Point positioning and counting network: A deep learning-based method for automatic axon counting

Accurate quantification of axon density is pivotal in optic nerve-related studies, as axonal degeneration is a hallmark of numerous neurological disorders. This study introduces the Point Positioning and Counting Network (PPCNet), a novel point-annotation-based deep learning framework that overcomes the limitations of manual counting and existing automated tools. PPCNet integrates a VGG16 backbone with multiscale feature extraction and lateral fusion to generate high-resolution feature maps. A dual-branch architecture regresses spatial coordinates and classifies candidate points, enabling axonal-center localization and confidence scoring. An optimized Hungarian algorithm, incorporating Euclidean distance and confidence metrics, ensures one-to-one correspondence between predicted candidates and ground-truth points. The model is trained end-to-end using a hybrid loss combining mean squared error and cross-entropy. Evaluated on a goat optic nerve semi-thin section dataset, PPCNet significantly outperformed current state-of-the-art methods (Axonet 2.0 and AxonDeepSeg). In the test set, mean ± SD axon counts were 901.6 ± 225.6 for manual counting, 890.2 ± 227.3 for PPCNet, 918.8 ± 297.9 for Axonet2.0, and 1045 ± 275 for AxonDeepSeg. Linear regression analysis demonstrated superior agreement with manual counts (R² = 0.939), surpassing Axonet 2.0 (R² = 0.8612) and AxonDeepSeg (R² = 0.9142). PPCNet also yielded a lower mean absolute error (MAE = 45.93) than those of the comparative models (97.50 and 146.33). Bland-Altman analysis confirmed narrower limits of agreement (-99.23 to 121.90) and reduced systematic bias. Confidence-interval analysis further supported PPCNet's reliability, showing substantial overlap with manual counts. In conclusion, PPCNet delivers sub-pixel-accurate automated axon quantification for optic nerve research, replacing tedious manual counting and traditional segmentation-based methods.