convex concave

convex concave

Eigenfaces Photobook/Eigenfaces (MIT Media Lab)

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

Query Example Photobook/Eigenfaces (MIT Media Lab)

Eigenfeatures Photobook/Eigenfaces (MIT Media Lab)

Eigenfeatures

Photobook/Eigenfaces (MIT Media Lab) Eigenfeatures

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

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

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

Relief Sculptures

Illumination Cone =0.5*+0.2*+0.3*

Empirical Study BallFacePhoneParrot # # # # # (Yuille et al.) Dimension:

BallFacePhoneParrot # # # # # # # # # #

Intuition lighting reflectance

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

Spherical Harmonics  ZYX XZYZXY

Harmonic Transform of Kernel n

Cumulative Energy N (percents)

Second Order Approximation

Other Low-D Approximations HemisphereForeshortenedBall (Exp.)Face ModelFace (Exp.) # # # # # # # # # (Ramamoorthi)

Harmonic Images 

Reconstruction

Motion + Illumination

Reconstruction Reconstruction Laser scan

Advantage of Our Method Disparity error Residue Std intensity Accounting for illumination variation Assuming brightness constancy

Mutual Information (Viola and Wells) Camera Rotation