Shock filter for image enhancement (source code)

= Shock filter for image enhancement
{title2=$u_t=-\operatorname{sign}(\Delta u)|\nabla u|$}

The formal shock-filter equation $u_t=-\operatorname{sign}(\Delta u)|\nabla u|$ steepens transitions around inflection boundaries. It is a Hamilton–Jacobi-type transport mechanism rather than positive diffusion. Combining it with controlled forward <image smoothing> limits noise amplification.