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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This is a very interesting and substantially novel paper that introduces an approach to solving continuous Markov random field energies with polynomial potentials. An insightful and well-motivated approach towards this end (ADMM-Poly) was published at CVPR 2013 [20] and is the obvious baseline to compare against. The present approach is convincingly shown to be preferable, as it is both elegant and computationally efficient. The main idea underlying the approach is to decompose the polynomials into a difference of convex functions.