The role of the extracellular matrix (ECM) in the evolution of certain diseases (e.g. fibrosis, cancer) is generally accepted but yet to be completely understood. A numerical model that captures the physical properties of the ECM, could convey certain connections between the topology of its constituents and their associated biological features. This study addresses the analysis and modeling of fibrillar networks containing Fi-bronectin (FN) networks, a major ECM molecule, from 2D confocal microscopy images. We leveraged the advantages of the fast discrete curvelet transform (FDCT), in order to obtain a multiscale and multidirectional representation of the FN fibrillar networks. This step was validated by performing a classification among the different variants of FN upregulated in disease states with a multi-class classification algorithm, DAG-SVM. Subsequently, we designed a method to ensure the invariance to rotation of the curvelet features. Our results indicate that the curvelets offer an appropriate discriminative model for the FN networks, that is able to characterize the local fiber geometry.