= Regularized Perona-Malik diffusion
{title2=$u_t=\operatorname{div}(c(|\nabla(G_\sigma*u)|)\nabla u)$}
Computing conductance from a smoothed <gradient> gives $u_t=\operatorname{div}(c(|\nabla(G_\sigma*u)|)\nabla u)$. The <image edge> detector is nonlocal, while the local highest-order diffusion has positive coefficient when conductance is positive. A smooth kernel, lower conductance bound and appropriate regularity/boundary hypotheses support a well-posed regularized filter.
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