Q12Digital Image Processing

Spatial Domain filtering operates directly on the physical pixel matrix. A sub-image (a "Mask" or "Kernel," typically $3\times 3$ or $5\times 5$) is mathematically slid across every single pixel in the original image. At each coordinate $(x,y)$, a specific mathematical operation is executed between the mask coefficients and the underlying image pixels to aggressively calculate the new intensity for the center pixel.

1. Linear Spatial Filters (Smoothing / Blurring)

These filters execute strict linear algebra (Convolution or Correlation). They are primarily designed to violently suppress high-frequency thermal noise.

• The Mean Filter (Averaging Filter): The mask coefficients are all mathematically equal (e.g., $1/9$ for a $3\times 3$). The filter aggressively sums the 9 physical pixels and calculates the absolute arithmetic mean. - Demerit: While it suppresses Gaussian noise, it causes catastrophic, irreversible blurring of sharp architectural edges in the image.

2. Non-Linear Spatial Filters (Order-Statistic Filters)

These filters do not use convolution. They rely on aggressive, non-linear sorting algorithms.

• The Median Filter: The absolute gold standard for eradicating "Salt and Pepper" (Impulse) noise. The $3\times 3$ filter violently extracts the 9 pixel intensities, sorts them in strict numerical order, and replaces the center pixel strictly with the median value. - Merit: Because a massive noise spike (255) will always be pushed to the end of the sorted list, it is mathematically guaranteed to NEVER be chosen as the median. The noise is absolutely annihilated while the sharp structural edges of the image remain perfectly intact.
• Max/Min Filters: The Max filter forcefully selects the absolute highest intensity in the neighborhood, violently expanding bright objects (used for finding the brightest points). The Min filter forcefully selects the absolute lowest intensity, expanding dark regions.