  Estimating 3D hand pose from 2D images is a difficult, inverse problem due to
the inherent scale and depth ambiguities. Current state-of-the-art methods
train fully supervised deep neural networks with 3D ground-truth data. However,
acquiring 3D annotations is expensive, typically requiring calibrated
multi-view setups or labor intensive manual annotations. While annotations of
2D keypoints are much easier to obtain, how to efficiently leverage such
weakly-supervised data to improve the task of 3D hand pose prediction remains
an important open question. The key difficulty stems from the fact that direct
application of additional 2D supervision mostly benefits the 2D proxy objective
but does little to alleviate the depth and scale ambiguities. Embracing this
challenge we propose a set of novel losses. We show by extensive experiments
that our proposed constraints significantly reduce the depth ambiguity and
allow the network to more effectively leverage additional 2D annotated images.
For example, on the challenging freiHAND dataset using additional 2D annotation
without our proposed biomechanical constraints reduces the depth error by only
$15\%$, whereas the error is reduced significantly by $50\%$ when the proposed
biomechanical constraints are used.
