“Deep Compositing Using Lie Algebras”

  • ©Tom Duff




    Deep Compositing Using Lie Algebras

Session/Category Title: Deep Image Processing



    Deep compositing is an important practical tool in creating digital imagery, but there has been little theoretical analysis of the underlying mathematical operators. Motivated by finding a simple formulation of the merging operation on OpenEXR-style deep images, we show that the Porter-Duff over function is the operator of a Lie group. In its corresponding Lie algebra, the splitting and mixing functions that OpenEXR deep merging requires have a particularly simple form. Working in the Lie algebra, we present a novel, simple proof of the uniqueness of the mixing function.The Lie group structure has many more applications, including new, correct resampling algorithms for volumetric images with alpha channels, and a deep image compression technique that outperforms that of OpenEXR.


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