Block matching algorithms (DIC), used in experimental mechanics and full-field process analysis, reach their limits in resolving complex, discontinuous, and multi-scale deformation patterns, are error-prone under industrial operating conditions, or fail when calculating spatio-temporal derivatives. However, motion and its spatio-temporal derivatives lay the foundation of modeling physical processes. This thesis pursues a fundamentally different approach, based on the calculus of variations – the optical flow methods. Newly designed regulariza-tions together with a novel framework for hyperparameter determination enable robust estimation of motion, its spatio-temporal derivatives, and discontinuities. The proposed methods allow analyzing strain, strain rate, and crack propagation during different shear cutting processes using high-speed imaging on a developed precision shear cutting tool.