  This paper develops and evaluates a new tensor field representation to
express the geometric affordance of one object over another. We expand the well
known bisector surface representation to one that is weight-driven and that
retains the provenance of surface points with directional vectors. We also
incorporate the notion of affordance keypoints which allow for faster decisions
at a point of query and with a compact and straightforward descriptor. Using a
single interaction example, we are able to generalize to previously-unseen
scenarios; both synthetic and also real scenes captured with RGBD sensors. We
show how our interaction tensor allows for significantly better performance
over alternative formulations. Evaluations also include crowdsourcing
comparisons that confirm the validity of our affordance proposals, which agree
on average 84% of the time with human judgments, and which is 20-40% better
than the baseline methods.
