## 4 Discussion  
The integration of the proposed pixel-weight map, combined with morphological operations, allows common semantic segmentation networks to infer instance-level information during runtime without additional computational costs. Designed to support AR rehabilitation applications, this approach achieves real-time CPU-based semantic segmentation inference of multiple hands while preserving instance information. The method was validated on two FCN architectures, ResNet and U-Net, using the EgoHands dataset. Although U-Net is recognized for its ability to retain positional precision, ResNet outperformed it, likely due to its network topology, specifically the modern skip connections and higher parameter count. [PERSON] et al. [53] demonstrated that residual connections contribute to convexifying the search space, which significantly enhances training by producing smoother, more optimizable surfaces. This effect helps explain the performance differences between U-Net and ResNet, particularly addressing the convergence issues observed with U-Net (Table 1). The original ResNet architecture was further optimized by tuning various hyperparameters. The optimal results (\(IoU=0.804\); \(precision=0.914\); \(recall=0.872\); \(CCC=0.839\)) were obtained by employing a dropout rate of 0.3, integrating the PReLU activation function, utilizing the FL with \(\alpha=0.5\) and \(\gamma=1.1\), and employing a monotonically decreasing cosine scheduler. The hyperparameters tested aim to enhance specific aspects of training or the model itself that have been deemed suboptimal. Based on the conducted tests and obtained results, the model's performance limit hovers around 0.8 IoU, and consistently surpassing this threshold may require significantly increasing the model's complexity. This can be achieved by adding more layers or increasing feature channels per layer, but constraints imposed by available GPU memory necessitate a more efficient approach. This was finally achieved by using PReLUs, that very efficiently increase model complexity. Introducing FL then allowed tuning the model for this specific application by adjusting precision and recall, which significantly enhanced the preservation of instance-level information (Table 4). Significant fluctuations appear in the validation results. These instabilities were mitigated by replacing the constant learning rate with a learning rate scheduler, which effectively guided the model towards convergence by progressively reducing the learning rate (Figure 6). To provide context for the performance of the proposed model, Table 6 compares its results with those achieved by other authors using the EgoHands dataset [39]. [PERSON] et al. [39] reported an IoU of 0.556 for hand detection and segmentation, employing a sliding-window-based CNN approach. [PERSON] and [PERSON] [54] utilized RefineNet for hand segmentation, achieving IoU, precision, and recall scores of 0.814, 0.879, and 0.919, respectively. [PERSON] et al. [55] proposed a method leveraging an RNN for hand segmentation, reporting IoU, precision, and recall values of 0.873, 0.935, and 0.924. Similarly, [PERSON] et al. [56] presented a video-based hand segmentation technique using optical flow, achieving an IoU of 0.872. [PERSON] et al. [57] reported an IoU of 0.466. [PERSON] et al. [58] achieved IoU, precision, and recall values of 0.902, 0.954, and 0.940, respectively. Finally, [PERSON] et al. [59], using RefineNet, reported an IoU of 0.824. Regarding processing efficiency, [PERSON] et al. [56] reported a latency of 20.28 ms (equivalent to 49 FPS) using a single NVIDIA P100 GPU. [PERSON] et al. [58] achieved 200 FPS on an RTX 2080 Ti GPU. [PERSON] et al. [59] recorded a processing time of 50.5 ms on a GeForce RTX 2080 Ti, translating to 19.8 FPS. [PERSON] et al. [60] achieved 65.4 FPS on an NVIDIA GeForce GTX 1080 Ti GPU. Although the proposed model falls behind some state-of-the-art methods in terms of performance, it successfully meets its primary objective of real-time performance.