Abstract

Optimal mass transport (OMT) theory, the goal of which is to move any irregular 3D object (i.e., the brain) without causing significant distortion, is used to preprocess brain tumor datasets for the first time in this paper. The first stage of a two-stage OMT (TSOMT) procedure transforms the brain into a unit solid ball. The second stage transforms the unit ball into a cube, as it is easier to apply a 3D convolutional neural network to rectangular coordinates. Small variations in the local mass-measure stretch ratio among all the brain tumor datasets confirm the robustness of the transform. Additionally, the distortion is kept at a minimum with a reasonable transport cost. The original 240 times 240 times 155 times 4 dataset is thus reduced to a cube of 128 times 128 times 128 times 4, which is a 76.6% reduction in the total number of voxels, without losing much detail. Three typical U-Nets are trained separately to predict the whole tumor (WT), tumor core (TC), and enhanced tumor (ET) from the cube. An impressive training accuracy of 0.9822 in the WT cube is achieved at 400 epochs. An inverse TSOMT method is applied to the predicted cube to obtain the brain results. The conversion loss from the TSOMT method to the inverse TSOMT method is found to be less than one percent. For training, good Dice scores (0.9781 for the WT, 0.9637 for the TC, and 0.9305 for the ET) can be obtained. Significant improvements in brain tumor detection and the segmentation accuracy are achieved. For testing, postprocessing (rotation) is added to the TSOMT, U-Net prediction, and inverse TSOMT methods for an accuracy improvement of one to two percent. It takes 200 seconds to complete the whole segmentation process on each new brain tumor dataset.

Highlights

  • Optimal mass transport (OMT) theory, the goal of which is to move any irregular 3D object without causing significant distortion, is used to preprocess brain tumor datasets for the first time in this paper

  • Since the two-stage OMT (TSOMT) procedure can skillfully represent the global information of a brain image, we propose a postprocessing scheme by applying the mirroring and rotation techniques to increase the Dice scores of the whole tumor (WT), tumor core (TC), and enhanced tumor (ET)

  • The two red curves corresponding to the loss functions in each subfigure of Fig. 6 form a variance when the number of epochs nears 400 and a bias when the number of epochs is near 10; the optimal number of epochs for the WT, TC and ET is between 45 and 55

Read more

Summary

Dice score

For a fixed brain tumor, as in [15], let A and B denote the positive ground truths and predictions, respectively, for the WT, TC, and ET. The HD is defined as HD max{max a∈∂ A min b∈∂ B a. HD95 is similar to the HD, and it calculates the 95th percentile of the distance between the boundary points in A and B. We consider applying the OMT technique on the MSD Challenge dataset to obtain a good training set and make highly accurate predictions

Results and discussion
Conclusions
Author contributions
Additional information
Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call