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. 2025 Sep 4;25(17):5495. doi: 10.3390/s25175495
Algorithm 1: Enhanced Multi-Modal Feature Fusion at scale  s (Equations (2)–(15))
Input:
 RGB image I∈RH×W×3
 Sparse depth map D∈RH×W×1
 Pre-processed dense depth (from BP) Dspre∈RH×W
 Camera intrinsics K∈R3×3
Output:
 Fused feature map Fs∈RH×W×C
Notion:
 ⊕: channel concatenation;
 ⊙: channel-wise multiplication;
 GAP: global average pooling;
 δ(⋅): ReLU;
 σ(⋅): Sigmoid
 Dspre: dense depth pre−processed via Bilateral Propagation
Procedure:
1: Step 1: Back-projection to 3D
2:  Construct sparse point cloud P=BackProjectS,K.
3: Step 2: 2D feature encoding
4:  Form 2D input X=[I⊕Dspre]
5:  F2D=U−NetX
6: Step 3: Dual-branch PointNet++-S
7:  For each branch b∈local,context:
8:   For each SA layer with config (nl,rl,kl):
9:    glb←PointNetSA(P;nl,rl,kl)
10:   End for
11:  End for
12:  Aggregate to multi-scale 3D feature F3D=ConcatFlocal2,Fcontext2
13: Step 4: Channel recalibration on 3D
14:  z=GAPF3D;
15:  s=σW2⋅δW1z;
16:  G3D=s⊙F3D.
17: Step 5: Spatial broadcasting of 3D feature
18:  G3D~=BroadcastG3D→H×W
19: Step 6: CAFFM: channel-attention fusion
20:  Fin=ConcatF2D,G3D~;
21:  z=GAPFin;
22:  α=σW2⋅δW1z);
23:  Fs=α⊙Fin.
24: return Fs.