We present variational models to perform texture analysis and/or extraction for image processing. We focus on second order decomposition models. Variational decomposition models have been studied extensively during the past decades. The most famous one is the Rudin-Osher-Fatemi model. We first recall most classical first order models . Then we deal with second order ones : we detail the mathematical framework, theoretical models and numerical implementation. We end with two 3D applications. Eventually, an appendix includes the mathematical tools that are used to perfom this study and Matlab codes are provided.