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Perona-Malik Anisotropic Diffusion

Edge-preserving smoothing via nonlinear diffusion

Original (Noisy)

After Diffusion

Diffusion Coefficient c(x,y)

Gradient Magnitude |∇I|

Diffusion Parameters

∂I/∂t = div(c(x,y,t)·∇I) = c·ΔI + ∇c·∇I

About Perona-Malik Diffusion

Perona and Malik (1990) introduced anisotropic diffusion as a technique for edge-preserving smoothing. Unlike isotropic diffusion (Gaussian blur), this method adapts the diffusion rate based on local image gradients.

Kappa (κ): Controls edge sensitivity. Higher values allow more diffusion across edges. Lower values preserve more edges but may leave noise.
Time Step (dt): Must be small (≤0.25) for stability.
Iterations: More iterations = more smoothing.

The conductance function c(|∇I|) approaches 1 in flat regions (allowing diffusion) and approaches 0 at edges (stopping diffusion), creating edge-preserving behavior.