# An Efficient Multiscale Scheme Using Local Zernike Moments for Face Recognition
## 4 Experimental Results
### Experiments on FERET
In addition, when red markings and green lines are compared, it is clear that better results were achieved with cascaded LZM transformations. As mentioned in Section 2, LZM is a linear transformation. Therefore, the filters used in the cascaded LZM transformation can be combined, and with the filters obtained in this way, complex LZM images can be generated. In Figure 8, we compare Dup2 results calculated using the cascaded and the combined filters which are obtained using different \(n\) and \(|m|\) values. As can be seen from these results, using the cascaded and the combined filters, very close results were obtained, as expected. The reason why the results were not exactly the same is that in the cascaded LZM transformation, the local regions were normalized separately before each transformation. Figure 6: Identification rates obtained for **(a)** Fb; **(b)** Fc; **(c)** Dup1; and **(d)** Dup2, using single LZM transformation. Blue markings indicate the performance per filter, and red markings indicate the cumulative performance. In this paper, as described in Section 3, a multi-scale feature extraction method, MS-LZM, is proposed. In this method, the features are computed around the facial points and the sizes of the feature vectors obtained for each point are reduced individually using WPCA. It was mentioned earlier that 21 facial points were specified. For the number of scales and the sizes of the face images, we performed comprehensive experiments, and we decided to use the images in five different sizes as follows: \(300\times 300,225\times 225,168\times 168,126\times 126\), and \(94\times 94\). For \(300\times 300\) images, the eye coordinates were set to \((110,122)\) and \((185,122)\). Aside from this, moment degrees and size of the filters used in the LZM transformations must also be determined. As a result of the experiments carried out, the best performance was achieved when the moment degree was \(n=4\) and the filter size was \(n=5\). Figure 8: Dup2 results calculated using cascaded and combined filters which were obtained using different \(n\) and \(|m|\) values. Figure 7: Per-filter and cumulative filter identification rates obtained for Dup1 **(top)** and Dup2 **(bottom)**, using single (yellow markings and green line) and cascaded LZM (red and blue markings) transformations. Blue markings indicate the performance per filter, and red markings indicate the cumulative performance. Green line and yellow markings indicate the best results and the performance per filter given in Figure 6, respectively. \(k=5\) for both LZM transformations. The results obtained are given in Table 1 together with the best known results in the literature. While these results were calculated, the feature vectors were constructed concatenating the PMHs with 18 bins which were calculated in each 4 \(\times\) 4 cells of 40 \(\times\) 40 grids. The dimension of the feature vectors was reduced to 1000 with WPCA. Using Equation (13), the similarity values between the vectors, whose dimensions were reduced, corresponding to the same facial point were calculated and further summed in order to obtain the similarity between two face images. In the results given in Table 1, it is obvious that the best identification results were obtained with the proposed method. Only four images from the Fb set could not be correctly identified. However, this is almost the same level as the highest results for this set. The results for the Fc set were all 100%. The superiority of MS-LZM is evidenced by the results obtained for Dup1 and Dup2. The images in these sets were recorded at different times from the gallery set and are the hardest sets in FERET. All studies compared in Table 1 use local feature extraction, methods as in MS-LZM. The results obtained in these studies using different local operators, including Gabor and LBP, were not better than the results obtained using LZM features in this study. On the other hand, our results are higher than those given in other studies [42; 53] using LZM features.