## 5 Case Studies  
### Study Setup  
In our case studies, the candidate images were gathered by a video camera monitoring the burning fire for a period of time. An oil pan was utilized as the burner, which was about 570 mm in diameter. Five liters of normal heptane were poured into the oil pan as fuel for the fire. Considering the security, the fuel was additionally mixed with twelve liters of water. An aerosol fire extinguisher was used to put out the flames. In order to evaluate the generalization capabilities of the proposed method, the candidate images were acquired at different times and in several different conditions. Meanwhile, the position and orientation of the flame in the scene and the flame-to-camera distance were also adjusted. What's more, some similar type of non-flame images were captured to test the robustness in handling false alarm sources. Finally, there were 3502 candidate images collected, with a size of \(266~{}\times~{}236\). Figure 2: The flow diagram of combustion state recognition based on IFA-WSVM model. Among them, the 1 st-2254 th candidate images contained the flame burning steadily, as shown in Figure 3a-e; the 2255 th-2779 th candidate images exhibited the flame being extinguished by a fire extinguisher, as shown in Figure 3f-j; the 2780 th-3194 th candidate images showed the extinguished flame, as shown in Figure 3k-o; the 3195 th-3502 nd candidate images contained flame-color objects, such as red flowers, lighting, sunset, and so on. Here, the first 2254 images were classified as stable burning state, the next 525 images were classified as extinguishing state; the following 415 images were classified as final extinguished state; the last 308 images were classified as non-flame state. However, it can be observed that some images with an extinguishing state are quite similar to those with a stable burning state, which increases the difficulty of recognition. First of all, the candidate images were segmented with the proposed rules and converted into pre-processed images. In order to eliminate noise, the closing operation and hole filling operation were also performed. Then, the edge images were obtained by applying the Canny edge detector to extract the potential flame contour. To extract the local and global multi-features, the RCMIs of pre-processed images and edge images were calculated to construct feature vectors. Finally, the IFA-WSVM model was used to recognize the combustion state of flame. Figure 4 shows some pre-processed images and edge images in our case studies respectively. Figure 4: \(Cont.\)  
Figure 3: Candidate images: (**a–e**) stable burning state; (**f–j**) extinguishing state; (**k–o**) final extinguished state; (**p–t**) non-flame state. From Figures 3 and 4, it can be observed that the stable burning flame has an irregular shape, containing a relatively large number of sharp angles. On the contrary, the shape of extinguishing flame is more regular and smooth. Due to that the flame was extinguished completely or absent, the images with final extinguished state and non-flame state show something small with strange shape, which are quite different from others. The basic idea of SVM is to separate two classes from each other. However, the combustion state recognition corresponds to a multi-class classification problem. A solution is to decompose the original multi-class problem into several binary sub-problems. One-against-one approach is one of the most suitable approaches for practical use. In the pairwise decomposition, \(c(c-1)/2\) different binary classifiers are built, each of which separates one class from another ignoring all the other classes. In the end, each classifier casts one vote for its preferred class, and the final result is the class with the most votes. For SVM, the one-against-one approach generally performs better than other SVM-based multi-class classification algorithms [40; 41]. Therefore, it is selected for the multi-class IFA-WSVM classifiers.