  Reasoning about 3D scenes from their 2D image projections is one of the core
problems in computer vision. Solutions to this inverse and ill-posed problem
typically involve a search for models that best explain observed image data.
Notably, images depend both on the properties of observed scenes and on the
process of image formation. Hence, if optimization techniques should be used to
explain images, it is crucial to design differentiable functions for the
projection of 3D scenes into images, also known as differentiable rendering.
Previous approaches to differentiable rendering typically replace
non-differentiable operations by smooth approximations, impacting the
subsequent 3D estimation. In this paper, we take a more general approach and
study differentiable renderers through the prism of randomized optimization and
the related notion of perturbed optimizers. In particular, our work highlights
the link between some well-known differentiable renderer formulations and
randomly smoothed optimizers, and introduces differentiable perturbed
renderers. We also propose a variance reduction mechanism to alleviate the
computational burden inherent to perturbed optimizers and introduce an adaptive
scheme to automatically adjust the smoothing parameters of the rendering
process. We apply our method to 3D scene reconstruction and demonstrate its
advantages on the tasks of 6D pose estimation and 3D mesh reconstruction. By
providing informative gradients that can be used as a strong supervisory
signal, we demonstrate the benefits of perturbed renderers to obtain more
accurate solutions when compared to the state-of-the-art alternatives using
smooth gradient approximations.
