{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T08:25:16Z","timestamp":1789719916063,"version":"4.0.1"},"reference-count":28,"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":[[2013,1]]},"abstract":"<jats:p>The main aim of this paper is to develop a histogram equalization algorithm for image contrast enhancement. Our idea is to propose a variational approach containing an energy functional to determine a local transformation such that the histogram can be redistributed locally, and the brightness of the transformed image can be preserved. In order to minimize the differences among the local transformation at the nearby pixel locations, the spatial regularization of the transformation is also incorporated into the functional for the equalization process. In the variational problem, we consider both $H_1$-norm regularization and total variation regularization of the transformation in the model. The existence and uniqueness of the minimizers of the two proposed models are studied and analyzed. Experimental results are reported to show that the performance of the proposed models are competitive with the other compared methods for several testing images.<\/jats:p>","DOI":"10.1137\/130909196","type":"journal-article","created":{"date-parts":[[2013,9,24]],"date-time":"2013-09-24T11:39:11Z","timestamp":1380022751000},"page":"1823-1849","source":"Crossref","is-referenced-by-count":18,"title":["A Variational Histogram Equalization Method for Image Contrast Enhancement"],"prefix":"10.1137","volume":"6","author":[{"given":"Wei","family":"Wang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael K.","family":"Ng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2013,9,24]]},"reference":[{"key":"atypb1","unstructured":"R. C. Gonzalez and R. E. Woods,<i>Digital Image Processing<\/i> 2nd ed., Prentice-Hall, 2002."},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1109\/30.580378"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1109\/30.754419"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1109\/TCE.2003.1261234"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1109\/TCE.2007.4341603"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1109\/TCE.2003.1261233"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1109\/83.388088"},{"key":"atypb8","doi-asserted-by":"crossref","first-page":"131","DOI":"10.3233\/ICA-2008-15204","volume":"15","author":"Jafar I.","year":"2008","journal-title":"Integrated Computer-Aided Engrg."},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1109\/TCE.2005.1561863"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1996.3237"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2009.2021548"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2007.891777"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2008.86"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1007\/s11263-009-0221-5"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1006\/cviu.1998.0723"},{"key":"atypb16","doi-asserted-by":"crossref","unstructured":"N. M. Kwok, Q. P. Ha, G. Fang, A. B. Rad, and D. Wang,<i>Color image contrast enhancement using a local equalization and weighted sum approach<\/i> in Proceedings of the 2010 IEEE Conference on Automation Science and Engineering (CASE), 2010, pp. 568-573.","DOI":"10.1109\/COASE.2010.5584719"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1109\/TCE.2011.5955195"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1016\/j.patcog.2012.03.019"},{"key":"atypb19","unstructured":"G. Golub and C. Van Loan,<i>Matrix Computations<\/i> The Johns Hopkins University Press, Baltimore, MD, 1993."},{"key":"atypb20","doi-asserted-by":"crossref","unstructured":"Y. Saad,<i>Iterative Methods for Sparse Linear Systems<\/i> 2nd ed., SIAM, Philadelphia, 2003.","DOI":"10.1137\/1.9780898718003"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1007\/BF01581204"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1137\/080725891"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2005.863935"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1016\/0734-189X(89)90166-7"},{"key":"atypb25","unstructured":"J. C. Russ,<i>The Image Processing Handbook<\/i> CRC Press, Boca Raton, FL, 1995."},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1137\/050626090"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-010-0251-1"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1109\/JSTSP.2007.910264"}],"container-title":["SIAM Journal on Imaging Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/130909196","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:27:09Z","timestamp":1787322429000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/130909196"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1]]},"references-count":28,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2013,1]]}},"alternative-id":["10.1137\/130909196"],"URL":"https:\/\/doi.org\/10.1137\/130909196","relation":{},"ISSN":["1936-4954"],"issn-type":[{"value":"1936-4954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,1]]}}}