standard_deviation σ (sigma)
Standard deviation measures how spread out values are from their mean. In a Gaussian distribution, σ controls the width of the bell curve. In a Gaussian blur, σ is the single parameter that determines how much blurring occurs — larger σ means more blur because the kernel samples a wider neighborhood and weights distant pixels more heavily.
Formula
σ = √(Σ(xᵢ − μ)² / N)
Key Insight
In Gaussian blur: σ = 1 blurs slightly, σ = 10 blurs heavily. Doubling σ roughly doubles the visual blur radius.