## 5 Experiments
### Experimental Results
#### 5.3.1 Flame Image Generation  
We compared our proposed method with other neural networks (GAN, VAE, and original DDPM). Figure 12 shows the performance of each model. In terms of SSIM, DDPM outperforms GAN and VAE, and our method, RE-DDPM, outperforms the original DDPM. In terms of LPIPS, our method achieved the lowest score, indicating that the images generated by our method are more in line with human perception. Figure 13 shows the FID scores for certain iterations, with the FID scores gradually decreasing with an increasing number of iterations. A lower FID score indicates more similarity, as the FID score between two identical datasets is almost zero. Although the DDPM shows promise in data augmentation, the sampling speed is still much slower compared to GAN and VAE. A GAN consists of a discriminator and  
Figure 12: (**a**) Score for each model in terms of structural similarity; (**b**) score for each model in terms of learned perceptual image-patch similarity. Figure 13: FID change graph. a generator. The generator is responsible for generating images, while the discriminator is used to judge the authenticity of the generated images. A trained GAN model can directly generate target images in one step. However, unlike aa GAN, a DDPM recovers images from noise in the form of a Markov chain in the reverse denoising process. This means that the more iterations we set, the longer it takes to generate images. Nevertheless, the images generated by a DDPM still achieve satisfactory results. Furthermore, due to improvements in network attention and the use of local redrawing methods in our method, the images generated by the model are more realistic, and the training speed of the network is also improved. Figure 14 shows images generated by different models. The images generated by VAE are too blurry to display the rich details of flame images. Compared to the DDPM, VAE's loss function typically includes a reconstruction loss, which measures the difference between the images generated by the decoder and the original input images. This reconstruction loss helps the model learn the data distribution but may result in generated images lacking detail and clarity, especially for complex structures or high-resolution images. Additionally, VAE assumes that the latent space is continuous, meaning that similar latent vectors generate similar images. This continuity may cause the model to converge to some blurry intermediate representations when generating images rather than producing clear images. The images generated by a GAN differ significantly from the real images in the distribution of flame texture features. The original DDPM achieves satisfactory results in terms of clarity and diversity, but there are significant differences in flame texture details compared to real images. For example, in the images of normal sintering generated by the original DDPM, there are large areas of bright flames, which severely deviate from the actual distribution of flames in real images and may cause the recognition network to identify them as over-sintering, reducing recognition accuracy. The images generated by our RE-DDPM are closer to real images. Traditional local redrawing focuses on the global generation of the redrawn region and does not consider the data distribution relationship between the redrawn region and other regions. This can cause a noticeable discontinuity at the boundary between the two regions, as shown in Figure 15. When RE-DDPM performs local redraw, it considers the distribution of flame characteristics between the redrawn region and other regions. Our proposed redrawing method can maintain the consistency around the furnace wall while achieving high similarity and diversity in the redrawn flame region. The generated images appear more realistic and natural at the boundary between the redrawn region and other regions. Figure 14: (**a**) Reference image; (**b**) image generated by VAE; (**c**) image generated by GAN; (**d**) image generated by DDPM; (**e**) image generated by RE-DDPM.