In this paper, authors have introduced a novel method for illumination invariant face recognition from 2D visual face images called the Vector faces. Theoretical analysis reveals that these new face images are illumination invariant and robust in terms of light shading. At each point of an image, normal component and tangent component are extracted. From every pair of normal and tangent components, a surface normal is computed. After that, normal components of an image are arranged together to form an intermediate matrix. This intermediate matrix is passed through bicubic interpolation for filling up of holes and then that is smoothed by Gaussian kernel to remove spikes, noisy points, and similar impairments. Resultant matrix, thus found called as Vector faces, uncover the prime structure of the face image by considering the relationship between neighboring intensity values. Authors have followed a SURF based feature extraction mechanism for investigating the Vector faces. To validate this method, the experiment will be conducted on Texas3D databases. Moreover, authors will investigate the illumination invariant 3D face images along with a comparison of recognition results for these methods and Vector faces of 2D visual face images.