{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:11:41Z","timestamp":1760177501358,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2020,5,12]],"date-time":"2020-05-12T00:00:00Z","timestamp":1589241600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61179031"],"award-info":[{"award-number":["61179031"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Shape registration, finding the correct alignment of two sets of data, plays a significant role in computer vision such as objection recognition and image analysis. The iterative closest point (ICP) algorithm is one of well known and widely used algorithms in this area. The main purpose of this paper is to incorporate ICP with the fast convergent extended Hamiltonian learning (EHL), so called EHL-ICP algorithm, to perform planar and spatial rigid shape registration. By treating the registration error as the potential for the extended Hamiltonian system, the rigid shape registration is modelled as an optimization problem on the special Euclidean group     S E ( n )         ( n = 2 , 3 )    . Our method is robust to initial values and parameters. Compared with some state-of-art methods, our approach shows better efficiency and accuracy by simulation experiments.<\/jats:p>","DOI":"10.3390\/e22050539","type":"journal-article","created":{"date-parts":[[2020,5,12]],"date-time":"2020-05-12T10:53:55Z","timestamp":1589280835000},"page":"539","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Rigid Shape Registration Based on Extended Hamiltonian Learning"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0579-8990","authenticated-orcid":false,"given":"Jin","family":"Yi","sequence":"first","affiliation":[{"name":"Department of Basic Courses, Beijing Union University, Beijing 100081, China"},{"name":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shiqiang","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8856-2902","authenticated-orcid":false,"given":"Yueqi","family":"Cao","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Erchuan","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, University of Western Australia, Crawley WA6009, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huafei","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,5,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2081","DOI":"10.1109\/TIP.2013.2244608","article-title":"Real-Time Continuous Image Registration Enabling Ultraprecise 2D Motion Tracking","volume":"22","author":"Cheng","year":"2013","journal-title":"IEEE Trans. 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