This paper proposes a new method based on implicit surfaces for medical organs reconstruction. The original data are noisy scattered points of an organ, that may be arranged in any non-uniform repartition. The knowledge of the normal vectors is not needed. Organs of any geometry and topology can be reconstructed, as for instance a vertebra that is characterized by a hole and by several branchings. The proposed method uses implicit iso-surfaces generated by skeletons, that are a particularly compact way of giving a smooth representation of a surface. Validity of the reconstructed shape is insured, since implicit surfaces bound a well defined volume. As in a previous work [Mur91] the principle is the minimization of an energy that represents the distance between the set of points and the iso-surface. Skeletons generating field functions are automatically subdivided when needed. But the algorithm we use is novel. Firstly, we introduce local control on the reconstructed shape thanks to local and less expensive field functions. Secondly, we propose a much more efficient skeleton subdivision process, based on a notion of “skeleton energy” that gives a robust criterion for choosing the next skeleton to subdivide. Another optimization consists in splitting the data space into several overlapping windows, where only local data points are used for reconstruction. Implemented as a semi-automatic process, the reconstruction module enables the user to take benefits of his initial knowledge of the surface to guide computations. We use an interactive system for visualizing the data, initially positioning some skeletons, defining local reconstruction areas, and visualizing intermediate results. We have successfully applied the method to both non-medical and medical data.