Deep | Cheeks 2

where σ denotes the sigmoid activation and [;] denotes channel‑wise concatenation. The fused feature is:

with “⊙” being element‑wise multiplication. The attention maps are learned end‑to‑end, encouraging the network to rely on the high‑resolution stream for texture‑rich regions (e.g., pores) and on the low‑resolution stream for ambiguous, occluded zones. The fused features are progressively up‑sampled using transposed convolutions and concatenated with the corresponding AGSC outputs (a UNet‑like skip). The final segmentation layer applies a 1 × 1 convolution followed by a sigmoid to produce M̂ . Deep Cheeks 2

[ \mathbfF^(\ell) = \mathbfA^(\ell) \odot \mathbfF_G^(\ell) + (1-\mathbfA^(\ell)) \odot \mathbfF_D^(\ell), ] where σ denotes the sigmoid activation and [;]

[ \mathbfA^(\ell) = \sigma\big( \textConv_1\times1\big([ \mathbfF_G^(\ell); \mathbfF_D^(\ell) ]\big) \big), ] For each level ℓ ∈ 1,2,3, we compute

| # | Contribution | Impact | |---|--------------|--------| | 1 | Dual‑stream multi‑scale architecture with AGSC | Improves robustness to pose/occlusion (↑ 8.7 % IoU) | | 2 | Cheek‑specific Dice loss + Perceptual Aesthetic loss | Aligns predictions with human perception (↑ 12.4 % correlation) | | 3 | CheekWILD‑2 dataset (45 k images, 23 k masks, 22 k scores) | Provides the largest public resource for cheek‑centric research | | 4 | Open‑source implementation (PyTorch, GPL‑3) | Facilitates reproducibility and downstream applications |

Both streams are frozen for the first 5 epochs (to retain generic facial priors) and then fine‑tuned jointly. For each level ℓ ∈ 1,2,3, we compute an attention map A ⁽ℓ⁾ that modulates the contribution of the two streams: