Diffusion tensor for image filtering
= Diffusion tensor for image filtering
{title2=$u_t=\operatorname{div}(D\nabla u)$}
A positive tensor $D=a_ne_ne_n^T+a_te_te_t^T$ selects different diffusion strengths normal and tangent to an estimated <image edge>. Taking $0<a_n\ll a_t$ smooths along the <image edge> while reducing mixing across it. A <structure tensor> provides robust orientation estimates. Positive <eigenvalues> ensure forward local parabolicity.