大气对红外辐射传输的影响引起的红外成像灰度变化, 是红外目标跟踪应用需要应对的问题。对红外成像灰度变化规律进行李群建模, 对设计高效、鲁棒的目标跟踪算法具有重要意义。首先分析了红外辐射传输模型, 并结合红外成像机理, 得到红外成像灰度变化模型。进一步从理论上证明了大气影响下红外成像灰度变化规律符合李群结构, 提出了红外图像灰度动态变化的一种非欧数学表征。最后根据红外成像灰度变化模型对不同环境下采集到的外场实验数据进行拟合, 回归分析结果表明了该模型的准确性, 进而说明了对红外成像灰度变化规律进行李群表达的合理性。

The infrared imaging grayscale variation caused by the influence of atmosphere on infrared radiation transmission is a problem that infrared target tracking application needs to cope with. The law of infrared imaging grayscale variation in Lie group was modeled, which was important to design an efficient and robust target tracking algorithm. Firstly the infrared radiation transmission model was analyzed, and then the brightness model of infrared imaging was derived by considering the mechanism of infrared imaging. Furthermore, it was theoretically proved that the infrared imaging grayscale variation caused by the atmosphere obeyed the Lie group structure, and a non-Euclidean mathematical representation of the infrared imaging grayscale variation was proposed. Finally, according to the infrared imaging grayscale variation model, the field experimental data collected under different environments were fitted. The regression analysis results demonstrate the correctness of the model, which validates the rationality of the Lie group representation of the infrared imaging grayscale variation.