The structure of the corneal endothelial cells can provide important information about the cornea health status. Particularly, parameters describing cell size and shape are important. However, these parameters are not widely used, because it requires segmentation of the cells from corneal endothelium images. Although several dedicated approaches exist, none of them is faultless. Therefore, this paper proposes a new approach to fully automatic segmentation of corneal endothelium images. The proposed approach combines a neural network which is thought to recognize pixels located at the cell boundaries, with postprocessing of the resulting boundary probability map. The postprocessing includes morphological reconstruction followed by coarse cell segmentation using local thresholding. The resulting cells are next separated from each other via iterative morphological opening. Finally, the region between cell bodies is skeletonized. The proposed method was tested on three publicly available corneal endothelium image datasets. The results were assessed against the ground truths and compared with the results provided by selected state-of-the-art methods. The resulting cell boundaries are well aligned with the ground truths. The mean absolute error of the determined cell number equals 6.78%, while the mean absolute error of cell size is at the level of 5.13%. Cell morphometric parameters were determined with the error of 5.69% for the coefficient of variation of cell side length and 11.64% for cell hexagonality. (C) 2018 Elsevier Ltd. All rights reserved.