Precision-based regularization comparametric calibration method for imaging system response functions

The radiometric calibration of imaging system response functions (ISRFs) is influenced by noise, the non-uniformity of the system response, and random disturbances. This leads to a lower accuracy in imaging system quantitative applications. In this work, we research a regularized comparametric calibration method focusing on measurement precision. First, we deduce the relationship between comparative radiometric calibration and absolute radiometric calibration of ISRF using the radiation chain of the imaging process, thereby elucidating the comparametric model. Then, based on the variational principle, we build an energy functional model for comparametric calibration in the Sobolev space and optimize the regularization term by the uncertainty of the estimated relative ISRFs. Finally, we verify the regularized comparametric calibration method and compare it with the weighted least squares method. The experimental results show that the regularized comparametric calibration method not only ensures the precision of the estimated relative ISRF curve but also can effectively overcome the ill-posed problem caused by noise and non-uniformity. This method is significant for applications using imaging system radiometric calibration, inverse radiometric measurement, image quantification, and dynamic range extension.