  In this paper, a low parameter deep learning framework utilizing the
Non-metric Multi-Dimensional scaling (NMDS) method, is proposed to recover the
3D shape of 2D landmarks on a human face, in a single input image. Hence, NMDS
approach is used for the first time to establish a mapping from a 2D landmark
space to the corresponding 3D shape space. A deep neural network learns the
pairwise dissimilarity among 2D landmarks, used by NMDS approach, whose
objective is to learn the pairwise 3D Euclidean distance of the corresponding
2D landmarks on the input image. This scheme results in a symmetric
dissimilarity matrix, with the rank larger than 2, leading the NMDS approach
toward appropriately recovering the 3D shape of corresponding 2D landmarks. In
the case of posed images and complex image formation processes like perspective
projection which causes occlusion in the input image, we consider an
autoencoder component in the proposed framework, as an occlusion removal part,
which turns different input views of the human face into a profile view. The
results of a performance evaluation using different synthetic and real-world
human face datasets, including Besel Face Model (BFM), CelebA, CoMA - FLAME,
and CASIA-3D, indicates the comparable performance of the proposed framework,
despite its small number of training parameters, with the related
state-of-the-art and powerful 3D reconstruction methods from the literature, in
terms of efficiency and accuracy.
