Explain Adaptive Filters. Describe Adaptive Local Noise Reduction Filter and Adaptive Median Filter with necessary conditions and equations.

Adaptive Filters are spatial filters whose behavior changes dynamically based on the local statistical properties (like mean and variance) of the image within a filter window. Unlike fixed filters, they adjust their computations based on image content, making them more effective at preserving edges and removing noise.

Advantages:

  • Adapts window size dynamically
  • Removes salt-and-pepper noise even when density is high (>20%)
  • Reduces unnecessary blurring by preserving uncorrupted pixels
  • Works better than standard median filter in mixed noise conditions

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