A morphable model for the synthesis of 3D faces
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
Multidimensional binary search trees used for associative searching
Communications of the ACM
From Few to Many: Illumination Cone Models for Face Recognition under Variable Lighting and Pose
IEEE Transactions on Pattern Analysis and Machine Intelligence
Lambertian Reflectance and Linear Subspaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Face Recognition Based on Fitting a 3D Morphable Model
IEEE Transactions on Pattern Analysis and Machine Intelligence
Overview of the Face Recognition Grand Challenge
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Shape from Shading: A Well-Posed Problem?
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Face transfer with multilinear models
ACM SIGGRAPH 2005 Papers
A Bilinear Illumination Model for Robust Face Recognition
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
IEEE Transactions on Pattern Analysis and Machine Intelligence
Using Bilinear Models for View-invariant Action and Identity Recognition
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2
3D and Infrared Face Reconstruction from RGB data using Canonical Correlation Analysis
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 01
Estimating Cast Shadows using SFS and Class-based Surface Completion
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 04
Recovering Facial Shape Using a Statistical Model of Surface Normal Direction
IEEE Transactions on Pattern Analysis and Machine Intelligence
Journal of Cognitive Neuroscience
Robust Estimation of Albedo for Illumination-Invariant Matching and Shape Recovery
IEEE Transactions on Pattern Analysis and Machine Intelligence
Non-Lambertian Reflectance Modeling and Shape Recovery of Faces Using Tensor Splines
IEEE Transactions on Pattern Analysis and Machine Intelligence
3D Face Reconstruction from a Single Image Using a Single Reference Face Shape
IEEE Transactions on Pattern Analysis and Machine Intelligence
Adaptive Noise Smoothing Filter for Images with Signal-Dependent Noise
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Statistical shape from shading under general light conditions can be thought of as a parameter-fitting problem to a bilinear model. Here, the parameters are personal attributes and light conditions. Parameters of a bilinear model are usually estimated using the alternating least squares method with a computational complexity of O((n"s+n"@f)^2n"p), where n"s,n"@f, and n"p are the dimensions of the light conditions, personal attributes, and face image features, respectively, for each iteration. In this paper, we propose an alternative algorithm with a computational complexity of O(n"sn"@f) for each iteration. Only the initial step requires a computational complexity of O(n"sn"@fn"p). This can be accomplished by reformulating the problem to that of a linear least squares problem, with a search space limited to a set of rank-one matrices. The rank-one condition is relaxed to obtain a possibly full-rank matrix. The algorithm then finds the best rank-one approximation of that matrix. By the Eckart-Young theorem, the best approximation is the outer product of the left and right singular vectors corresponding to the largest singular value. Since only this pair of singular vectors is needed, it is better to use the power iteration method, which has a computational complexity of O(n"sn"@f) for each iteration, than calculating the full singular value decomposition. The proposed method provides accurate reconstruction results and takes approximately 45ms on a PC, which is adequate for real-time applications.