1. Instant Dehazing of Images using Polarization
Yoav Schechner,
Srinivasa Narasimhan,
Shree Nayar
Department of Computer Science
Columbia University
Sponsors: DARPA HID, Morin Foundation, NSF

2. Imaging through Haze Recover: Previous work Object + haze layers
clear day
moderate haze
very hazy
Previous work
Pure image processing
Grewe & Brooks ’98, Kopeika ’98
Oakley & Satherley ’98
Physics based
Nayar & Narasimhan ’99
Polarization filtering
Shurcliff & Ballard ’64
Object + haze layers
Scene structure
Info about the aerosols
Recover:
Instant Dehazing: Yoav Schechner, Srinivasa Narasimhan, Shree Nayar

3. Imaging through Haze object R A direct T
camera
object
radiance R
Airlight A
scattering
direct
transmission T
Instant Dehazing: Yoav Schechner, Srinivasa Narasimhan, Shree Nayar

4. Multiplicative & additive models Color
Airlight A
camera
object
radiance R
scattering
direct
transmission T 1 z 1 z
z is a function of (x,y)
Multiplicative & additive models
- similar dependence
Color

5. Polarization and Haze A
polarizer
direct
transmission
Along the line of sight, polarization state is distance invariant
Assume: The object is unpolarized
@ all orientations
camera
Plane of rays determines airlight components A
> _ +
Airlight degree of polarization
p=0
unpolarized =
p=1
polarized =0
Instant Dehazing: Yoav Schechner, Srinivasa Narasimhan, Shree Nayar

6. Life is tough… Trivial case I
Instant Dehazing: Yoav Schechner, Srinivasa Narasimhan, Shree Nayar
Life is tough… I
Trivial case
… still, there is a dominant polarization

7. Experiment I = A T/2 + Best polarized image
Instant Dehazing: Yoav Schechner, Srinivasa Narasimhan, Shree Nayar

8. Experiment = I T/2 + A Worst polarized image
Instant Dehazing: Yoav Schechner, Srinivasa Narasimhan, Shree Nayar

9. Polarization measurement
polarizer
camera
180 o
3 general measurements suffice
Polarization vector determination

10. Model Recovery )/p e I R + = / ) ( e R T = A + = 2 / T I A
camera
object
radiance R
airlight A
transmission T + = 2 / T I A
2 input images:
Recovery
for known A p , βz e I R - + = / ) (
radiance
)/p z 1 b
depth I A _ βz e R T - =
transmission ÷ ø ö ç è æ A 1
airlight + p
polarization degree

11. airlight polarization
Model
saturated airlight A
airlight polarization p
camera
2 input images:
Recovery
for known A p , βz e I R - + = / ) (
radiance
)/p z 1 b
depth I + = 2 / T I A A
transmission βz e R T - =
airlight ÷ ø ö ç è æ - = βz e A 1 _ A + p
polarization degree

12. Dehazing Experiment I Best polarized image
Instant Dehazing: Yoav Schechner, Srinivasa Narasimhan, Shree Nayar

13. Dehazing Experiment R Dehazed image
Instant Dehazing: Yoav Schechner, Srinivasa Narasimhan, Shree Nayar

14. Range map ( ) = pA I e 1 log depth component images Airlight- = pA I e z 1 b
log
depth
component images
Airlight
saturation
polarization p

15. Aerosol distribution º å b b depends on the wavelength l l
Instant Dehazing: Yoav Schechner, Srinivasa Narasimhan, Shree Nayar l
400
600
500
700 nm b
Fog, heavy dust
Rayleigh (air)
Red b )
x,y z (
Green
Blue å ) (
x,y z
Blue b
Green
Red

16. Dehazing Experiment I Best polarized image
Instant Dehazing: Yoav Schechner, Srinivasa Narasimhan, Shree Nayar

17. Dehazing Experiment R Dehazed image
Instant Dehazing: Yoav Schechner, Srinivasa Narasimhan, Shree Nayar

18. Range map
Instant Dehazing: Yoav Schechner, Srinivasa Narasimhan, Shree Nayar

19. Conclusion Fast Acquisition Vision through Haze Depth
from Polarization
Aerosol
Size l b
Instant Dehazing: Yoav Schechner, Srinivasa Narasimhan, Shree Nayar