Generation of Stratified Samples for B-Spline Pixel Filtering

Michael Stark
University of California Irvine

Michael Ashikhmin
State University of New York Stony Brook

This paper appears in issue Volume 10, Number 1.
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Abstract

B-spline filter kernels have proved useful in many pixel-sampling applications. A cubic B-spline filter kernel, having a width of four pixels, is particularly effective. In distribution ray tracing, pixel filters are evaluated implicitly by having the density of sampling proportional to the filter value. In this work we present a simple method to generate random samples having an underlying B-spline density function. To reduce error it is important to stratify the samples, akin to jittering for uniform sampling. We provide an algebraic and a numerical technique for doing this for B-spline kernels of degree 1, 2, and 3.

Author Information

Michael Stark, University of California Irvine, Computer Science Department, Irvine, CA 92697 mstark@uci.edu

Peter Shirley, University of Utah Computer Science Department, 50 Central Campus Drive, Salt Lake City, UT 84112 shirley@cs.utah.edu

Michael Ashikhmin, State University of New York Stony Brook, 1434 Computer Science, Stony Brook, NY 11794 ash@cs.sunysb.edu

BibTeX Entry

@article{StarkEtAl05,
  author = "Michael Stark and Peter Shirley and Michael Ashikhmin",
  title = "Generation of Stratified Samples for B-Spline Pixel Filtering",
  journal = "journal of graphics tools",
  volume = "10",
  number = "1",
  pages = "39-48",
  year = "2005",
}