# A Display-Adaptive Pipeline for Dynamic Range Expansion of Standard Dynamic Range Video Content
## 3 Materials and Methods: A Pipeline for Dynamic Range Expansion of Video Sequences
### Saturation Enhancement  
The last step in our LDR-to-HDR conversion pipeline corresponds to the computation of the output HDR frame in color (tristimulus HDR RGB frame). For this purpose, [PERSON]'s formulation, as proposed in [49], was used as follows:  
\[c_{\text{out},i}(x,y)=\left(\left(\frac{c_{\text{in},i}(x,y)}{L_{\text{d}}(x,y) }-1\right)s+1\right)L_{\text{we}}(x,y)\qquad\text{s.t.}\qquad i\in r,g,b, \tag{6}\]  
where \(L_{\text{we}}(x,y)\) and \(L_{\text{d}}(x,y)\) are the HDR expanded luminance with enhanced highlights obtained from the highlight boosting step and the luminance of the filtered LDR input frame at \((x,y)\), respectively; \(c_{\text{in},i}(x,y)\) is the color component of the filtered LDR input frame at \((x,y)\) and \(c_{\text{out},i}(x,y)\) is the color component of the output HDR frame; \(r\), \(g\), and \(b\) are the red, green, and blue channels, respectively. Parameter \(s\), the color saturation enhancement parameter, should be set to a value greater than 1 to increase color saturation in the output HDR frame. The choice of [PERSON]'s formulation to compute the HDR RGB frame offers distinct benefits over alternatives like YUV color space-based approaches. It provides a robust method for adjusting the luminance of an image/frame in a manner that preserves the original color's hue and saturation, which is critical for maintaining visual consistency in HDR imaging. Moreover, [PERSON]'s formulation incorporates a color saturation enhancement parameter, \(s\), which offers additional control over the final image's vibrancy, mitigating the common issue of desaturated colors that occurs when the luminance of an image is increased. Following the methodology presented in [12], we conducted a subjective study to obtain the best subjective value for \(s\) across various scenes, each possessing distinct contrast and color characteristics. We aimed to investigate the correlation between the mid-level out parameter (\(m_{\text{o}}\)) used for the dynamic range expansion, considered as the scene-adaptive parameter, and the optimal saturation enhancement parameter (\(s\)). We employed a dataset of 178 LDR images. The dynamic range of each LDR image was expanded using our proposed dynamic range expansion function, and the subsequent HDR color images were derived from [PERSON]'s formulation. In the experiment, a domain expert  
Figure 7: Example of how highlights from the expanded luminance have been enhanced using expansion maps. False-color images are shown below each image for better visualization of the results. was tasked with identifying the optimal value for the saturation enhancement parameter \(s\) that generates an HDR color image that most faithfully captures the color characteristics of the original LDR image. The results of this experiment are summarized in Figure 8.  
Results revealed a weak correlation between the scene-specific mid-level out parameter (essentially, the nature of the scene) and the expert-chosen optimal value for \(s\). Further statistical analysis and hands-on experimentation were conducted to corroborate this finding. Notably, in numerous instances, the expert deemed it unnecessary to increase the saturation (indicated by green dots in Figure 8). Conversely, in scenarios where the expert considers increasing the saturation (indicated by black dots), values between 1.2 and 2.3 were typically used. These results differ from that reported in [12], where the authors found that saturation values between 1.2 and 1.8 are commonly used. This can be explained mainly because our resulting HDR images have a peak brightness much higher (6000 cd/m\({}^{2}\)) than those in their experiments (1000 cd/m\({}^{2}\)). As a result, our HDR images tend to appear more desaturated, necessitating a higher increase in saturation to achieve a similar perceptual impact. Our analysis determined that while the value of parameter \(s\) varies based on the nature of the input image, it cannot be reliably estimated using the mid-level out parameter.