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In this context, feature-aware denoising, hole filling and context-aware completion are three essential (but far from trivial) tasks. In this work, they are integrated within a geometric framework and realized through a unified variational model aiming at recovering triangulated surfaces from scanned, damaged and possibly incomplete noisy observations. The underlying non-convex optimization problem incorporates two regularisation terms: a discrete approximation of the Willmore energy forcing local sphericity and suited for the recovery of rounded features, and an approximation of the <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\ell _0$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>\u2113<\/mml:mi>\n                    <mml:mn>0<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> pseudo-norm penalty favouring sparsity in the normal variation. The proposed numerical method solving the model is parameterization-free, avoids expensive implicit volume-based computations and based on the efficient use of the Alternating Direction Method of Multipliers. Experiments show how the proposed framework can provide a robust and elegant solution suited for accurate restorations even in the presence of severe random noise and large damaged areas.<\/jats:p>","DOI":"10.1007\/s10851-022-01107-w","type":"journal-article","created":{"date-parts":[[2022,6,22]],"date-time":"2022-06-22T14:03:09Z","timestamp":1655906589000},"page":"82-98","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["A Unified Surface Geometric Framework for Feature-Aware Denoising, Hole Filling and Context-Aware Completion"],"prefix":"10.1007","volume":"65","author":[{"given":"Luca","family":"Calatroni","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Martin","family":"Huska","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8334-8798","authenticated-orcid":false,"given":"Serena","family":"Morigi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Giuseppe Antonio","family":"Recupero","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,6,22]]},"reference":[{"issue":"3","key":"1107_CR1","doi-asserted-by":"publisher","first-page":"878","DOI":"10.1145\/1015706.1015814","volume":"23","author":"A Sharf","year":"2004","unstructured":"Sharf, A., Alexa, M., Cohen-Or, D.: Context-based surface completion. 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