Sparse PDF Maps for Non-Linear Multi-Resolution Image Operations

Markus Hadwiger, Ronell Sicat, Johanna Beyer, Jens Krüger and Torsten Möller

ACM Transactions on Graphics, Vol.31, No.6 (Proceedings ACM SIGGRAPH Asia 2012), pp. 133:1-133:12 , 2012

We introduce a new type of multi-resolution image pyramid for high-resolution images called sparse pdf maps (sPDF-maps). Each pyramid level consists of a sparse encoding of continuous probability density functions (pdfs) of pixel neighborhoods in the original image. The encoded pdfs enable the accurate computation of non-linear image operations directly in any pyramid level with proper pre-filtering for anti-aliasing, without accessing higher or lower resolutions. The sparsity of sPDF-maps makes them feasible for gigapixel images, while enabling direct evaluation of a variety of non-linear operators from the same representation. We illustrate this versatility for antialiased color mapping, O(n) local Laplacian filters, smoothed local histogram filters (e.g., median or mode filters), and bilateral filters.

@article{Hadwiger2012SPDFMaps,
  title = {Sparse PDF Maps for Non-Linear Multi-Resolution Image Operations},
  author = {Hadwiger, Markus and Sicat, Ronell and Beyer, Johanna and Kr{\"u}ger, Jens and M{\"o}ller, Torsten},
  journal = {ACM Transactions on Graphics (Proceedings ACM SIGGRAPH Asia 2012)},
  year = {2012},
  volume = {31},
  number = {6},
  pages = {133:1--133:12}
}