Cultural Heritage Restoration of a Hemispherical Vault by 3D Modelling and Projection of Video Images with Unknown Parameters and from Unknown Locations

Reverse engineering applied to architectural restoration for the reconstruction of structural surfaces depends on metric precision. Sometimes there are elements on these surfaces whose value is even higher than the building itself. This is the case for many churches whose ceilings have pictorial works of art. Reconstruction requires the existence of some identifiable remainder and/or a surface geometry that enables mathematical development. In our case, the vault has an irregular hemispherical geometry (without possible mathematical development), and there are no significant remains of the painting (which was destroyed by a fire). Through the 3D modelling of the irregular vault and two historic frames with a camera of unknown geometry, an inverse methodology is designed to project the original painting without metric deformations. For this, a new methodology to locate the camera positions is developed. After, a 3D virtual mathematical model of the complete image on the vault is calculated, and from it, partial 3D virtual images are automatically calculated depending on the variable unknown positions of the video cannons (distributed along the upper corridor of the apse) that will project them (visually forming a perfect complete 3D image)