Since masonry arch is one of the most common structural forms in both historic bridges and in architecture across the world such as domes and vaults, its dimensional and structural analysis is still the subject of numerous investigations. Controlling the deformation in historic arch bridges involves a number of difficulties arising from the measurement technique and the analysis methodology. Important advances have been made on terrestrial laser scanning technology to allow measuring the 3D geometry of objects without making direct contact with them with very high rates of data acquisition, high accuracy and long range. However, the development of computer algorithms to automate the analysis of the clouds of points would be useful to take advantage of the potential of this technique in the field of dimensional and structural analysis of historic bridges. This article presents a methodology to estimate the deformation of arches or vaults based on the symmetry of sections obtained along the vault guideline. The accurate geometry of the arches is obtained by means of a 3D laser scanner survey, and the point cloud is processed by statistical nonparametric methods based on local bivariate kernel smoothers, allowing estimation of arch cross-sections without establishing any parametric shape a priori.