Face Detection and Modeling for Recognition - Biometrics Research ...

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of the cluster are computed by Eqs. (B.6)-(B.10). a i = √ λ 1 (B.6) b i = √ λ 2 (B.7) λ 1 = 1 ( √ ) (σ 2 · ) σx 2 + σy 2 + 2 x − σy 2 2 + 4σ 2 xy , (B.8) λ 2 = 1 2 · ( √ ) (σ ) σx 2 + σy 2 − 2 x − σy 2 2 + 4σ 2 xy , (B.9) ( α = tan −1 λ1 − σx 2 ) , (B.10) σ xy where a i and b i are the estimated lengths of the major and minor axes of the cluster, respectively; λ 1 and λ 2 are the largest and smallest eigenvalues of the covariance matrix C, respectively; and α is the orientation of the major axis of the cluster i. The orientation α is used to calculate the angle θ ij in Eq. (B.2). Therefore, the distance between clusters i and j is computed as d ij = d − R i − R j , where d is the Euclidean distance between the centroids of these two clusters. 159
Appendix C Image Processing Template Library (IPTL) The face detection algorithm has been implemented using our Image Processing Template Library (IPTL). This library brings the abstract data class, Image, from a class level to a container (a class template) level, Image Template. It has the advantages of easy conversion between images of different pixel types, a high reuse rate of image processing algorithms, and a better user interface for manipulating data in the image class level. C.1 Image and Image Template An image captures a scene. It is represented by a two-dimensional array of picture elements (so called pixels) in the digital format. Pixels can be of different data types, e.g., one bit for binary images, one byte or word for grayscale images, three bytes 160
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Face Detection and Modeling for Rec
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perimental results demonstrate succ
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To my parents; my lovely wife, Pei-
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for providing the range datasets; t
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4 Face Modeling 97 4.1 Modeling Met
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List of Figures 1.1 Applications us
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2.6 A breakdown of face recognition
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4.2 3D triangular-mesh model and it
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5.14 Fine alignment using geodesic
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Chapter 1 Introduction In recent ye
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(a) (b) Figure 1.1. Applications us
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(e) Figure 1.1. (Cont’d). (f) (a)
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esolutions and of poor quality (i.e
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can recognize known faces in carica
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the motivation for studies that att
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(a) Figure 1.10. Similarity of fron
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verify the face present in an image
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17 Figure 1.12. System diagram of o
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algorithm can also provide geometri
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commercial parametric face modeling
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1.5.1 Face Alignment Using 2.5D Sna
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1.5.3 Face Alignment Using Interact
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Using merely low-level features (e.
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such as eyes, mouth and face bounda
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can be applied to a 3D face model w
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Chapter 2 Literature Review We firs
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mation theory, geometrical modeling
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(e) (f) (g) (h) (i) (j) (k) (l) Fig
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esult in different recognition appr
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(a) (b) (c) Figure 2.2. Examples of
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(a) (b) (c) (d) Figure 2.4. Interna
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Figure 2.6. A breakdown of face rec
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2.3 Face Modeling Face modeling pla
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An advanced modeling approach which
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tionals to minimize, implementation
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are listed in Table 2.2. All of the
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low-level features can provide mean
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holistic 2D and geometrical 3D feat
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size) to generate potential face ca
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oundary. A face score is computed f
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normalized red-green (r-g) space [1
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(a) (b) Figure 3.3. The Y C b C r c
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(a) Figure 3.5. 2D projections of t
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3.3 Localization of Facial Features
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(a) (b) (c) Figure 3.9. Constructio
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The eye map from the chroma is enha
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mouth is performed within the face
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Figure 3.12. Computation of face bo
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center, and lengths of major and mi
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segment. The other term favors an u
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(a) (b) (c) (d) (e) Figure 3.15. Fa
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(a) (b) (c) (d) (e) Figure 3.18. Fa
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The number of false positives is al
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(a) (b) (c) (d) Figure 3.20. Face d
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Figure 3.22. Face detection results
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Figure 3.22. (Cont’d). 93
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3.5 Summary We have presented a fac
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Chapter 4 Face Modeling We first in
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and nose in frontal views), and bec
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4.3 Facial Measurements Facial meas
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4.4 Model Construction Our face mod
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a feature-dependent decay factor. F
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is to find appropriate external ene
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Page 165 and 166: 6.2 Future Directions Based on the
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Page 171 and 172: Appendices
Page 173 and 174: ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ Y
Page 175 and 176: and are shown as blue-dashed lines
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Page 185 and 186: Bibliography [1] Visionics Corporat
Page 187 and 188: [32] L. Wiskott, J.M. Fellous, N. K
Page 189 and 190: [59] M. Grudin, “On internal repr
Page 191 and 192: [84] M. Abdel-Mottaleb and A. Elgam
Page 193 and 194: [113] B. Kim and P. Burger, “Dept
Page 195 and 196: [141] M.D. Adams and F. Kossentini,
Page 197 and 198: [169] P.T. Jackway and M. Deriche,
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