The variational approach to shape from shading
Computer Vision, Graphics, and Image Processing
A Method for Enforcing Integrability in Shape from Shading Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Three-dimensional shape from color photometric stereo
International Journal of Computer Vision
New Constraints on Data-Closeness and Needle Map Consistency for Shape-from-Shading
IEEE Transactions on Pattern Analysis and Machine Intelligence
From Few to Many: Illumination Cone Models for Face Recognition under Variable Lighting and Pose
IEEE Transactions on Pattern Analysis and Machine Intelligence
Recovering 3-D shape and reflectance from a small number of photographs
EGRW '03 Proceedings of the 14th Eurographics workshop on Rendering
The CMU Pose, Illumination, and Expression Database
IEEE Transactions on Pattern Analysis and Machine Intelligence
A New Formulation for Shape from Shading for Non-Lambertian Surfaces
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2
A Riemannian Weighted Filter for Edge-sensitive Image Smoothing
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 03
Facial Gender Classification Using Shape from Shading and Weighted Principal Geodesic Analysis
ICIAR '08 Proceedings of the 5th international conference on Image Analysis and Recognition
Supervised Principal Geodesic Analysis on Facial Surface Normals for Gender Classification
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Learning a Self-organizing Map Model on a Riemannian Manifold
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
A Riemannian Self-Organizing Map
ICIAP '09 Proceedings of the 15th International Conference on Image Analysis and Processing
Estimating Facial Reflectance Properties Using Shape-from-Shading
International Journal of Computer Vision
Facial expression recognition using nonrigid motion parameters and shape-from-shading
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part II
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In this paper we show how arbitrary surface reflectance properties can be incorporated into a shape-from-shading scheme, by using a Riemannian minimisation scheme to minimise the brightness error. We show that for face images an additional regularising constraint on the surface height function is all that is required to recover accurate face shape from single images, the only assumption being of a single light source of known direction. The method extends naturally to colour images, which add additional constraints to the problem. For our experimental evaluation we incorporate the Torrance and Sparrow surface reflectance model into our scheme and show how to solve for its parameters in conjunction with recovering a face shape estimate. We demonstrate that the method provides a realistic route to non-Lambertian shape-from-shading for both grayscale and colour face images.