Tom Duff
Abstract:
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.
Paper (PDF)
To appear in ACM Transactions on Graphics