Integrated Frameworks for Three-Dimensional Scene Reconstruction - 3D Computer Vision: Efficient Methods and Applications - page 226

Sect. 1.5.2.5 ). Wolff and Angelopoulou ( 1994 ) propose a method to obtain dense
stereo correspondences based on photometric ratios. Two stereo image pairs of the
scene are acquired, where the camera positions remain fixed but the illumination
conditions change. The surfaces are assumed to be smooth and to consist of di-
electric material, such that a special reflectance model can be used which is more
complex than the Lambertian reflectance but does not represent specular reflections.
Wolff and Angelopoulou ( 1994 ) show that the pair of ratio images obtained by di-
viding two stereo image pairs acquired under different illumination conditions by
each other is invariant with respect to the exposure time and gain of the camera, the
viewpoint, and the albedo of the surface as long as no specular reflections occur.
Stereo correspondences between the computed pair of ratio images are established
by a pixel-wise comparison of the ratio values.
Jin et al. ( 2003 ) show that for several images acquired from different viewpoints,
the rank of the matrix containing the radiance values measured in all images for
a local neighbourhood of a certain pixel is not larger than two. As a reflectance
function, the fairly complex model of Ward ( 1992 ) is used, which is composed of
a diffuse and a specular component. Jin et al. ( 2003 ) utilise this constraint for the
three-dimensional reconstruction of non-Lambertian surfaces based on a level set
approach.
For images acquired from different viewpoints, where the scene is illuminated by
several light sources at fixed positions with variable irradiance values, Wang et al.
( 2007 ) rely on the 'light transport constancy' to establish stereo correspondences.
They show that the matrix containing the scene radiance values observed by the
cameras under the different illumination conditions has a rank which is lower than
the number of light sources. They introduce a criterion for establishing stereo cor-
respondences which is based on the singular values of that matrix and show that
it is equivalent to evaluating ratio images similar to the method of Wolff and An-
gelopoulou ( 1994 ). The method by Wang et al. ( 2007 ) is not restricted to Lambertian
surfaces but can be applied to surfaces with arbitrary reflectance functions. In their
experiments, variations of the illumination conditions are generated by two projec-
tors.
In the following, the method of Wöhler and d'Angelo ( 2009 ) for the three-
dimensional reconstruction of surfaces with non-Lambertian reflectance properties
based on stereo image analysis is described. Using the SfPRD technique described
in Sect. 5.3 as a basis, triangulation-based cues are combined with photopolari-
metric information into an iterative framework that allows one to establish stereo
correspondences in accordance with the specular reflectance behaviour and at the
same time to determine the surface gradient field based on the known photometric
and polarimetric reflectance properties. Illumination by a single point light source
is sufficient; no variable illumination is required. Disparities are refined based on a
comparison between observed and modelled pixel brightnesses. The approach yields
a dense three-dimensional reconstruction of the surface which is consistent with the
observed data.