GAUSSIAN PROCESSES FOR 3D SHAPE MODELLING OF NOISY AND INCOMPLETE DATA. AN APPLICATION TO HUMAN EARS RECONSTRUCTION

Mathematical modelling of 3D shapes is a requirement in a vast and increasing number of applications, especially when it comes to the human shape. Despite being an active branch of research, with many proposed solutions, some settings remain particularly challenging. An example of such an open problem is the modelling or reconstruction of human ears from 3D point clouds, the motivation behind this thesis. This specific problem proves to be a particularly challenging case due to the fine and non-linear details to be modelled, together with the extensive presence of missing data and outliers, originated from the data retrieval procedure. Gaussian Processes were recently proposed as a suitable framework for the formulation of shape modelling problems and have mostly been applied to the human face. We show that this is indeed the most promising setting for our particular kind of data, but it can not be trivially applied from existing solutions. Therefore, we propose a fully unsupervised pipeline from raw 3D scans to a complete ear model, able to cope with the specific challenges encountered. Nonetheless, the main bottleneck of the pipeline is found on the shape registration part, that hinders the quality of the final results. We address this problem by incorporating the registration task entirely within the Gaussian Processes framework, unlike previous approaches and we provide a method for parameter estimation based on Variational Bayesian Inference. Not only do we achieve better registration results in the presence of large regions of missing data, but we provide a more unified way to deal with shape modelling. This is a step towards a more coherent approach and away from complex pipelines, merging different and often contradictory assumptions.