# Multi-Focus Image Fusion Based on Decision Map and Sparse Representation
## 3 Experiment and Analyses
### Experimental Results and Discussions  
#### 3.4.1 Evaluation on Popular Multi-Focus Images  
In this section, we demonstrate the advantages of the proposed method (DMSR) on popular multi-focus images. An example, the fused images of the \"Lab\" pair (\(640\times 480\)) using different fusion methods is presented in Figure 8c-h. The \"Lab\" source images are shown in Figure 8a,b. For better comparison, we also present the normalized difference images between the correctly focused source image and the fusion results in Figure 9. It can be observed that the fused images obtained by DCHWT or SOMP methods showed serious artifacts and visible fake edges around the \"man\". The GF method had ringing artifacts and blurring effects near the \"men\". The IM method suffered from blurring effects near the \"men's hair\". The CNN method could achieve better fusion quality, but some small defects could still be found with careful observation, such as imperceptible artificial flaws on the \"table\" (see the lower middle in Figure 9e). Comparatively, the DMSR produced the best fused image. Another example, the fusion results of the \"Flowerpot\" image pair (\(944\times 736\)) are shown in Figure 10c-h. The normalized difference images between the correctly focused source image and  
Figure 8: The “Lab” source images and fusion results obtained by different fusion methods. DCHWT—discrete cosine harmonic wavelet transform, SOMP—synchronous orthogonal matching tracking sparse coding algorithm, GF—guided filtering, IM—image matting, CNN—convolutional neural network, DMSR—proposed method based on decision map and sparse representation. Figure 9: Normalized difference images between each of the fused images and Figure 8b. the fusion results are shown in Figure 11. Similar to the previous example, the DCHWT and SOMP method produced serious artifacts around the \"horologe\". The fused image obtained by the GF method suffered from a ringing effect, and the edges of the \"horologe\" were blurred. The results of the IM method also showed similar artifacts near the \"horologe\". Although the CNN method performed well overall, it exposed obvious artifacts on the \"ground\" and the \"wall\" of the fused image. Comparatively, the DMSR method exhibited the best visual quality. To evaluate fusion performance more objectively, each pair of popular multi-focus images was fused by six fusion methods. The values of metrics \(Q_{MI}\), \(Q^{AB/F}\), and _VIFF_ were calculated and are recorded in Table 1, with the best results indicated in bold. It can be seen that the DMSR method outperformed all other methods and won in almost all the quality metrics. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \begin{tabular}{c} **Source** \\ **Images** \\ \end{tabular} & \begin{tabular}{c} _Metric_ \\ \end{tabular} & \begin{tabular}{c} \\ **DCHWT [6]** \\ \end{tabular} & \begin{tabular}{c} **SOMP [19]** \\ \end{tabular} & \begin{tabular}{c} **Method** \\ **GF [15]** \\ \end{tabular} & \begin{tabular}{c} **IM [16]** \\ \end{tabular} & \
\begin{tabular}{c} **CNN [30]** \\ \end{tabular} &
\begin{tabular}{c} **DMSR** \\ \end{tabular} \\ \hline \multirow{3}{*}{Pepsi} & Q\({}_{MI}\) & 1.1167 & 0.9030 & 1.2164 & **1.3080** & 1.2911 & 1.3033 \\  & Q\({}^{AB/F}\) & 0.7315 & 0.6666 & 0.7510 & 0.7550 & **0.7591** & 0.7583 \\  & _VIFF_ & 0.9273 & 0.9235 & 0.9498 & 0.9335 & 0.9511 & **0.9543** \\ \hline \multirow{3}{*}{Clock} & Q\({}_{MI}\) & 1.0417 & 0.8485 & 1.1509 & 1.1837 & 1.2058 & **1.2351** \\  & Q\({}^{AB/F}\) & 0.7165 & 0.6510 & 0.7427 & 0.7429 & 0.7464 & **0.7478** \\  & _VIFF_ & 0.9279 & 0.9235 & 0.9404 & 0.9322 & 0.9432 & **0.9469** \\ \hline \multirow{3}{*}{Lab} & Q\({}_{MI}\) & 1.0611 & 0.9481 & 1.1928 & 1.2221 & 1.2363 & **1.2583** \\  & Q\({}^{AB/F}\) & 0.7162 & 0.6708 & 0.7552 & 0.7506 & 0.7573 & **0.7584** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Quantitative assessments of different image fusion methods for popular multi-focus images. Figure 11: Normalized difference images between each of the fused images and Figure 10b.