## 3 The Proposed Method  
### Hough Transform and Its Variants  
The Hough transform is a powerful instrument in computer vision and image processing for recognizing shapes in images. This approach is founded on the duality between points and lines in images. The Hough transform maps each point in image space to a corresponding point in a parametric space called Hough space. In Hough space, each line in the image can be represented as an individual point. The Hough Transformation has been widely used in many applications, including lane detection, edge detection, and text recognition. It has proven to be a robust and effective technique, particularly when dealing with images containing noisy or cluttered data. The Hough Transformation has also been extended to recognize other shapes, such as circles and ellipses, by modifying the parameter space and the corresponding algorithms. The formula for a straight line is as follows:  
\[y=k\times x+b \tag{1}\]  
In the Cartesian coordinate space, the variable \(k\) is used to represent the slope of a line, while the variable \(b\) is used to represent the intercept of the line. For any line passing through a point (\(x_{0}\), \(y_{0}\)) in the image space, \(y_{0}=k*x_{0}+b\) is fulfilled. The point (\(x_{0}\), \(y_{0}\)) produces \(a\) Hough space \(K\) and B straight line. It is written as \(b=-k*x_{0}+y_{0}\). The point \begin{table}
\begin{tabular}{p{85.4 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Article** & **Contribution** & **Shortcomings and Future Improvements** \\ \hline [PERSON] et al. [26] & This paper suggests using deep compression learning to calculate edges in high-resolution images of deep-sea mining. & Data compression is inevitably accompanied by the loss of accuracy, so it is necessary to extract and retain key information modules. \\ \hline [PERSON] et al. [27] & A multi-feature fusion network is proposed and a new end-to-end 3D object detection framework is designed. & The accuracy of single-stage detection algorithms is often lower than other methods, and the detection speed of this method has no obvious advantage. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._(\(k_{0}\), \(b_{0}\)) in Hough space can also be used to generate a line in the Cartesian coordinate system. The following is a representative expression:  
\[b_{0}=k_{0}\times x+y \tag{2}\]  
The Hough space represents all possible lines in the image space as a parameter space. In Hough space, each line is denoted by a point with two parameters, \(k\) and \(b\). These parameters describe the line's slope and the intercept of the line in Cartesian space. A mathematical expression can be used to describe the relationship between an image and Hough space:  
\[(x_{0},y_{0})\rightarrow(k_{0},b_{0})=(-\frac{x_{0}}{y_{0}},\frac{y_{0}}{k_{0}}) \tag{3}\]  
where \((x_{0},y_{0})\) is a point in the image space and \((k_{0},b_{0})\) is the corresponding point in the Hough space. The inverse mapping, from Hough space back to image space, is given by the equation:  
\[(k_{0},b_{0})\rightarrow(x_{0},y_{0})=\left(\frac{b_{0}}{k_{0}},-\frac{b_{0}}{ k_{0}^{2}+1}\right) \tag{4}\]  
The Hough space is typically discretized into a grid of cells, each representing a range of \(k\) and \(b\) values. The value of each cell in the Hough space is set to the number of image points that are mapped to that cell. This is known as the Hough accumulator. The highest value in the accumulator represents the most likely line in the image. The line in the image space can be obtained by mapping back the corresponding point in the Hough space using the inverse transformation. Utilizing the Hough transform, one can convert the task of detecting lines in an image area to finding corresponding points in the Hough space. Each line in image space corresponds to a specific \(k_{0}\) and \(b_{0}\) in Hough space, and finding these parameters in Hough space can be used to identify lines in image space.