{"version":1,"kind":"Article","sha256":"","slug":"139","location":"","dependencies":[],"doi":"10.54294/mamu6k","frontmatter":{"title":"Well-Composedness and the Topological Repairing of 2-D and 3-D Digital Images","abstract":"In an earlier submission, we considered 2-D and 3-D digital binary images topologically characterized by their well-composedness. Well-composed images exhibit important topological and geometrical properties not shared by their ill-composed counterparts. These properties have important implications for various algorithms used by the ITK community such as thinning algorithms and Marching Cubes. \r\n\r\nA natural follow-up inquiry to our original submission concerns the possible extension of the binary algorithm to accommodate images with multiple labels. In this paper, we describe such a generalization of our previous submission which also subsumes the binary approach. For completeness and clarity of exposition, we develop the idea of well-composedness within the binary image context and later generalize the discussion to include those images with multiple labels.","license":"You are licensing your work to Kitware Inc. under the\nCreative Commons Attribution License Version 3.0.\n\nKitware Inc. agrees to the following:\n\nKitware is free\n * to copy, distribute, display, and perform the work\n * to make derivative works\n * to make commercial use of the work\n\nUnder the following conditions:\n\\\"by Attribution\\\" - Kitware must attribute the work in the manner specified by the author or licensor.\n\n * For any reuse or distribution, they must make clear to others the license terms of this work.\n * Any of these conditions can be waived if they get permission from the copyright holder.\n\nYour fair use and other rights are in no way affected by the above.\n\nThis is a human-readable summary of the Legal Code (the full license) available at\nhttp://creativecommons.org/licenses/by/3.0/legalcode","keywords":["digital topology","digital images","well-composedness"],"authors":[{"name":"Tustison, Nicholas","email":"ntustison@gmail.com","affiliations":[],"corresponding":true},{"name":"Siqueira, Marcelo","affiliations":[]},{"name":"Gee, James","email":"gee@mail.med.upenn.edu","affiliations":[]}],"date_submitted":"2007-01-16T01:20:33Z","external_publication_id":139,"revision_cids":["bafkreib66hfpfw34r7x3cwjocomsudsjjldqy2noze5op5rp42obupom3y"]},"mdast":{"type":"root"},"downloads":[{"url":"https://ipfs.desci.com/ipfs/bafkreif4ro2xp2ge6z5lof6ckjagukqswihxc4ten54gktzj2atmgx7tym","title":"root/insight-journal-metadata.json","filename":"insight-journal-metadata.json","extra":{"size_bytes":5559,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreihsf6vjpiqnow637mu6fvp73atnisf4lbq4hnjpplvmgaub2jl5fa","title":"root/code/MultiValuedSource/.DS_Store","filename":".DS_Store","extra":{"size_bytes":6148,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreie7b7jnxip7tldksyoa637awhheab2a7z5vt3sqwtpf2prusitrne","title":"root/code/MultiValuedSource/CMakeLists.txt","filename":"CMakeLists.txt","extra":{"size_bytes":1991,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreiatekj56hyg737rvw5gkabmhk7ye6xg7bmajgtz5nqzoienkeah7y","title":"root/code/MultiValuedSource/IJMacros.txt","filename":"IJMacros.txt","extra":{"size_bytes":3973,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreia3vmvdi6k3lt7e6twomw4bikt67amlsltlsq7xtgsus46htwzwii","title":"root/code/MultiValuedSource/itkWellComposedImageFilter.h","filename":"itkWellComposedImageFilter.h","extra":{"size_bytes":4669,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreifmxd3pxzvrldiyvbwfolntd7uzkmlnwyveptr2lkooen6tp6sx6i","title":"root/code/MultiValuedSource/itkWellComposedImageFilter.txx","filename":"itkWellComposedImageFilter.txx","extra":{"size_bytes":40489,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreigypfvflvyfsgedlqtujqzgjcjccrwdh7cfsbz3b4kycgacojf45e","title":"root/code/MultiValuedSource/itkWellComposedImageFilterTest.cxx","filename":"itkWellComposedImageFilterTest.cxx","extra":{"size_bytes":2626,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreigw75pkpbx27qrr3mdu5tco5zqbvvf2stwcjvcajwgn3qzcaijgoq","title":"root/code/MultiValuedSource/progress.make","filename":"progress.make","extra":{"size_bytes":23,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreieh4jfbdfdkzv7zrmdzvrkvwau7rvj2ytimh7ztdraot7x62462sm","title":"root/code/MultiValuedSource/random2D.hdr","filename":"random2D.hdr","extra":{"size_bytes":348,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreia6km3apr5aq5pjjtoasrvle36oxijjrxkfxynjicphoehvr2t2qm","title":"root/code/MultiValuedSource/random2D.img","filename":"random2D.img","extra":{"size_bytes":900,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreigwkfsspeifzjtxggafabui35f5y2ncy63xc5jpbjdo6eqlp7moym","title":"root/code/MultiValuedSource/OutputImages/.DS_Store","filename":".DS_Store","extra":{"size_bytes":6148,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreifhk7j5eoity6jlnvgzdngcx3yih3d4u2fp4y3xfuzzqegazdwwp4","title":"root/code/MultiValuedSource/OutputImages/out2D.nii","filename":"out2D.nii","extra":{"size_bytes":1252,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafybeicieitrczphn2ct4txlifx5xwnyfdcpawmk72h7b3nuwavpmq2oeu","title":"root/code/MultiValuedSource/OutputImages/out3D.nii","filename":"out3D.nii","extra":{"size_bytes":28436900,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreigs4qg5532gd524muybflmxi2gjcrih6fq3o76g5fgeqtghwgf5em","title":"root/code/MultiValuedSource/InputImages/.DS_Store","filename":".DS_Store","extra":{"size_bytes":6148,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreid7l36brhjygstltgfshfm45yoatlr3d7fsmtwsjwogzxh37wmdli","title":"root/code/MultiValuedSource/InputImages/DS3/.DS_Store","filename":".DS_Store","extra":{"size_bytes":6148,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreifaomitj3razgsl6iy74kfvzkh6wqn7bmbg3atafyqucpeyrvnzz4","title":"root/code/MultiValuedSource/InputImages/DS3/ds3.hdr","filename":"ds3.hdr","extra":{"size_bytes":348,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafybeic2snm76jn7pnlyim4akf6dcrv2y5rohkza6x2axt5iu6epqpkzem","title":"root/code/MultiValuedSource/InputImages/DS3/ds3.img","filename":"ds3.img","extra":{"size_bytes":36700160,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreigwkfsspeifzjtxggafabui35f5y2ncy63xc5jpbjdo6eqlp7moym","title":"root/code/MultiValuedSource/InputImages/DS3/Binary/.DS_Store","filename":".DS_Store","extra":{"size_bytes":6148,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreifaomitj3razgsl6iy74kfvzkh6wqn7bmbg3atafyqucpeyrvnzz4","title":"root/code/MultiValuedSource/InputImages/DS3/Binary/pelvis.hdr","filename":"pelvis.hdr","extra":{"size_bytes":348,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafybeif6dvpijrnevs4nvigwcxq5e5zujjssvc2q2oixhpkm3itcabfpje","title":"root/code/MultiValuedSource/InputImages/DS3/Binary/pelvis.img","filename":"pelvis.img","extra":{"size_bytes":36700160,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreifaomitj3razgsl6iy74kfvzkh6wqn7bmbg3atafyqucpeyrvnzz4","title":"root/code/MultiValuedSource/InputImages/DS3/Binary/rbdv.hdr","filename":"rbdv.hdr","extra":{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