MULTIPLE STRUCTURE RECOVERY VIA PREFERENCE ANALYSIS IN CONCEPTUAL SPACE

Finding multiple models (or structures) that fit data corrupted by noise and outliers is an omnipresent problem in empirical sciences, includingComputer Vision, where organizing unstructured visual data in higher level geometric structures is a necessary and basic step to derive better descriptions and understanding of a scene. This challenging problem has a chicken-and-egg pattern: in order to estimate models one needs to first segment the data, and in order to segment the data it is necessary to know which structure points belong to. Most of the multi-model fitting techniques proposed in the literature can be divided in two classes, according to which horn of the chicken-egg-dilemma is addressed first, namely consensus and preference analysis. Consensus-based methods put the emphasis on the estimation part of the problem and focus on models that describe has many points as possible. On the other side, preference analysis concentrates on the segmentation side in order to find a proper partition of the data, from which model estimation follows. The research conducted in this thesis attempts to provide theoretical footing to the preference approach and to elaborate it in term of performances and robustness. In particular, we derive a conceptual space in which preference analysis is robustly performed thanks to three different formulations of multiple structures recovery, i.e. linkage clustering, spectral analysis and set coverage. In this way we are able to propose new and effective strategies to link together consensus and preferences based criteria to overcome the limitation of both. In order to validate our researches, we have applied our methodologies to some significant Computer Vision tasks including: geometric primitive fitting (e.g. line fitting; circle fitting; 3D plane fitting), multi-body segmentation, plane segmentation, and video motion segmentation.