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A fundamentally new approach that accurately estimates the camera response function from comparametric data, i.e., pixel data from two differently exposed images over a common field of view, is presented. It does so by solving for the camera response function from its associated comparametric relation. The approach offers several advantageous features, including having a complexity that is independent of the number of pixel data considered, allowing for the modeling of saturated pixels, enabling an inherently constrained optimization problem to be solved in an unconstrained manner, and the easy incorporation into an existing framework for joint image registration. This is accomplished by approximating the camera response function with a constrained piecewise linear model so that its solution, within the comparametric camera relation, can be obtained. This results in a semiparametric comparametric model, optimally determined from pixel data, which is directly parameterized in terms of the exposure parameter. Subsequently, it is shown how this semiparametric model is used for exposure estimation from captured images. Finally, we incorporate the semiparametric model within an existing and previously published framework for simultaneous and joint spatial and tonal image registration in order to illustrate the developed model's performance.