Clustered Principal Components for Precomputed Radiance Transfer

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Clustered Principal Components for Precomputed
Radiance Transfer real-time rendering with
shadows and inter-reflections for objects with
complex reflectance
Radiance transfer at p from source to transferred
incident to exitant. We use a transfer matrix at
each p to represent the linear transformation of
source radiance into exitant radiance. We use
the spherical harmonic basis for these radiance
functions.
We compress transfer matrices over many points
over the surface using CPCA (clustered principal
component analysis). It approximates the
transfer matrices using an affine subspace over a
small number (256) of clusters of points. Using
a few PCA vectors per cluster (n'), a good
approximation is obtained.
Equivalent Rendering Cost Comparison The three
left columns show various approximations that
take the same time to render (45Hz). CPCA
provides a much better approximation than a
global linear subspace over the whole object
(PCA), or a piecewise constant approximation (VQ).
59Hz
27Hz
Real-time rendering sample images, using
CPCA-encoded transfer matrices
43Hz
27Hz