2
CS152, Spring 2011
Intro Computer Vision
Photometric Stereo:
General BRDF
and
Reflectance Map
CS152, Spring 2011
Intro Computer Vision
Coordinate system
x
y
f(x,y)
Surface:
s
(x,y) =(x,y, f(x,y))
Tangent vectors:
Normal vector
n
=
∂
s
∂
x
×
∂
s
∂
y
=
∂
f
∂
x
,
∂
f
∂
y
,
−
1
Λ
Ν
Μ
Ξ
Π
Ο
CS152, Spring 2011
Intro Computer Vision
Gradient Space (p,q)
x
y
f(x,y)
Normal vector
Gradient Space : (p,q)
n
CS152, Spring 2011
Intro Computer Vision
Image Formation
For a given point A on the surface, the image
irradiance E(x,y) is a function of
1.
The BRDF at A
2.
The surface normal at A
3.
The direction of the light source
n
s
.
E(x,y)
A
CS152, Spring 2011
Intro Computer Vision
Reflectance Map
Let the BRDF be the same at all points on the surface, and let
the light direction
s
be constant.
1.
Then image irradiance is a function of only the direction
of the surface normal.
2.
In gradient space, we can write E(p,q)
3.
We can measure E(p,q) by taking an image of a sphere
made of a single material under distant lighting
n
s
E(x,y)
CS152, Spring 2011
Intro Computer Vision
Example Reflectance Map:
Lambertian surface
For lighting from front
E(p,q)