@article{Article_17,

title = {Apply Tensorial Methods for Detecting and Recovering Facial Shapes},

journal = {Communications in Combinatorics, Cryptography & Computer Science},

volume = {2021},

issue = {2},

issn = { 2783-5456 },

year = {2021},

url = {http://cccs.sgh.ac.ir/Articles/2021/issue 2/2-5-apply_tensorial_methods_for_detecting_and_recovering_facial_shapes-1638186773.pdf},

author = {Ali Reza Shojaeifard and Hamid Reza Yazdani and Mohsen Shahrezaee},

keywords = {Facial shape recovery, Image processing, Statistical face model, Tensorial methods.},

abstract = {This paper proposes a fast 3-D facial shape recovery algorithm from a single image with general, Unknown lighting. To derive the algorithm, we formulate a non-linear least-square problem with two-parameter vectors which are related to personal identity and light conditions. We then Combine the spherical harmonics for the surface normal of a human face with tensor algebra and show that in a certain condition, the dimensionality of the least-square problem can be further reduced to one-tenth of the regular subspace-based model by using tensor decomposition (N-mode SVD), which speeds up the computations. To enhance the shape recovery performance, we have incorporated prior information in updating the parameters. The proposed algorithm takes less than 0.4 s to reconstruct a face in the experiment and shows a significant performance improvement over other reported scheme.}

};