  In this work, we introduce the novel problem of identifying dense canonical
3D coordinate frames from a single RGB image. We observe that each pixel in an
image corresponds to a surface in the underlying 3D geometry, where a canonical
frame can be identified as represented by three orthogonal axes, one along its
normal direction and two in its tangent plane. We propose an algorithm to
predict these axes from RGB. Our first insight is that canonical frames
computed automatically with recently introduced direction field synthesis
methods can provide training data for the task. Our second insight is that
networks designed for surface normal prediction provide better results when
trained jointly to predict canonical frames, and even better when trained to
also predict 2D projections of canonical frames. We conjecture this is because
projections of canonical tangent directions often align with local gradients in
images, and because those directions are tightly linked to 3D canonical frames
through projective geometry and orthogonality constraints. In our experiments,
we find that our method predicts 3D canonical frames that can be used in
applications ranging from surface normal estimation, feature matching, and
augmented reality.
