Title: 3-D Shape from Shading
13-D Shape from Shading
- Image formation and the shape from shading problem
23D shape from shading
Prados Faugeras, 2005
3Image intensities depend on
- 3-D surface shape
- Surface reflectance properties
- Illumination in the scene
- Viewing geometry
Compute explicitly
General assumptions
4Viewing geometry
What fraction of the incident light is reflected
toward the viewer?
radiance
irradiance
Reflectance Function F(i,e,g)
surface radiance surface irradiance
5Reflectance functions
Fmirror(i,e,g) 1 if i e i e g
0 otherwise
Fmatte(i,e,g) ? cos i if i lt 90 0
otherwise ? albedo
6Representing surface orientation using
stereographic projection
sphere has radius 1
g
f
(f,g) (0, 2)
(f,g) (2, 0)
viewer
7Given surface brightness, can we determine
surface orientation?
8Reflectance Map R(f,g)
Given (1) light source (2) viewer position (3)
surface reflectance properties
R(f,g) relates brightness to surface orientation
Image Irradiance Equation I(x,y) I0 ?(x,y)
R(f,g)
9Ikeuchi Horn shape-from-shading algorithm
- Three sources of constraint
- (1) image intensity I(x,y)
- (2) surface smoothness
- e.g. minimize total variation in surface
- (3) points of known surface orientation
- e.g. occluding boundaries, shadow boundaries
(known viewer direction, light source direction,
surface reflectance properties)
I(x,y) I0 ?(x,y) R(f,g)
10Boundaries influence shape perception
Ramachandran, 1988