Gaussian Blur
A convolution operation that smooths data by weighting each value with a Gaussian distribution centered on that point. Standard deviation σ controls the radius of influence.
Mathematics
Operation: convolution
Kernel: G(x,y) = (1/2πσ²) × e^(-(x²+y²)/2σ²)
Separable means the 2D operation decomposes into two 1D passes, reducing cost from O(n²) to O(n).
Where It Appears
- Image Editing: noise reduction, skin smoothing
- Rendering: depth of field, bloom, glow
- Scientific Visualization: data smoothing before analysis
- Medical Imaging: pre-processing before segmentation
- Fluid Simulation: smoothing velocity fields
Physical Analog
Models optical diffusion — how light spreads through a translucent medium. Also models heat diffusion and atmospheric scattering.
Cross-Domain Insight
The same Gaussian blur that softens a portrait photograph is used to pre-process MRI scans, smooth velocity fields in fluid simulations, and simulate atmospheric haze in outdoor rendering. The math is identical. Only the domain changes.