4. REALIZATION – INTEGRATED APPROAC

4. REALIZATION – INTEGRATED APPROACH OF
DISPLACEMENT, SIMPLIFICATION AND
ENHANCEMENT
The realization of these features is achieved with an integrated
approach that combines different generalization procedures.
This approach is based on adjustment theory as a means to
achieve an integrated optimisation of different constraining
factors. Details can be found in [Sester 2000].
Adjustment theory is a means to determine a set of unknowns
based on given observations. The observations are described as
functions of unknowns in the so-called functional model; in
addition, the accuracy of the observations can be described in
the stochastic model. If the functional dependencies are not
linear, they have to be linearized, leading to the fact, that
approximate values for the unknowns have to be given. The
unknowns are determined by the following equation:
ˆ ( ) ( ( )) 0
x = AT PA −1 AT P l − f x ,
where A is the Jacobean Matrix of the derivations of the functions according to the unknowns x, P is the weight matrix of the observations, l are the observations and f(x0) is the value
of the function calculated at the approximate values x0. Obviously, the use of this scheme is straightforward, as soon as the observations and the unknowns for a given problem are identified. In the case of using adjustment theory for displacement, the unknowns are the coordinates of the points of the objects involved. The observations are distances between the objects, that have to be enforced and set to be at least as large as the minimum legible distance between the objects.
Additional object specific observations can be introduced in order to define the form and orientation of the objects. These additional observations are necessary in order to be able to specify the variability of these object properties: if the form observations are assigned a high weight, it enforces that the form is kept – a low weight allows the object to vary its form, i.e. leads to deformation of the object. Furthermore, the unknown coordinates are also introduced as observations, in order to be able to assign them a high or low weight, allowing
to fix an object at its original position, or allowing it to move, respectively. As distance constraints between all the objects are formulated, it is ensured that a global solution is found, where a displacement of one object occurs in accordance with all its surrounding objects, and no follow-up conflicts are triggered.
Thus it leads to a situation, where all the objects are clearly
legible, as the minimum distances between all the objects are
enforced. The result can be analysed by inspecting the residuals
of the observations and their accordance with the introduced
accuracies. E.g. the residuals in the object sides give an
indication for their deformation. As a measure for the absolute
positional accuracy, the change in the coordinates can be used.
In this way, these measures can be used to evaluate the quality
of the result and allow for self-inspection.