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In this work we introduce the idea of replacing these Euclidean distances with\n            <jats:italic>diffusion distances<\/jats:italic>\n            , which better account for the global distribution of pixels in their feature space. These distances are approximated using\n            <jats:italic>diffusion maps<\/jats:italic>\n            : a set of the dominant eigenvectors of a large affinity matrix, which may be computed efficiently by sampling a small number of matrix columns (the Nystr\u00f6m method). We demonstrate the benefits of using diffusion distances in a variety of image editing contexts, and explore the use of diffusion maps as a tool for facilitating the creation of complex selection masks. Finally, we present a new analysis that establishes a connection between the spatial interaction range between two pixels, and the number of samples necessary for accurate Nystr\u00f6m approximations.\n          <\/jats:p>","DOI":"10.1145\/1882261.1866171","type":"journal-article","created":{"date-parts":[[2010,12,1]],"date-time":"2010-12-01T20:18:10Z","timestamp":1291234690000},"page":"1-10","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":88,"title":["Diffusion maps for edge-aware image editing"],"prefix":"10.1145","volume":"29","author":[{"given":"Zeev","family":"Farbman","sequence":"first","affiliation":[{"name":"The Hebrew University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Raanan","family":"Fattal","sequence":"additional","affiliation":[{"name":"The Hebrew University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dani","family":"Lischinski","sequence":"additional","affiliation":[{"name":"The Hebrew University"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2010,12,15]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1360612.1360639"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1162\/089976603321780317"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/83.661192"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.patcog.2007.04.010"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/1276377.1276506"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2006.04.006"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/566654.566574"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/1360612.1360666"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/1276377.1276441"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531328"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2003.1190577"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2004.1262185"},{"key":"e_1_2_1_13_1","unstructured":"Golub G. 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Diffusion maps spectral clustering and eigenfunctions of Fokker-Planck operators. Neural Information Processing Systems (NIPS) 18.  Nadler B. Lafon S. Coifman R. and Kevrekidis I. 2005. Diffusion maps spectral clustering and eigenfunctions of Fokker-Planck operators. Neural Information Processing Systems (NIPS) 18."},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2006.302"},{"key":"e_1_2_1_26_1","unstructured":"Oppenheim A. V. and Schafer R. W. 1975. Digital Signal Processing. Prentice Hall.  Oppenheim A. V. and Schafer R. W. 1975. Digital Signal Processing. Prentice Hall."},{"key":"e_1_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1007\/11744085_44"},{"key":"e_1_2_1_28_1","doi-asserted-by":"publisher","DOI":"10.1109\/34.56205"},{"key":"e_1_2_1_29_1","doi-asserted-by":"crossref","unstructured":"Rhemann C. Rother C. Wang J. Gelautz M. Kohli P. and Rott P. 2009. A perceptually motivated online benchmark for image matting. In CVPR IEEE 1826--1833.  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