Original Research Article
Article volume = 2021 and issue = 2
Article publication Date: November, 1, 2021
You can download PDF file of the article here: Download
Visited 65 times and downloaded 14 times
Apply Tensorial Methods for Detecting and Recovering Facial Shapes
Ali Reza Shojaeifard(a), Hamid Reza Yazdani(b), Mohsen Shahrezaee(c)
(a)Imam Hossein Comprehensive University, Department of Mathematics and Statistics Tehran, Iran.
(b)Imam Hossein Comprehensive University, Department of Mathematics and Statistics Tehran, Iran.
(c)Imam Hossein Comprehensive University, Faculty of Defense and Engineering, Tehran, Iran.
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.
Facial shape recovery, Image processing, Statistical face model, Tensorial methods.
-  L. Qi, The Spectral Theory of Tensors, arXiv (2012): 1201.3424v1. 1, 2, 2.7
-  A. Rovi, Analysis of 222 Tensors, MAI mathematics: Master thesis (2010), Linkopings University. 2, 2.1, 2.5
-  Q. Song, H. Ge, J. Caverlee and X. Hu, Tensor Completion Algorithms in Big Data Analytics, ACM Trans- actions onKnowledge Discovery from Data (TKDD), 6 (13) (2019), 1–48. 1, 2.5, 2.8, 2.9
-  M. Lee, C-H. Choi, Fast facial shape recovery from a single image with general, unknown lighting by using tensor representation,Pattern Recognition, Elsevier, 44 (2011),1487–1496. 1
-  M. Lee, C-H. Choi, A robust real-time algorithm for facial shape recovery from a single image containing cast shadow undergeneral, unknown lighting, Pattern Recognition, Elsevier, 46 (2013), 38–44. 1, 2.6
-  M. Lee, C-H. Choi, Real-time facial shape recovery from a single image under general, unknown lighting by rank relaxation,Computer Vision and Image Understanding, Elsevier, 120 (2014), 59–69. 1
Cite this article as:
- Ali Reza Shojaeifard, Hamid Reza Yazdani, Mohsen Shahrezaee, Apply Tensorial Methods for Detecting and Recovering Facial Shapes, Communications in Combinatorics, Cryptography & Computer Science, 2021(2), PP.129–135, 2021
- Export citation to BibTeX