{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:32:52Z","timestamp":1787322772051,"version":"build-2736575974"},"reference-count":62,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Imaging Sci."],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>Image interpolation is the problem of increasing the resolution of a given image. An important aspect of interpolation is accurate estimation of edge orientations. This work introduces contour stencils, a new method for estimating the image contours based on total variation along curves. Contour stencils are able to distinguish lines of different orientations, curves, corners, and other geometric features with a computationally efficient formula. Contour stencils are applied in designing an edge directed color interpolation method. The method incorporates an efficient approximation of deconvolution. Although most interpolation methods that involve deconvolution require either solving a large linear system or running many iterations, this method has linear complexity in the number of pixels and can be computed in one or a small number of passes through the image. Comparisons show that the proposed interpolation is competitive with existing methods.<\/jats:p>","DOI":"10.1137\/100802785","type":"journal-article","created":{"date-parts":[[2011,9,29]],"date-time":"2011-09-29T18:11:15Z","timestamp":1317319875000},"page":"954-979","source":"Crossref","is-referenced-by-count":33,"title":["Contour Stencils: Total Variation along Curves for Adaptive Image Interpolation"],"prefix":"10.1137","volume":"4","author":[{"given":"Pascal","family":"Getreuer","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2011,9,29]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"V. R. Algazi, G. E. Ford, and R. A. Potharlanka,\n                      Directional interpolating of images based on visual properties and rank order filtering\n                      , in Proceedings of the 1991 IEEE International Conference on Acoustics, Speech, and Signal Processing, 1991, pp. 3005\u20133008.","DOI":"10.1109\/ICASSP.1991.151035"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"J. P. Allebach and P. W. Wong,\n                      Edge-directed interpolation\n                      , in Proceedings of the 1996 IEEE International Conference on Image Processing, Vol. 3, 1996, pp. 707\u2013710.","DOI":"10.1109\/ICIP.1996.560768"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1023\/B:JMIV.0000011318.77653.44"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2006.64"},{"key":"R5","unstructured":"D. H. Ballard and C. M. Brown,\n                      Computer Vision\n                      , Prentice\u2013Hall, Englewood Cliffs, NJ, 1982."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1007\/s11263-006-6852-x"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"A. Belahmidi and F. Guichard,\n                      A partial differential equation approach to image zoom\n                      , in Proceedings of the 2004 IEEE International Conference on Image Processing, 2004, pp. 649\u2013652.","DOI":"10.1109\/ICIP.2004.1418838"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"M. Bertalm\u00edo, G. Sapiro, V. Caselles, and C. Ballester,\n                      Image inpainting\n                      , in Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH '00, ACM Press, Addison-Wesley, New York, 2000, pp. 417\u2013424.","DOI":"10.1145\/344779.344972"},{"key":"R9","unstructured":"J. Big\u00fcn and G. H. Granlund,\n                      Optimal orientation detection of linear symmetry\n                      , in Proceedings of the First IEEE International Conference on Computer Vision, London, 1987, pp. 433\u2013438."},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/040616024"},{"key":"R11","doi-asserted-by":"crossref","unstructured":"T. F. Chan, S. Esedoglu, F. Park, and A. M. Yip,\n                      Total variation image restoration: Overview and recent developments\n                      , in Handbook of Mathematical Models in Computer Vision, Springer, New York, 2006, pp. 17\u201331.","DOI":"10.1007\/0-387-28831-7_2"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139900368844"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1145\/363156.363172"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/10.1.137"},{"key":"R15","doi-asserted-by":"crossref","unstructured":"A. Efros and T. Leung,\n                      Texture synthesis by non-parametric sampling\n                      , in Proceedings of the IEEE International Conference on Computer Vision, 1999, pp. 1033\u20131038.","DOI":"10.1109\/ICCV.1999.790383"},{"key":"R16","doi-asserted-by":"crossref","unstructured":"G. Facciolo, P. Arias, V. Caselles, and G. Sapiro,\n                      Exemplar-based interpolation of sparsely sampled images\n                      , in Energy Minimization Methods in Computer Vision and Pattern Recognition, D. Cremers, Y. Boykov, A. Blake, and F. R. Schmidt, eds., Lecture Notes in Comput. Sci. 5681, Springer, Berlin, Heidelberg, 2009, pp. 331\u2013344.","DOI":"10.1007\/978-3-642-03641-5_25"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1959-0110078-1"},{"key":"R18","doi-asserted-by":"crossref","unstructured":"Y. Fisher,\n                      Fractal Image Compression: Theory and Application to Digital Images\n                      , Springer-Verlag, New York, 1995.","DOI":"10.1007\/978-1-4612-2472-3"},{"key":"R19","unstructured":"W. F\u00f6rstner and E. G\u00fclch,\n                      A fast operator for detection and precise location of distinct points, corners, and centers of circular features\n                      , in Proceedings of the Intercommission Conference on Fast Processing of Photogrammetric Data, Interlaken, Switzerland, 1987, pp. 281\u2013305."},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1109\/38.988747"},{"key":"R21","doi-asserted-by":"crossref","unstructured":"P. Getreuer,\n                      Image interpolation with geometric contour stencils\n                      , Image Processing On Line, 2011, DOI:10.5201\/ipol.2011.g_igcs.","DOI":"10.5201\/ipol.2011.g_igcs"},{"key":"R22","doi-asserted-by":"crossref","unstructured":"P. Getreuer,\n                      Contour stencils for edge-adaptive image interpolation\n                      , in Proceedings of the SPIE, Vol. 7257, 2009, 725718.","DOI":"10.1117\/12.806014"},{"key":"R23","doi-asserted-by":"crossref","unstructured":"P. Getreuer,\n                      Image zooming with contour stencils\n                      , in Proceedings of the SPIE, Vol. 7246, 2009, 72460P.","DOI":"10.1117\/12.805934"},{"key":"R24","doi-asserted-by":"crossref","unstructured":"P. Getreuer,\n                      Image interpolation with contour stencils\n                      , Image Processing On Line, 2011, DOI:10.5201\/ ipol.2011.g_iics.","DOI":"10.1109\/ICDSP.2011.6004885"},{"key":"R25","doi-asserted-by":"crossref","unstructured":"D. Glasner, S. Bagon, and M. Irani,\n                      Super-resolution from a single image\n                      , in Proceedings of the 12th IEEE International Conference on Computer Vision, 2009.","DOI":"10.1109\/ICCV.2009.5459271"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1137\/080725891"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.1984.4767532"},{"key":"R28","unstructured":"Y.S. Ho and A. Gersho,\n                      Variable-rate contour-based interpolative vector quantization for image coding\n                      , in Proceedings of the 1988 IEEE Global Telecommunications Conference, 1988, pp. 750\u2013754."},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1109\/TASSP.1978.1163154"},{"key":"R30","doi-asserted-by":"publisher","DOI":"10.1109\/83.366477"},{"key":"R31","doi-asserted-by":"crossref","unstructured":"H. Jiang and C. Moloney,\n                      A new direction adaptive scheme for image interpolation\n                      , in Proceedings of the IEEE International Conference on Image Processing, Vol. 3, 2002, pp. 369\u2013372.","DOI":"10.1109\/ICIP.2002.1038982"},{"key":"R32","first-page":"228","volume":"92","author":"Jordan C.","year":"1881","journal-title":"C. R. Acad. Sci. Paris"},{"key":"R33","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2006.10.029"},{"key":"R34","doi-asserted-by":"publisher","DOI":"10.1109\/83.951537"},{"key":"R35","doi-asserted-by":"crossref","unstructured":"H. Q. Luong, A. Ledda, and W. Philips,\n                      Non-local interpolation\n                      , in Proceedings of the IEEE International Conference on Image Processing, 2006, pp. 693\u2013696.","DOI":"10.1109\/ICIP.2006.312429"},{"key":"R36","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142999362286"},{"key":"R37","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2010.2049927"},{"key":"R38","doi-asserted-by":"crossref","unstructured":"S. Masnou and J.M. Morel,\n                      Level lines based disocclusion\n                      , in Proceedings of the IEEE International Conference on Image Processing, Vol. 3, 1998, pp. 259\u2013263.","DOI":"10.1109\/ICIP.1998.999016"},{"key":"R39","doi-asserted-by":"publisher","DOI":"10.1109\/5.993400"},{"key":"R40","doi-asserted-by":"crossref","unstructured":"M. Moeller, T. Wittman, and A. L. Bertozzi,\n                      A variational approach to hyperspectral image fusion\n                      , in Proceedings of the SPIE, Vol. 7334, 2009.","DOI":"10.1117\/12.818243"},{"key":"R41","doi-asserted-by":"crossref","unstructured":"D. D. Muresan,\n                      Fast edge directed polynomial interpolation\n                      , in Proceedings of the IEEE International Conference on Image Processing, Vol. 2, 2005, pp. 990\u2013993.","DOI":"10.1109\/ICIP.2005.1530224"},{"key":"R42","unstructured":"I. P. Natanson,\n                      Theory of Functions of a Real Variable\n                      , Frederick Ungar, New York, 1955."},{"key":"R43","unstructured":"onOne Software,\n                      Genuine Fractals\n                      , http:\/\/www.ononesoftware.com (2008)."},{"key":"R44","doi-asserted-by":"publisher","DOI":"10.1007\/BF00252910"},{"key":"R45","doi-asserted-by":"publisher","DOI":"10.3934\/ipi.2011.5.511"},{"key":"R46","doi-asserted-by":"crossref","unstructured":"T. Q. Pham, L. J. van Vliet, and K. Schutte,\n                      Robust fusion of irregularly sampled data using adaptive normalized convolution\n                      , EURASIP J. Appl. Signal Process., 2006 (2006), 83268.","DOI":"10.1155\/ASP\/2006\/83268"},{"key":"R47","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2008.2008067"},{"key":"R48","unstructured":"T. Riemersma,\n                      Quick Image Scaling by\n                      2, http:\/\/www.compuphase.com\/graphic\/scale2.htm (2006)."},{"key":"R49","doi-asserted-by":"publisher","DOI":"10.1007\/s11263-008-0132-x"},{"key":"R50","unstructured":"M. Sajjad, N. Khattak, and N. Jafri,\n                      Image magnification using adaptive interpolation by pixel level data-dependent geometrical shapes\n                      , in Proceedings of World Academy of Science, Engineering and Technology, Vol. 25, 2007."},{"key":"R51","unstructured":"M. Stepin,\n                      hq4x Magnification Filter\n                      , http:\/\/www.hiend3d.com\/hq4x.html (2003)."},{"key":"R52","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2006.888330"},{"key":"R53","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2007.918028"},{"key":"R54","doi-asserted-by":"publisher","DOI":"10.1109\/42.875199"},{"key":"R55","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2005.87"},{"key":"R56","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2007.891794"},{"key":"R57","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2003.819861"},{"key":"R58","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7091-6586-7_13"},{"key":"R59","unstructured":"J. Weickert,\n                      Anisotropic Diffusion in Image Processing\n                      , ECMI Ser., Teubner-Verlag, Stuttgart, Germany, 1998."},{"key":"R60","doi-asserted-by":"publisher","DOI":"10.1006\/jvci.2001.0495"},{"key":"R61","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2005.864231"},{"key":"R62","first-page":"62","volume":"21","author":"Yu X.","year":"2001","journal-title":"IEEE Comput. Graph. Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0272-1716","issn-type":"print"}],"container-title":["SIAM Journal on Imaging Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/100802785","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:25:30Z","timestamp":1787318730000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/100802785"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,1]]},"references-count":62,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2011,1]]}},"alternative-id":["10.1137\/100802785"],"URL":"https:\/\/doi.org\/10.1137\/100802785","relation":{},"ISSN":["1936-4954"],"issn-type":[{"value":"1936-4954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,1]]}}}