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Results of Eigenface Detection Tests

Module by: Doug Kochelek, Matthew Escarra, Marshall B. Robinson, Jon Krueger. E-mail the authors

Summary: Hit rate results for various inputs and filtered inputs using the eigenface method for face recognition.

Undistorted Input Results

For both the averaging technique and removal technique undistorted duplicates of the original images were processed for recognition in order to determine a best-case rate for recognition. For both techniques and for all three data sets, rates of recognition stabilized as the number of eigenfaces used in the recognition scheme increased.

Figure 1: Rate of identification of the correct individual using undistorted inputs for the averaging technique.
Figure 1 (smallHR-AT.jpg)
Figure 2: Rate of identification of the correct individual using undistorted inputs for the removal technique.
Figure 2 (smallHR-RT.jpg)

For each image set stability was reached at the following hit rate and for the specified number of eigenfaces:

Table 1: Table 1. Number of Eigenfaces for Hit Rate Stability for All Image Sets
Image Set Stable Hit Rate Number of Eigenfaces
Rice (Average) 90% 11
AT&T (Average) 86% 17
Yale (Average) 68% 21
Rice (Removal) 67% 14
AT&T (Removal) 96% 12
Yale (Removal) 75% 20

For detection tests using a number of eigenfaces greater than that specified in Table 1 no significant improvement in detection success rate was achieved. In this way, undistorted tests suggest that implementations for both averaging and removal techniques do not achieve greater detection rates with numbers of eigenfaces greater than the minimum number needed for stability.

Occluded Input Results

For both averaging and removal techniques Rice image sets were tested for detection rates with horizontal and vertical occlusions centered on the vertical and horizontal axes respectively. Results show that hit rate stability, as before, is achieved as the number of eigenfaces used increases.

Figure 3: (a) the undistorted base image. (b) the image with a horizontal occlusion. (c) the image with a vertcal occlusion.
Figure 3 (mattie.jpg)
Figure 4: Rate of identification of the correct individual using horizontally obscured inputs with the averaging technique.
Figure 4 (smallHL-AT.jpg)
Figure 5: Rate of identification of the correct individual using horizontally obscured inputs with the removal technique.
Figure 5 (smallHL-RT.jpg)
Figure 6: Rate of identification of the correct individual using vertically obscured inputs with the averaging technique.
Figure 6 (smallVL-AT.jpg)
Figure 7: Rate of identification of the correct individual using vertically obscured inputs with the removal technique.
Figure 7 (smallVL-RT.jpg)

For each image set stability was reached at the following hit rate and for the specified number of eigenfaces:

Table 2: Table 2. Number of Eigenfaces for Hit Rate Stability for Rice Image Set, Averaging Technique
Occlusion Stable Hit Rate Number of Eigenfaces
Horizontal 1 pixel 90% 13
Horizontal 10 pixels 72% 7
Horizontal 40 pixels 28% 4
Vertical 1 pixel 90% 11
Vertical 10 pixels 83% 7
Vertical 40 pixels 71% 5
Table 3: Table 3. Number of Eigenfaces for Hit Rate Stability for Rice Image Set, Removal Technique
Occlusion Stable Hit Rate Number of Eigenfaces
Horizontal 1 pixel 72% 11
Horizontal 10 pixels 72% 12
Horizontal 40 pixels 56% 14
Vertical 1 pixel 72% 11
Vertical 10 pixels 74% 12
Vertical 40 pixels 72% 15

For detection tests using a number of eigenfaces greater than that specified in Tables 2 and 3 no significant improvement in detection success rate was achieved. In this way, occlusion tests suggest that implementations for both averaging and removal techniques do not achieve greater detection rates with numbers of eigenfaces greater than the minimum number needed for stability without occlusions.

Blurred Input Results

For both averaging and removal techniques, Rice image sets were tested for detection rates after being filtered with a two dimensional boxcar blur of various lengths. Results continue to indicate that the use of eigenfaces beyond the minimum necessary to achieve stability in the undistorted case is still unnecessary.

Figure 8: (a) undistorted base image. (b) same image with 20 pixel 2D boxcar blur.
Figure 8 (mattie2.jpg)
Figure 9: Rate of identification of the correct individual for blurred input images with the averaging technique.
Figure 9 (smallB-AT.jpg)
Figure 10: Rate of identification of the correct individual for blurred input images with the removal technique.
Figure 10 (smallB-RT.jpg)

For each image set stability was reached at the following hit rate and for the specified number of eigenfaces:

Table 4: Table 4. Number of Eigenfaces for Hit Rate Stability for Rice Image Set, Averaging Technique
Boxcar Length Stable Hit Rate Number of Eigenfaces
2 pixels 90% 12
20 pixels 80% 13
40 pixels 67% 15
Table 5: Table 5. Number of Eigenfaces for Hit Rate Stability for Rice Image Set, Averaging Technique
Boxcar Length Stable Hit Rate Number of Eigenfaces
2 pixels 72% 9
20 pixels 66% 14
40 pixels 44% 15

For detection tests using a number of eigenfaces greater than that specified in Tables 4 and 5 no significant improvement in detection success rate was achieved. In this way, blurring tests suggest that implementations for both averaging and removal techniques do not achieve greater detection rates with numbers of eigenfaces greater than the number needed for stability without blurring.

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