Multiple Relaxation Time Lattice Boltzmann Models for Multigrid Phase-Field Segmentation of Tumors in 3D Ultrasound Images

We address the problem of tumor segmentation in 3D ultrasound images. Although many studies have examined this subject, there is still a need to improve segmentation algorithms so as to obtain the best estimation of tumor volumes. In this paper we propose a new approach based on a variational formulation and a multigrid implementation of a multiple relaxation time lattice Boltzmann scheme. The data attachment term, resp., the regularization term, of the energy to be minimized is given by a log-likelihood, resp., the Allen-Cahn reaction diffusion equation. We investigate the stability and accuracy of the proposed scheme with D3Q7 and D3Q19 lattices. Specifically, we show how to choose the relaxation parameters to obtain a fourth-order exact scheme which is shown to be much more relevant than a single relaxation time Bhatnagar-Gross-Krook scheme. Experiments conducted on images with ground truth given by a dermatologist show that the proposed algorithm significantly increases the Dice index (by 10%) and the sensitivity (by 25%) compared with a level set algorithm and is consequently a good alternative to investigate the problem of volume underestimation.