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a range of distances from the camera. An extended bundle adjustment approach is
proposed which incorporates a regularisation term based on the depth-defocus func-
tion, such that the reprojection error is minimised simultaneously with the absolute
depth error of the tracked feature points. The proposed method has been imple-
mented as an offline and as an online algorithm and yields absolutely scaled three-
dimensional coordinates of the feature points without any prior knowledge about
the scene or the camera motion. Possible sources of random and systematic errors
have been discussed.
5.2 Self-consistent Combination of Shadow and Shading
Features
Information inferred from the analysis of shadows in an image (cf. Sect.
3.1
)may
be favourably used for refining the three-dimensional shape of a surface obtained by
other methods.
Schlüns (
1997
) uses shadow information in the context of photometric stereo (cf.
Sect.
3.3
) with multiple light sources in order to derive a unique solution for the
surface normal of those pixels for which only two rather than three intensity values
are available due to the presence of a shadow (classical photometric stereo requires
at least three intensity measurements per pixel to obtain a unique solution for the
surface normal, cf. Sect.
3.3
). This approach incorporates shadow information qual-
itatively rather than quantitatively in order to remove the ambiguity of a surface
reconstruction result obtained by photometric stereo resulting from the missing in-
tensity information.
Hogan and Smith (
2010
) propose a method to refine digital elevation models of
mountainous areas of the Earth constructed by synthetic aperture radar using in-
formation about the surface obtained from shadow analysis. Shadows are extracted
from multispectral satellite images based on the assumption that they appear dark
in all spectral bands. The refinement relies on geometric considerations inferred
from the shadow areas, taking into account the direction of the surface normal with
respect to the light source, the depth difference indicated by the shadow, the up-
per bound imposed on the depth between the starting point and the end point of a
shadow, and the gradient and second derivative of the surface at the starting point of
a shadow. For adjusting the elevation data to the shadow information, the reliability
of the radar measurements is taken into account.
This section describes a framework for three-dimensional surface reconstruction
by self-consistent fusion of shading and shadow features introduced by Wöhler and
Hafezi (
2005
). The presentation in this section is adopted from that work. Based on
the analysis of at least two pixel-synchronous images of the scene acquired under
different illumination conditions, this framework combines a shape from shading
approach (cf. Sect.
3.2
) for estimating surface gradients and depth variations on
small scales with a shadow analysis method (cf. Sect.
3.1
) that allows the determi-
nation of the large-scale properties of the surface. As a first step, the result of the
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