We present in this chapter fast operator-splitting-based algorithms for the solutions of variational problems from image processing. The models we consider use geometrical information and rely on the minimization of appropriate energy functionals. These energy functionals are nonquadratic, possibly nonconvex and nonsmooth, making their minimization a nontrivial endeavour. We show in this chapter that operator-splitting methods based on the Lie scheme, and variants of it, can provide algorithms that are efficient, robust and nearly parameter free. These new algorithms are simpler to use, and often more efficient, than those relying on alternating direction methods of multipliers (ADMM). We want to emphasize that one can use the methods discussed in this chapter for a wide range of applications; actually it has already been done for several of them.