eigenfaces photobook/eigenfaces (mit media lab)
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Database
7562 pictures of 3000 people
Photobook/Eigenfaces (MIT Media Lab)
Query ExamplePhotobook/Eigenfaces (MIT Media Lab)
Recognition with PCAAmano, Hiura, Yamaguti, and Inokuchi; Atick and Redlich; Bakry, Abo-Elsoud, and Kamel; Belhumeur, Hespanha, and Kriegman; Bhatnagar, Shaw, and Williams; Black and Jepson; Brennan and Principe; Campbell and Flynn; Casasent, Sipe and Talukder; Chan, Nasrabadi and Torrieri; Chung, Kee and Kim; Cootes, Taylor, Cooper and Graham; Covell; Cui and Weng; Daily and Cottrell; Demir, Akarun, and Alpaydin; Duta, Jain and Dubuisson-Jolly; Hallinan; Han and Tewfik; Jebara and Pentland; Kagesawa, Ueno, Kasushi, and Kashiwagi; King and Xu; Kalocsai, Zhao, and Elagin; Lee, Jung, Kwon and Hong; Liu and Wechsler; Menser and Muller; Moghaddam; Moon and Philips; Murase and Nayar; Nishino, Sato, and Ikeuchi; Novak, and Owirka; Nishino, Sato, and Ikeuchi; Ohta, Kohtaro and Ikeuchi; Ong and Gong; Penev and Atick; Penev and Sirivitch; Lorente and Torres; Pentland, Moghaddam, and Starner; Ramanathan, Sum, and Soon; Reiter and Matas; Romdhani, Gong and Psarrou; Shan, Gao, Chen, and Ma; Shen, Fu, Xu, Hsu, Chang, and Meng; Sirivitch and Kirby; Song, Chang, and Shaowei; Torres, Reutter, and Lorente; Turk and Pentland; Watta, Gandhi, and Lakshmanan; Weng and Chen; Yuela, Dai, and Feng; Yuille, Snow, Epstein, and Belhumeur; Zhao, Chellappa, and Krishnaswamy; Zhao and Yang.
Lambertian Reflectance
• Matt surface• Light source is distant• Light reflected equally
to all directions
n̂
cos ( 90 !)
ˆ ˆ( , )
o
T
I E
I l n l E l n n
or
l̂
Photometric Stereo: Factorization
• M is f x p (#images x #pixels)• L is f x 3 – light sources• S is 3 x p – surface normals (scaled by albedo)• Rank(M)=3 (if no noise present)• SVD:
• Ambiguity
Eliminate by forcing integrability
( )( )TM U V LS
M LS
1M LA AS
Ball Face Phone Parrot
#1 48.2 53.7 67.9 42.8
#2 84.4 75.2 83.2 69.7
#3 94.4 90.2 88.2 76.3
#4 96.5 92.1 92.0 81.5
#5 97.9 93.5 94.1 84.7
#6 98.9 94.5 95.2 87.2
#7 99.1 95.3 96.3 88.5
#8 99.3 95.8 96.8 89.7
#9 99.5 96.3 97.2 90.7
#10 99.6 96.6 97.5 91.7
Empirical Study
Spherical Harmonics
• Orthonormal basis for functions on the sphere
• n’th order harmonics have 2n+1 components
• Rotation = phase shift (same n, different m)
• In space coordinates: polynomials of degree n
• Funk-Hecke convolution theorem
( )!(2 1)( , ) (cos )
4 ( )!im
nm nm
n mnY P e
n m
2 / 22(1 )
( ) ( 1)2 !
m n mn
nm n n m
z dP z z
n dz
Harmonic Transform of Kernel
1.023
0.495
-0.111
0.05
-0.029
0.886
-0.5
0
0.5
1
1.5
0 1 2 3 4 5 6 7 8
00
( ) max(cos ,0) n nn
k k Y
nk
n
37.5
87.599.22 99.81 99.93 99.97
0
20
40
60
80
100
0 1 2 3 4 5 6 7 8
Cumulative Energy
N
1
N
nn
E
(percents)
Other Low-D Approximations
Hemisphere Foreshortened Ball (Exp.) Face Model Face (Exp.)
#1 51 62 48 61 54
#2 69 77 84 82 75
#3 88 92 94 92 90
#4 93 95 97 96 92
#5 95 97 98 97 94
#6 98 98 99 98 95
#7 98 99 99 99 95
#8 99 99 99 99 96
#9 99 99 100 99 96
(Ramamoorthi)
Harmonic Images( ) ( , , )nm nm x y zb p r n n n
zn xn yn
2(3 1)zn 2 2( )x yn n x yn n x zn n y zn n
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