Diffusion Filtering

PDE-based image smoothing: Perona-Malik, curvature flow, curvature diffusion, and gradient anisotropic diffusion.

Design

All diffusion filters operate on flat host buffers via substrate-agnostic pure functions. Each filter implements a host core shared by the Coeus-generic apply path and the native apply_native path. No Coeus tensor is constructed in the hot path.

Perona-Malik

Edge-preserving smoothing via the Perona-Malik PDE:

dI/dt = div(g(|∇I|) ∇I)

where g is the edge-stopping function. Two variants: g1 (exponential) and g2 (inverse quadratic).

Curvature Flow

dI/dt = ∇·(∇I/|∇I|) |∇I|

Smooths along edges while preserving across-edge structure.

Curvature Diffusion

∂I/∂t = |∇I| ∇·(c(|∇I|) ∇I/|∇I|)

RITK implements the Modified Curvature Diffusion Equation: each intensity level set evolves by conductance-modulated mean curvature. Unlike heat-equation diffusion, the gradient-normalized flux and edge-stopping conductance preserve strong boundaries while smoothing along their geometry.

Gradient Anisotropic Diffusion

dI/dt = ∇·(g(|∇I|) ∇I)

where g is a function of gradient magnitude. Smoothing is anisotropic: strong along edges, weak across edges.

Verification

Each filter is differentially tested against its Coeus-generic counterpart via assert_coeus_matches_coeus.