Computed tomography image representation using the Legendre polynomial and spherical harmonics functions

The representation of computed tomography (CT) images using the Legendre polynomial (LPF) and spherical harmonics (SHF) functions was investigated. We selected 100 two-dimensional (2D) CT images of 10 lung cancer patients and 33 three-dimensional (3D) CT images of head and neck cancer patients. The reproducibility of these special functions was evaluated in terms of the normalized cross-correlation (NCC). For the 2D images, the NCC was 0.990 ± 0.002 (1sd) with an LPF of order 70, whereas for the 3D images, the NCC was 0.971 ± 0.004 (1sd) with an SHF of degree 70. The results showed that the LPF was more efficient than the Fourier series. As the thoracic and head areas are cylindrical and spherical, respectively, expansions with the LPF and SHF achieved an efficient representation of the human body. CT image representation with analytical functions can be potentially beneficial, such as in X-ray scattering estimation.