Tomographic Volumetric Additive Manufacturing (TVAM) is an emerging 3D printing technology that can create complex objects in under a minute. The key idea is to project intense light patterns onto a rotating vial of photo-sensitive resin, causing polymerization where the cumulative dose of these patterns reaches the polymerization threshold. We formulate the pattern calculation as an inverse light transport problem and solve it via physically based differentiable rendering. In doing so, we address longstanding limitations of prior work by accurately modeling and correcting for scattering in composite resins, printing in non-symmetric vials, and supporting unusual printing geometries. We also introduce an improved discretization scheme that exploits the ray tracing operation to mitigate resolution-related artifacts in prints. We demonstrate the benefits of our method in real-world experiments, where our computed patterns produce prints with an improved fidelity.

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.

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.

Multi-view stereo can be used to rapidly create realistic virtual content, such as textured meshes or a geometric proxy for free-viewpoint Image-Based Rendering (IBR). These solutions greatly simplify the content creation process compared to traditional methods, but it is difficult to modify the content of the scene. We propose a novel approach to create scenes by composing (parts of) multiple captured scenes. The main difficulty of such compositions is that lighting conditions in each captured scene are different; to obtain a realistic composition we need to make lighting coherent. We propose a two-pass solution, by adapting a multi-view relighting network. We first match the lighting conditions of each scene separately and then synthesize shadows between scenes in a subsequent pass. We also improve the realism of the composition by estimating the change in ambient occlusion in contact areas between parts and compensate for the color balance of the different cameras used for capture. We illustrate our method with results on multiple compositions of outdoor scenes and show its application to multi-view image composition, IBR and textured mesh creation.