## 2 Materials and Methods
### Quantifying the Transferability of GEOBIA Rulesets  
While GEOBIA provides rich opportunities for expert (predefined) knowledge integration for the classification process, it also makes the classification more vulnerable to operator-/scene-/sensor-/target-dependency, which in turn hampers the repeatability and transferability of rules. Building a well-defined ruleset is a time-, labor-, and knowledge-intense task. Assuming that the segmentation process is optimal, robustness of GEOBIA rulesets rely heavily on the design goals of the ruleset describing the target classes of interest (e.g., class description) and their respective properties (e.g., low-level image object features) (see Figure 2). Table 2 lists important spectral, spatial, and textural properties, which we elected for developing the original ruleset.  
\begin{table}
\begin{tabular}{c} PAN \\ \end{tabular} & PAN \\ matrix (GLCM) contrast & PAN & PAN \\ \hline \hline \end{tabular}
\end{table}
Table 2: Image object properties and corresponding spectral bands.  
Use of fuzzy rules (which can take membership values between 0 and 1) is much favored in object-based classification over crisp rules (which can take membership values constrained to two logical values \"true\" (=1) and \"false\" (=0)) because the \"fuzzification\" of expert-steered thresholds improves transferability. In the case of GEOBIA, the classes of interest can be realized as a fuzzy set of image objects where a membership function(s) defines the degree of membership (\(\mu\in[0,1]\), \(\mu=0\) means no membership to the class of interest, \(\mu=1\) means the conditions for being a member of the class of interest is completely satisfied) of each image object to the class of interest with respect to a certain property. A fuzzy function describing a property \(p\) can be defined using: \(\alpha\) (lower border of \(p\)), \(\beta\) (upper border of \(p\)), a (mean of membership function), and \(v\) (range of membership function).  
In this study, we employed the framework proposed by [71] for quantifying the robustness of fuzzy rulesets. While briefly explaining the conceptual basis and implementation of the robustness measure, we encourage the reader to refer [71] for further details.  
A ruleset is considered to be more robust if it is capable of managing the variability of the target classes detected in different images given that the images are comparable and the segmentation results are optimal. [71] identified three types (C, O, F) of changes that a reference rule set (Rr) is exposed to during adaptation and used them to quantify the total deviation (\(d\)) of the adapted ruleset (Ra).  
Type C: Adding, removing, or deactivating a class.  
Type O: Change of the fuzzy-logic connection of membership functions.  
Type F: Inclusion or exclusion (Type F\({}^{q}\)) and changing the range of fuzzy membership functions (Type F\({}^{b}\)).  
The total deviation (\(d\)) occurring when adapting Rr to Ra is given by summation of individual changes of Types C, O, and F;  
\[d=\sum_{i=1}^{c}\mathrm{C}_{i}+\sum_{i=1}^{o}\mathrm{O}_{i}+\sum_{i=1}^{f_{a} }\mathrm{F}_{i}^{a}+\sum_{i=1}^{f_{b}}\delta F_{i}^{b} \tag{1}\]  
\[\delta F\ =\ \delta a+\delta v \tag{2}\]  
Figure 3 exhibits the possible changes of a membership function, which is subjected to adaptation under Type F\({}^{b}\). Let Rr be the master ruleset [72] developed based on the reference image (Ir) and Ra be the adapted version on Rr over a candidate image I (Ia). The robustness (\(r_{r}\)) of the master ruleset can be quantified by coupling with a quality parameter \(q\) (\(q_{a}\) and \(q_{r}\) denotes the classification accuracy of image Ia and Ir, respectively) and total deviations associated with Ra (\(d_{a}\)).  
\[r_{r}=\frac{\frac{q_{a}}{q_{r}}}{d_{a}+1} \tag{3}\]