By Schroll H.J., Svensson F.
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Extra info for A Bi-Hyperbolic Finite volume Method on Quadrilateral Meshes
In Tomasi and Kanade , the orthographic model was used and a matrix factorization principle was discovered. The factorization principle was extended to the paraperspective camera model in Poelman and Kanade . Factorization under uncertainty was considered in [175, 182]. The second difficulty is often resolved by imposing a subspace constraint on the face model. Bregler et al.  proposed to regularize the nonrigid face model by using the linear constrain. It was shown that factorization can be still be obtained.
Minimization approaches obtain the solution by minimizing an energy fimction. , singular points) to the whole image. Local approaches derive shape based on the assumption of surface type. Linear approaches compute the solution based on the linearization of the reflectance map. 5D structure from limited observations (image intensities), makes it an ill-posed problem in general. This is sometimes reflected in an interesting phenomenon: many SFS algorithms can recover a 'good' depth map for re-rendering the given image at the same lighting and viewing angles, but not good enough for rendering images at different lighting or viewing angles.
Its only weakness is a complicated fitting algorithm. Recently, a fitting algorithm more efficient than suggested in  is proposed in . In , the Fisher light field is proposed to handle both illumination and pose variations, where the light field is used to cover the pose variation and the LDA to cover the illumination variation. Since discriminant analysis is just a statistical analysis tool which minimizes the within-class scatter while 30 UNCONSTRAINED FACE RECOGNITION maximizing the between-class scatter and has no relationship with any physical illumination model, it is doubtable if discriminant analysis is able to generalize to new lighting conditions.