# 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 subjective and objective techniques are the two most used techniques for evaluating image quality. In the subjective assessment approach, a number of observers are chosen, and then they are presented a set of photographs. Following that, they are asked to judge image quality based on their assessment. Human inspection is used to give a rating to each image depending on its quality [72]. The objective image quality assessment (IQA) approaches rely on automated algorithms to assess image quality without the need for human intervention [72]. Since subjective assessment techniques differ from person to person, small distortions in the final stitched image cannot be detected. As a result, we employed objective IQA techniques to compare the quality of stitched images in this research. The quality of stitched images generated using different pairs of feature detectors and descriptors was compared based on objective IQA metrics. The objective image quality metrics utilized in this study to assess the quality of stitched images are listed below. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **Detector or Descriptor** & **Year Proposed** \\ \hline GFT & Detector & 1994 \\ SIFT & Detector + Descriptor & 1999 \\ MSER & Detector & 2004 \\ FAST & Detector & 2006 \\ SURF & Detector + Descriptor & 2006 \\ Star (CENSURE) & Detector & 2008 \\ BRIEF & Descriptor & 2010 \\ DAISY & Descriptor & 2010 \\ AGAST & Detector & 2010 \\ BRISK & Detector + Descriptor & 2011 \\ ORB & Detector + Descriptor & 2011 \\ FREAK & Descriptor & 2012 \\ KAZE & Detector + Descriptor & 2012 \\ AKAZE & Detector + Descriptor & 2013 \\ MSD & Detector & 2014 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Feature detectors and descriptors proposed over the years. Peak Signal to Noise Ratio (PSNR) is a metric for measuring how different two images are. The PSNR of comparable pixel values is expressed as (Equation (3)):  
\[\mathrm{PSNR}=\frac{10\log_{10}(\mathrm{max}(G(i,j),O(i,j)))^{2}}{\mathrm{MSE}} \tag{3}\]  
where G (i, j) and O (i, j) represent the (i, j)th pixel values in the input image and stitched image, respectively. MSE is the mean square error, which is defined as:  
\[\mathrm{MSE}=\frac{\sum_{i}\sum_{j}(G(i,j)-O(i,j))^{2}}{\mathrm{N}}\]  
where N is the total number of pixels in each image. A lower MSE value indicates that the difference between two images is low, thus resulting in higher PSNR values. The SSIM (Structural Similarity) index is used to determine the similarity of two images. The image that is being assessed is known as the target image, and the image that is used to compare the quality of the target image is known as the reference image. The SSIM index meets the requirements of symmetries, boundedness and having a unique maximum. The luminance measurement is assumed to be qualitatively consistent with [PERSON]'s law, which specifies that the visible change in luminance in the HVS is roughly proportional to the background luminance. Similarly, the contrast measurement follows the HVS by focusing primarily on the relative difference rather than the absolute difference in the contrast. The final SSIM index is a combination of these two values, as well as a structural similarity component determined using brightness and contrast values [73]. SSIM between two images x and y is described as follows (Equation (4)):  
\[\mathrm{SSIM}(\mathrm{x},\mathrm{y})=\frac{\left(2\mu_{x}\mu_{y}+C_{1}\right) \left(2\sigma_{xy}+C_{2}\right)}{\left(\mu_{x}^{2}+\mu_{y}^{2}+C_{1}\right) \left(\sigma_{x}^{2}+\sigma_{y}^{2}+C_{2}\right)} \tag{4}\]  
where \(\mu_{x}\) and \(\mu_{y}\) represent local means for x and y images, respectively. \(\sigma_{x}\) and \(\sigma_{y}\) represent standard deviations, and \(\sigma_{xy}\) is the cross-covariance for x and y images. The smaller the difference between the structure of x and y, the higher the SSIM index value. If there is no structural difference, SSIM (x, y) = 1.