Algorithm 1 The learning process of MAUNet

Input: The training images ${\mathbf{I}}_{train}$, max-epochs $E=12$, the number of ${\mathbf{I}}_{train}$$N_{train}$, The testing image ${\mathit{I}}_{test}$ and the  groundtruth labels G

Output: The output prediction $G^{{}^{\prime }}$, and its performance results $G_{Dice}^{{}^{\prime }}$, $G_{IoU}^{{}^{\prime }}$, $G_{RoC}^{{}^{\prime }}$ and $G_{time}^{{}^{\prime }}$

All the images are preprocessed according to the steps in Section 4.2.

Training Stage:

Initialize the network weights, learning rate, batch size, and other parameters

for $i=1$; $i\le E$; $i++$do

Get the data batch from ${\mathbf{I}}_{train}$

for $j=1$; $j\le N_{train}$; $j++$ do

Compute IoU loss function ${\mathcal{L}}_{IoU}$;

Compute Dice loss ${\mathcal{L}}_{Dice}$;

Compute Focal loss ${\mathcal{L}}_{Focal}$;

Train MAUNet by optimizing loss ${\mathcal{L}}_{MAUNet}$ and update the weights and parameters;

end for

end for

Testing Stage:

Feed ${\mathit{I}}_{test}$ into the well-trained MAUNet and then output the prediction segmentation $G^{{}^{\prime }}$;

Compute the performance results $G_{Dice}^{{}^{\prime }}$ (Equation (14)), $G_{IoU}^{{}^{\prime }}$ (Equation (15)), $G_{RoC}^{{}^{\prime }}$ (Equation (16)) and running time $G_{time}^{{}^{\prime }}$

return$G^{{}^{\prime }}$, $G_{Dice}^{{}^{\prime }}$, $G_{IoU}^{{}^{\prime }}$, $G_{RoC}^{{}^{\prime }}$ and $G_{time}^{{}^{\prime }}$.