The harmonic mean filter fails for images with pepper noise because it is better at removing positive outliers like salt noise but not negative outliers like pepper noise. The geometric mean filter was applied to an image with salt and pepper noise, replacing each pixel's color with the geometric mean of surrounding pixels. This filter performs better than the harmonic mean filter for this type of noise as it is susceptible to negative outliers like pepper noise. The larger the surrounding region, the stronger the noise reduction effect but with some increased blurring.

1. Question 1 Why does the harmonic mean filter fail for images with pepper noise?
Question 2 Filter the salt and pepper noise images with the geometric mean filter.
How does the filter perform?
Solution
1. The salt and pepper noise is a type of noise seen on images.It consists of white and black
pixels and the best method for noise reduction in this is a median filter.
While in the harmonic mean filter, each colour value of the pixel is replaced with the harmonic
mean of colour values of the pixels in the surrounding area.
This harmonic mean filter is best suitable for removing gaussian type noise as the edge features
are preserved .And it can work well for salt noise but not pepper noise.As it is good at removing
positive outliers.
2.Here the filtering is done by applying the geometric mean filter to an image.In this process,the
colour of each pixel is replaced by the geometric mean filter if the surrounding regions.The
larger the region,the stronger the effect with small amount of blurring. It is susceptible to
negative outliers.