform noise.

7.    Inverse Filter: - Inverse filtering is the process of recovering the input of a system from its output. For example, in the absence of noise the inverse filter would be a system that recovers u (m, n) from the observations v (m, n).

8.    Pseudoinverse Filer: - It is the stabilized version of the inverse filter.


9.    The Wiener Filter: - The main disadvantage of inverse filter and pseudoinverse filter is that these filters remain very sensitive to noise. Wiener filter is a method of restoring image in the presence of blur as well as noise. 

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