# Visual Saliency Detection Using a Rule-Based Aggregation Approach
## 2 Methodology
### Rough-Set-Based Rules  
The rough set theory was introduced by [PERSON] [36] as a mathematical tool for dealing with imperfect and inconsistent data, in order to extract useful knowledge. In a classification process, an object is described in terms of a set of attributes. The information contained on these sets of attributes usually has a certain level of vagueness and ambiguity. Rough set approaches handle inconsistencies of data using two types of approximation sets, the lower and the upper approximations. If we consider \(I\) as the information system used to approximate to decision class \(X\). The lower approximation \(IX\), determines according to \(I\), the objects that certainly correspond to class \(X\). The upper approximation, \(\overline{I}X\), defines the objects that possibly correspond to class \(X\). In Equations (1) and (2), we present the definition of the lower and upper approximations, respectively, where \([x]_{I}\) is the elementary set containing \(x\in X\).  
\[\underline{IX}=\{x|[x]_{I}\subseteq X\}, \tag{1}\]  
\[\overline{I}X=\{x|[x]_{I}\cap X\
eq\emptyset\}. \tag{2}\]  
The difference between the lower and upper approximations is known as the region boundary and is defined as in Equation (3). If the region boundary is not empty, the set is a rough set.  
\[IN_{I}(X)=\overline{I}X-\underline{IX}. \tag{3}\]  
From the given information, the rough set algorithm produces an ensemble of rules. Usually, the rules obtained are represented in the logical form of \(IF\) (_antecedent_) \(THEN\) (_consequent_). For our  
Figure 1: Overview of our proposed model. (**a**) Feature extraction is performed. Then, a learning process is carried out by using the MODLEM algorithm. (**b**) Using the obtained model, a saliency prediction is performed and the output is given in a binary form.  
purposes, the left side of the rule, called _antecedent_, is an attribute condition or feature. The right side of the rule is the _consequent_, i.e., the decision class or saliency.  
The rules created by using the rough set algorithm can be categorized into three types of rules sets [41]. The smallest set of rules needed to describe an object is known as the minimum set of rules. In contrast, the exhaustive set of rules consist of all the rules that can be generated from the examples given for learning. Finally, the satisfactory set of rules is conformed by those rules that satisfy requirements previously defined by the user. Therefore, several methods have been proposed to rough-set-based rule generation. One of the most commonly used rough-set-based approaches is the method proposed by [PERSON], named MODLEM [42].The main advantage of this method relies on the capability of handling discretization of the information and rule induction simultaneously. Additionally, the MODLEM algorithm generates a minimal set of rules for every decision class [35]. In the MODLEM algorithm, for numerical attributes, an elementary condition \(t\) is defined in the form of either \((a<v)\) or \((a>=v)\), where \(v\) is a threshold on the attribute domain and \(a\) is a numerical attribute value [43]. To determine the elementary condition, the values of a numerical attribute \(a\) are sorted in increasing order to find cut-points. The cut-points correspond to the mid-points between the sorted values. A cut-point is evaluated using either the class entropy technique or Laplace accuracy, and the elementary condition is selected by the largest coverage on the given learning examples. This procedure is repeated until the complete rule is induced and the set of rules obtained is minimum. In our experiments, we utilized the MODLEM implementation at WEKA [44], an open-source data mining tool.