Efficient 3D Geometric and Zernike moments computation from unstructured surface meshes
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- dc.contributor.author Pozo Soler, José Ma. (José María)
- dc.contributor.author Villa-Uriol, Maria-Cruz
- dc.contributor.author Frangi Caregnato, Alejandro
- dc.date.accessioned 2021-05-31T09:56:54Z
- dc.date.available 2021-05-31T09:56:54Z
- dc.date.issued 2010
- dc.description.abstract This paper introduces and evaluates a fast exact algorithm and a series of faster approximate algorithms for the computation of 3D geometric moments from an unstructured surface mesh of triangles. Being based on the object surface reduces the computational complexity of these algorithms with respect to volumetric grid-based algorithms. In contrast, it can only be applied for the computation of geometric moments of homogeneous objects. This advantage and restriction is shared with other proposed algorithms based on the object boundary. The proposed exact algorithm reduces the computational complexity for computing geometric moments up to order N with respect to previously proposed exact algorithms, from N 9 to N 6 . The approximate series algorithm appears as a power series on the rate between triangle size and object size, which can be truncated at any desired degree. The higher the number and quality of the triangles, the better the approximation. This approximate algorithm reduces the computational complexity to N 3 . In addition, the paper introduces a fast algorithm for the computation of 3D Zernike moments from the computed geometric moments, with a computational complexity N 4 , while the previously proposed algorithm is of order N 6 . The error introduced by the proposed approximate algorithms is evaluated in different shapes and the cost-benefit ratio in terms of error, and computational time is analyzed for different moment orders.
- dc.description.sponsorship This work was partially supported by Philips Healthcare (Best, The Netherlands), the @neurIST Integrated Project (co-financed by the European Commission through the contract no. IST-027703), the CDTI CENIT-CDTEAM grant funded by the Spanish Ministry of Industry and the research project STIMATH (TIN2009-14536-C02-01) funded by the Spanish Ministry of Science and Innovation (MICINN) and the European Regional Development Fund (ERDF)
- dc.format.mimetype application/pdf
- dc.identifier.citation Pozo JM, Villa-Uriol MC, Frangi AF. Efficient 3D Geometric and Zernike moments computation from unstructured surface meshes. IEEE Trans Pattern Anal Mach Intell. 2010;33(3):471-84. DOI: 10.1109/TPAMI.2010.139
- dc.identifier.doi http://dx.doi.org/10.1109/TPAMI.2010.139
- dc.identifier.issn 0162-8828
- dc.identifier.uri http://hdl.handle.net/10230/47698
- dc.language.iso eng
- dc.publisher Institute of Electrical and Electronics Engineers (IEEE)
- dc.relation.ispartof IEEE Transactions on Pattern Analysis and Machine Intelligence. 2010;33(3):471-84
- dc.relation.projectID info:eu-repo/grantAgreement/ES/3PN/TIN2009-14536-C02-01
- dc.relation.projectID info:eu-repo/grantAgreement/EC/FP7/027703
- dc.rights © 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The final published article can be found at http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5551145
- dc.rights.accessRights info:eu-repo/semantics/openAccess
- dc.subject.keyword Image analysis
- dc.subject.keyword Geometric moments
- dc.subject.keyword 3D Zernike moments
- dc.subject.keyword Shape characterization
- dc.subject.keyword Object characterization
- dc.title Efficient 3D Geometric and Zernike moments computation from unstructured surface meshes
- dc.type info:eu-repo/semantics/article
- dc.type.version info:eu-repo/semantics/acceptedVersion