A three-dimensional Fourier descriptor for human body representation/reconstruction from serial cross sections

Area of Science:

• Computer Vision
• Medical Imaging
• Geometric Modeling

Background:

• Accurate 3D shape representation is crucial for various applications, including medical imaging and geometric modeling.
• Existing methods may lack compactness, invariance, or the ability to retain all shape information.

Purpose of the Study:

• To introduce a novel three-dimensional Fourier descriptor (FD3) for 3D shape representation and reconstruction.
• To demonstrate the FD3's capability for compact, invariant representation and accurate shape reconstruction.
• To derive the error bound for 3D reconstruction using FD3.

Main Methods:

• The study utilizes a double Fourier transform of serial cross-sectional contours to create the FD3.
• An inverse Fourier transform is applied to the FD3 for shape reconstruction and volume estimation.
• The supremum norm is used to derive the upper bound of reconstruction error.

Main Results:

• The FD3 provides a compact and invariant representation of 3D shapes.
• The method successfully reconstructs 3D shapes from their contours, estimating volume.
• An upper bound for the reconstruction error was mathematically derived.

Conclusions:

• The three-dimensional Fourier descriptor (FD3) offers an effective method for 3D shape representation and reconstruction.
• FD3 is compatible with medical imaging modalities like CT and MRI, enabling applications in medical image analysis.
• The methodology was successfully illustrated by reconstructing a human head from MR images.