Nowadays, means of preventive management in various spheres of human life are actively developing. The task of automated screening is to detect hidden problems at an early stage without human intervention, while the cost of responding to them is low. Visual inspection is often used to perform a screening task. Deep artificial neural networks are especially popular in image processing. One of the main problems when working with them is the need for a large amount of well-labeled data for training. In automated screening systems, available neural network approaches have limitations on the reliability of predictions due to the lack of accurately marked training data, as obtaining quality markup from professionals is very expensive, and sometimes not possible in principle. Therefore, there is a contradiction between increasing the requirements for the precision of predictions of neural network models without increasing the time spent on the one hand, and the need to reduce the cost of obtaining the markup of educational data. In this paper, we propose the parametric model of the segmentation dataset, which can be used to generate training data for model selection and benchmarking; and the multi-task learning method for training and inference of deep neural networks for semantic segmentation. Based on the proposed method, we develop a semi-supervised approach for segmentation of salient regions for classification task. The main advantage of the proposed method is that it uses semantically-similar general tasks, that have better labeling than original one, what allows users to reduce the cost of the labeling process. We propose to use classification task as a more general to the problem of semantic segmentation. As semantic segmentation aims to classify each pixel in the input image, classification aims to assign a class to all of the pixels in the input image. We evaluate our methods using the proposed dataset model, observing the Dice score improvement by seventeen percent. Additionally, we evaluate the robustness of the proposed method to different amount of the noise in labels and observe consistent improvement over baseline version.