## 2 Cause of Halo Artifacts in Fused Images  
In HDR natural scenes, there is not only abundant information about brightness and color, but also plenty of sharp local brightness changes. In the process of multi-exposure fusion, if those sharp brightness changes cannot be fully considered, the halo artifacts will appear in the fused images. As seen in Figure 1a, which shows the fused result of [PERSON] et al. [18], halo artifacts have occurred in the sky outside the windows. By contrast, the sharp local brightness changes are fully considered in the proposed method. Thus, the fused image is more consistent with human visual perception through the removal of halo artifacts, as shown in Figure 1b.  
The cause of these halo artifacts are revealed in Figure 2. In the multi-exposure source images of Figure 2a-c, the exposure of the scenery outside the window is increasing until over-exposure, while the brightness contrast increases step-by-step between indoors and outdoors. In the local luminance gradient amplitude of Figure 2k-o, the maximal gradient is found in Figure 2m. However, the region around the maximal gradient in the corresponding source image in Figure 2c is over-exposed and unsuitable for the fused image. However, in the same position of Figure 2a,b, the well-exposed region can be found, which are more suitable for the fused image than that of Figure 2c. Therefore, the maximal gradient existing in Figure 2m is an invalid gradient and the primary cause of halo artifacts in the fused image. The reason for this phenomenon is that a single photograph has very limited dynamic range, compared to real HDR scenes. Thus, the invalid large-amplitude gradients occur in the multi-exposure source images. If these invalid gradients cannot be suppressed, halo artifacts are inevitable in the fused image.  
In most multi-exposure image fusion methods, the image features, such as contrast and saliency, are used as weight coefficients for image fusion, except for the gradient. However, these image features have more or less a direct connection with the gradient, which leads to halo artifacts of varying degrees in the fusion results. In the method by [PERSON] et al. [15], a Laplacian filter was applied to the grayscale version of each multi-exposure image to yield a simple indicator, C, for contrast. This indicator C was  
Figure 1: An example of multi-exposure image fusion. (**a**) The fused image by [PERSON] et al. [18], and (**b**) the fused image by the proposed method.  
then used as one of the weight coefficients for image fusion. Generally, pixels with larger contrast always have larger gradients, so the pixels with invalid large gradients inevitably take part in the image fusion process with larger weight, generating the halo artifacts. Like [PERSON] et al.'s method [15], the Laplacian filter was implemented to each source image in the Li method [18] to obtain a high-pass image. Then, the Gaussian filter was used in the high-pass image to obtain the saliency map of the source image, which was used as the winner-take-all weight coefficient for image fusion. It can be noted that pixels with larger gradients always have greater saliency, so the pixels with invalid large gradients are also involved in image fusion with larger weighting factors. In the Ma method [13; 14], signal contrast was used as one of benchmarks for image fusion, and the desired contrast of the fused image patch was determined by the highest contrast of all the source image patches, which would lead to the appearance of halo artifacts in the fused images.