Semantic Interpretation of Digital Aerial Images Utilizing ...

84 Chapter 4. From 3D to the Fusion of Redundant Pixel Observations
to the ground plane (we simply set the height coordinate to a fixed value). Hence, a collection
of multiple sampled points results in a highly redundant pool of image candidates
for the different modalities. In Figure 4.3, the corresponding image patches, transformed
to a common (orthographic) view, are given for color, height and semantic classification,
where we only display the most dominant object class. Due to missing data in the individual
height fields (e.g.caused by non-stationary objects or occlusions) the initial alignment
causes undefined areas, artifacts or outliers in the novel view.
In the following various regularized approaches, individually adapted to the considered
modality, are introduced to improve the final result with respect to these problems.
4.3 Fusion of Redundant Intensity Information
This section highlights our fusion model, that allows us to efficiently fuse redundant color
and height field observations into a single, high-quality result. Note that an integration
of multiple images at a city-scale demands fast and sophisticated methods, we thus make
use of energy minimization techniques defined in the continuous domain. These methods
provide a high parallelization capability and obtain in general a globally optimal solution.
The basic concept of energy minimization methods is to formulate the solution of a given
problem as an optimum of an functional, by taking into account of both the distance
of the solution to the observed data and the smoothness itself. First, we briefly discuss
related work. Then, we derive our fusion model, which is based on TV-L 1 denoising
model [Nikolova, 2004], capable to handle multiple input observations. In order to exploit
the particular characteristics of the involved modalities we individually adapt the fusion
model for color and height information. In case of color we replace the TV-norm by a
wavelet-based regularization, capable to preserve fine image structures and produces a
natural fusion result.
4.3.1 Background
The challenging task of reconstructing an original image from given (noisy) observations
is known to be an inverse ill-posed problem. In order to solve such optimization
problems, additional assumptions, such as the smoothness of the solution, have to be considered.
The optimization problem can be generally formulated as the minimization of
the functional
min
u
{ R(u) + λ D(u, f) } , (4.1)
where u is the sought solution, the function R(u) denotes the regularization, which forces
a smooth solution. Depending on the problem R(u) can be defined for different types