Q13Digital Image Processing

Spatial domain filtering is a mathematical architecture that operates directly on the raw pixel matrix $f(x,y)$, completely bypassing the complex Fourier frequency domain. A highly localized mathematical mask (a $3\times 3$ or $5\times 5$ kernel) is physically slid across every single pixel in the image to calculate a new center value.

A Linear Filter (like the Mean/Average Filter) simply calculates the mathematical average of the 9 pixels under a $3\times 3$ mask. While this blurs out Gaussian noise, it causes catastrophic damage to the image: it violently blurs sharp physical edges, making the image look out of focus.

The Median Filter completely abandons linear algebra in favor of Order-Statistics.

• Salt-and-Pepper Noise: This is impulse noise caused by a catastrophic hardware sensor failure. Random pixels violently spike to absolute maximum (255, Salt) or crash to absolute minimum (0, Pepper).
• The Execution: When the $3\times 3$ mask slides over a pixel, the algorithm physically extracts all 9 pixel values. It violently sorts them in ascending numerical order (e.g., $10,11,12,14,15,17,20,255,255$).
• The Mathematical Selection: It completely ignores the mean. It strictly selects the absolute median value (the 5th number in a sorted list of 9). In the example above, the median is $15$.
• The Result: The horrific Salt noise spike ($255$) is mathematically banished to the extreme right of the sorted list and is permanently ignored. The center pixel is replaced by $15$. The noise is violently annihilated, but because no averaging occurred, the sharp physical edges of the image remain perfectly intact.