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

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

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

  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}