# An Efficient Retrieval Technique for Trademarks Based on the Fuzzy Inference System
## 5 Experimental Results and Discussion
### Experiment Setup  
To achieve objective evaluation, an large trademark database is collected from three different image databases, including MPEG-7, [20; 22]. The aim is to observe the performance of the proposed technique in terms of its retrieval accuracy and efficiency through the large trademark database. The well-known MPEG-7 CE-2 region-based database consists of about three thousand binary trademarks. For the sake of simplicity, MPEG-7 is an abbreviation of the MPEG-7 CE-2 region-based database in this paper. Although MPEG-7 provides a set of trademarks, the images are not exclusively designed for performance evaluation of a TIR system. Further, classifying all the images of MPEG-7 is also extremely difficult work. Therefore, we use the existing seven group images from [20; 22], where five group images are from MPEG-7. These seven group images will be the query images for observing the retrieval performance of the proposed technique. As suggested above, the large trademark database of this paper contains about 1800 trademark images, including 12 different classes and 416 query images, as shown in Figure 8.  
As mentioned above, the performance indices, except efficiency, including (1) _precision_ and _recall_ (P-R) rates, (2) BES, and (3) ANMRR are described in the following. The precision and recall rates are presented as:  
\[\begin{array}{c}precision=n_{sl}/n_{rt}\\ recall=n_{sl}/n_{rt}\end{array} \tag{28}\]  
where \(n_{sl}\) is the total number of relevant retrieved images, \(n_{rt}\) is the total number of retrieved images, and \(n_{rt}\) is the total number of relevant images in the entire database.  
Figure 8: Trademark database in this study.  
The bull's eyes score is measured based on the top \(2\cdot n_{rq}\) retrieved images and defined as:  
\[BES=\frac{n_{sl}}{n_{rq}} \tag{29}\]  
where \(n_{sl}\) is the total number of relevant images in the top \(2\cdot n_{rq}\) retrieved images.  
The last performance index, ANMRR, is a normalized ranking method. This index is defined as:  
\[ANMRR=\frac{1}{n_{rq}}\sum_{i=1}^{n_{rq}}NMR(i) \tag{30}\]  
\[NMRR(q)=\frac{MRR(q)}{2\cdot n_{rq}+0.5-0.5\cdot n_{rq}} \tag{31}\]  
where the NMRR score ranges from 0 to 1, where 0 indicates perfect retrieval. The modified retrieval rank (MRR) is calculated from the average ranking rate (AVR) and is defined as:  
\[MRR(q)=AVR(q)-0.5-\frac{n_{rq}}{2} \tag{32}\]  
\[AVR(q)=\sum_{k=1}^{n_{rq}}\frac{Rank(k)}{n_{rq}} \tag{33}\]  
where \(Rank(k)\) is the rank of the relevant index in the retrieved images.  
After the indices are defined, the performances of the proposed technique and the other two competitive approaches are evaluated by those indices in the following experiments. In order to clearly certify our technique as better than the two competitive approaches, the experiential set up of the two competitive approaches is introduced below. In the first approach, ZMEG, there are two important factors to control the retrieved performance, which are the weighting values of the global feature, Zernike moments (ZM), and of the local feature, namely, the edge gradient co-occurrence matrix (EGCM), similarities, and similarity metric. In the following experiments, we set the weighting values to 0.3 and 0.7, respectively. Additionally, the similarity metric is using Manhattan distance for the global and local features. Regarding the second approach, ZMLDP, we analyze a variety of local features combined with the global features in the feature extraction. Therefore, we choose the best feature combination, ZM and local directional pattern (LDP), as the index of the literature. For the similarity metric, the global and local feature metrics use the Euclidean distance (\(L_{2}\) norm) and the Chi-square distance, respectively.