Over the last few years energy minimization has emerged as an indispensable tool in computer vision. The scale and form of computer vision problems introduce many challenges in energy minimization. This book focused on some aspects of these problems. The first problem it addresses relates to the efficient and exact minimization of groups of similar functions which are known to be solvable in polynomial time. A novel dynamic algorithm for minimizing such functions will be presented. This algorithm reuses computation from previous problem instances to solve new instances resulting in a substantial improvement in the running time. The second part of the book deals with the minimization of higher order functions which are able to model interactions among groups of random variables and can be used to formulate many vision problems. We will see how certain higher order energy functions can be minimized using the graph cut based expansion and swap move algorithms. The book presents results on the problems of interactive image segmentation, image segmentation in video, and human pose estimation and segmentation.