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Publication# Differentiable Physically Based Rendering: Algorithms, Systems and Applications

Résumé

Physically based rendering methods can create photorealistic images by simulating the propagation and interaction of light in a virtual scene. Given a scene description including the shape of objects, participating media, material properties, etc., the simulation computes an image representing the radiance reaching the sensor.This thesis, however, pursues the corresponding inverse problem: given observations such as pictures of a scene, we want to recover a plausible description of its components. Unfortunately, the rendering process is typically far too complex to invert analytically. We therefore turn to iterative gradient-based approximations of the inverse, that require efficiently estimating gradients of an objective function with respect to the scene parameters of interest.The first part of this thesis is dedicated to algorithms for gradient estimation. We consider the usage of automatic differentiation and examine the associated tradeoffs. Next, we introduce radiative backpropagation, an adjoint method that casts the gradient estimation problem into a modified light transport problem, unlocking vastly more efficient implementations. For the case of participating media, we propose differential ratio tracking, a sampling technique that addresses the bias and high variance found in existing gradient estimators.In the second part, we focus on the design of systems to support effective differentiable rendering research, including the efficient implementation of the algorithms above. We describe the architecture and features of Mitsuba 2, an open-source retargetable physically based renderer. Mitsuba 2 supports different representations of colors (RGB, spectral, polarized), computing platforms (scalar, CPU vectorized, GPU), and numerical precision, within a single codebase. Importantly, automatic differentiation can be applied throughout the system. Then, we extend this design by applying an automatic conversion from wavefront-style rendering to a megakernel-based approach, leveraging just-in-time compilation. We obtain a fast, flexible and memory-efficient framework for primal and differentiable physically based rendering.Finally, the third part showcases three applications of differentiable physically based rendering: caustic design, inverse volume rendering, and material & lighting estimation in real indoor scenes. In all cases, special care is taken to avoid sub-optimal local minima due to the ambiguous and non-convex nature of the reconstruction problems.

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Jean-Baptiste Francis Marie Juliette Cordonnier, Martin Jaggi, Sebastian Urban Stich

Huge scale machine learning problems are nowadays tackled by distributed optimization algorithms, i.e. algorithms that leverage the compute power of many devices for training. The communication overhead is a key bottleneck that hinders perfect scalability. Various recent works proposed to use quantization or sparsification techniques to reduce the amount of data that needs to be communicated, for instance by only sending the most significant entries of the stochastic gradient (top-k sparsification). Whilst such schemes showed very promising performance in practice, they have eluded theoretical analysis so far. In this work we analyze Stochastic Gradient Descent (SGD) with k-sparsification or compression (for instance top-k or random-k) and show that this scheme converges at the same rate as vanilla SGD when equipped with error compensation (keeping track of accumulated errors in memory). That is, communication can be reduced by a factor of the dimension of the problem (sometimes even more) whilst still converging at the same rate. We present numerical experiments to illustrate the theoretical findings and the good scalability for distributed applications.

2018Wenzel Alban Jakob, Merlin Eléazar Nimier-David, Sébastien Nicolas Speierer

Physically based differentiable rendering has recently evolved into a powerful tool for solving inverse problems involving light. Methods in this area perform a differentiable simulation of the physical process of light transport and scattering to estimate partial derivatives relating scene parameters to pixels in the rendered image. Together with gradient-based optimization, such algorithms have interesting applications in diverse disciplines, e.g., to improve the reconstruction of 3D scenes, while accounting for interreflection and transparency, or to design meta-materials with specified optical properties. The most versatile differentiable rendering algorithms rely on reverse-mode differentiation to compute all requested derivatives at once, enabling optimization of scene descriptions with millions of free parameters. However, a severe limitation of the reverse-mode approach is that it requires a detailed transcript of the computation that is subsequently replayed to back-propagate derivatives to the scene parameters. The transcript of typical renderings is extremely large, exceeding the available system memory by many orders of magnitude, hence current methods are limited to simple scenes rendered at low resolutions and sample counts. We introduce radiative backpropagation, a fundamentally different approach to differentiable rendering that does not require a transcript, greatly improving its scalability and efficiency. Our main insight is that reverse-mode propagation through a rendering algorithm can be interpreted as the solution of a continuous transport problem involving the partial derivative of radiance with respect to the optimization objective. This quantity is "emitted" by sensors, "scattered" by the scene, and eventually "received" by objects with differentiable parameters. Differentiable rendering then decomposes into two separate primal and adjoint simulation steps that scale to complex scenes rendered at high resolutions. We also investigated biased variants of this algorithm and find that they considerably improve both runtime and convergence speed. We showcase an efficient GPU implementation of radiative backpropagation and compare its performance arid the quality of its gradients to prior work.

Wenzel Alban Jakob, Merlin Eléazar Nimier-David, Delio Aleardo Vicini, Tizian Lucien Zeltner

Modern rendering systems are confronted with a dauntingly large and growing set of requirements: in their pursuit of realism, physically based techniques must increasingly account for intricate properties of light, such as its spectral composition or polarization. To reduce prohibitive rendering times, vectorized renderers exploit coherence via instruction-level parallelism on CPUs and CPUs. Differentiable rendering algorithms propagate derivatives through a simulation to optimize an objective function, e.g., to reconstruct a scene from reference images. Catering to such diverse use cases is challenging and has led to numerous purpose-built systems-partly, because retrofitting features of this complexity onto an existing renderer involves an error-prone and infeasibly intrusive transformation of elementary data structures, interfaces between components, and their implementations (in other words, everything). We propose Mitsuba 2, a versatile renderer that is intrinsically retargetable to various applications including the ones listed above. Mitsuba 2 is implemented in modern C++ and leverages template metaprogramming to replace types and instrument the control flow of components such as BSDFs, volumes, emitters, and rendering algorithms. At compile time, it automatically transforms arithmetic, data structures, and function dispatch, turning generic algorithms into a variety of efficient implementations without the tedium of manual redesign. Possible transformations include changing the representation of color, generating a "wide" renderer that operates on bundles of light paths, just-in-time compilation to create computational kernels that run on the GPU, and forward/reverse-mode automatic differentiation. Transformations can be chained, which further enriches the space of algorithms derived from a single generic implementation. We demonstrate the effectiveness and simplicity of our approach on several applications that would be very challenging to create without assistance: a rendering algorithm based on coherent MCMC exploration, a caustic design method for gradient-index optics, and a technique for reconstructing heterogeneous media in the presence of multiple scattering.