In this case, shape analysis becomes a problem of inverting Lambert’s law, i.e. the relationship between the surface normal and the light source direction causing an observed irradiance. The original ill-posed problem is known as shape-from-shading, however, when more than one light source is considered, new constraints allow numerical solutions to be included in the family of photometic stereo methods. I have been interested in studying the reflectance properties of both faces and diverse materials. My most recent research involves the development of a photometric stereo approach that is exclusive for face shape recovery, seeking for a coherent way to keeping facial proportions when estimating shape from several 2D images. This was one of the PhD contribution of former student, Dr. Felipe Hernández-Rodríguez. Examples of facial shape recovery are shown in the following figure, where the recovered surface is imposed over an image of the profile picture of two subjects:
Selected publications on this topic:
Felipe Hernández-Rodríguez and Mario Castelán. A photometric sampling method for facial shape recovery. Machine Vision and Applications, 27 (4): 483-497 (2016).
Mario Castelán, Elier Cruz-Pérez and Luz Abril Torres-Méndez. A Photometric sampling strategy for reflectance characterization and transference, Computación y Sistemas, 19 (2) : 255-272 (2015)
Jocelyn Miranda-Hernández, Mario Castelán and Luz Abril Torres-Méndez. Face colour synthesis using partial least squares and the luminance-a-b colour transform, IET Computer Vision, 6(4): 263-272 (2012).
Felipe Hernández Rodríguez and Mario Castelán. A method for improving consistency in photometric databases, Proc. British Machine Vision Conference, 1-1o (2012).