Cellular materials are characterized by a complex architecture where the material is most of times concentrated in small struts connected in different ways. Originally consisting of foams, i.e. exhibiting a random distribution of cells, it is now possible, with the advent of Additive Manufacturing, to produce so-called lattices where well-designed unit-cells are periodically repeated to achieve exceptional specific performances, such as unprecedent stiffness-to-weight ratios, high stretchability, etc. These meta-materials, however, are very difficult to model from a mechanical point of view: their response is intimately related to the local architecture, which may not be perfectly known a priori, either because of the random aspect in foams, or because of the process-induced defects in lattices. In this context, the purpose of this work is to build, from digital images, light yet accurate mechanical twins accounting for the real (as-manufactured) geometric architectures of lattice-type materials. More precisely, we consider the area of isogeometric image-based modelling, and develop a specific template-fitting strategy to build an explicit B-spline based beam model which is directly ready for isogeometric beam simulations. In order to do so, we extend the Virtual Image Correlation method to the case of curved beams with varying cross-sections, and to the situation of multiple interconnected beams. The principle is to create a virtual image representing the entity to be measured, and to look for the optimal position of the latter so that the virtual image best matches the real image. In case of a foam, an additional pre-processing step is required to learn its random topology from the images, which is addressed here by resorting to advanced image processing techniques. During the presentation, synthetic and real examples of increasing complexity will be presented to account for the performance of the developed workflow from digital images to isogeometric mechanical twins.