Systematically differentiating parametric discontinuities
| Autor: | Jesse Michel, Jonathan Ragan-Kelley, Kevin Mu, Tzu-Mao Li, Sai Praveen Bangaru, Gilbert Bernstein |
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| Rok vydání: | 2021 |
| Předmět: |
Computer graphics
Language primitive Automatic differentiation Computer science Semantics (computer science) ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION Classification of discontinuities Shader Algorithm Computer Graphics and Computer-Aided Design ComputingMethodologies_COMPUTERGRAPHICS Parametric statistics Rendering (computer graphics) |
| Zdroj: | ACM Transactions on Graphics. 40:1-18 |
| ISSN: | 1557-7368 0730-0301 |
| Popis: | Emerging research in computer graphics, inverse problems, and machine learning requires us to differentiate and optimize parametric discontinuities. These discontinuities appear in object boundaries, occlusion, contact, and sudden change over time. In many domains, such as rendering and physics simulation, we differentiate the parameters of models that are expressed as integrals over discontinuous functions. Ignoring the discontinuities during differentiation often has a significant impact on the optimization process. Previous approaches either apply specialized hand-derived solutions, smooth out the discontinuities, or rely on incorrect automatic differentiation. We propose a systematic approach to differentiating integrals with discontinuous integrands, by developing a new differentiable programming language. We introduce integration as a language primitive and account for the Dirac delta contribution from differentiating parametric discontinuities in the integrand. We formally define the language semantics and prove the correctness and closure under the differentiation, allowing the generation of gradients and higher-order derivatives. We also build a system, Teg, implementing these semantics. Our approach is widely applicable to a variety of tasks, including image stylization, fitting shader parameters, trajectory optimization, and optimizing physical designs. |
| Databáze: | OpenAIRE |
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