# Non-Local Image Dehazing - Supplementary Material

## Dana Berman, Tali Treibitz, Shai Avidan

### Outline

We present:
1) Various images before and after color-quantization, to support our prior. All the images are from the Berkeley Segmentation Dataset.
2) A comparison of our single image dehazing method to state-of-the-art algorithms. We compare:
a) Natural Images
b) Synthetic Images
c) Noisy Synthetic Images
We show here additional results that were not included in the paper for lack of space. Some of the results from the paper are included here as well, since we find it
easier to compare images in this interface.
3) A complete list of references is given at the end.

To switch between images please use the colored buttons on the left.
Please note that the result images are initialized to our results.

### Color Quantized Images

Our method is based on the observation that the number of distinct colors in an image is orders of magnitude smaller than the number of pixels. This assumption is used for saving color images using indexed colormaps. We validate and quantify it on the Berkeley Segmentation Dataset: we clustered the RGB pixel values using K-means to a maximum of 500 clusters, and replaced every pixel in the image with its respective cluster center. The result is an image with 500 different RGB values at most (two orders of magnitude smaller than image size). We show a random selection of outdoor scenes, before and after the color quantization.

### Natural Images

#### Lviv

| Input Hazy Image
Dehazing Methods | Output Dehazed Image
Dehazing Methods | Output Transmission Map

#### Stadium

| Input Hazy Image
Dehazing Methods | Output Dehazed Image

#### Wheat Field

| Input Hazy Image
Dehazing Methods | Output Dehazed Image

#### Florence

| Input Hazy Image
Dehazing Methods | Output Dehazed Image

#### Forest

| Input Hazy Image
Dehazing Methods | Output Dehazed Image
Dehazing Methods | Output Transmission Map

#### Hazy Day

| Input Hazy Image
Dehazing Methods | Output Dehazed Image

#### New York

| Input Hazy Image
Dehazing Methods | Output Dehazed Image

#### Pumpkins

| Input Hazy Image
Dehazing Methods | Output Dehazed Image
Dehazing Methods | Output Transmission Map

#### Signs

Dehazing Methods | Output Dehazed Image | Input Hazy Image

#### Swan

| Input Hazy Image
Dehazing Methods | Output Dehazed Image

#### Train

| Input Hazy Image
Dehazing Methods | Output Dehazed Image

#### House

Dehazing Methods | Output Dehazed Image | Input Hazy Image

### Synthetic Images

A synthetic dataset of hazy images of natural scenes was introduced by [Fattal 2014], and is available online. The dataset contains eleven haze free images, synthetic distance maps and corresponding simulated haze images. The following table summarizes the L1 errors on non-sky pixels (same metric used in [Fattal 2014]) of the transmission maps and the dehazed images. Our method is compared to the method of [Fattal 2014] and an implementation of [He et al. 2009] by [Fattal 2014].

Table: L1 errors of transmission maps and dehazed images

The transmission maps are displayed along with the images. They are color-mapped: warm colors indicate high values, while cold color indicate low values.
Please note that the buttons on the left switch both the image and the transmission map.

#### Flower 1

| Input Hazy Image
Dehazing Methods | Output Dehazed Image
Dehazing Methods | Output Transmission Map

#### Lawn 2

| Input Hazy Image
Dehazing Methods | Output Dehazed Image
Dehazing Methods | Output Transmission Map

#### Road2

| Input Hazy Image
Dehazing Methods | Output Dehazed Image
Dehazing Methods | Output Transmission Map

### Noisy Synthetic Images

#### Church, σ=0.05

| Input Noisy and Hazy Image
Dehazing Methods | Output Dehazed Image
Dehazing Methods | Output Transmission Map

#### Lawn1, σ=0.025

| Input Noisy and Hazy Image
Dehazing Methods | Output Dehazed Image
Dehazing Methods | Output Transmission Map

#### Road1, σ=0.05

| Input Noisy and Hazy Image
Dehazing Methods | Output Dehazed Image
Dehazing Methods | Output Transmission Map

### References

[Tan 2008] TAN, R. 2008. Visibility in bad weather from a single image. In CVPR.
[Kopf et al. 2008] KOPF, J., NEUBERT, B., CHEN, B., COHEN, M., COHEN-OR, D., DEUSSEN, O., UYTTENDAELE, M., AND LISCHINSKI, D. 2008. Deep photo: Model-based photograph enhancement and viewing. ACM Trans. Graph. 27, 5, 116.
[Tarel and Hautière 2009] TAREL J. P., AND HAUTIÈRE N. 2009. Fast visibility restoration from a single color or gray level image. In ICCV.
[He et al. 2009] HE, K., SUN, J., AND TANG, X. 2009. Single image haze removal using dark channel prior. In CVPR.
[Nishino et al. 2012] NISHINO, K., KRATZ, L., AND LOMBARDI, S. 2012. Bayesian defogging. IJCV, 98, 3, 263-278.
[Ancuti et al. 2013] ANCUTI, C. O., AND ANCUTI, C. 2013. Single image dehazing by multi-scale fusion. IEEE Trans. on Image Processing, 22, 8, 3271-3282.
[Gibson et al. 2013] GIBSON, K.B, AND NGUYEN, T.Q. 2013. An analysis of single image defogging methods using a color ellipsoid framework. EURASIP Journal on Image and Video Processing.
[Tang et al. 2014] TANG, K., YANG, J., AND WANG, J. 2014. Investigating haze-relevant features in a learning framework for image dehazing. In CVPR.
[Fattal 2014] FATTAL, R. 2014. Dehazing using color-lines. ACM Trans. Graph. 34, 1, 13.
[Luzón-González et al. 2014]LUZÓN-GONZÁLEZ, R., NIEVES, J. L., AND ROMERO, J. 2014. Recovering of weather degraded images based on RGB response ratio constancy. Appl. Opt.