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									Single Image Haze Removal
 Using Dark Channel Prior


Kaiming He    The Chinese University of Hong Kong
   Jian Sun   Microsoft Research Asia
Xiaoou Tang   The Chinese University of Hong Kong
Hazy Images




• Low visibility
• Faint colors
Goals of Haze Removal




                        depth
• Scene restoration
• Depth estimation
Haze Imaging Model                  Atmospheric light

             I  J  t  A  (1  t )




    Hazy image    Scene radiance        Transmission
Haze Imaging Model

             I  J  t  A  (1  t )


                 d    ln t



     Depth                              Transmission
Ambiguity in Haze Removal

         scene
        radiance



                            ….


input
         depth
Previous Works

• Using additional information
  – Polarization filter [Shwartz et al., CVPR’06]
  – Multiple images [Narasimhan & Nayar, CVPR’00]
  – Known 3D model [Kopf et al., Siggraph Asia’08]
  – User-assistance [Narasimhan & Nayar, CPMCV’03]
Previous Works

• Single image
  – Maximize local contrast   [Tan, CVPR 08]
Previous Works

• Single image
  – Maximize local contrast   [Tan, CVPR 08]
Previous Works

• Single image
  – Maximize local contrast     [Tan, CVPR 08]

  – Independent Component Analysis [Fattal, Siggraph 08]
Previous Works

• Single image
  – Maximize local contrast     [Tan, CVPR 08]

  – Independent Component Analysis [Fattal, Siggraph 08]
Priors in Computer Vision

                         prior
        Ill-posed                       well-posed
        problem                          problem


• Smoothness prior
• Sparseness prior
                                 Dark Channel Prior
• Exemplar-based prior
Dark Channel

• min (rgb, local patch)
Dark Channel

• min (rgb, local patch)
  – min (r, g, b)




                           min (r, g, b)
Dark Channel

• min (rgb, local patch)
  – min (r, g, b)
  – min (local patch) = min filter




  15 x15

                    darkest          dark channel
Dark Channel

• min (rgb, local patch)
  – min (r, g, b)
  – min (local patch) = min filter

J dark (x)  min ( min J c (y ))
           y ( x ) c{r,g,b}


  – Jc: color channel of J

  – Jdark: dark channel of J         dark channel
Dark Channel

• min (rgb, local patch)
  – min (r, g, b)
  – min (local patch) = min filter

     J   dark
                 min (min J )
                             c
                       c


  – Jc: color channel of J

  – Jdark: dark channel of J         dark channel
A Surprising Observation
                           Haze-free
A Surprising Observation
                           Haze-free
A Surprising Observation
                           Haze-free
A Surprising Observation
                           Haze-free
A Surprising Observation
                           Haze-free
A Surprising Observation
                           Haze-free
A Surprising Observation
          1

 Prob.
         0.8


                          86% pixels
         0.6               in [0, 16]
                                                  5,000 haze-free
         0.4
                                                      images
         0.2




          0
               0         64       128       192       256

                   Pixel intensity of dark channels
Dark Channel Prior

• For outdoor haze-free images


              min (min J )  0
                           c
                     c
What makes it dark?

• Shadow


• Colorful object


• Black object
Dark Channel of Hazy Image




         hazy image             dark channel

• The dark channel is no longer dark.
Transmission Estimation
Haze imaging model     I  J  t  A  (1  t )

                       Ic   Jc
Normalize
                         c
                            c t 1 t
                       A    A
Compute dark channel

                     I     
                           c
                                    J 
                                     c
            min (min c )  min (min c )t  1  t
                 c A
                                c A
                                        
Transmission Estimation
Dark Channel Prior


                     min (min J c )  0
                              c




                                             0
Compute dark channel

                      I    c
                                    J 
                                      c
             min (min c )  min (min c )t  1  t
                  c A
                                 c A
                                         
Transmission Estimation
Estimate transmission
                                   c
                                   I
                  t  1  min (min c )
                               c A




Compute dark channel

                      I c
                                    J 
                                      c
             min (min c )  min (min c )t  1  t
                  c A
                                 c A
                                         
Transmission Estimation
Estimate transmission
                                        c
                                        I
                       t  1  min (min c )
                                    c A




           input   I                        estimated   t
Transmission Optimization
Haze imaging model     I  J  t  A  (1  t )
  Matting model       I  F    B  (1   )


                  +


                        tri-map                       
                                                     Refined
                  +
                                                  transmission
Transmission Optimization

                           ~2 T
             (t )   t  t  t Lt
                   Data term         Smoothness term


• L - matting Laplacian [Levin et al., CVPR ‘06]
• Constraint - soft, dense (matting - hard, sparse)
Transmission Optimization




           before optimization
Transmission Optimization




            after optimization
Atmospheric Light Estimation
 A: most hazy                   brightest pixels




 brightest pixel   hazy image    dark channel
Scene Radiance Restoration
                                       Atmospheric
                                          light


                I  J  t  A  (1  t )




   Hazy image        Scene radiance        Transmission
Results




          input
Results




          recovered image
Results




          depth
Results




          input
Results




          recovered image
Results




          depth
Results




          input
Results




          recovered image
Results




          depth
Comparisons




       input   [Fattal Siggraph 08]
Comparisons




       input   our result
Comparisons




      input   [Tan, CVPR 08]
Comparisons




      input   our result
Comparisons




   input   [Kopf et al, Siggraph Asia 08]   our result
Results: De-focus


                                  input




                                  depth

       recovered scene radiance
Results: De-focus


                      input




                      depth

           de-focus
Results: Video

    output




     input
Results: Video

    output




     input
Limitations

• Inherently white or grayish objects




         input        our result    transmission
Limitations

• Haze imaging model is invalid
  – e.g. non-constant A




           input                  our result
Summary

• Dark channel prior
  – A natural phenomenon
  – Very simple but effective
  – Put a bad image to good use
Thank you

								
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