{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T01:37:49Z","timestamp":1775871469160,"version":"3.50.1"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2022,4,17]],"date-time":"2022-04-17T00:00:00Z","timestamp":1650153600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,4,17]],"date-time":"2022-04-17T00:00:00Z","timestamp":1650153600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Pattern Anal Applic"],"published-print":{"date-parts":[[2022,11]]},"DOI":"10.1007\/s10044-022-01074-3","type":"journal-article","created":{"date-parts":[[2022,4,17]],"date-time":"2022-04-17T14:03:08Z","timestamp":1650204188000},"page":"795-806","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Harmonic image inpainting using the charge simulation method"],"prefix":"10.1007","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1434-2541","authenticated-orcid":false,"given":"El Mostafa","family":"Kalmoun","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohamed M. S.","family":"Nasser","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,4,17]]},"reference":[{"key":"1074_CR1","doi-asserted-by":"crossref","unstructured":"Bertalmio M, Sapiro G, Caselles V, Ballester C (2000) Image inpainting. In: Proceedings of the 27th annual conference on computer graphics and interactive techniques, pp 417\u2013424","DOI":"10.1145\/344779.344972"},{"issue":"2\u20133","key":"1074_CR2","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1007\/s10851-008-0087-0","volume":"31","author":"I Gali\u0107","year":"2008","unstructured":"Gali\u0107 I, Weickert J, Welk M, Bruhn A, Belyaev A, Seidel H-P (2008) Image compression with anisotropic diffusion. J Math Imaging Vis 31(2\u20133):255\u2013269","journal-title":"J Math Imaging Vis"},{"key":"1074_CR3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511734304","volume-title":"Partial differential equation methods for image inpainting","author":"C-B Sch\u00f6nlieb","year":"2015","unstructured":"Sch\u00f6nlieb C-B (2015) Partial differential equation methods for image inpainting, vol 29. Cambridge University Press, Cambridge"},{"issue":"3","key":"1074_CR4","doi-asserted-by":"publisher","first-page":"376","DOI":"10.1109\/83.661188","volume":"7","author":"V Caselles","year":"1998","unstructured":"Caselles V, Morel J-M, Sbert C (1998) An axiomatic approach to image interpolation. IEEE Trans Image Process 7(3):376\u2013386","journal-title":"IEEE Trans Image Process"},{"issue":"3","key":"1074_CR5","doi-asserted-by":"publisher","first-page":"1019","DOI":"10.1137\/S0036139900368844","volume":"62","author":"J Shen","year":"2002","unstructured":"Shen J, Chan TF (2002) Mathematical models for local nontexture inpaintings. SIAM J Appl Math 62(3):1019\u20131043","journal-title":"SIAM J Appl Math"},{"key":"1074_CR6","doi-asserted-by":"crossref","unstructured":"Mainberger M, Hoffmann S, Weickert J, Tang CH, Johannsen D, Neumann F, Doerr B (2011) Optimising spatial and tonal data for homogeneous diffusion inpainting. In: International conference on scale space and variational methods in computer vision. Springer, pp 26\u201337","DOI":"10.1007\/978-3-642-24785-9_3"},{"issue":"1","key":"1074_CR7","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1016\/0165-1684(88)90028-X","volume":"15","author":"S Carlsson","year":"1988","unstructured":"Carlsson S (1988) Sketch based coding of grey level images. Signal Process 15(1):57\u201383","journal-title":"Signal Process"},{"issue":"1","key":"1074_CR8","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1137\/080716396","volume":"70","author":"Z Belhachmi","year":"2009","unstructured":"Belhachmi Z, Bucur D, Burgeth B, Weickert J (2009) How to choose interpolation data in images. SIAM J Appl Math 70(1):333\u2013352","journal-title":"SIAM J Appl Math"},{"issue":"9","key":"1074_CR9","doi-asserted-by":"publisher","first-page":"1859","DOI":"10.1016\/j.patcog.2010.08.004","volume":"44","author":"M Mainberger","year":"2011","unstructured":"Mainberger M, Bruhn A, Weickert J, Forchhammer S (2011) Edge-based compression of cartoon-like images with homogeneous diffusion. Pattern Recognit 44(9):1859\u20131873","journal-title":"Pattern Recognit"},{"key":"1074_CR10","doi-asserted-by":"crossref","unstructured":"Hoeltgen L, Setzer S, Weickert J (2013) An optimal control approach to find sparse data for Laplace interpolation. In: International workshop on energy minimization methods in computer vision and pattern recognition. Springer, pp 151\u2013164","DOI":"10.1007\/978-3-642-40395-8_12"},{"key":"1074_CR11","unstructured":"Chen Y, Ranftl R, Pock T (2014) A bi-level view of inpainting-based image compression. In: Computer vision winter workshop"},{"issue":"7","key":"1074_CR12","doi-asserted-by":"publisher","first-page":"1945","DOI":"10.1016\/j.sigpro.2012.12.008","volume":"93","author":"A Gholami","year":"2013","unstructured":"Gholami A, Hosseini SM (2013) A balanced combination of Tikhonov and total variation regularizations for reconstruction of piecewise-smooth signals. Signal Process 93(7):1945\u20131960","journal-title":"Signal Process"},{"key":"1074_CR13","doi-asserted-by":"publisher","first-page":"64","DOI":"10.1016\/j.patcog.2019.03.009","volume":"92","author":"W Wei","year":"2019","unstructured":"Wei W, Zhou B, Po\u0142ap D, Wo\u017aniak M (2019) A regional adaptive variational pde model for computed tomography image reconstruction. Pattern Recognit 92:64\u201381","journal-title":"Pattern Recognit"},{"key":"1074_CR14","doi-asserted-by":"crossref","unstructured":"Kalmoun EM (2020) A new Tikhonov-TV regularization for optical flow computation. In: Pan Z, Wang X (eds) Eleventh international conference on graphics and image processing (ICGIP 2019), vol 11373. International Society for Optics and Photonics, SPIE, pp 644\u2013648","DOI":"10.1117\/12.2557210"},{"issue":"9","key":"1074_CR15","doi-asserted-by":"publisher","first-page":"1095","DOI":"10.1109\/26.623074","volume":"45","author":"R Distasi","year":"1997","unstructured":"Distasi R, Nappi M, Vitulano S (1997) Image compression by b-tree triangular coding. IEEE Trans Commun 45(9):1095\u20131100","journal-title":"IEEE Trans Commun"},{"issue":"3","key":"1074_CR16","doi-asserted-by":"publisher","first-page":"222","DOI":"10.1007\/s11263-014-0702-z","volume":"108","author":"C Schmaltz","year":"2014","unstructured":"Schmaltz C, Peter P, Mainberger M, Ebel F, Weickert J, Bruhn A (2014) Understanding, optimising, and extending data compression with anisotropic diffusion. Int J Comput Vis 108(3):222\u2013240","journal-title":"Int J Comput Vis"},{"key":"1074_CR17","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1016\/j.image.2016.05.002","volume":"46","author":"P Peter","year":"2016","unstructured":"Peter P, Hoffmann S, Nedwed F, Hoeltgen L, Weickert J (2016) Evaluating the true potential of diffusion-based inpainting in a compression context. Signal Process Image Commun 46:40\u201353","journal-title":"Signal Process Image Commun"},{"issue":"1\u20132","key":"1074_CR18","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1007\/s10851-006-6865-7","volume":"26","author":"TF Chan","year":"2006","unstructured":"Chan TF, Kang SH (2006) Error analysis for image inpainting. J Math Imaging Vis 26(1\u20132):85\u2013103","journal-title":"J Math Imaging Vis"},{"issue":"8","key":"1074_CR19","first-page":"195","volume":"37","author":"M Katsurada","year":"1998","unstructured":"Katsurada M (1998) A mathematical study of the charge simulation method by use of peripheral conformal mappings. Mem Inst Sci Tech Meiji Univ 37(8):195\u2013212","journal-title":"Mem Inst Sci Tech Meiji Univ"},{"key":"1074_CR20","doi-asserted-by":"publisher","first-page":"1660","DOI":"10.1109\/TPAS.1974.293898","volume":"5","author":"H Singer","year":"1974","unstructured":"Singer H, Steinbigler H, Weiss P (1974) A charge simulation method for the calculation of high voltage fields. IEEE Trans Power Apparatus Syst 5:1660\u20131668","journal-title":"IEEE Trans Power Apparatus Syst"},{"key":"1074_CR21","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-17079-4","volume-title":"A method of fundamental solutions in poroelasticity to model the stress field in geothermal reservoirs","author":"MA Augustin","year":"2015","unstructured":"Augustin MA (2015) A method of fundamental solutions in poroelasticity to model the stress field in geothermal reservoirs. Springer, Heidelberg"},{"key":"1074_CR22","volume-title":"Methods of fundamental solutions in solid mechanics","author":"H Wang","year":"2019","unstructured":"Wang H, Qin Q-H (2019) Methods of fundamental solutions in solid mechanics. Elsevier, Amsterdam"},{"key":"1074_CR23","doi-asserted-by":"publisher","first-page":"118","DOI":"10.1016\/j.enganabound.2020.08.013","volume":"120","author":"AHD Cheng","year":"2020","unstructured":"Cheng AHD, Hong Y (2020) An overview of the method of fundamental solutions\u2014solvability, uniqueness, convergence, and stability. Eng Anal Bound Elem 120:118\u2013152","journal-title":"Eng Anal Bound Elem"},{"key":"1074_CR24","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1023\/A:1018981221740","volume":"9","author":"G Fairweather","year":"1998","unstructured":"Fairweather G, Karageorghis A (1998) The method of fundamental solutions for elliptic boundary value problems. Adv Comput Math 9:69\u201395","journal-title":"Adv Comput Math"},{"issue":"2","key":"1074_CR25","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1016\/0021-9991(87)90140-9","volume":"73","author":"L Greengard","year":"1987","unstructured":"Greengard L, Rokhlin V (1987) A fast algorithm for particle simulations. J Comput Phys 73(2):325\u2013348","journal-title":"J Comput Phys"},{"key":"1074_CR26","doi-asserted-by":"publisher","first-page":"1169","DOI":"10.1137\/S1064827595294307","volume":"19","author":"K Amano","year":"1998","unstructured":"Amano K (1998) A charge simulation method for numerical conformal mapping onto circular and radial slit domains. SIAM J Sci Comput 19:1169\u20131187","journal-title":"SIAM J Sci Comput"},{"key":"1074_CR27","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1016\/S0377-0427(02)00722-7","volume":"152","author":"D Okano","year":"2003","unstructured":"Okano D, Ogata H, Amano K (2003) A method of numerical conformal mapping of curved slit domains by the charge simulation method. J Comput Appl Math 152:441\u2013450","journal-title":"J Comput Appl Math"},{"key":"1074_CR28","doi-asserted-by":"publisher","first-page":"53","DOI":"10.14495\/jsiaml.2.53","volume":"2","author":"K Amano","year":"2010","unstructured":"Amano K, Okano D (2010) A circular and radial slit mapping of unbounded multiply connected domains. JSIAM Lett 2:53\u201356","journal-title":"JSIAM Lett"},{"key":"1074_CR29","first-page":"35","volume":"26","author":"K Amano","year":"2003","unstructured":"Amano K, Okano D, Ogata H, Sugihara M (2003) Numerical conformal mappings of unbounded multiply-connected domains using the charge simulation method. Bull Malays Math Sci Soc 26:35\u201351","journal-title":"Bull Malays Math Sci Soc"},{"key":"1074_CR30","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1017\/S0962492904000212","volume":"14","author":"M Benzi","year":"2005","unstructured":"Benzi M, Golub GH, Liesen J (2005) Numerical solution of saddle point problems. Acta Numerica 14:1\u2013137","journal-title":"Acta Numerica"},{"issue":"3","key":"1074_CR31","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1080\/00036818608839589","volume":"21","author":"WL Wendland","year":"1986","unstructured":"Wendland WL, Christiansen S (1986) On the condition number of the influence matrix belonging to some first kind integral equations with logarithmic kernel. Appl Anal 21(3):175\u2013183","journal-title":"Appl Anal"},{"key":"1074_CR32","doi-asserted-by":"crossref","unstructured":"Hoffmann S, Plonka G, Weickert J (2015) Discrete Green\u2019s functions for harmonic and biharmonic inpainting with sparse atoms. In: International workshop on energy minimization methods in computer vision and pattern recognition. Springer, pp 169\u2013182","DOI":"10.1007\/978-3-319-14612-6_13"},{"key":"1074_CR33","unstructured":"Greengard L, Gimbutas Z (2012) FMMLIB2D: A MATLAB toolbox for fast multipole method in two dimensions, version 1.2. edition. http:\/\/www.cims.nyu.edu\/cmcl\/fmm2dlib\/fmm2dlib.html. Accessed 1 Jan 2018"},{"key":"1074_CR34","unstructured":"Parisotto S, Sch\u00f6nlieb C (2020) Matlab codes for the image inpainting problem. GitHub repository, MATLAB Central File Exchange, September 2016. Retrieved September 23, 2020"}],"container-title":["Pattern Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10044-022-01074-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10044-022-01074-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10044-022-01074-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,19]],"date-time":"2022-10-19T04:14:19Z","timestamp":1666152859000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10044-022-01074-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,17]]},"references-count":34,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2022,11]]}},"alternative-id":["1074"],"URL":"https:\/\/doi.org\/10.1007\/s10044-022-01074-3","relation":{},"ISSN":["1433-7541","1433-755X"],"issn-type":[{"value":"1433-7541","type":"print"},{"value":"1433-755X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,4,17]]},"assertion":[{"value":"11 June 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 March 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 April 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}