A multitude of computer vision challenges can be cast as problems of energy minimization. In my presentation I will introduce optimization methods which allow to segment moving objects in image sequences, to detect obstacles in traffic videos, to estimate the similarity of 2D shapes, to reconstruct 3D shapes from a collection of 2D images and to track humans in videos. I will detail how respective cost functionals can be minimized both by continuous (PDE and level set methods) and by discrete (graph theoretic) methods.