Triangulation-Based Approaches to Three-Dimensional Scene Reconstruction - 3D Computer Vision: Efficient Methods and Applications - page 75

A useful assumption is that the edges extracted by the interest operator are as-
sociated with the same objects in both images. Accordingly, Barrois et al. ( 2010 )
introduce the minimum weighted matching constraint, which determines the three-
dimensional reconstruction result given by the maximum number of correspon-
dences. This constraint is similar to the constraint proposed by Fielding and Kam
( 1997 ) but is based on a minimum rather than a maximum overall SSD measure.
The correspondence problem is then regarded as an assignment problem in a bipar-
tite graph and is solved by the Hungarian method (Kuhn, 1955 ).
1.6.1 Plane Model
In the domain of mobile robotic systems or intelligent vehicle applications, mod-
elling the scene or parts of it by a plane is a well-known approach. The plane then
provides an approximate scene description, as described e.g. by Biber et al. ( 2004 ).
A plane model is applicable to a variety of objects with repetitive structures, es-
pecially human-made ones such as wall tiles, fences, or buildings. The repetitive
structures are usually equidistant in the scene but not necessarily in the image, as
the objects are generally not oriented parallel to the image plane. The plane model
is especially useful for scene parts located far away from the camera (i.e. at dis-
tances at least one to two orders of magnitude larger than the baseline distance of
the stereo camera system), even when they are not very accurately described by a
plane. In such a case, the repetitive structures are associated with the background
of the scene, which is modelled by the plane at infinity. The deviations in disparity
space from the configuration implied by a plane can then be assumed to be small
due to the smallness of the disparity values themselves.
1.6.1.1 Detection and Characterisation of Repetitive Structures
Repetitive structures are characterised by a repeating grey value pattern which leads
to a significant peak in the associated amplitude spectrum, which is favourably deter-
mined by a fast Fourier transform (FFT). Horizontal image lines of fixed length, e.g.
128 pixels, are extracted from each image row with an overlap of half the length of
a line. In the amplitude spectrum, the maximum peak apart from the zero-frequency
component is extracted if its significance exceeds a given threshold that depends on
the mean and the standard deviation of the spectrum, and the corresponding wave-
length is calculated. To obtain a continuous representation, a plane is adapted to
the extracted wavelengths using an M-estimator technique. Outliers are eliminated,
and image areas displaying repetitive structures are marked in the image based on
the determined wavelengths. The same procedure is applied to vertical image lines
extracted in an analogous manner. The results of these horizontal and vertical spec-
tral analyses are image areas displaying repetitive structures and plane functions
λ h (U, V ) and λ v (U, V ) providing a wavelength value for each marked image posi-
tion with coordinates (U, V ) .