Symbols	Description
$ℝ$	real number space
$X$	input tensor
$A_{mask}^k$	attention mask map of the kth stage
$S_{side}^{\mathrm{k}}$	side output of the kth stage
$\mathsf{\Gamma }$	tensor concatenation operation
$\sigma$	Sigmoid activation function
$U{p}_{H\times W}$	upsampling to the input image size $H\times W$
$S_{fuse}$	Output prediction map after multi-stage fusion, i.e., the final prediction result map
$\otimes$	convolution operation
$\oplus$	element-wise addition operation
$\odot$	element-wise multiplication operation
P	the predicted segmentation result
G	the ground truth binary label
N	the total number of pixels in a crack image
$\alpha$	predicting the error weights
$\beta$	predicting the correct weights
$\left|Y^{+}\right|$	the number of positive samples in a crack image
$\left|Y^{-}\right|$	the number of negative samples in a crack image
$\lambda$	the loss ratio to balance the positive and negative samples
$L_{BWCE}(W)$	the balanced weighted cross-entropy loss
${\alpha }_1$	false positive weights
${\beta }_1$	false negative weights
$L_{Tversky}(W)$	Tversky loss
$L(W)$	$L_{BWCE}(W)$ and $L_{Tversky}(W)$ weighted losses
$\eta$	the weight of loss $L_{BWCE}(W)$
$L_{total}(W)$	The final total loss function
$w_{side}^k$	the loss weight of the kth stage
$w_{fuse}$	the loss weight of the final fusion stage
${\displaystyle \sum }$	Summation