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3D models of seafloor interest areas having a strong 3D relief are a rich source of information for scientists. In the recent years, the computer vision community has been developing techniques to achieve the discrete reconstruction of these interest areas from a set of images. However, 3D reconstruction methods output a 3D point cloud as a representation of the shape of the observed object/area. This representation lacks connectivity information, and a surface that describes the underlying object is needed for both performing computations on the object and to achieve its correct visualization. In this article we aim to survey the State-of-the-Art of the problem of reconstructing the surface of an object represented by a cloud of points. This set of points is assumed to be the result of a Computer Vision based 3D reconstruction pipeline.