Height and gradient from shading
International Journal of Computer Vision
Estimation of Illuminant Direction, Albedo, and Shape from Shading
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
IEEE Transactions on Pattern Analysis and Machine Intelligence
Symmetric Shape-from-Shading Using Self-ratio Image
International Journal of Computer Vision
Lambertian Reflectance and Linear Subspaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multilinear Analysis of Image Ensembles: TensorFaces
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
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
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Recovering Facial Shape Using a Statistical Model of Surface Normal Direction
IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust Estimation of Albedo for Illumination-Invariant Matching and Shape Recovery
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient 3D reconstruction for face recognition
Pattern Recognition
3D Face Reconstruction from a Single Image Using a Single Reference Face Shape
IEEE Transactions on Pattern Analysis and Machine Intelligence
Automatic 3D reconstruction for face recognition
FGR' 04 Proceedings of the Sixth IEEE international conference on Automatic face and gesture recognition
Adaptive Noise Smoothing Filter for Images with Signal-Dependent Noise
IEEE Transactions on Pattern Analysis and Machine Intelligence
Molding face shapes by example
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Shape from recognition: a novel approach for 3-D face shape recovery
IEEE Transactions on Image Processing
A Coupled Statistical Model for Face Shape Recovery From Brightness Images
IEEE Transactions on Image Processing
Computer Vision and Image Understanding
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It is difficult to find a non-iterative solution for statistical shape from shading (SFS) for a single image containing cast shadow under unknown, arbitrary light conditions. This is because it is not trivial to find a mapping from a convex cone in the image space to a point in the depth space. To find a non-iterative solution for the statistical SFS, which has not been done yet to our knowledge, we show that it is possible to approximate a cone of images (illumination cone) to a polytope by a nonlinear function, which is a transform from Cartesian coordinates to hyperspherical coordinates. The images of a subject form a convex cone in the image space, and it can be better to use the direction of an image in hyperspherical coordinates as an input feature for the mapping rather than the image itself. The maximum error occurs on one of the vertices of the polytope if we choose the objective function to be the squared error of a linear function in the hyperspherical space. Hence, we can solve the least square problem using the cost only for the vertices. In deriving the solution, we use the generalized Rayleigh quotient, canonical correlation analysis (CCA), and prior information on input images, to reduce the solution space and improve 3-D reconstruction performance. In experiments, the proposed scheme performs robustly under light variations, and is fast enough for real-time applications.