Gaussian processes for 3D measurements

n this dissertation we explore the usage of probabilistic machine learning techniques for calibrating 3D measuring devices and applications. More specifically, we focus on Gaussian processes and line geometry. The research focuses on four main topics: galvanometric setup calibration, surface approximation, camera calibration, and the clinical application of mapping visuospatial neglect. We present a semi-data-driven approach to calibrate galvanometric setups. We perform Gaussian process regression to learn the mapping from the two galvanometric controlled mirrors to the resulting laser lines. Purely data-driven methods bypass the underlying geometric model of the device completely. We re-introduce one geometric assumption: lasers are straight lines. Building upon this approach, we impose constraints on both the inputs and the outputs of the Gaussian process models. The angles of the two galvanometric controlled mirrors can be seen as points on the surface of a torus. The Pl¨ucker coordinates of the straight lines themselves obey a quadratic constraint. We formulate several ways to handle these constraints. We implement Gaussian Process Latent Variable Models, which are a form of non-linear probabilistic dimensionality reduction, to approximate several surfaces. By relaxing the linear assumption of Principal Component Analysis, we can handle many more surfaces than classical methods. The exploration extends to camera calibration, addressing checkerboard pattern detection through corner detection and sub-pixel refinement. A mapping from virtual perfect checkerboard corners to real image pixels is learned, providing a solution for inferring missing corners and correcting existing ones. This idea is taken further in camera calibration by reversing this mapping. Now we learn from pixels of real checkerboard corners to a perfect virtual checkerboard. This approach turns cameras into perfect pinhole models. The research concludes by extending its scope to the application of visuospatial neglect assessment and treatment. Active learning methods are applied in a virtual reality environment to lower the number of measurements and thus the burden on patients suffering from this cognitive disorder. In summary, the dissertation highlights significant contributions to the field of 3D measurements and applications, offering a variety of innovative techniques and practical applications for future exploration.

Publication year:2024

Keywords:Engineering sciences. Technology

Accessibility:Open