Title :
Fast Recursive Computation of 3D Geometric Moments from Surface Meshes
Author_Institution :
Dept. of Comput. Sci., Univ. of California, Davis, CA, USA
Abstract :
A new exact algorithm is proposed to compute the 3D geometric moments of a homogeneous shape defined by an unstructured triangulation of its surface. This algorithm relies on the analytical integration of the moments on tetrahedra defined by the surface triangles and a central point and on a set of recurrent relationships between the corresponding integrals, and achieves linear running time complexities with respect to the number of triangles in the surface mesh and with respect to the number of moments that are computed. This effectively reduces the complexity for computing moments up to order N from N6 to N3 with respect to the fastest previously proposed exact algorithm.
Keywords :
computational complexity; computational geometry; mesh generation; 3D geometric moments; analytical integration; fast recursive computation; homogeneous shape; linear running time complexities; surface meshes; surface triangles; tetrahedra; unstructured triangulation; Approximation algorithms; Approximation methods; Computational complexity; Equations; Mathematical model; Shape; 3D geometric moments; discrete convolution; exact algorithm; Algorithms; Artificial Intelligence; Image Enhancement; Image Interpretation, Computer-Assisted; Imaging, Three-Dimensional; Numerical Analysis, Computer-Assisted; Pattern Recognition, Automated; Reproducibility of Results; Sensitivity and Specificity;
Journal_Title :
Pattern Analysis and Machine Intelligence, IEEE Transactions on
DOI :
10.1109/TPAMI.2012.23
