Deriving a Compact Analytical Model for Camera Response Functions with Application to Chartless Radiometric Calibration

Radiometric calibration (RC) is an essential pre-processing step to correct the non-linearity of camera output images. The chartless RC is a novel RC approach that does not need a color checker to do the calibration and attracts intensive research interests. A challenging issue in the chartless RC is how to reveal the parameters of the camera response function (CRF) more effectively from limited camera images. In this work, we take a general strategy for this issue by deriving more compact parametric CRF models. Firstly, a novel exponential exponent gamma curve (EEGC) model is proposed as a more compact superset to characterize the functional space of CRF. Then the general criteria for monotonic EEGCs (MEEGC) are derived. Fi-nally, the analytical solution to low-order MEEGCs (AMEEGC) is proposed to get some nice constraint-free low-order analytical CRF models. The curve fitting experiments showed that the proposed models gave a more compact representation for real-world CRFs when compared to some existing models. We also demonstrated how to improve the efficiency of chartless RC algorithms with the 2nd-AMEEGC model by revisiting Taka-matsu's noise-based method, and the results proved our method's superiority.