# 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
### Highlight Boosting  
The main goal of the highlight boosting step is to restore high-brightness areas to a substantially higher output brightness (relative to the mid-level point) within the display system's capabilities, e.g., 6000 cd/m\({}^{2}\) for the SIM2 HDR display used in our experiments.  
In the dynamic range expansion operation, we initially constrained the maximum luminance intensity of the expanded luminance (\(L_{\text{w}}\)) to 4000 cd/m\({}^{2}\). Considering the capabilities of the SIM2 HDR display, this leaves a margin of 2000 cd/m\({}^{2}\) for additional highlight boosting. This approach ensures that highlights are enhanced in a way that maximizes the dynamic range and visual impact of the resulting HDR content, staying within the technical limits of the display device.  
The highlight boosting step specifically targets the identification and enhancement of highlights, aiming to intensify them up to a luminance of 6000 cd/m\({}^{2}\). To accomplish this, we proposed a novel method to identify and boost highlights. Our method utilizes an \"expansion map\", which identifies the positions of highlights in the current LDR frame under consideration and specifies the extent of boosting required at each pixel.  
The process begins by analyzing the artifact-free LDR input frame and its luminance channel to detect highlights and generate the expansion map. Initially, a \"binary map\" is created by selecting pixels from the artifact-free LDR input frame that are identified as highlights. In this binary map, a pixel value is set to 1 if it is determined to be a highlight and set to 0 if it is not. Given that the maximum pixel value for an LDR frame is 255, the decision to  
The resulting expansion map yields values within the range of 0 to 1. A value of 0 indicates that the expanded luminance (\(L_{\mathrm{w}}\)) at the current pixel location will remain unchanged, whereas a value of 1 indicates that it will be boosted up to 6000 cd/m\({}^{2}\). Examples of binary maps and their corresponding expansion maps derived from two distinct LDR frames can be seen in Figure 6. As observed, fine details and smooth gradients in highlights found in the original image have been incorporated into the expansion map. Finally, the expansion map (\(M\)) is used to enhance the highlights present on the expanded luminance as follows:  
\[L_{\mathrm{we}}(x,y)=L_{\mathrm{w}}(x,y)+rM(x,y)^{\alpha}\] \[\mathrm{s.t.}\qquad x\in 0,\ldots,w-1\qquad y\in 0,\ldots,h-1 \qquad\alpha>0,\]  
where \(L_{\mathrm{we}}(x,y)\) is the value of the HDR expanded luminance with \"enhanced\" highlights at \((x,y)\), \(M(x,y)\) is the value in expansion map at \((x,y)\), \(r\) is the peak luminance value added to the highlights (2000 cd/m\({}^{2}\)), and \(\alpha\) is a parameter to control how highlights will be boosted. An \(\alpha\) value greater than one (\(\alpha>1\)) will make strong highlights more pronounced in the output, while values smaller than one (\(\alpha<1\)) will make diffuse highlights more pronounced. The \(w\) and \(h\) values are the width and the height of \(L_{\mathrm{w}}\).  
Figure 7 shows the results of highlight boosting. False-color images in a logarithmic scale have been included to facilitate the visualization of the results. We found that an \(\alpha\) value around 2.0 (\(\alpha\approx 2.0\)) is a good trade-off between giving more priority to boosting the strong highlights and suppressing the enhancement of diffuse lights.  
Figure 6: Binary and expansion maps obtained from two different LDR images. The expansion map is used to enhance the highlights of the HDR expanded luminance (\(L_{\mathrm{w}}\)). (The image on the right was obtained from the movie “Star Wars: Episode III Revenge of the Sith”, property of Lucasfilm).