The digitisation of heritage is being rapidly realised in many parts of the world thanks to LiDAR technology. In addition to the simple digital preservation of heritage, 3D acquisition makes it possible to monitor the structural condition and assess possible damage. This paper presents a method for modelling the lost volume of a heritage bridge. The selected case study is the Fillaboa bridge, in Salvaterra de Miño, Spain, which has two cutwaters with the same cutting angle, one of which is damaged and has a stone loss. The bridge was acquired with a Terrestrial Laser Scanner. The method consists of the following processes. First, the walls of the whole cutwater are segmented and aligned by Iterative Closest Point algorithm over the damaged cutwater. Second, the distance between the two point clouds is calculated and the damaged area is delimited in both point clouds. And third, the alpha shape algorithm is applied to model the point cloud of the damaged area to a polygon. By searching for the optimal alpha radius, the polygon that best fits the damaged volume is generated. The proposed method also allows digital reconstruction of the damaged area, although it is sensitive to acquisition problems, which require manual interventions in the processing. The accuracy of the method is mainly dependent on the acquired point cloud registration (with an RMS error of 60mm) and the ICP registration error (31mm). Its use is limited to the existence of two geometries that allow superposition: one in good condition and one damaged to compare.
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