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Tomography refers to imaging by sections. Computed tomography (CT) is a non-invasive imaging technique that uses computers to analyze several cross-sectional X-rays to reveal minute details about structures in the body.
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Computed tomography image representation using the Legendre polynomial and spherical harmonics functions.

Taisei Shimomura1, Akihiro Haga2

  • 1Graduate School of Biomedical Sciences, Tokushima University, 3-18-15 Kuramoto-cho, Tokushima city, Tokushima, 770-8503, Japan.

Radiological Physics and Technology
|January 11, 2021
PubMed
Summary
This summary is machine-generated.

Legendre polynomial functions (LPF) and spherical harmonics functions (SHF) efficiently represent computed tomography (CT) images. LPF and SHF offer superior reproducibility for 2D and 3D CT scans compared to traditional methods.

Keywords:
Legendre polynomial functionMedical imagesSpherical harmonicsX-ray CT

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Area of Science:

  • Medical Imaging
  • Computational Physics
  • Applied Mathematics

Background:

  • Computed tomography (CT) imaging is crucial for medical diagnosis.
  • Representing complex anatomical structures in CT scans efficiently is an ongoing challenge.
  • Traditional methods may not fully capture the nuances of 3D anatomical data.

Purpose of the Study:

  • To investigate the efficacy of Legendre polynomial functions (LPF) and spherical harmonics functions (SHF) for representing CT images.
  • To evaluate the reproducibility of LPF and SHF in 2D and 3D CT data.
  • To compare the performance of LPF and SHF against existing methods like Fourier series.

Main Methods:

  • Utilized 100 two-dimensional (2D) CT images from lung cancer patients.
  • Employed 33 three-dimensional (3D) CT images from head and neck cancer patients.
  • Assessed function reproducibility using normalized cross-correlation (NCC) with LPF order 70 and SHF degree 70.

Main Results:

  • Achieved high reproducibility for 2D CT images with LPF (NCC: 0.990 ± 0.002).
  • Demonstrated strong reproducibility for 3D CT images with SHF (NCC: 0.971 ± 0.004).
  • LPF showed greater efficiency than Fourier series for image representation.

Conclusions:

  • LPF and SHF provide efficient and reproducible representations of CT images, particularly for cylindrical (thoracic) and spherical (head) anatomical regions.
  • This analytical function-based approach offers potential benefits for applications like X-ray scattering estimation.
  • The findings suggest a promising new direction for CT image analysis and data compression.