We consider the problem of aggregating the geometrical information provided by sensors such as rangefinders and its applications to scene modelling. This information consists of collections of three-dimensional surface points that form a discrete subspace of the objects-to-free-space boundaries within the world to be modelled. We introduce a graph-theoretic definition for model validity which we use to guide the process of aggregating the different views. We propose a global algorithm based on the concept convex layers in computational geometry. The decision process relies solely on geometrical intersection predicates between lines and faces. Physically, the lines correspond to lines of sight of the sensor, and faces to approximations of the hull of the observed object. See Figures a-d
S. Aubry, V. Hayward
Figure a: A round object with a deep concavity. The pyramidal marks are fiducial points. Figure b: The zeroth-order approximation of the object (the convex hull). The black lines are the rangefinder's line-of-sight rays for those points which make up the next order's approximation. Figure c: The first-order approximation of the object. Artifacts on the round part of the object are caused by calibration inaccuracies. The concavity is now only partially carved. Figure d: The second-order approximation of the object. The concavity is still being carved (note the many rays in the bottom part of the figure) while the round part of the object is fully modelled.