Computational vision in UV-Mapping of textured meshes coming from photogrammetric recovery: Unwrapping frescoed vaults

Sometimes it is difficult to represent "on paper" the existing reality of architectonic elements, depending on the complexity of his geometry, but not only in cases with complex geometries: non-relief surfaces, can need a "special planar format" for its graphical representation. Nowadays, there are a lot of methods to obtain tridimensional recovery of our Cultural Heritage with different ranges of the relationship accuracy / costs, even getting high accuracy using "low-cost" recovery methods as digital photogrammetry, which allow us easily to obtain a graphical representation "on paper": ortho-images of different points of view. This can be useful for many purposes but, for others, an orthographic projection is not really very interesting. In non-site restoration tasks of frescoed vaults, a "planar format" representation in needed to see in true magnitude the paintings represented on the intrados vault, because of the general methodology used: gluing the fresco on a fabric, removing the fresco-fabric from the support, moving to laboratory, removing the fresco from the fabric, restoring the fresco, gluing back the restored fresco on another fabric, laying the restored fresco on the original location and removing the fabric. Because of this, many times, an unfolded model is needed, in a similar way a cylinder or cone can be unfolded, but in this case with a texture included: UV unwrapping. Unfold and fold-back processes, can be especially interesting in restoration field of frescoed vaults and domes at: chromatic recovery of paintings, reconstruction of partially missed geometries, transference of paintings on surfaces, etc.