The geometric mean filter is a type of filter used in image processing to smooth and reduce noise in images while preserving edge features. Unlike the arithmetic mean filter, which calculates the average of pixel values in the neighborhood, the geometric mean filter calculates the geometric mean of pixel values. This filter is particularly effective in reducing multiplicative noise (e.g., speckle noise) and preserving edges better than the arithmetic mean filter.
Advantages of the Geometric Mean Filter
Noise Reduction: Effective in reducing multiplicative noise such as speckle noise.
Edge Preservation: Better at preserving edges and fine details compared to the arithmetic mean filter.
Robustness: Less sensitive to outliers in the neighborhood.
Disadvantages
Computational Complexity: More computationally intensive than the arithmetic mean filter due to the multiplication and exponentiation operations.
Handling Zero Values: Cannot directly handle zero pixel values, as the geometric mean involves multiplication; zero values must be addressed separately (e.g., by adding a small constant to all pixel values).
Steps to Apply the Geometric Mean Filter
Select a Neighborhood:
Define the size of the neighborhood (eg m*m Window) around each pixel.
Compute the Geometric Mean:
For each pixel (i,j), compute the geometric mean of the pixel values in the neighborhood.
Replace the Pixel Value:
Replace the pixel value at (i,j) with the computed geometric mean.
