# Improved Combined Metric for Automatic Quality Assessment of Stitched Images
## 3 The Proposed Approach
The local entropy values can be determined for the fragments of the stitched (\(ent^{s}_{local}\)) and constituent images (\(ent^{c}_{local}\)) in a similar way, assuming the use of the 9 \(\times\) 9 pixel sliding window for the calculation of the local entropy for each pixel's neighborhood. They are further averaged for all positions of the sliding window to obtain the average features (\(\overline{ent^{s}}_{local}\) and \(\overline{ent^{s}}_{local}\)). After the numerical experiments, it was found that the differential local entropy and the average local entropy determined for the constituent images did not increase the metric's performance. Therefore, the average local entropy of the stitched image \(\overline{ent^{s}}_{local}\) is used as the feature \(f_{3}\). Nevertheless, the differential variance of the local entropy values is used as the feature \(f_{4}\), determined as  
\[f_{4}=var(ent^{c}_{local})-var(ent^{s}_{local}). \tag{5}\]  
Two sub-metrics (\(ES\) and \(K\)) incorporated from the MIQM [29; 30], used as features \(f_{5}\) and \(f_{6}\), reflect the distortion level; hence, their values close to 1 indicate high quality, whereas their small values denote strongly distorted images. The sub-metric \(K\) is sensitive to sharp local changes in luminance and contrast around the structured regions in the \(21\times 21\) pixel macroblocks. This is based on the comparison of mean intensities and standard deviations similar to the well-known Structural Similarity (SSIM) metric [33]. Then, the weighted average of the luminance and contrast index of each macroblock is calculated with weights dependent on the texture randomness index of the reference image (the constituent image in our case) for each macroblock. The calculated texture randomness is also the basis for the edge-based structural index \(ES\). Both sub-metrics are calculated for regions of interest (ROIs), selected from each of the constituent images and the corresponding ROIs detected in the stitched images, and are subject to quality evaluation. Since the third component of the MIQM--spatial motion index--is partially dependent on the local entropy, it was not utilized in our study due to the use of three entropy-based features. The next two features (\(f_{7}\) and \(f_{8}\)) are the variances of these sub-metrics (\(ES\) and \(K\)). The last feature (\(f_{9}\)) included in the developed combined CombSIQE metric, is the absolute difference of standard deviations calculated for the stitched and respective constituent images (obviously the values are averaged for 4 or 5 constituent images, depending on the number of them available in the ISIQA dataset). The optimization procedure of the parameters (weights and exponents) of the combined metric was conducted in a MATLAB environment using the Nelder-Mead method implemented in the _fminsearch_ function. Some additional experiments, however, leading to worse results (PLCC = 0.8425, refer to Table 1 for comparison), were also conducted using neural networks. The illustration of the experimental procedure is presented in Figure 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Metric**} & \multicolumn{4}{c}{**Correlation with MOS**} \\ \cline{2-4}  & **PLCC** & **SROCC** & **KROCC** \\ \hline \multicolumn{4}{c}{Results provided by other researchers for 80\% training and 20\% testing sets} \\ \hline SIQE reported in [20] & 0.8395 & 0.8318 & - \\ SIQE (median) reported in [44] & 0.8030 & 0.7820 & - \\ [PERSON] and Mo [44] & 0.8432 & 0.8013 & - \\ \hline \multicolumn{4}{c}{Results obtained for the whole ISIQA database} \\ \hline SIQE [20] & 0.7488 & 0.7057 & 0.5308 \\ EntSIQE\({}_{1}\)[43] & 0.8012 & 0.7920 & 0.5971 \\ EntSIQE\({}_{2}\)[43] & 0.8101 & 0.7945 & 0.5990 \\ EntSIQE\({}_{1}^{+}\)[31] & 0.8338 & 0.8338 & 0.6418 \\ EntSIQE\({}_{2}^{+}\)[31] & 0.8337 & 0.8341 & 0.6432 \\ \hline \multicolumn{4}{c}{CombSIQE (proposed)} & **0.8684** & **0.8665** & **0.6810** \\ \hline \hline \end{tabular}
\end{table}