{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T10:54:58Z","timestamp":1768906498548,"version":"3.49.0"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2019,7,29]],"date-time":"2019-07-29T00:00:00Z","timestamp":1564358400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,7,29]],"date-time":"2019-07-29T00:00:00Z","timestamp":1564358400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Image Video Proc."],"published-print":{"date-parts":[[2019,12]]},"DOI":"10.1186\/s13640-019-0475-y","type":"journal-article","created":{"date-parts":[[2019,7,29]],"date-time":"2019-07-29T14:03:34Z","timestamp":1564409014000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Optimum design of chamfer masks using symmetric mean absolute percentage error"],"prefix":"10.1186","volume":"2019","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7551-0107","authenticated-orcid":false,"given":"Baraka Jacob","family":"Maiseli","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,7,29]]},"reference":[{"key":"475_CR1","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/j.patrec.2015.04.006","volume":"76","author":"PK Saha","year":"2016","unstructured":"PK Saha, G Borgefors, GS di Baja, A survey on skeletonization algorithms and their applications. Pattern Recogn. Lett.76:, 3\u201312 (2016).","journal-title":"Pattern Recogn. Lett."},{"issue":"6","key":"475_CR2","doi-asserted-by":"publisher","first-page":"922","DOI":"10.1109\/83.503909","volume":"5","author":"P Maragos","year":"1996","unstructured":"P Maragos, Differential morphology and image processing. IEEE Trans. Image Process.5(6), 922\u2013937 (1996).","journal-title":"IEEE Trans. Image Process."},{"key":"475_CR3","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/978-0-387-68413-0_2","volume-title":"Deformable Models","author":"GJ Grevera","year":"2007","unstructured":"GJ Grevera, in Deformable Models. Distance transform algorithms and their implementation and evaluation (SpringerNew York, 2007), pp. 33\u201360."},{"issue":"9","key":"475_CR4","doi-asserted-by":"publisher","first-page":"1763","DOI":"10.1109\/TPDS.2012.300","volume":"24","author":"W Liu","year":"2013","unstructured":"W Liu, H Jiang, X Bai, G Tan, C Wang, W Liu, K Cai, Distance transform-based skeleton extraction and its applications in sensor networks. Parallel Distrib. Syst. IEEE Trans.24(9), 1763\u20131772 (2013).","journal-title":"Parallel Distrib. Syst. IEEE Trans."},{"key":"475_CR5","doi-asserted-by":"publisher","first-page":"304","DOI":"10.1007\/978-3-642-37195-0_30","volume-title":"Research in Computational Molecular Biology","author":"D Xu","year":"2013","unstructured":"D Xu, H Li, Y Zhang, in Research in Computational Molecular Biology. Fast and accurate calculation of protein depth by Euclidean distance transform (SpringerNew York, 2013), pp. 304\u2013316."},{"key":"475_CR6","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1007\/s11760-012-0419-9","volume":"9","author":"Y Mishchenko","year":"2015","unstructured":"Y Mishchenko, A fast algorithm for computation of discrete Euclidean distance transform in three or more dimensions on vector processing architectures. SIViP. 9:, 19\u201327 (2015).","journal-title":"SIViP"},{"key":"475_CR7","doi-asserted-by":"publisher","first-page":"757","DOI":"10.1109\/WACV.2015.106","volume-title":"Applications of Computer Vision (WACV), 2015 IEEE Winter Conference on","author":"D Salvi","year":"2015","unstructured":"D Salvi, K Zheng, Y Zhou, S Wang, in Applications of Computer Vision (WACV), 2015 IEEE Winter Conference on. Distance transform based active contour approach for document image rectification (IEEENew York, 2015), pp. 757\u2013764."},{"key":"475_CR8","doi-asserted-by":"publisher","first-page":"266","DOI":"10.5772\/56581","volume":"10","author":"JC Elizondo-Leal","year":"2013","unstructured":"JC Elizondo-Leal, EF Parra-Gonz\u00e1lez, JG Ram\u00edrez-Torres, The exact Euclidean distance transform: a new algorithm for universal path planning. Int. J. Adv. Robot. Syst.10:, 266\u2013275 (2013).","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"475_CR9","first-page":"88","volume-title":"Discrete Geometry for Computer Imagery","author":"E Linn\u00e9r","year":"2014","unstructured":"E Linn\u00e9r, R Strand, in Discrete Geometry for Computer Imagery. Anti-aliased Euclidean distance transform on 3D sampling lattices (SpringerNew York, 2014), pp. 88\u201398."},{"issue":"3","key":"475_CR10","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1007\/s10851-010-0232-4","volume":"39","author":"KC Ciesielski","year":"2011","unstructured":"KC Ciesielski, X Chen, JK Udupa, GJ Grevera, Linear time algorithms for exact distance transform. J. Math. Imaging Vis.39(3), 193\u2013209 (2011).","journal-title":"J. Math. Imaging Vis."},{"issue":"2","key":"475_CR11","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1109\/TPAMI.2003.1177156","volume":"25","author":"CR Maurer","year":"2003","unstructured":"CR Maurer, R Qi, V Raghavan, A linear time algorithm for computing exact Euclidean distance transforms of binary images in arbitrary dimensions. IEEE Trans. Pattern. Anal. Mach. Intell.25(2), 265\u2013270 (2003).","journal-title":"IEEE Trans. Pattern. Anal. Mach. Intell."},{"issue":"3","key":"475_CR12","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1016\/0734-189X(84)90035-5","volume":"27","author":"G Borgefors","year":"1984","unstructured":"G Borgefors, Distance transformations in arbitrary dimensions. Comput. Vis. Graph. Image Proc.27(3), 321\u2013345 (1984).","journal-title":"Comput. Vis. Graph. Image Proc."},{"key":"475_CR13","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1016\/j.tcs.2012.05.010","volume":"448","author":"R Strand","year":"2012","unstructured":"R Strand, N Normand, Distance transform computation for digital distance functions. Theor. Comput. Sci.448:, 80\u201393 (2012).","journal-title":"Theor. Comput. Sci."},{"key":"475_CR14","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1007\/11907350_25","volume":"4245","author":"R Strand","year":"2006","unstructured":"R Strand, B Nagy, C Fouard, G Borgefors, Generating distance maps with neighbourhood sequences. Lect. Notes Comput. Sci. 4245:, 295 (2006).","journal-title":"Lect. Notes Comput. Sci"},{"key":"475_CR15","doi-asserted-by":"publisher","first-page":"292","DOI":"10.1007\/978-3-642-38294-9_25","volume-title":"International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing","author":"B Nagy","year":"2013","unstructured":"B Nagy, R Strand, N Normand, in International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing. A weight sequence distance function (SpringerNew York, 2013), pp. 292\u2013301."},{"key":"475_CR16","doi-asserted-by":"publisher","first-page":"875","DOI":"10.1007\/978-3-642-42057-3_110","volume-title":"Intelligence Science and Big Data Engineering","author":"J Dong","year":"2013","unstructured":"J Dong, C Sun, W Yang, in Intelligence Science and Big Data Engineering. An improved method for oriented chamfer matching (SpringerNew York, 2013), pp. 875\u2013879."},{"key":"475_CR17","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1007\/978-3-642-40602-7_14","volume-title":"Pattern Recognition","author":"D Tzionas","year":"2013","unstructured":"D Tzionas, J Gall, in Pattern Recognition. A comparison of directional distances for hand pose estimation (SpringerNew York, 2013), pp. 131\u2013141."},{"issue":"12","key":"475_CR18","doi-asserted-by":"publisher","first-page":"1151","DOI":"10.1109\/LSP.2013.2283254","volume":"20","author":"P Kaliamoorthi","year":"2013","unstructured":"P Kaliamoorthi, R Kakarala, Directional chamfer matching in 2.5 dimensions. Signal Process. Lett. IEEE. 20(12), 1151\u20131154 (2013).","journal-title":"Signal Process. Lett. IEEE"},{"key":"475_CR19","doi-asserted-by":"publisher","first-page":"2425","DOI":"10.1109\/CVPR.2014.311","volume-title":"Computer Vision and Pattern Recognition (CVPR), 2014 IEEE Conference on","author":"DT Nguyen","year":"2014","unstructured":"DT Nguyen, in Computer Vision and Pattern Recognition (CVPR), 2014 IEEE Conference on. A novel chamfer template matching method using variational mean field (IEEENew York, 2014), pp. 2425\u20132432."},{"key":"475_CR20","first-page":"56","volume":"54","author":"DW Paglieroni","year":"1992","unstructured":"DW Paglieroni, Distance transforms: Properties and machine vision applications. CVGIP: Graph. Model. Image Process.54:, 56\u201374 (1992).","journal-title":"CVGIP: Graph. Model. Image Process."},{"key":"475_CR21","doi-asserted-by":"publisher","first-page":"376","DOI":"10.1109\/IROS.2013.6696379","volume-title":"2013 IEEE\/RSJ International Conference on Intelligent Robots and Systems","author":"L Dantanarayana","year":"2013","unstructured":"L Dantanarayana, R Ranasinghe, G Dissanayake, in 2013 IEEE\/RSJ International Conference on Intelligent Robots and Systems. C-LOG: A Chamfer Distance based method for localisation in occupancy grid-maps (IEEENew York, 2013), pp. 376\u2013381."},{"key":"475_CR22","doi-asserted-by":"publisher","first-page":"450","DOI":"10.1007\/978-3-642-15555-0_33","volume-title":"Computer Vision\u2013ECCV 2010","author":"T Ma","year":"2010","unstructured":"T Ma, X Yang, LJ Latecki, in Computer Vision\u2013ECCV 2010. Boosting chamfer matching by learning chamfer distance normalization (SpringerNew York, 2010), pp. 450\u2013463."},{"key":"475_CR23","doi-asserted-by":"publisher","first-page":"537","DOI":"10.1007\/978-1-4899-0715-8_51","volume-title":"Visual Form","author":"E Thiel","year":"1992","unstructured":"E Thiel, A Montanvert, in Visual Form. Shape splitting from medial lines using the 3\u20134 chamfer distance (SpringerNew York, 1992), pp. 537\u2013546."},{"key":"475_CR24","unstructured":"MP Tran, 3D Contour Closing: A local operator based on Chamfer distance transformation (2013). \n                              https:\/\/hal.archives-ouvertes.fr\/hal-00802068\/file\/cclose_tran.pdf\n                              \n                           ."},{"issue":"4","key":"475_CR25","doi-asserted-by":"publisher","first-page":"607","DOI":"10.1007\/s13042-013-0158-4","volume":"5","author":"MK Bhuyan","year":"2014","unstructured":"MK Bhuyan, VV Ramaraju, Y Iwahori, Hand gesture recognition and animation for local hand motions. Int. J. Mach. Learn. Cybern.5(4), 607\u2013623 (2014).","journal-title":"Int. J. Mach. Learn. Cybern."},{"key":"475_CR26","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1109\/MSP.2008.930649","volume":"26","author":"Z Wang","year":"2009","unstructured":"Z Wang, AC Bovik, Mean squared error: love it or leave it? A new look at signal fidelity measures. IEEE Signal Proc. Mag.26:, 98\u2013117 (2009).","journal-title":"IEEE Signal Proc. Mag."},{"issue":"3","key":"475_CR27","doi-asserted-by":"publisher","first-page":"669","DOI":"10.1016\/j.ijforecast.2015.12.003","volume":"32","author":"S Kim","year":"2016","unstructured":"S Kim, H Kim, A new metric of absolute percentage error for intermittent demand forecasts. Int. J. Forecast.32(3), 669\u2013679 (2016).","journal-title":"Int. J. Forecast."},{"key":"475_CR28","volume-title":"From crystal ball to computer","author":"JS Armstrong","year":"1985","unstructured":"JS Armstrong, LR Forecasting, From crystal ball to computer (Wiley, New York, 1985)."},{"issue":"10","key":"475_CR29","doi-asserted-by":"publisher","first-page":"1477","DOI":"10.1109\/83.718487","volume":"7","author":"MA Butt","year":"1998","unstructured":"MA Butt, P Maragos, Optimum design of chamfer distance transforms. Image Proc. IEEE Trans.7(10), 1477\u20131484 (1998).","journal-title":"Image Proc. IEEE Trans."},{"issue":"3","key":"475_CR30","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1002\/tee.21858","volume":"8","author":"OK Kwon","year":"2013","unstructured":"OK Kwon, JW Suh, Improved 3 \u00d7 3 sequential Euclidean distance transform. IEEJ Trans. Electr. Electron. Eng.8(3), 305\u2013307 (2013).","journal-title":"IEEJ Trans. Electr. Electron. Eng."},{"issue":"12","key":"475_CR31","doi-asserted-by":"publisher","first-page":"381","DOI":"10.14257\/ijmue.2015.10.12.36","volume":"10","author":"Y Dou","year":"2015","unstructured":"Y Dou, M Ye, P Xu, Pei L, Z Liu, Object detection based on two level fast matching. International Journal of Multimedia and Ubiquitous Engineering. 10(12), 381\u2013394 (2015).","journal-title":"International Journal of Multimedia and Ubiquitous Engineering"},{"issue":"2","key":"475_CR32","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1006\/cviu.1999.0783","volume":"76","author":"O Cuisenaire","year":"1999","unstructured":"O Cuisenaire, B Macq, Fast Euclidean distance transformation by propagation using multiple neighborhoods. Comp. Vision Image Underst.76(2), 163\u2013172 (1999).","journal-title":"Comp. Vision Image Underst."},{"issue":"11","key":"475_CR33","doi-asserted-by":"publisher","first-page":"1551","DOI":"10.1016\/0031-3203(94)90133-3","volume":"27","author":"T Saito","year":"1994","unstructured":"T Saito, JI Toriwaki, New algorithms for euclidean distance transformation of an n-dimensional digitized picture with applications. Pattern Recog.27(11), 1551\u20131565 (1994).","journal-title":"Pattern Recog."},{"issue":"2","key":"475_CR34","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1016\/j.cviu.2003.09.004","volume":"93","author":"FY Shih","year":"2004","unstructured":"FY Shih, YT Wu, Fast Euclidean distance transformation in two scans using a 3 \u00d7 3 neighborhood. Comp. Vision Image Underst.93(2), 195\u2013205 (2004).","journal-title":"Comp. Vision Image Underst."},{"issue":"11","key":"475_CR35","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1016\/0167-8655(91)90004-6","volume":"12","author":"BJ Verwer","year":"1991","unstructured":"BJ Verwer, Local distances for distance transformations in two and three dimensions. Pattern Recogn. Lett.12(11), 671\u2013682 (1991).","journal-title":"Pattern Recogn. Lett."},{"key":"475_CR36","doi-asserted-by":"crossref","unstructured":"BJ Maiseli, L Bai, X Yang, Y Gu, H Gao, Robust cost function for optimizing chamfer masks. Vis. Comput., 1\u201316 (2017).","DOI":"10.1007\/s00371-017-1367-8"},{"key":"475_CR37","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1007\/978-3-642-10210-3_7","volume-title":"International Workshop on Combinatorial Image Analysis","author":"J Hulin","year":"2009","unstructured":"J Hulin, \u00c9 Thiel, in International Workshop on Combinatorial Image Analysis. Farey sequences and the planar Euclidean medial axis test mask (SpringerNew York, 2009), pp. 82\u201395."}],"container-title":["EURASIP Journal on Image and Video Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1186\/s13640-019-0475-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1186\/s13640-019-0475-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1186\/s13640-019-0475-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,7,27]],"date-time":"2020-07-27T23:07:59Z","timestamp":1595891279000},"score":1,"resource":{"primary":{"URL":"https:\/\/jivp-eurasipjournals.springeropen.com\/articles\/10.1186\/s13640-019-0475-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,29]]},"references-count":37,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["475"],"URL":"https:\/\/doi.org\/10.1186\/s13640-019-0475-y","relation":{},"ISSN":["1687-5281"],"issn-type":[{"value":"1687-5281","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,7,29]]},"assertion":[{"value":"29 August 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 July 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 July 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare that they have no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"74"}}