Quantigraphic Imaging: Estimating the camera response and exposures from differently exposed images

Multiple differently exposed pictures of the same subject matter arise naturally whenever a video camera having automatic exposure captures multiple frames of video with the same subject matter appearing in regions of overlap between at least some of the successive video frames. Almost all cameras have some kind of automatic exposure feature. Generally automatic exposure is center weighted, so that when a light object falls in the center of the frame the exposure is automatically decreased, whereas the exposure is automatically increased when the camera swings around to point at a darker object. In this paper, it is assumed that the spatial (e.g. projective) coordinate transformation between successive frames of the sequence is known (or equivalently that it is the identity), and the contribution of the paper is an efficient way to estimate the tonal relationship between successive frames of the sequence. In particular methods are proposed to simultaneously estimate the unknown camera response function, as well as the set of unknown relative exposure changes among images, up to a single unknown scalar constant. The method comprises a succession of guesses each of which is a refinement of the previous. The first guess is often sufficient, so that no initial solution needs to be provided by the user. Each subsequent guess is a least squares solution so that no computationally expensive optimization is required. Since the method makes use of all the data, it is extremely immune to noise. The method is tested against state-of-the art laboratory measurement instruments to confirm the accuracy of the results.