【Practical Exercise】Image Dehazing Based on Retinex Algorithm (Implemented in Matlab)

# 2.1 The Principle of Retinex Algorithm

The Retinex algorithm is an image defogging algorithm proposed based on the characteristics of human visual perception. Its fundamental principle is to decompose an image into reflection components and illumination components, and then to restore a clear image by enhancing the reflection components.

Specifically, the Retinex algorithm assumes that the brightness value of each pixel in an image is determined by both the reflection component and the illumination component. The reflection component reflects the inherent color and texture of the object itself, while the illumination component reflects the effect of lighting conditions. The Retinex algorithm performs local processing on the image to estimate the illumination component of each pixel, and then removes it from the image to obtain the enhanced reflection component, ultimately restoring a clear image.

# 2. The Theoretical Foundation of Retinex Algorithm

The Retinex algorithm is an important algorithm in the field of image defogging, based on the principle of human visual system's perception of image brightness, by simulating the human eye's ability to adapt to different brightness areas, effectively removing haze and noise from images.

### 2.1 The Principle of Retinex Algorithm

The principle of the Retinex algorithm is to decompose the image into reflection components and illumination components, and then to remove the haze by enhancing the reflection components. The reflection component represents the inherent color and texture of objects in the image, while the illumination component represents the influence of the lighting conditions in the image.

The Retinex algorithm assumes that each pixel point in the image is obtained by multiplying the reflection component and the illumination component:

I(x, y) = R(x, y) * L(x, y)

Where:

* I(x, y) is the pixel value in the image
* R(x, y) is the reflection component
* L(x, y) is the illumination component

The Retinex algorithm performs local contrast enhancement on the image to separate the reflection component and the illumination component. Local contrast enhancement operations can eliminate brightness changes in the image caused by haze or noise, resulting in a clearer reflection component.

### 2.2 The Mathematical Model of Retinex Algorithm

The mathematical model of the Retinex algorithm can be represented as:

R(x, y) = I(x, y) / L(x, y)

Where:

* R(x, y) is the reflection component
* I(x, y) is the pixel value in the image
* L(x, y) is the illumination component

The illumination component L(x, y) can be estimated by various methods, such as:

***Gaussian filtering:** Using a Gaussian filter to smooth the image, obtaining an approximate illumination component.
***Median filtering:** Using a median filter to filter the image, obtaining a noise-removed illumination component.
***Guided filtering:** Using a guided filter to filter the image, obtaining an illumination component similar to the structure of the original image.

By using different methods to estimate the illumination component, the Retinex algorithm can produce different defogging effects.

# 3. Implementation of Retinex Algorithm Based on Matlab

### 3.1 The Foundation of Matlab Image Processing

As a powerful scientific computing software, Matlab has a wide range of applications in the field of image processing. It provides a rich set of image processing functions and toolboxes, making it easy to implement various image processing algorithms.

**Matlab Image Data Types**

The image data type in Matlab is uint8, representing an unsigned 8-bit integer, with a range of [0, 255]. Each pixel value represents the grayscale value or color component value of tha