Gaze Tracing in a Bounded Log-Spherical Space for Artificial Attention Systems

Human gaze is one of the most important cue for social robotics due to its embedded intention information. Discovering the location or the object that an interlocutor is staring at, gives the machine some insight to perform the correct attentional behaviour. This work presents a fast voxel traversal algorithm for estimating the potential locations that a human is gazing. Given a 3D occupancy map in log-spherical coordinates and the gaze vector, we evaluate the regions that are relevant for attention by computing the set of intersected voxels between an arbitrary gaze ray in the 3D space and a log-spherical bounded section defined by $$\rho \in (\rho _{min},\rho _{max}),\theta \in (\theta _{min},\theta _{max} ),\phi \in (\phi _{min},\phi _{max})$$. The first intersected voxel is computed in closed form and the rest are obtained by binary search guaranteeing no repetitions in the intersected set. The proposed method is motivated and validated within a human-robot interaction application: gaze tracing for artificial attention systems.