## 4 Results and Discussion
### Spectral Polarization Image Clustering Rendering
#### 4.2.2 Spectral Polarization Image Rendering  
In the previous section, points for six materials in the image were randomly selected, and a good clustering result was obtained. In this section, the proposed HAC-FCM algorithm is used to cluster the actual image at the pixel level, and the clustering results are assigned colors, which provides a more intuitive view compared to the polarized grayscale image at each characteristic band. Finding equally spaced single-wavelength images, 11 wavelengths (ranging from 372 nm to 757 nm) are selected from the spectral image. The operation is performed on the image, and the value of the Stokes vector and Dolp are calculated from the intensity value of each pixel to form a three-dimensional reconstruction matrix. Dimensionality reduction was performed on the matrix before applying the fusion algorithm. For the space debris material part in the image, the cluster center obtained in Section 4.2.1 was used as the initial value. After clustering each pixel, the results were color-coded and re-projected onto the original image pixel range to produce the final rendering. The physical sample of the field experiment is depicted in Figure 8a. The image size of the experiment was 325 \(\times\) 250, and pixels were colored based on different intensity values. The resulting coloring of the original image at an incident polarization angle of 135\({}^{\circ}\) and a wavelength of 442 nm is shown in Figure 8b, with similar results obtained for the other wavelengths. It can be seen that due to high noise interference of background pixels during shooting, the classification effect may be poor. To remove image noise, the Full Average Filter (FAF) method was used to denoise the image, with a filter kernel of 9 \(\times\) 9 pixels used to smooth the original image. The resulting coloring of the filtered image is shown in Figure 8c, which shows that the background noise is significantly reduced after using the mean filtering method. \begin{table}
\begin{tabular}{c c c c} \hline
**Algorithm** & **Total Points** & **Correct Points** & **Recognition Rates** \\ \hline K-means & 726 & 551 & 75.90\% \\ HAC & 726 & 604 & 83.20\% \\ Ours & 726 & 726 & **100\%** \\ \hline \end{tabular}
\end{table} 
Table 2: Three different algorithm cluster results comparison. Figure 7: Results scattered point diagram and iteration change diagram. (**a**) FCM algorithm in a 2D scatter plot (**b**) FCM target function J iteration change diagram. Clustering algorithm processing is performed on the image after denoising. As the dataset is large and fuzzy, the FCM threshold is adjusted to \(10^{-5}\), while the maximum number of iterations remains 1000. After obtaining the clustering result, the result is colored and reshaped from a one-dimensional vector to the original image shape, and the coloring result is output as an image. The result of denoising image clustering is shown in Figure 9. The image demonstrates that, following mean filtering, the fusion method is able to categorize the filtered image extremely well, with excellent border characteristics. Although there are seven different types of color blocks in the result graph, the algorithm unfortunately recognizes the two coating materials as the same material and separates the material's outside circle into another category. This is due to the fact that both coating materials are white and have similar surface topography (as shown in Figure 8a), which results in very similar polarization behaviors of the two materials. The image rendering shows that, except for the very thin iron sheet material, there is a circle of yellow edges around the other material images. This is because the polarization characteristics are extremely sensitive to changes in the material structure, and the thickness of the material cannot be neglected. At the edge where the debris material is in contact with the background, the sudden change in thickness causes a change in its polarization properties.