  We propose a differentiable sphere tracing algorithm to bridge the gap
between inverse graphics methods and the recently proposed deep learning based
implicit signed distance function. Due to the nature of the implicit function,
the rendering process requires tremendous function queries, which is
particularly problematic when the function is represented as a neural network.
We optimize both the forward and backward passes of our rendering layer to make
it run efficiently with affordable memory consumption on a commodity graphics
card. Our rendering method is fully differentiable such that losses can be
directly computed on the rendered 2D observations, and the gradients can be
propagated backwards to optimize the 3D geometry. We show that our rendering
method can effectively reconstruct accurate 3D shapes from various inputs, such
as sparse depth and multi-view images, through inverse optimization. With the
geometry based reasoning, our 3D shape prediction methods show excellent
generalization capability and robustness against various noises.
