Document

Multiple Light Source
Optical Flow
Robert J. Woodham
ICCV’90
Introduction
Optical Flow Definition
Is a vector field that shows the direction and magnitude
of the intensity changes from one image to the other
Main Idea
Use the intensity color values recorded from multiple
Images of moving objects acquired simultaneously
under different illumination conditions
to calculate optical flow
Some considerations
Object Motion vs. brightness change
Not purely geometric
Depends on radiometric factors
(illumination, reflectance)
The idea is based on. . .
Photometric stereo uses multiple conditions of
illumination to determine shape from shading
Theory
Optical Flow Constraint Equation
dE/dt=Exu + Eyv + Et
where
E = E(x,y,t) be the image brightness at point (x,y) as a function of time t
Ex = E/x, Ey = E/y, Et = E/t (partial derivatives of E with respect
to x, y and t)
u =dx/dt and v= dy/dt (instantaneous flow in the point (x,y).
Theory (2)
If the brightness does not change as consequence of
motion . . .
Exu + Eyv + Et = 0
Validity conditions
Purely translational motion,
Orthographic projection
Uniform incident illumination
Theory (3)
Equation properties
Exu + Eyv + Et = 0
•Cannot be solved locally – 1 equation with 2 unknowns
•Variation in scene illumination cause dE/dt0
•Objects acts as indirect sources of illumination (inter-reflection)
•Locations of brightness discontinuity – undefined points.
Using Multiple Light Sources
E1xu + E1yv + E1t = 0
E2xu + E2yv + E2t = 0
:
For 2 light sources
 E1x
u 
v    E
 
 2x
1
E1 y   E1t 
E2 y   E2t 
3 Light Sources
E1xu + E1yv + E1t = 0
E2xu + E2yv + E2t = 0
E3xu + E3yv + E3t = 0
Overdetermined Problem
Standard Least
Square solution
Ax = b
x = [u,v]T
b = -[E1t,, E2t ,E3t]T
 E1x

A   E2 x
 E3 x

E1 y 

E2 y 
E3 y 
x = (ATA)-1ATb
Implementation
6 images
3 under different illumination condition at time t0
3 same illumination as time t0, with same
background but different object position
3 images taken under different illumination condition in t0
Implementation
(2)
v
u
Multiple light source optical flow
computation at one point
3 Flow constraint lines
Results
•Estimation is good where the
surface is smoothly shaded
•In the collar dark points
degenerate the results
•In the discontinuities, due change
of image brightness the estimates
is also inaccurate
Optical Flow vectors
•Vector in the background due the
shadows and inter-reflection
Practical Implementation
Can be used 3 light sources (red, green and
blue) continuously illuminating a workspace
The capture can be made using cameras to
capture different spectral channels
Conclusion
•The method works better in smoothly curves
(not distinct surface markings and the local
brightness depends on local shading)
•Restrictions in surface discontinuities and
surface markings because local brightness
change is dominated by scene features (largely
independent of the illumination direction)

Download Report