Intensity-Based and Polarisation-Based Approaches to Three-Dimensional Scene Reconstruction - 3D Computer Vision: Efficient Methods and Applications - page 157

non-uniform reflectance function from a set of images acquired under different il-
lumination conditions. The surface material is assumed to be composed of a small
number of 'fundamental materials', where the material of a specific surface loca-
tion is additionally constrained to consist of a mixture of only two materials. The
proposed optimisation scheme estimates the surface normals, the reflectance pa-
rameters of the fundamental materials, and the pixel-specific material fractions. It
is shown by Goldman et al. ( 2010 ) that their approach is especially suitable for
generating synthetically rendered images of the reconstructed objects under illu-
mination and viewing conditions different from those encountered during image
acquisition.
Hernandez et al. ( 2007 ) use the method of 'multispectral photometric stereo',
which consists of acquiring three colour channels simultaneously using an RGB
camera, where the surface to be reconstructed is illuminated by a red, a green,
and a blue light source emitting in non-overlapping wavelength ranges. This ap-
proach avoids the requirement of classical photometric stereo to acquire the images
subsequently and thus to keep the surface stationary. Under the assumption of a
Lambertian surface with a non-uniform albedo, a photometric stereo scheme sim-
ilar to the method described at the beginning of this section is applied in order to
obtain the surface gradients. The depth map is then inferred by integration, and a
temporal tracking of the variations of the three-dimensional surface shape is per-
formed, using the surface derived from the first image as a deformable template.
Correspondences between subsequent frames are established based on optical flow
information inferred from the surface gradient images. This method is applied by
Hernandez et al. ( 2007 ) to the three-dimensional reconstruction of clothes. The mul-
tispectral photometric stereo approach employed using standard RGB cameras does
not yield more than three images, and under these conditions images of complex
surfaces are nearly never shadow-free for all colour channels. Thus Hernandez et
al. ( 2008 ) propose a method to obtain unambiguous surface gradients for pixels ly-
ing inside shadow areas in one of the images by imposing a combined integrability
and direction-dependent smoothness constraint. The framework of Hernandez et al.
( 2007 , 2008 ) is applied by Hernandez and Vogiatzis ( 2010 ) to the three-dimensional
reconstruction of faces. Their method is calibrated by estimating the object mo-
tion using structure from motion and by applying stereo image analysis to derive a
three-dimensional reconstruction of the face. The reconstruction, which is accurate
on large spatial scales but noisy on small scales, is then used to estimate the light
source directions. A refined three-dimensional reconstruction of the facial surface is
obtained by multispectral photometric stereo with correction for shadows according
to the method of Hernandez et al. ( 2007 , 2008 ).
3.3.2 Photometric Stereo Approaches Based on Ratio Images
This section regards photometric stereo approaches which are suited for non-
uniform surface albedos, coplanar illumination vectors (which may be of high prac-
tical relevance, especially in the field of remote sensing applications, as pointed out