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

Jens Krüger; Markus Hadwiger; Ronell Sicat; Johanna Beyer; Torsten Möller
In: Julie Dorsey (Hrsg.). ACM Transactions on Graphics (TOG), Vol. 31, Pages 133:1-133:12, ACM, 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.