##### Document Text Contents

Page 65

53

corresponding to ith feature point. The vector qi is a set of spatial and angular

distances from feature point i to its N nearest neighbors denoted by Qi(x,y,θj),

where j is the jth of the N neighbors. Ni represents a set of neighbors. The

neighbors satisfying both maximum number N and minimum Euclidean distance

dij between two points Vi and Vj are said to be of consequence for i

th feature point.

In order to identify an input graph with a stored one, which might be

different either in total number of feature points or in the location of the respective

faces, two cost values are evaluated [36]. One is the topological cost and the other

is a similarity cost. If i, j refer to nodes in the input graph I and nmyx ′′′′ ,,, refer

to nodes in the stored graph O then the two graphs are matched as follows [36]:

1. The centroids of the feature points of I and O are aligned.

2. Let Ni be the i

th feature point { Vi }of I. Search for the best feature point {Vi’ }

in O using the criterion

mi

Nm

ii

ii

ii S

qq

qq

S

i

′

∈′

′

′

′ =−= min

.

1 (2.45)

3. After matching, the total cost is computed taking into account the topology of

the graphs. Let nodes i and j of the input graph match nodes i ′ and j ′ of the

stored graph and let iNj ∈ (i.e., Vj is a neighbor of Vi). Let

��

�

�

�

��

�

�

�

= ′′

′′

′′

ij

ji

ji

ij

jjii

d

d

d

d

,minρ . The topology cost is given by

.1 jjijjii ′′′′ −=Τ ρ (2.46)

Page 129

117

[113] G. Chow and X. Li, “Towards a system for automatic facial feature

detection,” Pattern Recognition, vol. 26, no. 12, pp. 1739-1755, 1993.

[114] L. Stringa, “Eyes detection for face recognition,” Applied Artificial

Intelligence, vol. 7, pp. 365-382, Oct-Dec 1993.

[115] P. Burt, “Smart sensing within a pyramid vision machine,” Proc. of IEEE,

vol. 76, pp. 1006-1015, August 1988.

[116] D. Beymer, “Face recognition under varying pose,” Proc. of 23rd Image

understanding Workshop, vol.2, pp. 837-842, 1994.

[117] M. Lades, J Vorbruggen, J, Buhmann, J. Lange, von der Malsburg, and R.

Wurtz, “ Distortion invariant object recognition in the dynamic link

architecture,” IEEE Trans. Comput., vol. 42, no. 3, pp. 300-311, 1993.

[118] T. S. Lee, “Image representation using 2-d Gabor wavelets,” IEEE Trans.

On Pattern Analysis Pattern Analysis and Machine Intelligence, vol. 18,

no.10, October, 1996.

[119] J. G. Daugman, “Two dimensional spectral analysis of cortical receptive

field profile”, Vision Research, vol. 20, pp. 847-856, 1980.

[120] D. Gabor, “Theory of communication,” J. IEE, vol. 93, pp. 429-459, 1946.

[121] D. H. Hubel and T. N. Wiesel, “Functional architecture of macaque

monkey visual cortex,” Proc. Royal Soc. B (London), vol. 198, pp.1-59,

1978.

[122] S. Marcelja, “Mathematical description of the responses of simple cortical

cells,” J. Optical Soc. Am., vol. 70, pp. 1297-1300, 1980.

[123] A. M. Burton, and V. Bruce, and I. Craw, “Modeling face recognition,”

Philosophical Trans. Of the Royal Soc. B, vol. 1, p. 457-480, 1993.

[124] V. Bruce and S. Langton, “The use of pigmentation and shading

information in recognizing the sex and identities of faces,” Perception,

vol. 23, pp.803-822, 1994.

[125] R. Kemp, G. Pike, P. White, and A. Musselman, “A perception and

recognition of normal and negative faces- the role of shape from shading

and pigmentation cues,” Perception, vol. 25, pp. 37-52, 1996.

[126] R. E. Galper, “Recognition of faces in photographic negative”,

Psychonomic Science, vol. 19, pp. 207-208, 1970.

53

corresponding to ith feature point. The vector qi is a set of spatial and angular

distances from feature point i to its N nearest neighbors denoted by Qi(x,y,θj),

where j is the jth of the N neighbors. Ni represents a set of neighbors. The

neighbors satisfying both maximum number N and minimum Euclidean distance

dij between two points Vi and Vj are said to be of consequence for i

th feature point.

In order to identify an input graph with a stored one, which might be

different either in total number of feature points or in the location of the respective

faces, two cost values are evaluated [36]. One is the topological cost and the other

is a similarity cost. If i, j refer to nodes in the input graph I and nmyx ′′′′ ,,, refer

to nodes in the stored graph O then the two graphs are matched as follows [36]:

1. The centroids of the feature points of I and O are aligned.

2. Let Ni be the i

th feature point { Vi }of I. Search for the best feature point {Vi’ }

in O using the criterion

mi

Nm

ii

ii

ii S

S

i

′

∈′

′

′

′ =−= min

.

1 (2.45)

3. After matching, the total cost is computed taking into account the topology of

the graphs. Let nodes i and j of the input graph match nodes i ′ and j ′ of the

stored graph and let iNj ∈ (i.e., Vj is a neighbor of Vi). Let

��

�

�

�

��

�

�

�

= ′′

′′

′′

ij

ji

ji

ij

jjii

d

d

d

d

,minρ . The topology cost is given by

.1 jjijjii ′′′′ −=Τ ρ (2.46)

Page 129

117

[113] G. Chow and X. Li, “Towards a system for automatic facial feature

detection,” Pattern Recognition, vol. 26, no. 12, pp. 1739-1755, 1993.

[114] L. Stringa, “Eyes detection for face recognition,” Applied Artificial

Intelligence, vol. 7, pp. 365-382, Oct-Dec 1993.

[115] P. Burt, “Smart sensing within a pyramid vision machine,” Proc. of IEEE,

vol. 76, pp. 1006-1015, August 1988.

[116] D. Beymer, “Face recognition under varying pose,” Proc. of 23rd Image

understanding Workshop, vol.2, pp. 837-842, 1994.

[117] M. Lades, J Vorbruggen, J, Buhmann, J. Lange, von der Malsburg, and R.

Wurtz, “ Distortion invariant object recognition in the dynamic link

architecture,” IEEE Trans. Comput., vol. 42, no. 3, pp. 300-311, 1993.

[118] T. S. Lee, “Image representation using 2-d Gabor wavelets,” IEEE Trans.

On Pattern Analysis Pattern Analysis and Machine Intelligence, vol. 18,

no.10, October, 1996.

[119] J. G. Daugman, “Two dimensional spectral analysis of cortical receptive

field profile”, Vision Research, vol. 20, pp. 847-856, 1980.

[120] D. Gabor, “Theory of communication,” J. IEE, vol. 93, pp. 429-459, 1946.

[121] D. H. Hubel and T. N. Wiesel, “Functional architecture of macaque

monkey visual cortex,” Proc. Royal Soc. B (London), vol. 198, pp.1-59,

1978.

[122] S. Marcelja, “Mathematical description of the responses of simple cortical

cells,” J. Optical Soc. Am., vol. 70, pp. 1297-1300, 1980.

[123] A. M. Burton, and V. Bruce, and I. Craw, “Modeling face recognition,”

Philosophical Trans. Of the Royal Soc. B, vol. 1, p. 457-480, 1993.

[124] V. Bruce and S. Langton, “The use of pigmentation and shading

information in recognizing the sex and identities of faces,” Perception,

vol. 23, pp.803-822, 1994.

[125] R. Kemp, G. Pike, P. White, and A. Musselman, “A perception and

recognition of normal and negative faces- the role of shape from shading

and pigmentation cues,” Perception, vol. 25, pp. 37-52, 1996.

[126] R. E. Galper, “Recognition of faces in photographic negative”,

Psychonomic Science, vol. 19, pp. 207-208, 1970.