{"data":{"id":"10.6084/m9.figshare.1323266","type":"dois","attributes":{"doi":"10.6084/m9.figshare.1323266","prefix":"10.6084","suffix":"m9.figshare.1323266","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Castillo, Enrique Del","nameType":"Personal","givenName":"Enrique Del","familyName":"Castillo","affiliation":[],"nameIdentifiers":[]},{"name":"Colosimo, Bianca M.","nameType":"Personal","givenName":"Bianca M.","familyName":"Colosimo","affiliation":[],"nameIdentifiers":[]},{"name":"Tajbakhsh, Sam Davanloo","nameType":"Personal","givenName":"Sam Davanloo","familyName":"Tajbakhsh","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"Geodesic Gaussian Processes for the Parametric Reconstruction of a Free-Form Surface"}],"publisher":"Taylor \u0026 Francis","container":{},"publicationYear":2020,"subjects":[{"subject":"Physiology"},{"subject":"FOS: Biological sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Biological sciences","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"59999 Environmental Sciences not elsewhere classified","subjectScheme":"FOR"},{"subject":"FOS: Earth and related environmental sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Earth and related environmental sciences","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"39999 Chemical Sciences not elsewhere classified","subjectScheme":"FOR"},{"subject":"FOS: Chemical sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Chemical sciences","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"80699 Information Systems not elsewhere classified","subjectScheme":"FOR"},{"subject":"FOS: Computer and information sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Computer and information sciences","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"19999 Mathematical Sciences not elsewhere classified","subjectScheme":"FOR"},{"subject":"FOS: Mathematics","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Mathematics","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Cancer"}],"contributors":[],"dates":[{"date":"2015-03-04","dateType":"Created"},{"date":"2020-08-21","dateType":"Updated"},{"date":"2020","dateType":"Issued"}],"language":null,"types":{"ris":"DATA","bibtex":"misc","citeproc":"dataset","schemaOrg":"Dataset","resourceType":"Dataset","resourceTypeGeneral":"Dataset"},"relatedIdentifiers":[{"relationType":"IsSupplementTo","relatedIdentifier":"10.1080/00401706.2013.879075","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":["409002 Bytes"],"formats":[],"version":null,"rightsList":[{"rights":"Creative Commons Attribution 4.0 International","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rightsIdentifier":"cc-by-4.0","rightsIdentifierScheme":"SPDX"}],"descriptions":[{"description":"Reconstructing a free-form surface from 3-dimensional (3D) noisy measurements is a central problem in inspection, statistical quality control, and reverse engineering. We present a new method for the statistical reconstruction of a free-form surface patch based on 3D point cloud data. The surface is represented parametrically, with each of the three Cartesian coordinates (\u003ci\u003ex\u003c/i\u003e, \u003ci\u003ey\u003c/i\u003e, \u003ci\u003ez\u003c/i\u003e) a function of surface coordinates (\u003ci\u003eu\u003c/i\u003e, \u003ci\u003ev\u003c/i\u003e), a model form compatible with computer-aided-design (CAD) models. This model form also avoids having to choose one Euclidean coordinate (say, \u003ci\u003ez\u003c/i\u003e) as a “response” function of the other two coordinate “locations” (say, \u003ci\u003ex\u003c/i\u003e and \u003ci\u003ey\u003c/i\u003e), as commonly used in previous Euclidean kriging models of manufacturing data. The (\u003ci\u003eu\u003c/i\u003e, \u003ci\u003ev\u003c/i\u003e) surface coordinates are computed using parameterization algorithms from the manifold learning and computer graphics literature. These are then used as locations in a spatial Gaussian process model that considers correlations between two points on the surface a function of their \u003ci\u003egeodesic\u003c/i\u003e distance on the surface, rather than a function of their Euclidean distances over the \u003ci\u003exy\u003c/i\u003e plane. We show how the proposed geodesic Gaussian process (GGP) approach better reconstructs the true surface, filtering the measurement noise, than when using a standard Euclidean kriging model of the “heights”, that is, \u003ci\u003ez\u003c/i\u003e(\u003ci\u003ex\u003c/i\u003e, \u003ci\u003ey\u003c/i\u003e). The methodology is applied to simulated surface data and to a real dataset obtained with a noncontact laser scanner. Supplementary materials are available online.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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