Abstract : Medial surfaces are well-known and interesting surface skeletons. As such, they can describe the topology and the geometry of a 3D closed object. Many applications in computer graphics can benefit from their properties, if we use them as Shape Representation Models (SRMs). However, visualizing the shape described by a medial surface remains a challenging problem. In this paper, we propose a method to build a mesh for any closed surface described by a medial surface. This method is based on the construction of an adaptive voxelisation from the geometry encoded with the medial surface. This discretization has the same topology as the described object, regardless its genus. Then, we mesh the boundary of this voxel-based representation to get a coarse approximation. Finally we refine this mesh using an original migration algorithm, in order to smooth the result and be as close as possible to the described object. An empirical study, on both CAO and laser scan models, shows the efficiency of our method in providing high quality surfaces with a reasonable computational complexity.