Inverse reconstruction from images is a central problem in many scientific and engineering disciplines. Recent progress on differentiable rendering has led to methods that can efficiently differentiate the full process of image formation with respect to millions of parameters to solve such problems via gradient-based optimization. At the same time, the availability of cheap derivatives does not necessarily make an inverse problem easy to solve. Mesh-based representations remain a particular source of irritation: an adverse gradient step involving vertex positions could turn parts of the mesh inside-out, introduce numerous local self-intersections, or lead to inadequate usage of the vertex budget due to distortion. These types of issues are often irrecoverable in the sense that subsequent optimization steps will further exacerbate them. In other words, the optimization lacks robustness due to an objective function with substantial non-convexity. Such robustness issues are commonly mitigated by imposing additional regularization, typically in the form of Laplacian energies that quantify and improve the smoothness of the current iterate. However, regularization introduces its own set of problems: solutions must now compromise between solving the problem and being smooth. Furthermore, gradient steps involving a Laplacian energy resemble Jacobi's iterative method for solving linear equations that is known for its exceptionally slow convergence. We propose a simple and practical alternative that casts differentiable rendering into the framework of preconditioned gradient descent. Our pre-conditioner biases gradient steps towards smooth solutions without requiring the final solution to be smooth. In contrast to Jacobi-style iteration, each gradient step propagates information among all variables, enabling convergence using fewer and larger steps. Our method is not restricted to meshes and can also accelerate the reconstruction of other representations, where smooth solutions are generally expected. We demonstrate its superior performance in the context of geometric optimization and texture reconstruction.

Inria (a) Or i g i n a l I ma g e (b) S e l e c t i o n (c) Co mp o s i t e Re s u l t Figure 1: Example of a composition of two captured historical landmarks using our method. We extract the geometry of one (b) from a multi-view dataset, and import it into the other (a). Our method ensures coherent treatment of lighting and shadows, producing a realistic result (c).

We present a method for reducing errors---variance and bias---in physically based differentiable rendering (PBDR). Typical applications of PBDR repeatedly render a scene as part of an optimization loop involving gradient descent. The actual change introduced by each gradient descent step is often relatively small, causing a significant degree of redundancy in this computation. We exploit this redundancy by formulating a gradient estimator that employs a recursive control variate , which leverages information from previous optimization steps. The control variate reduces variance in gradients, and, perhaps more importantly, alleviates issues that arise from differentiating loss functions with respect to noisy inputs, a common cause of drift to bad local minima or divergent optimizations. We experimentally evaluate our approach on a variety of path-traced scenes containing surfaces and volumes and observe that primal rendering efficiency improves by a factor of up to 10.