In this paper, the robustness of tessellation images segmentation using Convolutional Neural Network (CNN) is presented. Particularly, this paper aims to study the effect of the quality and number of the images used for training on the robustness of the edge segmentation and completion. Three kinds of image deterioration are considered: the absence of a part of the tessellation, the discontinuity of the edges constituting the tessellation and the presence of a background noise. Five CNNs are trained with several kinds of deteriorated images and the trained models are then compared according to the results obtained with four classes of images.