Kernel-PCA Analysis of Surface Normals for Shape-from-Shading

We propose a kernel-based framework for computing components from a set of surface normals. This framework allows us to easily demonstrate that component analysis can be performed directly upon normals. We link previously proposed mapping functions, the azimuthal equidistant projection (AEP) and principal geodesic analysis (PGA), to our kernel-based framework. We also propose a new mapping function based upon the cosine distance between normals. We demonstrate the robustness of our proposed kernel when trained with noisy training sets. We also compare our kernels within an existing shape-from-shading (SFS) algorithm. Our spherical representation of normals, when combined with the robust properties of cosine kernel, produces a very robust subspace analysis technique. In particular, our results within SFS show a substantial qualitative and quantitative improvement over existing techniques.