Differentiable Rendering of Neural SDFs through Reparameterization

We present a method to automatically compute correct gradients with respect to geometric scene parameters in neural SDF renderers. Recent physically-based differentiable rendering techniques for meshes have used edge-sampling to handle discontinuities, particularly at object silhouettes, but SDFs do not have a simple parametric form amenable to sampling. Instead, our approach builds on area-sampling techniques and develops a continuous warping function for SDFs to account for these discontinuities. Our method leverages the distance to surface encoded in an SDF and uses quadrature on sphere tracer points to compute this warping function. We further show that this can be done by subsampling the points to make the method tractable for neural SDFs. Our differentiable renderer can be used to optimize neural shapes from multi-view images and produces comparable 3D reconstructions to recent SDF-based inverse rendering methods, without the need for 2D segmentation masks to guide the geometry optimization and no volumetric approximations to the geometry.

Opt: A Domain Specific Language for Non-linear Least Squares Optimization in Graphics and Imaging

Many graphics and vision problems can be expressed as non-linear least squares optimizations of objective functions over visual data, such as images and meshes. The mathematical descriptions of these functions are extremely concise, but their implementation in real code is tedious, especially when optimized for real-time performance on modern GPUs in interactive applications. In this work, we propose a new language, Opt (available under http://optlang.org), for writing these objective functions over image- or graph-structured unknowns concisely and at a high level. Our compiler automatically transforms these specifications into state-of-the-art GPU solvers based on Gauss-Newton or Levenberg-Marquardt methods. Opt can generate different variations of the solver, so users can easily explore tradeoffs in numerical precision, matrix-free methods, and solver approaches. In our results, we implement a variety of real-world graphics and vision applications. Their energy functions are expressible in tens of lines of code, and produce highly-optimized GPU solver implementations. These solver have performance competitive with the best published hand-tuned, application-specific GPU solvers, and orders of magnitude beyond a general-purpose auto-generated solver.