In the paper, we propose an approach for selection a correction parameter for images
damaged by backlighting. We consider the photos containing underexposed areas due to backlit conditions. Such areas are dark and have poorly discernible details. The correction parameter controls the level of amplification of local contrast in shadow tones. Besides, the correction parameter can be considered as a quality estimation factor for such photos. For an automatic selection of the correction parameter, we apply regression by supervised machine learning. We propose new features calculated from the co-occurrence matrix for the training of the regression model. We compare the performance of the following techniques: the least square method, support vector machine, random forest, CART, random forest, two shallow neural networks as well as blending and staking of several models. We apply two-stage approach for the collection of a big dataset for training: initial model is trained on a manually labeled dataset containing about two hundred of photos, after that we use the initial model for searching for photos damaged by backlit in social networks having public API. Such approach allowed to collect about 1000 photos in conjunction with their preliminary quality assessments that were corrected by experts if it was necessary. In addition, we investigate an application of several well-known blind quality metrics for the estimation of photos affected by backlit.