In the image deformation process of the moving least squares based algorithm, the coefficient matrix of the solved linear equations is irreversible and unstable. In this study, we apply a constraint term to the coefficient matrix to obtain the exact solution and avoid the formation of ill-conditioned equations by introducing Tikhonov regularization and using the L-curve method to solve the regular parameters. To overcome the limitation of a large number of manually localized feature points and an insufficient number of feature points in the process of image deformation, the Dlib library is employed to automatically extract 68 feature points covering facial features and contours. Simulation results demonstrate that, compared to the original algorithm, the proposed algorithm can produce clear and accurate image deformation.