Following the recent progress of surface acquisition systems, geometry processing algorithms quickly evolve to deal with the variety of data types and acquisition quality. This habilitation manuscript details some recent approaches to tackle this challenge. First, for low-quality data, it is necessary to improve the measure by denoising or super-resolution algorithms. Self-similarity analysis yields efficient methods for improving the acquisition quality either for real object surfaces, or generalized shapes (shapes whose intrinsic dimension is not constant). Beyond low-resolution acquisition, taking this similarity into account also permits to compress point set surfaces, that can then be resampled during decompression.
While geometric data are per se a research topic, additional image data or other type of measures can be acquired simultaneously, which allows to complete or augment the geometric information through a joint analysis. This manuscript addresses this multi-captor data problem to augment urban scenes point sets by using a collection of pictures, which permits to colorize point clouds, once images are accurately registered. Finally, for specific purposes, it is interesting to represent surfaces as polygonal meshes potentially replacing several points by a single planar facet. To do so, this manuscript describes an Optimal Transportation metric between the initial point cloud and a mesh. The reconstruction and optimization of the mesh can then be driven by the minimization of this distance.