{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T19:26:27Z","timestamp":1783106787290,"version":"3.54.6"},"reference-count":16,"publisher":"Association for Computing Machinery (ACM)","issue":"5","license":[{"start":{"date-parts":[[2009,12,1]],"date-time":"2009-12-01T00:00:00Z","timestamp":1259625600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2009,12]]},"abstract":"<jats:p>\n            We present a new Laplacian solver for\n            <jats:italic>minimal<\/jats:italic>\n            surfaces---surfaces having a mean curvature of zero everywhere except at some fixed (Dirichlet) boundary conditions. Our solution has two main contributions: First, we provide a robust rasterization technique to transform continuous boundary values (diffusion curves) to a discrete domain. Second, we define a\n            <jats:italic>variable stencil size<\/jats:italic>\n            diffusion solver that solves the minimal surface problem. We prove that the solver converges to the right solution, and demonstrate that it is at least as fast as commonly proposed multigrid solvers, but much simpler to implement. It also works for arbitrary image resolutions, as well as 8 bit data. We show examples of robust diffusion curve rendering where our curve rasterization and diffusion solver eliminate the strobing artifacts present in previous methods. We also show results for real-time seamless cloning and stitching of large image panoramas.\n          <\/jats:p>","DOI":"10.1145\/1618452.1618462","type":"journal-article","created":{"date-parts":[[2009,12,8]],"date-time":"2009-12-08T20:53:14Z","timestamp":1260305594000},"page":"1-8","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":54,"title":["A GPU Laplacian solver for diffusion curves and Poisson image editing"],"prefix":"10.1145","volume":"28","author":[{"given":"Stefan","family":"Jeschke","sequence":"first","affiliation":[{"name":"Arizona State University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David","family":"Cline","sequence":"additional","affiliation":[{"name":"Arizona State University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter","family":"Wonka","sequence":"additional","affiliation":[{"name":"Arizona State University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2009,12]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1276377.1276495"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882364"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/34.910881"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531373"},{"key":"e_1_2_1_5_1","volume-title":"HWWS '03: Proceedings of the ACM SIGGRAPH\/EUROGRAPHICS conference on Graphics hardware, 102--111","author":"Goodnight N.","unstructured":"Goodnight , N. , Woolley , C. , Lewin , G. , Luebke , D. , and Humphreys , G . 2003. A multigrid solver for boundary value problems using programmable graphics hardware . In HWWS '03: Proceedings of the ACM SIGGRAPH\/EUROGRAPHICS conference on Graphics hardware, 102--111 . Goodnight, N., Woolley, C., Lewin, G., Luebke, D., and Humphreys, G. 2003. A multigrid solver for boundary value problems using programmable graphics hardware. In HWWS '03: Proceedings of the ACM SIGGRAPH\/EUROGRAPHICS conference on Graphics hardware, 102--111."},{"key":"e_1_2_1_6_1","volume-title":"ICIP '05: IEEE International Conference on Image Processing","volume":"2","author":"Grady L.","unstructured":"Grady , L. , Tasdizen , T. , and Whitaker , R . 2005. A geometric multigrid approach to solving the 2D inhomogeneous Laplace equation with internal Dirichlet boundary conditions . In ICIP '05: IEEE International Conference on Image Processing , vol. 2 , 642--645. Grady, L., Tasdizen, T., and Whitaker, R. 2005. A geometric multigrid approach to solving the 2D inhomogeneous Laplace equation with internal Dirichlet boundary conditions. In ICIP '05: IEEE International Conference on Image Processing, vol. 2, 642--645."},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-88688-4_19"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/311535.311567"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/1360612.1360620"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827501389229"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/1360612.1360692"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/1360612.1360691"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882269"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/1342250.1342281"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/1111411.1111431"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1109\/83.503906"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1618452.1618462","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1618452.1618462","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T12:18:06Z","timestamp":1750249086000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1618452.1618462"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,12]]},"references-count":16,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2009,12]]}},"alternative-id":["10.1145\/1618452.1618462"],"URL":"https:\/\/doi.org\/10.1145\/1618452.1618462","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,12]]},"assertion":[{"value":"2009-12-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}