1
CSE252A
Illumination Cones
and
Uncalibrated Photometric Stereo
CS252A, Fall 2010
Computer Vision I
Photometric stereo
•
Single viewpoint, multiple images under
different lighting.
1.
Arbitrary known BRDF, known lighting
2.
Lambertian BRDF, known lighting
3.
Lambertian BRDF, unknown lighting.
CS252A, Fall 2010
Computer Vision I
Three Source Photometric stereo:
Step1
Offline:
Using source directions & BRDF, construct reflectance map
for each light source direction. R
1
(p,q), R
2
(p,q), R
3
(p,q)
Online:
1.
Acquire three images with known light source directions.
E
1
(x,y), E
2
(x,y), E
3
(x,y)
2.
For each pixel location (x,y), find (p,q) as the intersection
of the three curves
R
1
(p,q)=E
1
(x,y)
R
2
(p,q)=E
2
(x,y)
R
3
(p,q)=E
3
(x,y)
3.
This is the surface normal at pixel (x,y).
Over image, the
normal field is estimated
CS252A, Fall 2010
Computer Vision I
Reflectance Map of Lambertian Surface
What does the intensity
(Irradiance) of one pixel in one
image tell us? (e..g, let’s say the
Then, the normal lies on
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
R(p,q)
CS252A, Fall 2010
Computer Vision I
One viewpoint, two images, two light sources
Two super imposed reflectance maps
E
measured
E
measured
1
A third image would disambiguate between two possible n
R
1
(p,q)
R
2
(p,q)
CS252A, Fall 2010
Computer Vision I
Recovering the surface f(x,y)
Many methods: Simplest approach
1.
From estimate
n
=(n
x
,n
y
,n
z
), p=n
x
/n
z
, q=n
y
/n
z
2.
Integrate p=df/dx along a row (x,0) to get f(x,0)
3.
Then integrate q=df/dy along each column
starting with value of the first row
f(x,0)