Perona-Malik Anisotropic Diffusion
Edge-preserving image smoothing via nonlinear PDE
Original (noisy)
Diffused
Edges detected
Controls
Test image
Geometric shapes
Gradient ramp
Stripe pattern
Pure noise
Noise level σ
0.15
Conductance K
0.20
λ (step size)
0.20
Diffusion function
PM1: exp(-|∇u|²/K²)
PM2: 1/(1+|∇u|²/K²)
Run Diffusion
Reset
Iterations:
0
Mean gradient:
—
PSNR:
—
dB
Perona-Malik (1990)
: ∂u/∂t = div(c(|∇u|)·∇u)
The conductance c(s) decreases at edges, halting diffusion there while smoothing flat regions. Unlike Gaussian blur, PM preserves sharp edges and can even sharpen them (K < edge gradient).