{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:53:29Z","timestamp":1760151209628,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,3,9]],"date-time":"2022-03-09T00:00:00Z","timestamp":1646784000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>This paper introduces a new method for determining the shape similarity of complex three-dimensional (3D) mesh structures based on extracting a vector of important vertices, ordered according to a matrix of their most important geometrical and topological features. The correlation of ordered matrix vectors is combined with perceptual definition of salient regions in order to aid detection, distinguishing, measurement and restoration of real degradation and digitization errors. The case study is the digital 3D structure of the Camino Degli Angeli, in the Urbino\u2019s Ducal Palace, acquired by the structure from motion (SfM) technique. In order to obtain an accurate, featured representation of the matching shape, the strong mesh processing computations are performed over the mesh surface while preserving real shape and geometric structure. In addition to perceptually based feature ranking, the new theoretical approach for ranking the evaluation criteria by employing neural networks (NNs) has been proposed to reduce the probability of deleting shape points, subject to optimization. Numerical analysis and simulations in combination with the developed virtual reality (VR) application serve as an assurance to restoration specialists providing visual and feature-based comparison of damaged parts with correct similar examples. The procedure also distinguishes mesh irregularities resulting from the photogrammetry process.<\/jats:p>","DOI":"10.3390\/info13030145","type":"journal-article","created":{"date-parts":[[2022,3,9]],"date-time":"2022-03-09T01:53:54Z","timestamp":1646790834000},"page":"145","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Method for Determining the Shape Similarity of Complex Three-Dimensional Structures to Aid Decay Restoration and Digitization Error Correction"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4081-0203","authenticated-orcid":false,"given":"Iva","family":"Vasic","sequence":"first","affiliation":[{"name":"Department of Civil and Building Engineering and Architecture (DICEA), Universit\u00e0 Politecnica delle Marche, 60131 Ancona, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5637-6582","authenticated-orcid":false,"given":"Ramona","family":"Quattrini","sequence":"additional","affiliation":[{"name":"Department of Civil and Building Engineering and Architecture (DICEA), Universit\u00e0 Politecnica delle Marche, 60131 Ancona, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9160-834X","authenticated-orcid":false,"given":"Roberto","family":"Pierdicca","sequence":"additional","affiliation":[{"name":"Department of Civil and Building Engineering and Architecture (DICEA), Universit\u00e0 Politecnica delle Marche, 60131 Ancona, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8893-9244","authenticated-orcid":false,"given":"Emanuele","family":"Frontoni","sequence":"additional","affiliation":[{"name":"VRAI Lab, Universit\u00e0 di Macerata, 62100 Macerata, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8667-1507","authenticated-orcid":false,"given":"Bata","family":"Vasic","sequence":"additional","affiliation":[{"name":"Faculty of Electronic Engineering, University of Nis, 18000 Nis, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.culher.2006.10.007","article-title":"Methods for 3D digitization of Cultural Heritage","volume":"8","author":"Pavlidis","year":"2007","journal-title":"J. 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[2nd ed.].","DOI":"10.1017\/CBO9780511811685"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1052","DOI":"10.1109\/TPAMI.2007.1049","article-title":"MonoSLAM: Real-Time Single Camera SLAM","volume":"29","author":"Davison","year":"2007","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_6","unstructured":"Osada, R., Funkhouser, T., Chazelle, B., and Dobkin, D. (2001, January 7\u201311). Matching 3D models with shape distributions. Proceedings of the International Conference on Shape Modeling and ApplicationsMay, Genova, Italy."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1109\/34.121791","article-title":"A Method for Registration of 3-D Shapes","volume":"14","author":"Besl","year":"1992","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1016\/j.cag.2010.11.010","article-title":"Surface Partial Matching & Application to Archaeology","volume":"35","author":"Itskovich","year":"2011","journal-title":"Comput. Graph."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2532548","article-title":"Context-based Coherent Surface Completion","volume":"33","author":"Harary","year":"2014","journal-title":"ACM Trans. Graph. (TOG)"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1016\/S0926-5805(98)00053-3","article-title":"Generating, evaluating and visualizing construction schedules with CAD tools","volume":"7","author":"McKinney","year":"1998","journal-title":"Autom. Constr."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Kersting, O., and D\u00f6llner, J. (2002, January 8\u20139). Interactive 3D visualization of vector data in GIS. Proceedings of the 10th ACM International Symposium on Advances in Geographic Information, McLean, VA, USA.","DOI":"10.1145\/585147.585170"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1109\/CVPR.2000.854916","article-title":"Structure from motion without correspondence","volume":"Volume 2","author":"Deleart","year":"2000","journal-title":"Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2000 (Cat. No.PR00662)"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Van den Hengel, A., Dick, A.R., Thorm\u00e4hlen, T., Ward, B., and Torr, P.H.S. (2007). Videotrace: Rapid Interactive Scene Modelling from Video. ACM SIGGRAPH 2007 Papers, Association for Computing Machinery.","DOI":"10.1145\/1275808.1276485"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1145\/588272.588279","article-title":"A search engine for 3D models","volume":"22","author":"Funkhouser","year":"2003","journal-title":"ACM Trans. Graph."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Qin, S., Li, Z., and Chen, Z. (2018, January 29\u201331). Similarity Analysis of 3D Models Based on Convolutional Neural Networks with Threshold. Proceedings of the 2018 the 2nd International Conference on Video and Image Processing, Tokyo, Japan.","DOI":"10.1145\/3301506.3301529"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3267346","article-title":"Corner-operated Tran-similar (COTS) Maps, Patterns, and Lattices","volume":"39","author":"Rossignac","year":"2020","journal-title":"ACM Trans. Graph."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1145\/1073204.1073229","article-title":"Mean value coordinates for closed triangular meshes","volume":"24","author":"Ju","year":"2005","journal-title":"ACM Trans. Graph."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/cgf.12010","article-title":"Symmetry in 3D geometry: Extraction and applications","volume":"32","author":"Mitra","year":"2013","journal-title":"Comput. Graph. Forum"},{"key":"ref_19","unstructured":"Chang, M.C., and Kimia, B.B. (October, January 27). Measuring 3D Shape Similarity by Matching the Medial Scaffolds. Proceedings of the IEEE 12th International Conference on Computer Vision Workshops, ICCV Workshops, Kyoto, Japan."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1145\/1118890.1118893","article-title":"Feature-based similarity search in 3D object databases","volume":"37","author":"Bustos","year":"2005","journal-title":"ACM Comput. Surv."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1591","DOI":"10.1109\/TMM.2015.2457676","article-title":"Covariance-Based Descriptors for Efficient 3D Shape Matching, Retrieval, and Classification","volume":"17","author":"Tabia","year":"2015","journal-title":"IEEE Trans. Multimed."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1007\/s11042-007-0181-0","article-title":"A survey of content based 3D shape retrieval methods","volume":"39","author":"Tangelder","year":"2007","journal-title":"Multimed. Tools Appl."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"878","DOI":"10.1145\/1015706.1015814","article-title":"Context-Based Surface Completion","volume":"23","author":"Sharf","year":"2004","journal-title":"ACM Trans. Graph."},{"key":"ref_24","first-page":"191","article-title":"Simplification and Repair of Polygonal Models Using Volumetric Techniques","volume":"9","author":"Nooruddin","year":"2003","journal-title":"IEEE Educ. Act. Dep."},{"key":"ref_25","unstructured":"Khorramabadi, D. (1991). A Walk through the Planned CS Building, University of California at Berkeley. [1st ed.]."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1111\/1467-8659.00669","article-title":"On Visual Similarity Based 3D Model Retrieval","volume":"22","author":"Chen","year":"2003","journal-title":"Comput. Graph. Forum"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"25","DOI":"10.4316\/AECE.2012.04004","article-title":"Ordered Statistics Vertex Extraction and Tracing Algorithm (OSVETA)","volume":"12","author":"Vasic","year":"2012","journal-title":"Adv. Electr. Comput. Eng."},{"key":"ref_28","unstructured":"Spivak, M. (1999). A Comprehensive Introduction to Differential Geometry, Publish or Perish. [3rd ed.]."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Hege, H.C. (2003). Discrete Differential-Geometry Operators for Triangulated 2-Manifolds. Visualization and Mathematics III, Springer Berlin\/Heidelberg.","DOI":"10.1007\/978-3-662-05105-4"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/s001380050055","article-title":"A comparison of local surface geometry estimation methods","volume":"10","author":"McIvor","year":"1997","journal-title":"Mach. Vis. Appl."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2325","DOI":"10.1109\/18.720541","article-title":"Quantization","volume":"44","author":"Gray","year":"1998","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1532","DOI":"10.1109\/TMM.2013.2265673","article-title":"Simplification Resilient LDPC-Coded Sparse-QIM Watermarking for 3D-Meshes","volume":"15","author":"Vasic","year":"2013","journal-title":"IEEE Trans. Multimed."},{"key":"ref_33","first-page":"387","article-title":"Neuro-OSVETA: A Robust Watermarking of 3D Meshes","volume":"Volume 55","author":"Vasic","year":"2019","journal-title":"Proceedings of the International Telemetering Conference"},{"key":"ref_34","unstructured":"Vasic, B., and Vasic, I. (2022, January 08). Angeli Similarity Research. Available online: http:\/\/iva.silicon-studio.com\/AngeliSImilarityResearch.zip."}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/13\/3\/145\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:33:23Z","timestamp":1760135603000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/13\/3\/145"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,9]]},"references-count":34,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,3]]}},"alternative-id":["info13030145"],"URL":"https:\/\/doi.org\/10.3390\/info13030145","relation":{},"ISSN":["2078-2489"],"issn-type":[{"type":"electronic","value":"2078-2489"}],"subject":[],"published":{"date-parts":[[2022,3,9]]}}}