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Optimization with graph cuts became very popular in recent years. While exact optimization is possible in a few cases, many useful energy functions are NP hard to optimize. One approach to approximate optimization is the so-called move making algorithms. At each iteration, a move-making algorithm makes a proposal (move) for a pixel p to either keep its old label or switch to a new label. Two move-making algorithms based on graph cuts are in wide use, namely the swap and expansion. Both of these moves are binary in nature, that is they give each pixel a choice of only two labels. An evaluation of optimization techniques shows that the expansion and swap algorithms perform very well for energies where the underlying MRF has the Potts prior. However for more general priors, the swap and expansion algorithms do not perform as well. The main contribution of this paper is to develop multi-label moves. A multi-label move, unlike expansion and swap, gives each pixel has a choice of more than two labels to switch to. In particular, we develop several multi-label moves for truncated convex priors. We evaluate our moves on image restoration, inpainting, and stereo correspondence. We get better results than expansion and swap algorithms, both in terms of the energy value and accuracy. [ABSTRACT FROM AUTHOR]