Fig. 1. Examples of matching problems using MHD. Solid lines represent the line segments in the model and dashed lines represent the line segments in the test image.

Fig. 2. An example of matching problem on broken line using MHD.

Fig. 3. Line displacement measures.

Fig. 4. The rotation effect of two lines. (a) The original line pair. (b) Rotate the shorter line. (c) Rotate the longer line. (d) Rotate both lines with half of their angle difference in opposite directions. Solid lines represent lines before rotation. Dashed lines represent lines after rotation.

Fig. 5. All cases with d(m,t)=0.

Fig. 10. An example of misaligned model and input faces.

Fig. 6. The effect of W_a on recognition of misaligned profiles.

Fig. 7. Sample pairs of frontal face edge maps with detected dominant points.

Fig. 8. Sample pairs of profile edge maps with detected dominant points.

Fig. 9. Sample pairs of face profiles together with the detected dominant points.

Fig. 11. Illustration of average LHD composition.

Fig. 12. Sample cropped images of model (first row) and test faces (second and third rows).

Fig. 13. Recognition results when left light was on.

Fig. 14. Recognition results when right light was on.

Fig. 15. Recognition results when both lights were on.

Fig. 16. Recognition results with background lighting after two weeks.

Fig. 18. Recognition results on smiling expression.

Fig. 19. Recognition results on angry expression.

Fig. 20. Recognition results on screaming expression.

Fig. 17. An illustration of large variation between the model and the scream expression face.

Fig. 21. The Yale face database contains 165 frontal face images covering 15 individuals taken under 11 different conditions. The faces in the first 4 rows are original images while the last 4 rows show the cropped faces used in our experiment.

Table 1. Face recognition results of MHD and LHD with W_a=20

Table 2. Legends of symbols in Table 1

Table 3. “Leave-one-out” test of Yale face database

Table 4. Average storage requirements of profile and frontal faces in the experiments

Table 5. Average computational time of MHD and LHD