Integrated Frameworks for Three-Dimensional Scene Reconstruction - 3D Computer Vision: Efficient Methods and Applications - page 223

Figure 5.16 g shows the reconstruction result using only the sparse depth values,
effectively smoothing and interpolating the sparse depth values shown in Fig. 5.16 b.
The overall shape is correct, but smaller details like the flattened top of the object
are missing in the reconstructed three-dimensional profile. Adding intensity and
polarisation terms improves the results and captures the finer details which are not
visible in the sparse depth data (cf. Figs. 5.16 h-i).
The values for the weight parameters of the error terms according to ( 5.21 )
and ( 5.32 ) are related to the magnitudes of the intensity and polarisation features
and their measurement uncertainties. The influence of the weight parameters on the
reconstruction accuracy has been evaluated using the previously described synthetic
data. As a typical example, Fig. 5.17 shows the root-mean-square depth error of the
reconstructed surface profile obtained from one intensity and one polarisation an-
gle image for different weight parameters λ and μ . For noise-free image data, the
reconstruction error decreases with increasing λ and μ until the algorithm starts to
diverge at fairly well-defined critical values. For noisy input images (cf. Fig. 5.16 c)
the reconstruction error displays a weaker dependence on λ and μ and a less pro-
nounced minimum. This is a favourable property, since small changes in the weight
parameters do not lead to large differences in the reconstruction accuracy as long
as the values chosen for λ and μ are well below their critical values for which the
algorithm begins to diverge.
5.3.5 Discussion
In this section we have presented an image-based three-dimensional surface recon-
struction method relying on simultaneous evaluation of intensity and polarisation
features and its combination with depth data.
The shape from photopolarimetric reflectance (SfPR) technique is based on the
analysis of single or multiple intensity and polarisation images. The surface gradi-
ents are determined based on a global optimisation method involving a variational
framework and based on a local optimisation method which consists of solving a
set of nonlinear equations individually for each image pixel. These approaches are
suitable for strongly non-Lambertian surfaces and surfaces of diffuse reflectance
behaviour.
The shape from photopolarimetric reflectance and depth (SfPRD) method in-
tegrates independently measured absolute depth data into the SfPR framework in
order to increase the accuracy of the three-dimensional reconstruction result. In this
context we concentrated on dense but noisy depth data obtained by depth from de-
focus and on sparse but more accurate depth data obtained e.g. by stereo analysis
or structure from motion. However, our framework is open for independently mea-
sured three-dimensional data obtained from other sources such as laser triangula-
tion.
We have shown that depth from defocus information can be used for determining
the large-scale properties of the surface and for appropriately initialising the sur-
face gradients. At the same time it provides an estimate of the surface albedo. For