【Field Test】Logarithmic Image Processing Model Based on MATLAB: Dehazing and Dark Channel Prior Image Enhancement

# 1. Fundamentals of Logarithmic Image Processing

Logarithmic image processing is an image enhancement technique that enhances the contrast and details of an image by transforming the image pixel values into the logarithmic domain. This technology is particularly effective when dealing with images with poor visibility, such as low light or haze.

The basic principle of logarithmic image processing is to map image pixel values to the logarithmic domain, as follows:

I_log = log(1 + I)

Where:

* `I_log` is the pixel value in the logarithmic domain
* `I` is the original pixel value

Through logarithmic transformation, the contrast in the darker areas of the image is enhanced, while the contrast in the brighter areas is reduced. This makes the details of the image clearer, thereby improving the overall visibility of the image.

# 2. Haze Removal Algorithm

### 2.1 Logarithmic Image Haze Removal Model

#### 2.1.1 Model Principle

The logarithmic image haze removal model converts a hazy image into a logarithmic image and assumes that the minimum value of the product of scene radiance and atmospheric light in the logarithmic image equals the minimum value of scene radiance. Based on this assumption, the following logarithmic image haze removal model can be established:

log(I(x, y)) = log(J(x, y)) - βt(x, y)

Where:

* `I(x, y)`：Hazy image
* `J(x, y)`：Dehazed image
* `β`：Atmospheric scattering coefficient
* `t(x, y)`：Transmittance

#### 2.1.2 Parameter Estimation

To estimate the parameters in the model, the following formulas are used:

β = arg min ∑(log(I(x, y)) - log(J(x, y)))^2

t(x, y) = arg min ∑(log(I(x, y)) - log(J(x, y)) + βt(x, y))^2

### 2.2 Implementation of Haze Removal Algorithm

#### 2.2.1 Code Structure

import numpy as np
import cv2

def dehaze(image, beta):
     # Convert the image to a logarithmic image
     log_image = np.log(image)

     # Estimate the transmittance
     t = np.min(log_image)

     # Dehaze
     dehazed_image = np.exp(log_image - beta * t)

     return dehazed_image

#### 2.2.2 Experimental Results

The table below shows the experimental results of the haze removal algorithm on different images:

| Image | Hazy Image | Dehazed Image |
|---|---|---|
| Image 1 | [Hazy Image](*** [Dehazed Image](***
*** [Hazy Image](*** [Dehazed Image](***
*** [Hazy Image](*** [Dehazed Image](***

***

**`dehaze` function:**

* Convert the image to a logarithmic image: `log_image = np.log(image)`
* Estimate the transmittance: `t = np.min(log_image)`
* Dehaze: `dehazed_image = np.exp(log_image - beta * t)`

**Parameter Description:**

* `image`: Input hazy image
* `beta`: Atmospheric scattering coefficient

# 3. Dark Channel Prior Image Enhancement Algorithm

### 3.1 Dark Channel Prior Image Enhancement Model

#### 3.1.1 Model Principle

The dark channel prior image enhancement algorithm is based on the dark channel prior, which assumes that the distribution of dark channels in the image follows a Poisson distribution. The Poisson distribution is a discrete probability di