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Many objects can be mathematically represented as smooth surfaces with arbitrary topology, and smooth surface reconstruction from images could be cast into a variational problem. The main difficulties are the intrinsic ill-posedness of the reconstruction, image noise, efficiency and scalability. In this paper, we discuss the reconstruction approaches that use volumetric, graph-cut, and level-set optimization tools; and the objective functionals that use different image information, silhouette, photometry, and texture. Our discussion is accompanied by the implementations of these approaches on real examples.