Algorithm 2 The learning process of SASAPD

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 $G_{Dice}^{{}^{\prime }}$, $G_{Recall}^{{}^{\prime }}$, $G_{Precision}^{{}^{\prime }}$ and $G_{FPS}^{{}^{\prime }}$

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$i=1$; $t\le 6$; $i++$ do

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

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

Compute loss function ${\mathcal{L}}_l$ (Equation (7))

Each instance is assigned to the pyramid level which has the minimal loss ${\mathcal{L}}_l$

Train SASAPD by optimizing loss $\mathcal{L}$ (Equation (10)) where $w_l=1$, and update the weights and parameters;

end for

end for

for $i=7$; $i\le E$; $i++$ do

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

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

Compute loss function ${\mathcal{L}}_l$ (Equation (7))

Train SASAPD by optimizing loss $\mathcal{L}$ (Equation (10)), and update the weights and parameters;

end for

end for

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

Compute the performance results $G_{Dice}^{{}^{\prime }}$ (Equation (14)), $G_{Recall}^{{}^{\prime }}$ (Equation (17)), $G_{Precision}^{{}^{\prime }}$ (Equation (17)) and running  time $G_{FPS}^{{}^{\prime }}$

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