Understanding the effect of lighting in images Ronen Basri

Light field Rays travel from sources to objects There they are either absorbed or reflected Energy decreases with distance and number of bounces Camera captures the set of rays that travel through the focal center

Specular reflectance (mirror) When a surface is smooth light reflects in the opposite direction of the surface normal

Specular reflectance When a surface is slightly rough the reflected light will fall off around the specular direction

Diffuse reflectance When the surface is very rough light may be reflected equally in all directions

Diffuse reflectance When the surface is very rough light may be reflected equally in all directions

BRDF

Lambertian reflectance

Lambert’s law

Preliminaries

Photometric stereo Given several images of the a lambertian object under varying lighting Assuming single directional source

Photometric stereo We can solve for S if L is known (Woodham) If L is unknown we can use SVD factorization (Hayakawa)

Factorization Use SVD to find a rank 3 approximation Define Factorization is not unique, since invertible To reduce ambiguity we impose integrability – up to generalized bas relief transformation (Belhumeur et al.)

Integrability

Shape from shading (SFS)

Shape from shading

Distance transform

Solution

Example