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The many-light formulation provides a general framework for rendering variousillumination effects using hundreds of thousands of virtual point lights(VPLs). To efficiently gather the contributions of the VPLs, lightcuts and itsextensions cluster the VPLs, which implicitly approximates the lighting matrixwith some representative blocks similar to vector quantization. In this paper,we propose a new approximation method based on the previous lightcut method anda low-rank matrix factorization model. As many researchers pointed out, thelighting matrix is low rank, which implies that it can be completed from asmall set of known entries.  We first generate a conservative global light cut with bounded error andpartition the lighting matrix into slices by the coordinate and normal of thesurface points using the method of lightslice. Then we perform two passes ofrandomly sampling on each matrix slice. In the first pass, uniformlydistributed random entries are sampled to coarsen the global light cut, furtherclustering the similar light for the spatially localized surface points of theslices. In the second pass, more entries are sampled according to thepossibility distribution function estimated from the first sampling result.Then each matrix slice is factorized into a product of two smaller low-rankmatrices constrained by the sampled entries, which delivers a completion of thelighting matrix. The factorized form provides an additional speedup for addingup the matrix columns which is more GPU friendly. Compared with the previouslightcut based methods, we approximate the lighting matrix with some signalspecialized bases via factorization. The experimental results shows that we canachieve significant acceleration than the state of the art many-light methods.

Sparse Sampling and Completion for Light Transport in VPL-based Rendering