# A Comparative Analysis of Feature Detectors and Descriptors for Image Stitching
## 3 Materials and Methods
### Method: Comparative Analysis
#### 3.2.2 Stitched Image Quality
The Feature Similarity (FSIM) index is based on how the HVS interprets an image based on its low-level features [74]. Two characteristics, phase congruency (PC) and gradient magnitude (GM), have to be considered in order to calculate the FSIM index. PC and GM are complementary for describing local quality of the image. The FSIM measurement is divided into two components, f\({}_{1}\)(x) and f\({}_{2}\)(x), one for PC and one for GM. The measure of similarity in terms of PC\({}_{1}\)(x) and is described as (Equation (5)):  
\[\mathrm{S_{PC}(x)}=\frac{2\mathrm{PC_{1}(x)\cdot PC_{2}(x)+T_{1}}}{\mathrm{ PC_{1}^{2}(x)+PC_{2}^{2}(x)+T_{1}}} \tag{5}\]  
where T\({}_{1}\) is a positive constant. The measure of similarity in terms of G\({}_{1}\)(x) and G\({}_{2}\)(x) is described as (Equation (6)):  
\[\mathrm{S_{G}(x)}=\frac{2\mathrm{G_{1}(x)\cdot G_{2}(x)+T_{2}}}{\mathrm{G_{1}^ {2}(x)+G_{2}^{2}(x)+T_{2}}} \tag{6}\]  
where T\({}_{2}\) is a positive constant. The combination of and gives the similarity of \(\rm f_{1}(x)\) and \(\rm f_{2}(x)\), which is represented as:  
\[\rm S_{L}(x)=\rm S_{PC}(x)\cdot S_{G}(x)\]  
The FSIM index between \(\rm f_{1}\) and \(\rm f_{2}\) is described as (Equation (7)):  
\[\rm FSIM=\frac{\sum_{x\in\Omega}S_{L}(X)\cdot PC_{m}(X)}{\sum_{x\in\Omega}PC_{ m}(X)} \tag{7}\]  
where \(\rm PC_{m}(X)=max(PC_{1}(x)\cdot PC_{2}(x))\). The FSIM index was designed to be used with grayscale images or the luminance component of color images. As chrominance information influences the HVS's interpretation of images, including chrominance information in FSIM for color IQA may result in improved performance. A simple addition to the FSIM framework may be used to accomplish this purpose. The RGB color images are first transformed to a different color space, where luminance and chrominance may be segregated. The commonly used YIQ color space, in which Y contains luminance information and I and Q provide chrominance information, is utilized to achieve this. The following equation (Equation (8)) may be used to convert from RGB to YIQ space:  
\[ \begin{bmatrix}Y\\ I\\ Q\end{bmatrix} = \begin{bmatrix}0.299&0.587&0.114\\ 0.596&-0.274&-0.322\\ 0.211&-0.523&0.312\end{bmatrix}\begin{bmatrix}R\\ G\\ B\end{bmatrix}  \tag{8}\]  
The similarity between chromatic features is represented as follows:  
\[\rm S_{I}(x)=\frac{2I_{1}(x)\cdot I_{2}(x)+T_{3}}{I_{1}^{2}(x)+I_{2}^{2}(x)+T_ {3}}\]  
\[\rm S_{Q}(x)=\frac{2Q_{I}(x)\cdot Q_{2}(x)+T_{4}}{Q_{I}^{2}(x)+Q_{2}^{2}(x)+T_ {4}}\]  
where \(\rm I_{1}(I_{2})\) and \(\rm Q_{1}(Q_{2})\) are the I and Q chromatic channels of the image \(\rm f_{1}(f_{2})\), respectively. \(\rm T_{3}\) and \(\rm T_{4}\) are positive constants. \(\rm T_{3}=T_{4}\) is used for convenience since the I and Q components have almost the same dynamic range. The chrominance similarity between \(\rm f_{1}(x)\) and \(\rm f_{2}(x)\) is the obtained by combining the \(\rm S_{I}(x)\) and \(\rm S_{Q}(x)\), which is represented by \(\rm S_{C}(x)\) as follows:  
\[\rm S_{C}(x)=\rm S_{I}(x)\cdot S_{Q}(x)\]  
Finally, by simply adding chromatic information to the FSIM index, it may be easily modified to \(\rm FSIM_{C}(Equation (9))\). \[\rm FSIM_{C}=\frac{\sum_{x\in\Omega}S_{L}(x)\cdot\left[S_{C}(x)\right]^{\lambda }PC_{m}(x)}{\sum_{x\in\Omega}PC_{m}(x)} \tag{9}\]  
where \(\lambda>0\) is the parameter that is used to alter the significance of the chromatic components. Visual Saliency Induced Index  
Over the past decade, visual saliency (VS) has been extensively investigated in psychology, neuroscience and computer science to determine which portions of an image would grab the major attention of the HVS. [PERSON] et al. [75] introduced the visual saliency induced (VSI) index, a simple but highly effective full-reference IQA approach based on VS.