Diffusion tensor for image filtering ($u_t=\mathrm{div}(D\nabla u)$)

A positive tensor $D=a_n{e}_n{e}_n^T+a_t{e}_t{e}_t^T$ 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.