Image Filters: Mean, Median, Gaussian

Three smoothers

• Mean filter — average of all pixels in a window. Cheap, fast, blurs edges aggressively.
• Median filter — sort the window's pixels into a 1D list, take the middle value. Excellent at killing salt-and-pepper noise without smearing edges.
• Gaussian filter — weighted average where the weights fall off with distance. Given σ and a kernel size (e.g. 5: [-2,-1,0,1,2]), the 1D kernel looks like [0.0549, 0.2431, 0.4026, 0.2431, 0.0549] — separable, edge-aware, the workhorse of low-level CV.

Visualizer · noise → clean

Crank up the noise, then sweep through filters and kernel sizes. The right canvas is the filtered output; the small panel on the right shows the actual kernel weights being applied.

When to use which

• Mean — when speed matters more than quality (preview pipelines, motion blur).
• Median — when noise is impulsive (dead pixels, sensor read errors, salt & pepper). Notice in the viz: crank S&P to 15%, switch to median, and the speckle just vanishes — but text edges stay sharp.
• Gaussian — when you need a smooth derivative downstream. Edge detectors (Sobel, Canny) blur Gaussian-first because the convolution of derivatives is well-behaved on Gaussians.