1. Introduction
Multi-structure recovery (also known as multi-model fitting) aims at organising a set of input data in multiple geometric structures described by a few underlying parametric models. This is a fundamental step in many Computer Vision and Pattern Recognition applications such as motion segmentation [40], template detection [17], primitive fitting in point clouds [12], and multi-body Structure-From-Motion [10], [22], [26]. The vast majority of fitting methods identifies multiple structures from a single-class of models (e.g. 3D planes to fit building facades) [7], [13], [18], [32], and cannot solve multi-class structure recovery problems, where structures have to be identified from several classes of models (e.g. cylinders, planes). Multi-class recovery problems have been much less investigated [3],[4],[21],[42],[43], despite they are frequently met in practical applications and their solution typically enrich the interpretation of raw data. Dealing with diverse classes of models enables a higher level of abstraction and, in a broader perspective, can be reckoned as an attempt to bridge the semantic gap separating raw visual content from reasoning. For instance, consider the 3D point cloud X in Fig. 1, where the underlying structures (groups of 3D points) can be identified by solving a 2-class multi-model fitting problem with respect to Θp and Θc, the class of planes and cylinders, respectively. Here, the proposed MultiLink successfully partitions the point cloud in s structures X = U1 ∪ ... ∪ Us, and for each structure it decides whether to fit a plane or a cylinder, providing an high-level description of the Cathedral.