Integrated Frameworks for Three-Dimensional Scene Reconstruction - 3D Computer Vision: Efficient Methods and Applications - page 208

by shape from shading. Their approach, however, requires dense depth data and
integrates the independently obtained results of two separate algorithms.
Samaras et al. ( 2000 ) introduce a surface reconstruction algorithm that performs
stereo analysis of a scene and quantifies the reliability of the stereo data using a
'minimum description length metric', such that shape from shading is applied to un-
structured surface parts selectively. A surface model described by facets is adjusted
to minimise a combined error term relying on the depth inferred by stereo analysis,
shape from shading using Lambertian reflectance with an additional constant term,
and the smoothness of the surface.
A related approach by Fassold et al. ( 2004 ) integrates stereo depth measurements
into a variational shape from shading algorithm and estimates surface shape, illumi-
nation conditions, and the parameters of an empirically modified Lambertian re-
flectance function. In their approach, the influence of a depth point is restricted to a
small local neighbourhood of the corresponding image pixel.
Horovitz and Kiryati ( 2004 ) propose a method that incorporates sparse depth
point data into the gradient field integration stage of the shape from shading algo-
rithm. It involves a heuristically chosen parameterised weight function governing
the local influence of a depth point on the reconstructed surface. A second approach
is proposed by Horovitz and Kiryati ( 2004 ), suggesting a subtraction of the large-
scale deviation between the depth data independently obtained by stereo and shape
from shading, respectively, from the shape from shading solution. For sparse stereo
data, the large-scale deviation is obtained by fitting a sufficiently smooth parame-
terised surface model to the depth difference values. Both approaches combine the
independently obtained results of two separate algorithms.
The method of Nehab et al. ( 2005 ) combines directly measured surface normals
obtained e.g. by photometric stereo with dense depth data directly measured with a
range scanning device. The surface obtained by integration of the measured surface
normals is assumed to be inaccurate on large spatial scales, while the surface nor-
mals inferred from the measured depth data tend to be inaccurate on small spatial
scales. In the first step, Nehab et al. ( 2005 ) combine the high-pass filtered com-
ponent of the measured surface normals with the low-pass filtered component of
the surface normals inferred from the depth data, which results in corrected sur-
face normals. In the second step, the final surface is constructed by simultaneously
minimising its deviation from the measured depth data and the deviation from or-
thogonality between its gradients and the corrected surface normals determined in
the first step. This approach is formulated as a computationally efficient linear opti-
misation scheme.
A method to simultaneously estimate the depth on small spatial scales along with
the albedo map of the surface based on a single image is introduced by Barron and
Malik ( 2011 ). The proposed approach relies on a training procedure during which
the statistical properties of the albedo map and those of the depth map are inferred
from a set of examples. A Lambertian reflectance function is assumed. Large-scale
depth information obtained by other methods, such as stereo image analysis or active
range scanning, can be integrated into the optimisation procedure and thus combined
with the inferred small-scale depth information.