# Dual-level weighted cross-entropy loss function and multi-object region segmentation network evaluation for dynamic knee joint X-ray radiography based on a novel scoring criterion

## TL;DR

This paper introduces a new method for accurately segmenting key regions in dynamic knee X-rays using a novel loss function and evaluation metrics to improve diagnostic efficiency.

## Contribution

A dual-level weighted cross-entropy loss function and a novel scoring criterion for multi-object region segmentation in dynamic knee X-ray imaging.

## Key findings

- The proposed loss function improves segmentation performance compared to traditional methods.
- The optimal model achieved a mean IoU of 0.8921 and mean Dice of 0.9373 across key knee regions.
- The model shows high potential for enhancing quantitative motion analysis of the knee joint.

## Abstract

The knee joint is one of the largest and most complex joints in the human body, serving as the main support point for body weight, which allows the legs to bend and extend. Dynamic knee joint X-ray radiography provides the necessary imaging conditions for motion-function assessment of these key multi-object regions, including the patella, femur, tibia, and patellar tendon. An accurate, automatic segmentation model will not only assist radiologists and physicians in the diagnostic process but also further alleviate the significant labor they must invest. Meanwhile, the network architecture and the loss function are the primary factors influencing the segmentation model. Therefore, an optimal multi-object region segmentation model should be proposed for dynamic knee joint X-ray radiography to segment the patella, femur, tibia, and patellar tendon.

First, a dual-level weighted cross-entropy loss function based on multi-object region areas for dynamic knee joint X-ray radiography is proposed to balance losses across the patella, femur, tibia, and patellar tendon. Second, two comprehensive evaluation metrics, constructed based on the characteristics of existing evaluation metrics, are developed to reduce the dimensionality of evaluation metrics and enable comprehensive evaluation of multi-object region segmentation models. Third, a novel scoring criterion is proposed based on the two constructed comprehensive evaluation metrics to determine the optimal multi-object region segmentation model, with an appropriate ratio for each loss function in the mixed loss function.

Compared to the traditional weighted cross-entropy loss function, the proposed dual-level weighted cross-entropy loss function improves the segmentation model's performance. Meanwhile, the multi-object region segmentation model with the optimal combination of network (DeepLabV3+_R50c) and mixed loss function (τ1*LCE2 + τ2*LDICE + τ3*LBD, τ1:τ2:τ3 = 0.50:0.25:0.25) is determined based on the proposed two comprehensive evaluation metrics and scoring criterion, achieves a mean IoU of 0.8921, a mean Dice of 0.9373, a mean Precision of 0.9316, a mean Recall of 0.9490, a mean HD95 of 2.9145, and a mean ASSD of 1.0309, respectively.

The proposed multi-object region segmentation model has the potential to greatly enhance the accuracy and effectiveness of quantitative analysis of the knee joint motion.