Spectral Processing and Optimization of Static and Dynamic 3D Geometries

Geometry processing of 3D objects is of primary interest in many areas of computer vision and graphics, including robot navigation, 3D object recognition, classification, feature extraction, etc. The recent introduction of cheap range sensors has created a great interest in many new areas, driving the need for developing efficient algorithms for 3D object processing. Previously, in order to capture a 3D object, expensive specialized sensors were used, such as lasers or dedicated range images, but now this limitation has changed. The current approaches of 3D object processing require a significant amount of manual intervention and they are still time-consuming making them unavailable for use in real-time applications. The aim of this thesis is to present algorithms, mainly inspired by the spectral analysis, subspace tracking, etc, that can be used and facilitate many areas of low-level 3D geometry processing (i.e., reconstruction, outliers removal, denoising, compression), pattern recognition tasks (i.e., significant features extraction) and high-level applications (i.e., registration and identification of 3D objects in partially scanned and cluttered scenes), taking into consideration different types of 3D models (i.e., static and dynamic point clouds, static and dynamic 3D meshes).