# A Feature-Based Structural Measure: An Image Similarity Measure for Face Recognition
## 4 Experimental Results and Performance
### Results and Discussion  
The new FSM technique was implemented as per Equation (9), with the well-known measures SSIM as per Equation (1) and FSIM as per Equation (2). These three methods were implemented simultaneously on 1100 images from two datasets; all images of AT&T database and 700 images of FEI database to compare their performance. The distance between the first and second maxima of the similarity curve (peaks) is used for all recognition methods. A greater distance means more confidence in the facial recognition decision. Almost for all cases, the proposed FSM keeps larger difference between the test image and other individuals; better confidence in the recognition process is obtained. Figure 3 shows the poses of the fourth person in the AT&T database, used for testing; Figure 4 shows the poses of the eighth person, also used for testing. Figure 5 shows the poses of the fifth person in FEI database and Figure 6 shows the poses of the fifteenth person in FEI database also used for testing. The reference pose, used as the test image, is indicated. A pose with no significant angle is chosen for the purposes of testing and comparison, although eye-glasses are considered in the first test (see Figure 3), which increases the difficulty of face recognition. Figure 1: Various face poses for a single person from The AT&T (American Telephone & Telegraph) Face Database. Figure 2: Various face poses for a single person from The FEI (Brazilian) Face Database. Figure 4: Poses for person No. 8 in AT&T database. Figure 5: Poses for person No. 5 in FEI database. Figure 3: Poses for person No. 4 in AT&T database. Figure 6: Poses for person No. 15 in FEI database. In Figures 7-10, the proposed FSM gives better performance in terms of recognition confidence. In spite of the fact that the other measures SSIM and FSIM correctly decide the proper person with maximum similarity, they give low confidence in their decision because there are many cases of distrust (big similarities with wrong persons) in their decisions (similarities); this is a big challenge when we employ these measures in security recognition tasks. FSM gives more confidence to decide the proper person from a database. Figure 11 shows the performance of similarity measures using person No. 15 in FEI database. Pose 8 is the Reference Image, while a different pose (pose 10) is used for testing for all database images (including the target person). FSIM fails, while confidence of SSIM, and FSM is 0.0364, 0.12 respectively. Figure 10: Performance of similarity measures using person No. 15 (pose 8) in the FEI database. Confidence in recognition for SSIM, FSIM and FSM is 0.2430, 0.1916 and 0.8697 respectively. Figure 9: Performance of similarity measures using person No. 5 (pose 7) in the FEI database. Confidence in recognition for SSIM, FSIM and FSM is 0.2354, 0.2103 and 0.8791 respectively. Figures 12-15 we simulated the confidence measure as per Equation (11) to show the efficiency of the proposed measure (FSM) in giving the highest confidence versus the well-known SSIM and FSIM. Figure 11: Performance of similarity measures using person No. 15 in the FEI database. Pose 8 is the Reference Image, while pose 10 is used for testing for all database images (including the target person). FSIM fails, while confidence in recognition for SSIM, and FSM is 0.0364, 0.12 respectively. Figure 12: Recognition confidence for similarity measures SSIM, FSIM and FSM using person No. 4 (pose 10) in the AT&T database. In Figures 16-19, the proposed measure FSM produces near-one (maximal) similarity for similar images under Gaussian noise, while giving near-zero similarity when the images are dissimilar. The other measures SSIM and FSIM gave non-trivial amounts of similarity when the two images are quite different, which indicates a shortcoming in these measures. Figure 2:0 Recognition confidence for similarity measures SSIM, FSIM and FSM using person No. 5 (pose 7) in FEI database. Figure 2:1 Recognition confidence for similarity measures SSIM, FSIM and FSM using person No.