Partial iterates for symmetrizing non-parametric color correction

Mosaic generation is a central tool in various fields ranging way beyond the scope of photogrammetry and requires the radiometry and color of the images to be corrected. Correction can either be done by a global parametric approach (looking for an optimal gain or gamma for each image of the mosaic), or by iteratively correcting image pairs with a non-parametric approach. Such non-parametric approaches allow for much finer correction but are asymmetric, i.e. they require the choice of a source image that will be corrected to match a target image. Thus the result on the whole mosaic will be very dependant on the order in which images are corrected. In this paper, we propose to use partial iterates to symmetrize non-parametric correction in order to solve this problem. Partial iterates formalize what partially applying a bijective function means and we explain how this can be done in both the continuous and discrete domain. This mechanism is applied to a simple non-parametric approach (histogram transfer of the luminance) to show its potential.