# NYU CSCI-GA 2271 - Lighting affects appearance (27 pages)

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## Lighting affects appearance

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- Pages:
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- School:
- New York University
- Course:
- Csci-Ga 2271 - Computer Vision

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Lighting affects appearance What is the Question based on work of Basri and Jacobs ICCV 2001 Given an object described by its normal at each surface point and its albedo we will focus on Lambertian surfaces 1 What is the dimension of the space of images that this object can generate given any set of lighting conditions 2 How to generate a basis for this space Empirical Study Epstein Hallinan and Yuille see also Hallinan Belhumeur and Kriegman 1 3 5 7 9 Ball 48 2 94 4 97 9 99 1 99 5 Face 53 7 90 2 93 5 95 3 96 3 Phone Parrot 67 9 42 8 88 2 76 3 94 1 84 7 96 3 88 5 97 2 90 7 Dimension 5 2D Domain Lambertian No cast shadows convex objects Lights are distant n l Lighting to Reflectance Intuition Lambert Law 1 k max cos 0 Lighting to Reflectance Intuition 1 l 0 5 0 0 1 2 3 0 0 1 2 3 2 1 5 Three point light sources l Illuminating a sphere and its reflection r r r 1 0 5 Profiles of l and Lighting Reflectance r r r 2 k r r l l l l l sin l d l d l S 1 where k r r l l k r l max cos r l 0 Images Spherical Harmonics S H Orthonormal basis Ynm 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 2n 1 n m Ynm Pnm cos eim 4 n m 2 m2 1 z Pnm z 2 n n n m d 2 n z 1 n m dz S H analog to convolution theorem Funk Hecke theorem Convolution in function domain is multiplication in spherical harmonic domain filter k Ynm n Ynm 4 n kn 2n 1 k Harmonic Transform of Kernel k q max cosq 0 kn hYnn00 n 0 2 k n 3 n 1 n 2 2 n 1 2 1 n n n 2 1 1 2 2 0 n 0 n 1 n 2 even n 2 odd An Amplitudes of Kernel 1 k 2n 1 n 2 nm m n An n Energy of Lambertian Kernel in low order harmonics k is a low pass filter 1 1 5 k cos cos 2 4 2 16 Reflectance Functions Near Low dimensional Linear Subspace n r k l K K nm n 0 m n 2 n nm Lnm Y hnm nm Lnm hYnm nm n 0 m n Yields 9D linear subspace Forming Harmonic Images b nm p rnm X Y Z 2 Z2 X 2 Y 2 X 2 Y 2 Z X Y XY XZ YZ How accurate is approximation Point light source r k l n K n 0

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