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DTSTART:19911015T033000
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BEGIN:VEVENT
DTSTAMP:20251218T030653Z
LOCATION:Meeting Room S426+S427\, Level 4
DTSTART;TZID=Asia/Hong_Kong:20251216T113400
DTEND;TZID=Asia/Hong_Kong:20251216T114500
UID:siggraphasia_SIGGRAPH Asia 2025_sess118_papers_1042@linklings.com
SUMMARY:SZ Sequences: Binary-Constructed $(0, 2^q)$-Sequences
DESCRIPTION:Abdalla G. M. Ahmed (Shenzhen University), Matt Pharr (NVIDIA)
 , Victor Ostromoukhov (Université Claude Bernard Lyon), and Hui Huang (She
 nzhen University)\n\nLow-discrepancy sequences have seen widespread adopti
 on in computer graphics thanks to the superior rates of convergence that t
 hey provide.\nBecause rendering integrals often are comprised of products 
 of lower-dimensional integrals, recent work has focused on developing sequ
 ences that are also well-distributed in lower-dimensional projections. To 
 this end, we introduce a novel construction of binary-based $(0, 4)$-seque
 nces; that is, progressive fully multi-stratified sequences of 4D points, 
 and extend the idea to higher power-of-two dimensions. We further show tha
 t not only it is possible to nest lower-dimensional sequences in higher-di
 mensional ones---for example, embedding a $(0, 2)$-sequence within our $(0
 , 4)$-sequence---but that we can ensemble two $(0, 2)$-sequences into a $(
 0, 4)$-sequence, four $(0, 4)$-sequences into a $(0, 16)$-sequence, and so
  on. Such sequences can provide excellent rates of convergence when integr
 als include lower-dimensional integration problems in 2, 4, 16,$\ldots$ di
 mensions. Our construction is based on using 2$\times$2 block matrices as 
 symbols to construct larger matrices that potentially generate a sequence 
 with the target $(0, s)$-sequence in base $s$ property. We describe how to
  search for suitable alphabets and identify two distinct, cross-related al
 phabets of block symbols, which we call $s$ and $z$, hence \emph{SZ} for t
 he resulting family of sequences.\nGiven the alphabets, we construct candi
 date generator matrices and search for valid sets of matrices. We then inf
 er a simple recurrence formula to construct full-resolution (64-bit) matri
 ces.\nBecause our generator matrices are binary, they allow highly-efficie
 nt implementation using bitwise operations and can be used as a drop-in re
 placement for Sobol matrices in existing applications. \nWe compare SZ seq
 uences to state-of-the-art low discrepancy sequences, and demonstrate mean
  relative squared error improvements up to $1.93\times$ in common renderin
 g applications.\n\nRegistration Category: Full Access, Full Access Support
 er\n\nSession Chair: Oliver Deussen (University of Konstanz)\n\n
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