Maximum a posteriori approach to 2.5D image reconstruction using Laplacian-Gaussian mixture model

This paper explored the issue of separating illumination from 2D human face images. A novel statistical approach is introduced which is based on seeking maximum possibility of independency between illumination and object shape at the extreme case where the number of observation is less than the number of input images. It allows only two images of an individual under different illumination conditions via the same view point to be applied, which breaks the lower boundary condition of the least input number of images in classical photometric stereo. The proposed mathematical framework is formulated using the Bayesian statistics and the parameters are estimated using the maximum a posteriori (MAP) approach. A novel Laplacian-Gaussian mixture model (LGMM) is developed to model the noisy captured images. This model enhances the parameter estimation accuracy while reduces the overall computational complexity. In addition, the ambiguity of generalized Bas-relief transformation is resolved due to the uniqueness of 'statistical independent' solution rendered by the proposed approach.