4. convex concave

5. convex concave

8. Eigenfaces Photobook/Eigenfaces (MIT Media Lab)

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

10. Query Example Photobook/Eigenfaces (MIT Media Lab)

11. Eigenfeatures Photobook/Eigenfaces (MIT Media Lab)

12. Eigenfeatures

13. Photobook/Eigenfaces (MIT Media Lab) Eigenfeatures

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

15. 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.

16. Lambertian Reflectance Matt surface Light source is distant Light reflected equally to all directions  or

17. 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

18. Relief Sculptures

19. Illumination Cone =0.5*+0.2*+0.3*

20. Empirical Study BallFacePhoneParrot #148.253.767.942.8 #394.490.288.276.3 #597.993.594.184.7 #799.195.396.388.5 #999.596.397.290.7 (Yuille et al.) Dimension:

21. BallFacePhoneParrot #148.253.767.942.8 #284.475.283.269.7 #394.490.288.276.3 #496.592.192.081.5 #597.993.594.184.7 #698.994.595.287.2 #799.195.396.388.5 #899.395.896.889.7 #999.596.397.290.7 #1099.696.697.591.7

22. Intuition lighting reflectance

23. 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

24. Spherical Harmonics  ZYX XZYZXY

25. Harmonic Transform of Kernel n

26. Cumulative Energy N (percents)

27. Second Order Approximation

28. Other Low-D Approximations HemisphereForeshortenedBall (Exp.)Face ModelFace (Exp.) #15162486154 #26977848275 #38892949290 #49395979692 #59597989794 #698 999895 #79899 95 #899 96 #999 1009996 (Ramamoorthi)

29. Harmonic Images 

30. Reconstruction

32. Motion + Illumination

33. Reconstruction Reconstruction Laser scan

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

35. Mutual Information (Viola and Wells) Camera Rotation