Utilizing the optimal mass transportation (OMT) technique to convert an irregular 3D brain image into a cube, a required input format for a U-net algorithm, is a brand new idea for medical imaging research. We develop a cubic volume-measure-preserving OMT (V-OMT) model for the implementation of this conversion. The contrast-enhanced histogram equalization grayscale of fluid-attenuated inversion recovery (FLAIR) in a brain image creates the corresponding density function. We then propose an effective two-phase residual U-net algorithm combined with the V-OMT algorithm for training and validation. First, we use the residual U-net and V-OMT algorithms to precisely predict the whole tumor (WT) region. Second, we expand this predicted WT region with dilation and create a smooth function by convolving the step-like function associated with the WT region in the brain image with a 5 × 5 × 5 blur tensor. Then, a new V-OMT algorithm with mesh refinement is constructed to allow the residual U-net algorithm to effectively train Net1–Net3 models. Finally, we propose ensemble voting postprocessing to validate the final labels of brain images. We randomly chose 1000 and 251 brain samples from the Brain Tumor Segmentation (BraTS) 2021 training dataset, which contains 1251 samples, for training and validation, respectively. The Dice scores of the WT, tumor core (TC) and enhanced tumor (ET) regions for validation computed by Net1–Net3 were 0.93705, 0.90617 and 0.87470, respectively. A significant improvement in brain tumor detection and segmentation with higher accuracy is achieved.
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