Measuring displacement and strain fields at low observable scales of complex microstructures such as cellular materials still remains a challenge in experimental mechanics, often because of images with low definition and poor texture at this scale. Here, we develop a Digital Volume Correlation (DVC) method that allows to measure the deformation of the cell-struts of a cellular material undergoing crushing. It consists of a DIC method assisted with a physically sound weak regularization using an elastic finite-element image-based model at the architecture scale. With this technique, the non-linear response at the architecture scale, in particular local buckling, of a polyurethane foam under compression, is properly described.