Systematically differentiating parametric discontinuities

نویسندگان

چکیده

Emerging research in computer graphics, inverse problems, and machine learning requires us to differentiate optimize parametric discontinuities. These discontinuities appear object boundaries, occlusion, contact, sudden change over time. In many domains, such as rendering physics simulation, we the parameters of models that are expressed integrals discontinuous functions. Ignoring during differentiation often has a significant impact on optimization process. Previous approaches either apply specialized hand-derived solutions, smooth out discontinuities, or rely incorrect automatic differentiation. We propose systematic approach differentiating with integrands, by developing new differentiable programming language. introduce integration language primitive account for Dirac delta contribution from integrand. formally define semantics prove correctness closure under differentiation, allowing generation gradients higher-order derivatives. also build system, Teg, implementing these semantics. Our is widely applicable variety tasks, including image stylization, fitting shader parameters, trajectory optimization, optimizing physical designs.

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ژورنال

عنوان ژورنال: ACM Transactions on Graphics

سال: 2021

ISSN: ['0730-0301', '1557-7368']

DOI: https://doi.org/10.1145/3450626.3459775