This paper proposes a method of automatic facial reconstruction from a facial image partially corrupted by noise or occlusion. There are two key features of this method; the one is the automatic extraction of the correspondences between the corrupted input face and reference face without additional manual tasks; the other is the reconstruction of the complete facial information from corrupted facial information based on these correspondences. In this paper, we propose a non-iterative approach that can match multiple feature points in order to obtain the correspondences between the input image and the reference face. Furthermore, shape and texture of the whole face are reconstructed by SVDD (Support Vector Data Description) from the partial correspondences obtained by matching. The experimental results of facial image reconstructions show that the proposed SVDD-based reconstruction method gives smaller reconstruction errors for a facial image corrupted by Gaussian noise and occlusion than the existing linear projection reconstruction method with a regulation factor. The proposed method also reduces the mean intensity error per pixel by an average of 35 %, especially in the reconstruction of a facial image corrupted by Gaussian noise.