## 2 Materials and Methods
### Image-Based Fire Heat Release Rate Prediction Methods
#### 2.1.1 YOLO-YCbCr Segmentation-Model-Based HRR Prediction
This rule comprises two distinct conditions: the first targets desaturated but high-luminance white flames, and \(\tau_{R,E}=2\) is a narrow chrominance difference threshold tailored for detecting nearly achromatic flames. The second condition focuses on the segmentation of yellow-white flames with low Cr intensity, because these light-toned boundary flames are often undetectable by Cr-centric approaches. For flames classified as yellow-dominant in Rule 1, Rule 3 is employed. Yellow-white or nearly white flames under low-light conditions often appear with high luminance but low chrominance contrast due to camera auto-exposure or light reflections. Rule 3-1 identifies regions with a low Cr-Cb difference, suitable for detecting visually flat but bright flames. Rule 3-2 targets low-Cr but high-luminance pixels, often corresponding to yellow-white flames in bright areas. As shown in Figure 2, the proposed HRR prediction procedure consists of two key phases: (1) flame segmentation and (2) HRR estimation. In the segmentation phase, the YOLO-YCbCr segmentation model is applied to mask the flame regions from fire images or video frames. In the HRR estimation phase, the spatial information from the segmented flame is obtained to calculate the flame height and fire diameter. The flame height is calculated as the pixel distance between the topmost and bottommost positions along the vertical (\(y\)-) axis within the segmented flame region, where each position is defined as a horizontal line (\(y\)-value) containing at least five flame pixels. This criterion is applied to reduce the influence of segmentation noise and enhance robustness in flame height estimation. This method reflects the maximum visible flame extension in each frame and is suitable for detecting transient flame fluctuations. The fire diameter is defined as the horizontal distance between the leftmost and rightmost x-coordinates of the outermost flame pixels. To improve robustness against irregular flame shapes at the top, this calculation is  
Figure 1: Architecture of YOLO-YCbCr. conducted only within the bottom 30% of the flame region. This region typically reflects the stable combustion zone and provides more consistent diameter estimates. The pixel-based distances are converted to physical units by using a scaling factor derived from the known physical size of the combustible material in each experiment. Finally, the calculated flame sizes are used to estimate the HRR values by applying the Zukoski correlation [14], which establishes a quantitative relationship between flame size and HRR, as follows:  
\[\frac{z_{f}}{D}=3.3Q_{D}^{*2/3} \tag{1}\]  
where \(z_{f}\) and \(D\) are the flame height and fire diameter, respectively. \(Q_{D}^{*}\) is the non-dimensional heat release rate and is defined as follows:  
\[Q_{D}^{*}=\frac{\dot{Q}}{\rho_{\infty}c_{p}T_{\infty}\sqrt{g\overline{D}D^{2}}} \tag{2}\]  
where \(\rho_{\infty}\), \(c_{p}\), \(T_{\infty}\), \(g\), and \(\dot{Q}\) represent the ambient density, specific heat of air at constant pressure, ambient temperature, gravitational acceleration, and heat release rate, respectively.