Instant Dehazing of Images using Polarization

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Presentation transcript:

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

Imaging through Haze Recover: Previous work Object + haze layers clear day moderate haze very hazy www.hazecam.net 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

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

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

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

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

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

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

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

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 + º p polarization degree

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 + º p polarization degree

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

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

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

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 º ) ( x,y z Blue b Green Red

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

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

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

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