*3.3. Contribution of Multiple-Order Feature*

To illustrate the contribution of multiple-order features to promote performance, we compare the AlexNet and ResNet, which are the backbone in SiamRPN and SiamRPN++, respectively, with the backbone proposed in this paper. The results are listed in Table 2, embedding the above-mentioned backbones in our framework and discussing the percentage of the added second-order information. By comparing the first-order features, it can be seen that as the depth increases, the network feature description capability is improved and ResNet50 achieved better results than AlexNet with a 0.08 and 0.04 improvement in precision and success rate, respectively. With the injection of second-order information, the performance of the network increases significantly. The framework with 30% and 50% second-order features obtained the highest precision of 0.979 and 0.980, an improvement of 0.020 and 0.021 compared to the first-order Resnet50. The multi-order features benefit the localization success rate, which was improved by 0.11 (*p* = 10%), 0.21 (*p* = 30%), 0.19 (*p* = 50%), and 0.19 (*p* = 100%), respectively, compared with the first-order backbone ResNet50. Considering the processing speed and centering error, *p* = 30% is used in practical applications.

**Table 2.** Ablation studies on the backbone of M-O SiamRPN with weight adaptive joint multiple intersection over union loss function.


### *3.4. Contribution of Weight Adaptive Joint MIoU Loss Function*

The uniform metric Average Precision (AP) is chosen for performance measurement in order to demonstrate in detail the role of weight adaption and multiple intersection over union. AP is the area under the curve of precision versus recall, which is a widely accepted criterion for target detection tasks. We set different *IoU* thresholds, i.e., *IoU* = {0.5, 0.6, 0.7, 0.8, 0.9} and used *IoU*, *DIoU*, and *GIoU* as comparisons. The results are reported in Table 3. *L*MIoU with weight adaptive gained the highest AP and *L*MIoU achieved the second-best

results for all different thresholds of IoU. In addition, *L*MIoU with weight adaptive showed the most significant improvement under the harsher conditions with higher thresholds.


**Table 3.** Quantitative comparison of M-O SiamRPN using *LIoU*, *LCIoU*, *LDIoU*, *LGIoU*, *L*MIoU.
