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The characterization is given by several topological properties described in terms of critical points relative to the region. We formally prove the necessary and sufficient conditions that a region needs to satisfy to be a slope region. We also provide a prototype of slope regions which is general and contains, as particular cases, the prototypes studied and published in previous conference papers.<\/jats:p>","DOI":"10.1007\/s10878-021-00783-5","type":"journal-article","created":{"date-parts":[[2021,7,27]],"date-time":"2021-07-27T05:02:49Z","timestamp":1627362169000},"page":"2661-2680","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Characterizing slope regions"],"prefix":"10.1007","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9937-0033","authenticated-orcid":false,"given":"Rocio","family":"Gonzalez-Diaz","sequence":"first","affiliation":[]},{"given":"Darshan","family":"Batavia","sequence":"additional","affiliation":[]},{"given":"Rocio M.","family":"Casablanca","sequence":"additional","affiliation":[]},{"given":"Walter G.","family":"Kropatsch","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,7,27]]},"reference":[{"key":"783_CR1","doi-asserted-by":"crossref","unstructured":"Batavia D, Hladuvka J, Kropatsch WG (2019a) Partitioning 2D images into prototypes of slope region. 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