Denoising 3D biomedical images with fractional-order integral calculus

The investigation is conducted a volumetric fractional-order integral calculus. Due to fractional-order integral calculus performing well in denoising of two-dimensional (2D) images, it is applied widely in the 2D field. In this paper, the 2D fractional-order integral operator is extended to the three-dimensional (3D) field, called the volumetric fractional-order integral calculus (VFIC). Furthermore, according to 2D discrete templates, the 3D discrete templates of the VFIC are also generalized. The 3D high precision (sub-voxel) edge surfaces are extracted from the volumetric data filtered by the proposed VFIC. Finally, the experimental results based on 3D biomedical volumetric data filtered by the VFIC method are demonstrated to show that the method has better denoising effect than the conventional 3D Gaussian filter method.