We propose a new way to estimating interparticle contact forces in granular materials, based on the combination of experimental measurements and numerical techniques that take the contact laws respectively from Molecular Dynamics and Non-Smooth Contact Dynamics discrete element methods. Tests are performed in quasi-static conditions on a two-dimensional granular assembly; 80 MPixel pictures of the assembly are shot throughout each test. Image processing and Digital Image Correlation are used in order to get information on the geometry of the assembly (particles and contact points position) and the rigid-body motion of particles (displacements and rotation); based on this information, numerical methods can be applied to assess contact forces. 2D DEM simulations are also performed and the same information is extracted and used for contact force estimation, so that the numerical methods can be validated. The reproducibility of the original set of contact forces is shown to be dependent on the displacement history for the first method, based on contact elasticity, and on the degree of force indeterminacy for the Contact Dynamics-based one. The validation phase also includes a perturbation analysis to predict the influence of measurement error (bad contact detection) when applying the Contact Dynamics-based method, which shows the robustness of this method. After this validation phase, the methods are applied to experimental data. Measurement error on kinematic measurements turns out to be quite significant for the first approach, while it does not affect the second, for which the accuracy of the force estimation can be assumed to be mainly dependent on the degree of force indeterminacy of the system.