{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T06:44:00Z","timestamp":1759041840566},"reference-count":17,"publisher":"Elsevier BV","issue":"2-3","license":[{"start":{"date-parts":[[1994,11,1]],"date-time":"1994-11-01T00:00:00Z","timestamp":783648000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Signal Processing"],"published-print":{"date-parts":[[1994,11]]},"DOI":"10.1016\/0165-1684(94)90064-7","type":"journal-article","created":{"date-parts":[[2003,8,8]],"date-time":"2003-08-08T06:11:51Z","timestamp":1060323111000},"page":"129-154","source":"Crossref","is-referenced-by-count":27,"title":["Precision of morphological-representation estimators for translation-invariant binary filters: Increasing and nonincreasing"],"prefix":"10.1016","volume":"40","author":[{"given":"Edward R.","family":"Dougherty","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert P.","family":"Loce","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"issue":"No. 6","key":"10.1016\/0165-1684(94)90064-7_BIB1","doi-asserted-by":"crossref","first-page":"1782","DOI":"10.1137\/0151091","article-title":"Minimal representation of translation invariant set mappings by mathematical morphology","volume":"Vol. 51","author":"Banon","year":"1991","journal-title":"SIAM J. Appl. Math."},{"issue":"No. 1","key":"10.1016\/0165-1684(94)90064-7_BIB2","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/1049-9660(92)90005-N","article-title":"Optimal mean-square N-observation digital morphological filters Part I: Optimal binary filters","volume":"Vol. 55","author":"Dougherty","year":"1992","journal-title":"JCVGIP \u2014 Image Understanding"},{"issue":"No. 1","key":"10.1016\/0165-1684(94)90064-7_BIB3","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/1049-9660(92)90006-O","article-title":"Optimal mean-square N-observation digital morphological filters Part II: Optimal gray scale filters","volume":"Vol. 55","author":"Dougherty","year":"1992","journal-title":"JCVGIP \u2014 Image Understanding"},{"key":"10.1016\/0165-1684(94)90064-7_BIB4","doi-asserted-by":"crossref","unstructured":"E.R. Dougherty, \u201cExistence and synthesis of minimal-basis morphological solutions for a restoration-based boundary-value problem\u201d, J. Math. Imaging Vision, to appear.","DOI":"10.1007\/BF00123350"},{"key":"10.1016\/0165-1684(94)90064-7_BIB5","first-page":"534","article-title":"A digital version of Matheron's theorem for increasing \u03c4-mappings in terms of a basis for the kernel","author":"Dougherty","year":"1986","journal-title":"IEEE Comput. Vis. Patt. Rec."},{"issue":"No. 3","key":"10.1016\/0165-1684(94)90064-7_BIB6","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1007\/BF00129879","article-title":"Hole-spectrum representation and model-based optimal morphological restoration for binary images degraded by subtractive noise","volume":"Vol. 1","author":"Dougherty","year":"1992","journal-title":"J. Math. Imaging Vision"},{"key":"10.1016\/0165-1684(94)90064-7_BIB7","series-title":"Mathematical Morphology in Image Processing","article-title":"Efficient design strategies for the optimal binary digital morphological filter: Probabilities, constraints, and structuring-element libraries","author":"Dougherty","year":"1992"},{"issue":"No. 4","key":"10.1016\/0165-1684(94)90064-7_BIB8","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1117\/12.132376","article-title":"Optimal mean-absolute-error hit-or-miss filters: Morphological representation and estimation of the binary conditional expectation","volume":"Vol. 32","author":"Dougherty","year":"1993","journal-title":"SPIE J. Optical Engrg."},{"key":"10.1016\/0165-1684(94)90064-7_BIB9","series-title":"Morphological Methods in Image and Signal Processing","author":"Giardina","year":"1988"},{"issue":"No. 5","key":"10.1016\/0165-1684(94)90064-7_BIB10","doi-asserted-by":"crossref","first-page":"1008","DOI":"10.1117\/12.56144","article-title":"Facilitation of optimal morphological filter design via structuring element libraries and design constraints","volume":"Vol. 31","author":"Loce","year":"1992","journal-title":"SPIE J. Optical Engrg."},{"issue":"No. 4","key":"10.1016\/0165-1684(94)90064-7_BIB11","doi-asserted-by":"crossref","first-page":"412","DOI":"10.1016\/1047-3203(92)90043-S","article-title":"Optimal morphological restoration: The morphological filter mean-absolute-error theorem","volume":"Vol. 3","author":"Loce","year":"1992","journal-title":"J. Visual Comm. Image Representation"},{"key":"10.1016\/0165-1684(94)90064-7_BIB12","series-title":"Proc. Internat. Conf. Acoust. Speech Signal Process.","article-title":"A unification of linear, median, order-statistics and morphological filters under mathematical morphology","author":"Maragos","year":"1985"},{"key":"10.1016\/0165-1684(94)90064-7_BIB13","doi-asserted-by":"crossref","first-page":"1153","DOI":"10.1109\/TASSP.1987.1165259","article-title":"Morphological filters\u2014Part I: Their set-theoretic analysis and relations to linear shift-invariant filters","volume":"Vol. ASSP-35","author":"Maragos","year":"1987","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"10.1016\/0165-1684(94)90064-7_BIB14","doi-asserted-by":"crossref","first-page":"1170","DOI":"10.1109\/TASSP.1987.1165254","article-title":"Morphological filters\u2014Part II: Their relations to median, order statistic, and stack-filters","volume":"Vol. ASSP-35","author":"Maragos","year":"1987","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"10.1016\/0165-1684(94)90064-7_BIB15","series-title":"Random Sets and Integral Geometry","author":"Matheron","year":"1975"},{"issue":"No. 3","key":"10.1016\/0165-1684(94)90064-7_BIB16","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1007\/BF01223318","article-title":"Efficient derivation of the optimal mean-square morphological filter from the conditional expectation via a switching algorithm for the discrete power-set lattice","volume":"Vol. 12","author":"Mathew","year":"1993","journal-title":"J. Circuits Systems Signal Process."},{"key":"10.1016\/0165-1684(94)90064-7_BIB17","series-title":"Image Analysis and Mathematical Morphology","author":"Serra","year":"1983"}],"container-title":["Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:0165168494900647?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:0165168494900647?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,3,15]],"date-time":"2019-03-15T00:52:33Z","timestamp":1552611153000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/0165168494900647"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,11]]},"references-count":17,"journal-issue":{"issue":"2-3","published-print":{"date-parts":[[1994,11]]}},"alternative-id":["0165168494900647"],"URL":"https:\/\/doi.org\/10.1016\/0165-1684(94)90064-7","relation":{},"ISSN":["0165-1684"],"issn-type":[{"value":"0165-1684","type":"print"}],"subject":[],"published":{"date-parts":[[1994,11]]}}}