In the collections of natural history, mounted skeletons are among the most complex objects. They are composed of hundreds of different bones, tedious to digitize accurately in 3D because many surfaces remain hidden to the scanning device. A group of researchers from Pierre et Marie Curie (Paris 6) and Grenoble Universities teamed up with researchers from the National Museum of Natural History in Paris in order to design and implement a mathematical model of the bone surface deformation through optimization. The goal is to produce a surface triangulation adapted to the underlying surface intrinsic geometric properties from the sole datum of point clouds of skeleton bones. Outlier points will be removed from the data and the remaining inlier points will be labeled according to their membership to a specific bone structure. The results will be validated from the anatomical point of view and will be used to conduct functional morphology analysis. In our approach, each bone reconstruction of a skeleton will be obtained by morphing a generic representative surface of the same equivalence class using a mathematical derivative-based model. The resolution of this problem will lead to a definition of a closed orientable surface and will allow to account for the conservation of specifically labeled components.