## 2 Materials and Methods
### Image-Based Fire Heat Release Rate Prediction Methods
#### 2.1.1 YOLO-YCbCr Segmentation-Model-Based HRR Prediction  
The core component of the proposed HRR prediction method is accurate segmentation of flame regions from fire imagery. While deep learning-based segmentation models can achieve high performance, they typically require pixel- or polygon-level annotations and incur high computational costs. To address these limitations, our research team previously proposed the YOLO-YCbCr segmentation model [32], which combines efficient YOLO object detection with lightweight rule-based segmentation in the YCbCr color space. In this model, segmentation is applied only to flame-containing regions identified through object detection. This proposed segmentation reduces training costs by eliminating the need for complex mask annotations, reducing background noise, and lowering the computational load. In this study, an improved YOLO-YCbCr model was used, in which the segmentation rules were refined and the YOLO detector was retrained with an expanded fire image dataset. Figure 1 illustrates the architecture of the YOLO-YCbCr segmentation model employed in this study. The model consists of two main stages: object detection and rule-based color segmentation. First, YOLOv8 is used to detect bounding boxes surrounding flame regions, effectively acting as a spatial filter. This allows the subsequent color-based segmentation to be performed only within the detected bounding boxes. The cropped regions are then converted into the YCbCr color space, which is suitable for flame segmentation [34], and the flame region is segmented using the YCbCr rules. Based on an analysis of flame image characteristics observed under various environments and the segmentation results of the YCbCr model proposed by [PERSON] and [PERSON] [35], it was found that the flame segmentation performance varies significantly depending on the presence of objects with flame-like colors and the color characteristics of flames as influenced by fire conditions and image acquisition environments. Therefore, the YCbCr rules were proposed to account for such variations, enabling the detection of flame regions by categorizing them into red-dominant and yellow-dominant flames. As shown in Figure 1, the proposed YCbCr rules consist of the following components: Rule 1, which classifies the dominant flame color (red or yellow); Rule 2, which detects red-dominant flames; and Rule 3, which detects yellow-dominant flames. In Rule 1, bounding boxes obtained from YOLO detection are analyzed to classify the enclosed flame regions as either red-dominant or yellow-dominant based on their average luminance and overall image brightness. This classification is important, as each flame type exhibits different color distribution patterns that necessitate different segmentation strategies. When the average luminance within the bounding box exceeds a predefined threshold, the flame is classified as yellow-dominant, which typically exhibits high luminance. However, inenvironments with strong ambient lighting, such as outdoor scenes or artificial illumination, even red flames can exhibit elevated luminance, potentially leading to misclassification. To enhance robustness under such lighting variations, the global average luminance of the image is also considered. The thresholds were empirically determined via statistical performance analysis on a fire dataset consisting of 1000 images, resulting in \(\tau_{white}=130\) and \(\tau_{day}=90\). For flames classified as red-dominant, Rule 2 is applied. This stage consists of two sub-rules: Rule 2-1 builds upon the classical YCbCr method proposed by [PERSON] and [PERSON] [35], identifying flame pixels as those with high Cr, low Cb, and high Y values. The threshold, \(\tau=35\), ensures sufficient color contrast to differentiate flames from the background. Rule 2-2 serves as a complementary condition to detect yellow-white or white flame regions that often appear near the flame boundaries or in high-temperature zones within red flames.