The 2D variation procedure can be performed for the binary image of fig. 9 with the button 2D binary (fig. 26). In the popup menu the distance metric has to be defined [4] by mouseclick. Fig. 30 left shows a distance metric of 3,5,7,9 and 11 pixels, which was used for the analysis of fig. 31.
Figure 30: Defining the distance metric
The result of the 2D variation analysis is shown in fig. 31.
Figure 31: Binary 2D variation result
For binary images of low resolution the 2D variation algorithm is no proper
procedure [4], since there is a saturation region for
large distance metrics. Nevertheless the dimension can be estimated
by the usage of small pixel sizes as depicted in fig. 31.
The binary 2D dimension is calculated with formulas and specifications
given in [4] as ,
which matches with the dimensions in
sect. 5.1.
2D variation analysis for greyscale images is performed by mouse click on the 2D greyscale button in fig. 26.
The distance metric of fig. 30 right was used for the analysis of fig. 32. The result is given in fig. 32.
Figure 32: Grey 2D variation result
The linear fit for greyscale images is much better than for binary images
(comp. fig. 31). With the formulas and specifications
given in [4] the greyscale 2D variation dimension is
.