## 3 HAFNet and HAFNetE  
In this section, we introduce HAFNetE, an efficient hybrid attention-aware fusion network for building extraction, starting from its predecessor HAFNet or Hybrid Attention-aware Fusion Network. HAFNet is a multi-modal building extraction segmentation network that utilizes cross-modal and individual features to perform building footprint extraction, and it accepts HRI RGB images and LiDAR data as its inputs. The overall architecture is comprised of three streams: RGB, DSM, and cross-modal. All the streams are built as parallel SegNets [26], where the encoder part is characterized by a VGG-16 structure. The RGB and DSM streams are designed to learn individual modal features. These features are then fused together after each set of convolutional operations with an Attention-Aware Multi-modal Fusion Block (Att-MFBlock) in the cross-modal stream. The extracted features from each stream are decoded in their respective decoder stream and finally combined at the decision stage using again an Attention-Aware Multi-modal Fusion Block to produce the final segmented output. By using both individual and cross-modal streams, it is possible to learn more discriminative features and, therefore, achieve a comprehensive building extraction result. Starting from this existing scheme, HAFNetE preserves the three-stream network concept but utilizes both a completely different single stream architecture and encoder structure. The model architecture is shown in Figure 2.  
The network is comprised of three subnetworks (streams): the RGB stream, the DSM stream, and the cross-modal stream. RGB HRI images and LiDAR-derived DSM data are fed as input to the model where features are extracted, respectively, by the RGB stream encoder and the DSM stream encoder. The extracted features are then combined in the cross-modal stream encoder by using the previously discussed Attention-aware multi-fusion block. The cross-modal specific stream is added to combine different modalities at an early stage and, therefore, to learn more discriminative cross-modal features [27]. After the decoding phase, predictions coming from the three streams are fused using the Att-MFBlock [8] to provide a comprehensive building extraction result. Unlike the previous HAFNet model, whose architecture was based on three parallel SegNet-like streams using VGG16-style encoders in each of them, HAFNetE introduces modifications both at the encoder level and at the single stream level. VGG-16 encoders are substituted with EfficientNet encoders. This family of models is specifically designed for good encoding performance even with limited available resources. This translates to simple networks with fewer parameters. Small models yield multiple advantages: faster training, shorter inference times, and bearable memory footprint on the system where the model is deployed. Multiple networks characterized by these features exist (MobileNet, MobileNetV2, etc. ); however, an EfficientNet-B0-type encoder was selected across the candidates because it offers a good compromise in the performance/computational cost trade-off. As a matter  
Figure 2: Scheme of the HAFNetE network. of fact, by reducing the number of parameters in the model, performance is likely to decrease. However, EfficientNet, by scaling the number of parameters according to the Compounding Scaling method [16], attains high performances with approximately 11\(\times\) fewer parameters than classical models, such as ResNet-50 [28]. An efficiency comparison between EfficientNet models and classical models is reported in Table 1.  
At the individual stream level, the SegNet structure is substituted with a U-Net network [31]. U-Net has a similar architecture to the previously utilized SegNet and offers a suitable alternative to it, thanks to its effective feature re-localization capability. The conceptually simple architecture of U-Net makes it easy and elegant to implement.