# Improved Combined Metric for Automatic Quality Assessment of Stitched Images
## 3 The Proposed Approach  
The main idea of the proposed approach was an extension of the SIQE metric using some additional features that may be sensitive to some other types of distortions leading to an increase in the correlations between the developed combined metric and subjective scores (the MOS values available from the ISIQA dataset used in the experiments). Since the original SIQE implementation utilized 36 features based on statistical data (GGD and GMM models) for the subbands, a substantial increase in the correlation between the developed combined metric and the MOS values may be expected by utilizing some additional features of a different \"nature\". Considering the experiences related to the general-purpose IQA, the presence of image distortions usually leads to some changes in entropy and variance in the degraded image (higher values may be expected); hence, the first experimental results provided in earlier papers [31; 43], contained the effects of applying two models based on the weighted product and weighted sum of the SIQE, entropy-based features, and simplified implementation of two features originating from the MIQM [29; 30]. In comparison to the original correlation values for the SIQE metric (PLCC = 0.7488, SROCC = 0.7057, and KROCC = 0.5308), the \"best\" combinations led to a PLCC = 0.8338, SROCC = 0.8341, and KROCC = 0.6432. Some other competitive results can be found in the paper written by [PERSON] and [PERSON] [44], where the fusion of global and local features was proposed. Nevertheless, the authors randomly divided the dataset into training and testing sets, achieving a PLCC = 0.8432 and SROCC = 0.8013 for the proposed method based on the extension of the BRISQUE metric [45], compared to the median SIQE performance reported in [44], with a PLCC = 0.8030 and SROCC = 0.7820 for the train/test split 80/20 with an additional SVR score fitting. All these values may be considered the starting point for the further extensions provided in this paper. The approach to the design of the combined metric proposed in this paper was based on the joint application of the weighted sum and the weighted product of the same set of metrics. Therefore, the additional memory resources were not necessary for storing the additional values of the features, and the advantages of both combination methods may demonstrate the synergy effect. The general formula for the designed combined metric based on the SIQE and additional features can be defined as  
\[\text{CombSIQE}=w_{1}\cdot(\text{SIQE})^{a_{1}}+\sum_{i=2}^{N}w_{i}\cdot(f_{ i})^{a_{i}}+(\text{SIQE})^{b_{1}}\cdot\prod_{j=2}^{N}\left(f_{j}\right)^{b_{j}}\ \, \tag{4}\]  
where weight \(w\) and exponents \(a\) and \(b\) are subject to optimization. The list of additional features used in Formula (4) contains the following (in this study, \(N=7\) features have been used in aggregate):  
* \(f_{2}\)--differential entropy;
* \(f_{3}\)--average local entropy for the stitched image;
* \(f_{4}\)--differential variance of the local entropy;
* \(f_{5}\)--median edge-based structural index (\(ES\)--a part of the MIQM [29; 30]);
* \(f_{6}\)--median luminance and contrast index (\(K\)--a part of the MIQM [29; 30]);
* \(f_{7}\)--variance of the edge-based structural index (var(\(ES\)));
* \(f_{8}\)--variance of the luminance and contrast index (var(\(K\)));
* \(f_{9}\)--absolute difference of standard deviations. The entropy-based features (\(f_{2}\)-\(f_{4}\)) can be determined, calculating the local and global entropy values for the constituent and stitched images. The global entropy can be calculated independently for each stitched image (\(ent^{s}_{global}\)) and as the average for four or five constituent images (\(ent^{c}_{global}\)), and then the differential entropy is determined as the difference of these two values.