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Given a specific large target filter to approximate, we first use numerical optimization to design a set of small kernels, which are then used to perform the analysis and synthesis steps of our multiscale transform. Once the optimization has been done, the resulting transform can be applied to any signal in linear time. We demonstrate that our method is well suited for tasks such as gradient field integration, seamless image cloning, and scattered data interpolation, outperforming existing state-of-the-art methods.<\/jats:p>","DOI":"10.1145\/2070781.2024209","type":"journal-article","created":{"date-parts":[[2011,11,30]],"date-time":"2011-11-30T13:58:46Z","timestamp":1322661526000},"page":"1-8","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":52,"title":["Convolution pyramids"],"prefix":"10.1145","volume":"30","author":[{"given":"Zeev","family":"Farbman","sequence":"first","affiliation":[{"name":"The Hebrew University"}]},{"given":"Raanan","family":"Fattal","sequence":"additional","affiliation":[{"name":"The Hebrew University"}]},{"given":"Dani","family":"Lischinski","sequence":"additional","affiliation":[{"name":"The Hebrew University"}]}],"member":"320","published-online":{"date-parts":[[2011,12,12]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1276377.1276495"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-88688-4_9"},{"key":"e_1_2_2_3_1","unstructured":"Brigham E. O. 1988. The fast Fourier transform and its applications. Prentice-Hall Inc. Upper Saddle River NJ USA.   Brigham E. O. 1988. The fast Fourier transform and its applications . Prentice-Hall Inc. Upper Saddle River NJ USA."},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCOM.1983.1095851"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/0146-664X(81)90092-7"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/604471.604495"},{"volume":"4","volume-title":"Proc. ICIP","author":"Derpanis K.","key":"e_1_2_2_7_1"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2003.815389"},{"key":"e_1_2_2_9_1","unstructured":"Evans L. C.\n     1998.\n      \n  \n   \n  Partial Differential Equations vol. \n  19\n   of \n  Graduate Series in Mathematics\n  . \n  American Mathematical Society\n  .  Evans L. C. 1998. Partial Differential Equations vol. 19 of Graduate Series in Mathematics . 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