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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,\n            <jats:italic>O<\/jats:italic>\n            (\n            <jats:italic>n<\/jats:italic>\n            ) local Laplacian filters, smoothed local histogram filters (e.g., median or mode filters), and bilateral filters.\n          <\/jats:p>","DOI":"10.1145\/2366145.2366152","type":"journal-article","created":{"date-parts":[[2012,11,14]],"date-time":"2012-11-14T20:36:17Z","timestamp":1352925377000},"page":"1-12","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":13,"title":["Sparse PDF maps for non-linear multi-resolution image operations"],"prefix":"10.1145","volume":"31","author":[{"given":"Markus","family":"Hadwiger","sequence":"first","affiliation":[{"name":"KAUST"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ronell","family":"Sicat","sequence":"additional","affiliation":[{"name":"KAUST"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Johanna","family":"Beyer","sequence":"additional","affiliation":[{"name":"KAUST"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jens","family":"Kr\u00fcger","sequence":"additional","affiliation":[{"name":"IVDA, DFKI, Intel VCI"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Torsten","family":"M\u00f6ller","sequence":"additional","affiliation":[{"name":"Simon Fraser University"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2012,11]]},"reference":[{"key":"e_1_2_2_1_1","unstructured":"Aubry M. Paris S. Hasinoff S. W. Kautz J. and Durand F. 2011. Fast and Robust Pyramid-based Image Processing. Tech. rep. MIT. MIT-CSAIL-TR-2011-049.  Aubry M. Paris S. Hasinoff S. W. Kautz J. and Durand F. 2011. Fast and Robust Pyramid-based Image Processing. Tech. rep. MIT. 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