{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T11:18:01Z","timestamp":1790767081665,"version":"4.1.0"},"reference-count":167,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2018,2,1]],"date-time":"2018-02-01T00:00:00Z","timestamp":1517443200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Imaging"],"abstract":"<jats:p>The theory of hierarchical image representations has been well-established in Mathematical Morphology, and provides a suitable framework to handle images through objects or regions taking into account their scale. Such approaches have increased in popularity and been favourably compared to treating individual image elements in various domains and applications. This survey paper presents the development of hierarchical image representations over the last 20 years using the framework of component trees. We introduce two classes of component trees, partitioning and inclusion trees, and describe their general characteristics and differences. Examples of hierarchies for each of the classes are compared, with the resulting study aiming to serve as a guideline when choosing a hierarchical image representation for any application and image domain.<\/jats:p>","DOI":"10.3390\/jimaging4020033","type":"journal-article","created":{"date-parts":[[2018,2,2]],"date-time":"2018-02-02T04:20:50Z","timestamp":1517545250000},"page":"33","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":47,"title":["Partition and Inclusion Hierarchies of Images: A Comprehensive Survey"],"prefix":"10.3390","volume":"4","author":[{"given":"Petra","family":"Bosilj","sequence":"first","affiliation":[{"name":"Lincoln Centre for Autonomous Systems Research, University of Lincoln, Lincoln LN6 7TS, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ewa","family":"Kijak","sequence":"additional","affiliation":[{"name":"Univ. Rennes I, UMR 6074 IRISA, Campus de Beaulieu, 35042 Rennes, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2384-8202","authenticated-orcid":false,"given":"S\u00e9bastien","family":"Lef\u00e8vre","sequence":"additional","affiliation":[{"name":"Univ. Bretagne Sud, UMR 6074, IRISA, F-56000 Vannes, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,2,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Soille, P. (2003). Morphological Image Analysis: Principles and Applications, Springer.","DOI":"10.1007\/978-3-662-05088-0"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1109\/83.841934","article-title":"Binary Partition Tree as an Efficient Representation for Image Processing, Segmentation, and Information Retrieval","volume":"9","author":"Salembier","year":"2000","journal-title":"IEEE Trans. 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