Stable evaluation of 3D Zernike moments for surface meshes

Autor: Patrice Koehl, Jérôme Houdayer
Přispěvatelé: Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Department of Computer Science [Univ California Davis] (CS - UC Davis), University of California [Davis] (UC Davis), University of California (UC)-University of California (UC)
Jazyk: angličtina
Rok vydání: 2022
Předmět:
Zdroj: Algorithms
Algorithms, 2022, 15 (11), pp.406. ⟨10.3390/a15110406⟩
Volume 15
Issue 11
Pages: 406
ISSN: 1999-4893
DOI: 10.3390/a15110406⟩
Popis: Special Issue Computational Methods and Optimization for Numerical Analysis; International audience; The 3D Zernike polynomials form an orthonormal basis of the unit ball. The associated 3D Zernike moments have been successfully applied for 3D shape recognition; they are popular in structural biology for comparing protein structures and properties. Many algorithms have been proposed for computing those moments, starting from a voxel-based representation or from a surface based geometric mesh of the shape. As the order of the 3D Zernike moments increases, however, those algorithms suffer from decrease in computational efficiency and more importantly from numerical accuracy. In this paper, new algorithms are proposed to compute the 3D Zernike moments of a homogeneous shape defined by an unstructured triangulation of its surface that remove those numerical inaccuracies. These algorithms rely on the analytical integration of the moments on tetrahedra defined by the surface triangles and a central point and on a set of novel recurrent relationships between the corresponding integrals. The mathematical basis and implementation details of the algorithms are presented and their numerical stability is evaluated.
Databáze: OpenAIRE
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