Single Image Haze Removal Using Dark Channel Prior Kaiming He Jian Sun Xiaoou Tang The Chinese University of Hong Kong Microsoft Research Asia The Chinese University of Hong Kong

Hazy Images Low visibility Faint colors

Goals of Haze Removal depth Scene restoration Depth estimation

Haze Imaging Model I  J  t  A  (1 t) Atmospheric light 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 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 Ill-posed problem well-posed problem Smoothness prior • Sparseness prior Exemplar-based prior Dark Channel 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 dark channel darkest

Dark Channel Jdark (x)  min ( min Jc (y)) min (rgb, local patch) min (local patch) = min filter Jdark (x)  min ( min Jc (y)) y(x) c{r,g,b} Jc: color channel of J Jdark: dark channel of J dark channel

Dark Channel Jdark  min (min Jc ) min (rgb, local patch) min (local patch) = min filter Jdark  min (min Jc )  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 in [0, 16] 0.6 5,000 haze-free images 0.4 0.2 64 128 192 Pixel intensity of dark channels 256

Dark Channel Prior For outdoor haze-free images min (min Jc )  0  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) I  J c c Normalize t 1 t Ac Ac Compute dark channel Ic Jc   min (min  c )  min (min c )t 1 t c  A A   c

Transmission Estimation Dark Channel Prior min (min Jc )  0  c Compute dark channel  0 Ic Jc   min (min  c )  min (min c )t 1 t c  A A   c

Transmission Estimation Estimate transmission c I t  1 min (min ) Ac  c Compute dark channel  Jc  min (min c )t    c A  I c min (min  c )  1 t Ac

Transmission Estimation Estimate transmission c I t  1 min (min  c ) Ac estimated t input I

Transmission Optimization Haze imaging model I  J  t  A  (1 t) I  F   B  (1 ) Matting model +  tri-map Refined transmission +

Transmission Optimization ~ 2 (t)   t  t tTLt 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

Imatest Imatest LLC is a company that produces image quality testing software and offers a range of consulting services. Imatest was founded by photographer/engineer Norman Koren in Boulder, Colorado in 2004 to develop software for testing digital camera image quality.

Wedge The Wedge module (described in this document) can analyze any arrangement of horizontal or vertical (but not diagonal) wedges, using manual region selection.

ISO 12233:2000 The ISO 12233:2000 resolution test chart and its variants are by far the best-know charts with wedge patterns.

For the Wedge module, select the regions of interest (ROIs) to be analyzed.

ROI Fine adjustment window The boundaries of the selected region should be inside the ends of the wedge (top and bottom, above) and outside the sides, allowing a little “breathing room”.

MTF and Aliasing onset results MTF: Modulation Transfer Function MTF and Aliasing onset results