## 4 Object Recognition
### Retrieval  
Much of the existing literature assesses retrieval results with a method called the bull's eye score. The bull's eye score exemplifies the most typical use of a system that retrieves images based on their content. Given a query image, the \(N\) most similar images are retrieved from the database and the number of images belonging to the same class of the query is counted. After collecting the signaturesfor all shapes in a given class, as described in Section 3, a set of \(c\) centroids is determined. The process is repeated for each one of the 70 classes in the database determining in this way the \(c\times 70\) centroids. Then each of the 1400 images is used to query the database. The class of the query image is determined first. Independently of the fact that the class is correct or not, the \(c\) centroids corresponding to the class are used to retrieve \(N\) images that have minimum Euclidean distance with any of the \(c\) centroids. Finally, the number of images belonging to the original class of the query image is counted. The scores of the bull's eye retrieval are compared in Table 1 with results in the existing literature.  
For \(c=6\) centroids and \(N=40\), our method significantly improves upon the best result previously reported in the literature (93.06% as compared to 85.4%). It is noteworthy that the improvement achieved by the \(RBRC\) algorithm is based on feature extraction that also improves the state-of-the-art in both texture segmentation and classification. The feature extraction in _FPFT_ proves to be a powerful representation of image features that can be used in \(RBRC\) to address a very different problem.  
Table 1 reports results for \(N=40\); that is, the number of correct shapes out of the top 40 retrieved. The choice of \(N=40\) is natural for the MPEG-7 CE-Shape-1 database because it is twice the number of shapes in each class, allowing for a reasonable but not overly large number returned for a given query (40) as compared to the maximum possible number of correct answers for a given query (20). Although \(N=40\) is the standard used in literature, it is worthwhile to note that performance of \(RBRC\) changes gracefully with \(N\). In fact even at \(N=20\), \(RBRC\) about equals the best of the past results shown in Table 1 that use \(N=40\). Table 2 shows these results, with the top row having the value of \(N\) and the bottom row showing the percent success when the number of correct classification out of the top \(N\) retrieved is counted.  
\begin{table}
\begin{tabular}{l c} \hline
**Method** & **Score** \\ \hline
**CSS** ([PERSON], [PERSON], and [PERSON] [12]) & 75.44\% \\
**Visual Parts** ([PERSON], [PERSON], and [PERSON] [17]) & 76.45\% \\
**SC** + **TPS** ([PERSON], [PERSON], and [PERSON] [14]) & 76.51\% \\
**Curve Edit** ([PERSON], [PERSON], and [PERSON] [18]) & 78.71\% \\
**Distance Set** ([PERSON] and [PERSON] [19]) & 78.38\% \\
**MCSS** ([PERSON], [PERSON], and [PERSON] [20]) & 78.80\% \\
**Generative Models** ([PERSON] and [PERSON] [21]) & 80.03\% \\
**MDS** + **SC** + **DP** ([PERSON] and [PERSON] [15]) & 84.35\% \\
**IDSC** + **DP** ([PERSON] and [PERSON] [15]) & 85.40\% \\
**\(RBRC\), \(c=6\)** & **93.06\%** \\ \hline \end{tabular}
\end{table}
Table 1: Retrieval rate (bull’s eye measure, \(N=40\)).  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**20** & **25** & **30** & **35** & **40** & **45** & **50** & **55** & **60** \\ \hline
88.2 & 90.5 & 88.7 & 90.3 & 93.1 & 93.5 & 93.9 & 94.3 & 94.4 \\ \hline \end{tabular}
\end{table}
Table 2: RBRC retrieval rate (%) for different parameters \(N\).