Eigenfaces PhotobookEigenfaces MIT Media Lab Database PhotobookEigenfaces MIT

Eigenfaces Photobook/Eigenfaces (MIT Media Lab)

Database Photobook/Eigenfaces (MIT Media Lab) 7562 pictures of 3000 people

Query Example Photobook/Eigenfaces (MIT Media Lab)

Eigenfeatures Photobook/Eigenfaces (MIT Media Lab)

Eigenfeatures Photobook/Eigenfaces (MIT Media Lab) Receiver Operating Characteristic (ROC) Curve

Recognition with PCA Amano, 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 or q

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

Illumination Cone =0. 5* +0. 2* +0. 3*

Empirical Study 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

Intuition lighting reflectance

Spherical Harmonics • Orthonormal basis for functions on the sphere • n’th order harmonics have 2 n+1 components • Rotation = phase shift (same n, different m) • In space coordinates: polynomials of degree n • Funk-Hecke convolution theorem

Spherical Harmonics 1 Z X Y XY XZ YZ

Harmonic Transform of Kernel n

Cumulative Energy (percents) N

Second Order Approximation

Other Low-D Approximations (Ramamoorthi) 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 96 #9 99 99 100 99 96