Summary: We present a variational model for image texture identification. We first use a second order model introduced in J.-P. M. M. Bergounioux and L. Piffet [Set-Valued Var. Anal. 18, No. 3–4, 277–306 (2010; Zbl 1203.94006)] for image denoising. The model involves a \(L^{2}\)-data fitting term and a Tychonov-like regularization. We choose here the \(BV^{2}\) norm, where \(BV^{2}\) is the bounded hessian function space. We observe that results are not satisfying since geometrical information appears in the oscillating component and should not. So we propose an anisotropic strategy, by setting components of the discrete hessian operator to 0 in order to focus on gradient directions. We precisely describe and illustrate the numerical methodology. Finally, we propose some numerical tests.
For the entire collection see [Zbl 1217.90006].