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In this paper, a low parameter deep learning framework utilizing theNon-metric Multi-Dimensional scaling (NMDS) method, is proposed to recover the3D shape of 2D landmarks on a human face, in a single input image. Hence, NMDSapproach is used for the first time to establish a mapping from a 2D landmarkspace to the corresponding 3D shape space. A deep neural network learns thepairwise dissimilarity among 2D landmarks, used by NMDS approach, whoseobjective is to learn the pairwise 3D Euclidean distance of the corresponding2D landmarks on the input image. This scheme results in a symmetricdissimilarity matrix, with the rank larger than 2, leading the NMDS approachtoward appropriately recovering the 3D shape of corresponding 2D landmarks. Inthe case of posed images and complex image formation processes like perspectiveprojection which causes occlusion in the input image, we consider anautoencoder component in the proposed framework, as an occlusion removal part,which turns different input views of the human face into a profile view. Theresults of a performance evaluation using different synthetic and real-worldhuman 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 relatedstate-of-the-art and powerful 3D reconstruction methods from the literature, interms of efficiency and accuracy.

Deep-MDS Framework for Recovering the 3D Shape of 2D Landmarks from a Single Image