The paper deals with the construction of interpretable machine learning models. The approximation problem is solved for a set of shapes on a contour image. Assumptions that the shapes are second-order curves are introduced. When approximating the shapes, information about the type, location, and shape of curves as well as about the set of their possible transformations is used. Such information is called expert information, and the machine learning method based on expert information is called expert-augmented learning. It is assumed that the set of shapes is approximated by the set of local models. Each local model based on expert information approximates one shape on the contour image. To construct the models, it is proposed to map second-order curves into a feature space in which each local model is linear. Thus, second-order curves are approximated by a set of linear models. In a computational experiment, the problem of approximating an iris on a contour image is considered.