Convolution of 3D Gaussian surfaces for volumetric intensity inhomogeneity estimation and correction in 3D brain MR image data

Magnetic resonance (MR) imaging technique has become indispensable in image‐guided diagnosis and clinical research. However, present MR image acquisition leads to a slow varying intensity inhomogeneity (IIH) in MR image data. This study presents a novel technique based on convolution of three‐dimensional (3D) Gaussian surfaces, which is denoted as ‘Co3DGS’, for volumetric IIH estimation and correction for 3D brain MR image data. A 3D Gaussian surface is approximated using local voxel gradients on each tissue volume corresponding to grey matter, white matter and cerebrospinal fluid of the 3D brain MR image data and then convolved to partially estimate the IIH, which is subsequently removed from the image data. The above processes are repeated until there is no such significant change in the voxel gradients. The Co3DGS technique has been tested on both synthetic and in‐vivo human 3D brain MR image data of different pulse sequences. The empirical results both in qualitatively and quantitatively, which include coefficient of joint variation, index of variation, index of joint variation, index of class separability and root mean square error, collectively demonstrate that the Co3DGS efficiently estimates and removes the IIH from the 3D brain MR image data and stands superior to some state‐of‐the‐art methods