LD-IoU: A Novel Lorentzian Distance-based Localization Loss for Enhanced Bounding-box Regression with Faster Convergence in YOLOv8-based Knee Osteoarthritis Detection

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Knee osteoarthritis (KOA) is one of the most prevalent musculoskeletal disorders, making accurate and automated knee joint detection essential for computer-aided diagnosis.Although YOLO-based object detectors have demonstrated promising performance, most existing approaches rely on the conventional Intersection over Union (IoU) localization loss, which primarily measures geometric overlap between predicted and ground-truth bounding boxes.Consequently, it provides limited optimization when the bounding boxes are partially overlapped or spatially displaced, leading to less accurate localization, higher Box Loss, and slower convergence during training.To overcome these limitations, this study proposes a Lorentzian Distance Intersection over Union (LD-IoU) localization loss integrated into the YOLOv8 framework.By incorporating the Lorentzian distance into the conventional IoU formulation, the proposed loss provides a more robust representation of spatial discrepancy, enabling more accurate bounding-box regression.Experiments conducted on the OAI dataset demonstrate that the proposed framework consistently outperforms the baseline YOLOv8 and existing IoU-based localization losses.The proposed LD-IoU-YOLOv8 achieved 99.1% precision, 94.2% mAP@0.5:0.95,99.6% mAP@0.5, and 98.8% recall, while reducing the Box Loss from 0.291 to 0.093, corresponding to an approximately 68% relative reduction.Furthermore, the proposed localization loss demonstrated faster convergence than the conventional IoU loss, achieving high mAP@0.5 in fewer training epochs and providing more efficient optimization.These findings indicate that the proposed LD-IoU is a promising localization loss that can be readily integrated into modern object detection frameworks for reliable medical image analysis and real-time computer-aided diagnosis.