{"version":1,"kind":"Article","sha256":"","slug":"37","location":"","dependencies":[],"doi":"10.54294/jd5eba","frontmatter":{"title":"Cumulative Gaussian Curve Fitter for Boundary Parameterization","abstract":"We have previously developed an algorithm for locating boundaries in an image with sub-pixel resolution, as well as estimating boundary width and image intensity within the adjoining objects. The algorithm operates by finding the parameters of a cumulative Gaussian curve that best approximates an intensity profile taken across a boundary. If intensity is sampled along the image gradient across a boundary, it is reasonable to assume the profile approximates a finite portion of a cumulative Gaussian. Given that assumption, the first derivative of the profile should be the corresponding portion of a Gaussian, completely described by its mean, standard deviation, and amplitude. We present here a simple and rapid method to find those parameters, given that we only have a potentially skewed sample of the Gaussian. The parameters are approximated first for the finite sample, and then both ends of the Gaussian are extrapolated using the resulting parameters. New parameters are then calculated and the procedure is repeated. The optimization rapidly converges, yielding boundary location (mean) with sub-pixel accuracy as well boundary width (standard deviation). Integration then reproduces the cumulative Gaussian, and a least-squares fit is applied to estimate the constant of integration, from which intensity of the adjoining regions can be estimated.","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":["Cumulative Gaussian","Optimization","Image Analysis","Boundary Detection"],"authors":[{"name":"Wang, David","email":"david@wangmd.com","affiliations":["University of Pittsburgh"],"corresponding":true},{"name":"Tamburo, Robert","email":"robert.tamburo@gmail.com","affiliations":[]},{"name":"Stetten, George","email":"email@stetten.com","affiliations":[]}],"date_submitted":"2005-08-05T21:30:12Z","external_publication_id":37,"revision_cids":["bafkreicnik627hwpt35o6dx5woxgtpq6qldezcq2cws6ta6gvhkzugohdq"]},"mdast":{"type":"root"},"downloads":[{"url":"https://ipfs.desci.com/ipfs/bafkreibaauomscr2ndx3k4q5bj4tgb73ikcijpvz7ncfdg2wlngbqs3jau","title":"root/insight-journal-metadata.json","filename":"insight-journal-metadata.json","extra":{"size_bytes":13382,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreih4tatiqs6ejkh7ll5ha72mqqwhhdvpwq5cfvtrlu33mcouncfyye","title":"root/code/itkWAMoptimizer/CMakeLists.txt","filename":"CMakeLists.txt","extra":{"size_bytes":1602,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreibvxmo5pweuixrsozjvosrxkkyxxibj3dgrg6obeyxqueru53j4qq","title":"root/code/itkWAMoptimizer/EI1.gif","filename":"EI1.gif","extra":{"size_bytes":1114,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreicnlnofv2p7ogs6srit64uigk6lkqhzettvnzk7jtcu63wgj36zg4","title":"root/code/itkWAMoptimizer/EI2.gif","filename":"EI2.gif","extra":{"size_bytes":1147,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreia3qckeszv6vxncfjt5jf2qhcz5lqab6l7j2p2fd733gzn6s2sx5q","title":"root/code/itkWAMoptimizer/Emu.gif","filename":"Emu.gif","extra":{"size_bytes":1079,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreihrpzc5qfsfwafjv5y72zuy6hwxn5ne3b5o3mx3bdbccexzmfwtui","title":"root/code/itkWAMoptimizer/Esigma.gif","filename":"Esigma.gif","extra":{"size_bytes":1074,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreicn7kfngtq673ewxcvxgdzkw74pbiztcbn2rccrqdclwzndjq7ohi","title":"root/code/itkWAMoptimizer/I1.gif","filename":"I1.gif","extra":{"size_bytes":581,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreib6xwbv5ldw7dhzuohc4of6nf2n6ogypmixvvlo55g4ynqex5whni","title":"root/code/itkWAMoptimizer/I2.gif","filename":"I2.gif","extra":{"size_bytes":606,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreiaxbfe2iyooz2mcz6qqalb6zzzjr3qwtileuj43zyjuehlszkfvbu","title":"root/code/itkWAMoptimizer/ReadMe.doc","filename":"ReadMe.doc","extra":{"size_bytes":132608,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreifcqmo76yfdehpmaapojrlk2umrwuczm7gg6ent3zr7serwpnlxsa","title":"root/code/itkWAMoptimizer/ReadMe.pdf","filename":"ReadMe.pdf","extra":{"size_bytes":175843,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreiav7b55mwd4nrwisug4rq6kyz2lodskvqjrdcul3bzqqynbih62my","title":"root/code/itkWAMoptimizer/cumulativeGaussian.gif","filename":"cumulativeGaussian.gif","extra":{"size_bytes":2853,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreih3qbfvxtszca6kcpwevjv7xfl64yb2ruyfvv5hzogkm6ngg3nrsa","title":"root/code/itkWAMoptimizer/fltkCommandEvents.h","filename":"fltkCommandEvents.h","extra":{"size_bytes":1179,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreifcrzd2ncrcmml3qmkbbaicpzzna6ek5az43g7qlnccixr54u7zzm","title":"root/code/itkWAMoptimizer/itkCumulativeGaussianCostFunction.cxx","filename":"itkCumulativeGaussianCostFunction.cxx","extra":{"size_bytes":11604,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreigm73x2qltrxw5b6tsviz7hv3qkl7z4jwfrtpqma45veylxxzkeia","title":"root/code/itkWAMoptimizer/itkCumulativeGaussianCostFunction.h","filename":"itkCumulativeGaussianCostFunction.h","extra":{"size_bytes":5021,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreieyijpsybtmfvx3gzhe36f57r6rvlba7w6q4mhoddjd2kit5t6cxu","title":"root/code/itkWAMoptimizer/itkCumulativeGaussianOptimizer.cxx","filename":"itkCumulativeGaussianOptimizer.cxx","extra":{"size_bytes":16625,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreiepsunpfd3qbjmfuwcebpax6sucbhj7pfrw5gbns6krjoj7h55jae","title":"root/code/itkWAMoptimizer/itkCumulativeGaussianOptimizer.h","filename":"itkCumulativeGaussianOptimizer.h","extra":{"size_bytes":6577,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreicbdbinpwrwu54jonl3ns4ymerhsmcqlhtos7wwkpaq5lbo5yaqqu","title":"root/code/itkWAMoptimizer/itkWAMoptimizer.cxx","filename":"itkWAMoptimizer.cxx","extra":{"size_bytes":2171,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreidwa2qprgjqa7dmjs3eyw3vrz6rrrwssj76e2eg3byaxeljzzvdcu","title":"root/code/itkWAMoptimizer/itkWAMoptimizer.h","filename":"itkWAMoptimizer.h","extra":{"size_bytes":1758,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreihq4ejlxgpwtmbz6vem6euwib5jh733jpekfknx6ydi76lm64miu4","title":"root/code/itkWAMoptimizer/itkWAMoptimizerBase.cxx","filename":"itkWAMoptimizerBase.cxx","extra":{"size_bytes":23244,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreiayvejmcxpuo2udeq4drdvmd3xulpq6em4xm3vqlfoqhui2liz4nu","title":"root/code/itkWAMoptimizer/itkWAMoptimizerBase.h","filename":"itkWAMoptimizerBase.h","extra":{"size_bytes":4968,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreiek3hejn7gf35rz3xjxyezfapjpaqkw2zynr64wd36e4cfydmm7aa","title":"root/code/itkWAMoptimizer/itkWAMoptimizerGUI.cxx","filename":"itkWAMoptimizerGUI.cxx","extra":{"size_bytes":129896,"type":"file"}},{"url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Profiles for Automated Unsupervised Boundary Classification and their Application to Core Atoms Towards Shape Analysis+International Journal of Image and Graphics+1+4+659+680+2001+R. Tamburo"}}}}