Algorithms for face image mutual reconstruction by means of two-dimensional projection methods

In this paper, we consider the problem of mutual reconstruction of face image pairs. We addressed this problem in our previous article, where the proposed solutions were discussed in connection with Heterogeneous Face Recognition and Cross-Modal Multimedia Retrieval problems. Those solutions are based on one-dimensional and two-dimensional Principal Component Analysis performed over two original face images followed by their projection on independent eigenspaces, estimation of a transformation matrix and mutual reconstruction of the face image by means of one-dimensional and two-dimensional Karhunen-Loève Transform.
In this article, we propose new approaches and solutions, which are based solely on the two-dimensional eigenspace projection methods, and two regression models — Multiple Linear Regression and Partial Least Squares regression.
We present the experiments on mutual reconstruction of face images in sketch/photo pairs, in pairs of face images with age-related changes, and in pairs of 2D/3D face images. In order to conduct the experiments, we selected two variants of the proposed approach. First one is based on two-dimensional Principal Component Analysis and Partial Least Squares regression, and the second one is based on two-dimensional Partial Least Squares and Multiple Linear Regression. Both variants showed acceptable performance for practical applications involving the mutual reconstruction of face images. Furthermore, we consider the method to improve the quality of reconstructed face images in the case of mixed datasets. This method involves classification of the dataset by means of two-dimensional Linear Discriminant Analysis and fitting of a separate regression model for each class.
In addition, we show that generally, mutual reconstruction of face images is also achievable in conditions when original images are not a part of training sets of face images.