single image haze removal using dark channel prior

Single Image Haze Removal Using Dark

Channel Prior

Professor : 王聖智教授

Student : 戴玉書

CVPR 2009 . Best Paper Award Kaiming He, Dept. of Inf. Eng., Chinese Univ. of Hong Kong, Hong Kong, ChinaJian Sun Xiaoou Tang, Dept. of Inf. Eng., Chinese Univ. of Hong Kong, Hong Kong, China

OutlineOutline

Background Background What is the Dark Channel Prior?What is the Dark Channel Prior? How to estimate How to estimate atmospheric light?? Estimating the transmission t(x) & Soft MaEstimating the transmission t(x) & Soft Ma

ttingtting Recovering the Scene RadianceRecovering the Scene Radiance ResultResult

BackgroundBackground

( ) ( ) ( ) (1 ( ))I x J x t x A t x ��

Observed intensity

Scene radiance

The global atmospheric light

The medium transmission,

( ) :

( ) :

:

( ) :

I x

J x

A

t x

��

( )( ) d xt x e

OutlineOutline

Background Background What is the Dark Channel Prior?What is the Dark Channel Prior? How to estimate How to estimate atmospheric light? light? Estimating the transmission t(x) & Soft MaEstimating the transmission t(x) & Soft Ma


Dark Channel PriorDark Channel Prior Observation on haze-free outdoor images: Observation on haze-free outdoor images: In most of the non-sky patches, at least one colIn most of the non-sky patches, at least one col

or channel has very low intensity at some pixelor channel has very low intensity at some pixelss

{ , , } ( )( ) min ( min ( ( )))dark c

c r g b y xJ x J y

��

��

Mainly due to three factorsMainly due to three factors

ShadowsShadows Colorful of objects or surfacesColorful of objects or surfaces Dark objectsDark objects

haze-free image The dark channel of haze-free image

Statistics of the dark Statistics of the dark channelschannels

Except for the sky region, the intensity of is low and Except for the sky region, the intensity of is low and tends to be zerotends to be zero

( )darkJ x��

Visually, the intensity of the dark channel is rough

approximation of the thickness of the haze

haze image The dark channel of haze image

OutlineOutline

Background Background What is the Dark Channel Prior?What is the Dark Channel Prior? To estimate of To estimate of atmospheric light light Estimating the transmission t(x) & Soft MaEstimating the transmission t(x) & Soft Ma


To estimate of To estimate of atmospheric light

Pick the top 0.1% brightest pixels in the dark Pick the top 0.1% brightest pixels in the dark channelchannel

OutlineOutline



Estimating the transmission Estimating the transmission

( ) ( )min ( ( )) ( ) min ( ( )) (1 ( ))c c c

y x y xI y t x J y t x A

��

��

( ) ( )

( ) ( )min( min ( )) ( ) min( min ( )) (1 ( ))

c c

c cc cy x y x

I y J yt x t x

A A ��

��

( ) ( )

( ) ( )min ( ) ( ) min ( ) (1 ( ))

c c

c cy x y x

I y J yt x t x

A A ��

��

( ) ( )

( )( ) min( min ( ( ))) min( min ( )) 0

cdark c

cc cy x y x

J yJ x J y

A ��

��

( )

( )( ) 1 min( min ( ))

c

cc y x

I yt x

A ��

��

( )

( )( ) 1 min( min ( ))

c

cc y x

I yt x

A

��

�� 0.95

( ) ( ) ( ) (1 ( ))I x J x t x A t x ��

Soft MattingSoft Matting

Image matting equation:Image matting equation:

(1 )I F B ��

( ) ( ) ( )T TE t t Lt t t t t

13

|( , )

1( (1 ( ) ( ) ( )))

| | | |k

Ti jij k kk

k i j k k

I U I

410

L ij :

( )L U t t

Minimize the following cost function:

A. Levin, D. Lischinski, and Y. Weiss. A closed form solutionto natural image matting. CVPR, 1:61–68, 2006. 4, 5, 7

OutlineOutline



( ) ( ) ( ) (1 ( ))I x J x t x A t x ��

0

( )( )

max( ( ), )

I x AJ x A

t x t

��

(t0=0.1)

OutlineOutline



ResultResult

The patch size is set to 15x15 The patch size is set to 15x15 Soft matting: Preconditioned Conjugate GSoft matting: Preconditioned Conjugate G

radient (PCG) algorithmradient (PCG) algorithm Local min operator using Marcel van HerkLocal min operator using Marcel van Herk

’s ’s fast algorithmfast algorithm

► Tan's resultTan's result

► Fattal's resultFattal's result

► Dark channelDark channel

► Kopf et al's resultKopf et al's result

► Dark channelDark channel

( )( ) d xt x e

single image haze removal using dark channel prior

Documents