Generative models of shapes for 2D boundaries have applications in object detection and inference from 2D images.We investigate how to learn this generative model from a training set of shape functions.The quality of the correspondence establishment significantly affects the quality of the shape models.A state-of-the-art approach for establishing correspondence is to define a regularized empirical risk for generative models, and by minimizing this risk, the correspondence between shapes is determined.The choice of the regularization parameters of the risk has a significant effect on the quality of the correspondence.In this article, by estimating the effective dimension of the principal component analysis model and using the entropy estimation of eigenvalues algorithm, we consider the effect of error variance in determining the regularization parameter for correspondence establishment.Using Our proposed algorithm leads to the following improvements in the correspondence establishment for shape models of the objects that exist in JSRT chest radiography images: 0.5 mm specificity improvement, and training time reduction from 600 seconds to 300 seconds, compared to the minimum description length method.Moreover, the specificity of the correspondence established by our proposed method is better than that established by experts' manual landmarks in terms of specificity.