# An Efficient Retrieval Technique for Trademarks Based on the Fuzzy Inference System
###### Abstract
On the other hand, several approaches based on geometric-based features are proposed for TIR, including Fourier description, curvature scaled space [14], edge directions histograms [15], Triangle-Area Representation (TAR) [16], the local patterns of an image [17], etc. A comparative retrieval study between a region and a geometric-based feature found that the matching of the geometric-based feature was significantly more effective than the matching of the region-based feature [18]. There is consensus that the use of multiple region-based features or the integration of region and geometric-based features work better than any single ones, while integrating various shape descriptors is generally necessary. Although an effective approach has been employed for feature representation, an inappropriate choice of feature similarity measure leads to poor retrieval results in a TIR system. To achieve both the advantage of the region and geometric-based features, a two-component solution (TCS) has been proposed with region and geometric-based features [15; 19; 20]. [PERSON] et al. [20] present two-component feature matching, which employs the Euclidean distance with a threshold and penalty value. It is important to decide the appropriate threshold and penalty value in the TCS. To avoid this problem, [PERSON] et al. [15] proposed a TIR technique employing two shape descriptors, the ZMs and edge gradient co-occurrence matrix (EGCM), with the TCS. In the first stage of TCS, the authors utilized the superior properties of the ZMs to retrieve similar trademarks in a database, which are fed into the next stage. In the second stage, a weighting strategy was employed to combine the similarity coefficients of the ZMs and EGCM for the candidate trademarks in the first stage. However, relying on a single feature is not a good way to effectively find the relevant image, despite the advantages of ZMs. Therefore, a number of studies have proposed structures to bridge the global and local properties of an image. [PERSON] et al. [21] propose a curvature tree (CT) with a TAR feature to describe the topology of the trademark (foreground) and the holes (background), and they report better accuracy with this than by employing single region-based descriptors in a medical image database. For further retrieving a complex trademark with multiple objects, [PERSON] et al. [22] presented the fusion of geometric features, including a blurred shape model, a Voronoi diagram for the density of an object and the spatial location of an object, based on a tree representation model (TRM) for retrieving similar trademarks. This TRM is similar to the CT, but it outperforms TIR. Although the CT and TRM have good retrieval results for complex multi-object images, both of these image representations have two drawbacks in termsof similarity measurement. The first drawback of the tree similarity algorithm is that it has a heavy computational burden in finding the maximum similarity subtree isomorphism (MSSI) with a recursive procedure. In additional, another drawback is a selection problem of the weighting values between multiple features in a tree node. A similar selection problem also existed in the TCS, the threshold value of a feature similarity. There are many techniques that aim to avoid these selection problems such as Machine Learning techniques [19; 23; 24] and Relevance Feedback techniques [25]. The property of the image retrieval requires that the computer retrieves images that are similar to human perception and does not depend on rigid distance metrics to measure feature similarity. [PERSON] et al. [24] used a learning-based feature using Convolutional Neural Networks (CNN), which is the first study using CNN for trademark retrieval. It relies on finding an end-to-end mapping directly from the raw input to the required output, whereby the best representation for the problem at hand is obtained from the data directly.