Methods for characterizing a sample of porous media using a measuring device along with a multipoint statistical (MPS) model. Retrieving a set of reflected measured data provided by the measuring device of a surface of the sample in order to produce a sample imaging log, wherein the retrieved set of measured data is communicated to a processor. Selecting depth-defined surface portions of the sample from the sample imaging log as a training image for inputting in the MPS model. Determining pattern based simulations from the training image using one of a pixel-based template which is applied to the training image. Constructing from the pattern based simulations a complete-sampling image log of surface portions of the sample. Repeat the above steps in order to construct three dimensional (3D) sample images from stacked successive pattern based simulations so as to construct at least one 3D model of the sample.