Integrated Frameworks for Three-Dimensional Scene Reconstruction - 3D Computer Vision: Efficient Methods and Applications - page 209

The technique proposed in this section is based on the analysis of single or multi-
ple intensity and polarisation images. To compute the surface gradients, we present
a global optimisation method based on a variational framework and a local optimi-
sation method based on solving a set of nonlinear equations individually for each
image pixel. These approaches are suitable for strongly non-Lambertian surfaces
and those of diffuse reflectance behaviour and can also be adapted to surfaces of
non-uniform albedo. We describe how independently measured absolute depth data
are integrated into the shape from photopolarimetric reflectance framework in or-
der to increase the accuracy of the three-dimensional reconstruction result. In this
context we concentrate on dense but noisy depth data obtained by depth from de-
focus and on sparse but accurate depth data obtained by stereo or structure from
motion analysis. We show that depth from defocus information should preferen-
tially be used for initialising the optimisation schemes for the surface gradients. For
integration of sparse depth information, we suggest an optimisation scheme that si-
multaneously adapts the surface gradients to the measured intensity and polarisation
data and to the surface slopes implied by depth differences between pairs of depth
points. Furthermore, Sect. 5.5 describes a related method for combining image in-
tensity information with active range scanning data.
5.3.1 Shape from Photopolarimetric Reflectance
In our scenario we assume that the surface z(x,y) to be reconstructed is illuminated
by a point light source and viewed by a camera, both situated at infinite distance
in the directions s and v , respectively (cf. Fig. 3.2 ). The xy plane is parallel to
the image plane. Parallel unpolarised incident light and an orthographic projection
model are assumed. For each pixel location (u, v) of the image we intend to derive
a depth value z uv . The surface normal n , the illumination vector s , the vector v to
the camera, the incidence and emission angles θ i and θ e , the phase angle α , and the
surface albedo ρ uv are defined according to Sect. 3.2 .
In the framework of shape from photopolarimetric reflectance (SfPR) according
to d'Angelo and Wöhler ( 2005a , b ), the light reflected from a surface point located
at the world coordinates (x,y,z) with corresponding image coordinates (u, v) is
described by the observed pixel grey value I uv , the polarisation angle Φ uv (i.e. the
direction in which the light is linearly polarised), and the polarisation degree D uv .
This representation is analogous to the one chosen in the context of shape from
shading (cf. Sect. 3.2 ) and photometric stereo (cf. Sect. 3.3 ). The measurement of
polarisation properties is thus limited to linear polarisation; circular or elliptic polar-
isation is not taken into account. It is assumed that models are available that express
these photopolarimetric properties in terms of the surface orientation n , illumination
direction s , and viewing direction v . These models may either be physically moti-
vated or empirical (cf. Sects. 3.2.1 and 3.4.2 ) and are denoted here by R I (intensity
reflectance), R Φ (polarisation angle reflectance), and R D (polarisation degree re-
flectance). The aim of surface reconstruction in the presented framework is to deter-
mine for each pixel (u, v) the surface gradients p uv and q uv , given the illumination