# An Improved Method for Evaluating Image Sharpness Based on Edge Information
## 2 Principle and Design of the Sharpness Evaluation Method
### Analysis of Edge Width
#### 2.3.2 Solution of Edge Width  
To calculate the edge width of an edge point, it is necessary to find the grayscale extreme points at the two ends closest to the edge point in the edge direction [10]. When the grayscale values of one side are larger than those of the other side, the maximum value point of the side with the larger grayscale values and the minimal value point of the side with the smaller grayscale values are selected as the start and end points of the edge width;  
Figure 6: Determination of edge direction: (**a**) \(-45^{\circ}\) edge direction; (**b**) horizontal edge direction; (**c**) vertical edge direction; (**d**) \(-45^{\circ}\) edge direction.  
Figure 7: Typical edge direction diagram: (**a**) vertical edge direction; (**b**) \(45^{\circ}\) edge direction; (**c**) \(-45^{\circ}\) edge direction; (**d**) horizontal edge direction.  
the distance between the two end points is the corresponding edge width of the edge point. Figure 8 shows the variation of the grayscale values in the 257 th row along the horizontal direction of the reference image \"parrots\" in the LIVE database [17] after Gaussian blurring. As can be seen in the figure below, the edge widths of the edge points P1 and P3 are P2-P2\({}^{\prime}\) and P4\({}^{\prime}\)-P4, respectively.  
In this paper, the above rule is also followed when calculating the edge width. The upper and lower rows of the images in Figure 9 are \"parrots\" and \"planes\" in the Gaussian blurred images of the LIVE database, respectively. According to the method in this paper, the edge widths of the edge points in the upper and lower rows of the images were calculated separately; the calculation results are shown in Figure 10.  
Randomly select 100 edge points of \"parrots\" and \"planes\" and divide these 100 points into equal parts by 360\({}^{\circ}\) so that each edge point corresponds to an angle within 0-360\({}^{\circ}\), which is the polar angle corresponding to that edge point. Then, the edge width of the edge point is selected as the corresponding polar diameter; so, the edge point with a certain edge width can be mapped to the polar coordinate system. Plot (a) and plot (b) in Figure 10 correspond to the upper and lower rows of images in Figure 9, respectively (each row of images in Figure 9, from left to right, can be numbered as a, b, c, and d). According to the definition of points in the polar coordinate system, the more the line is located outside, the more edge points with large edge widths will be in the image corresponding to the line. It can be clearly seen from Figure 10 that the pink line is the most inward, the blue line is outward, the yellow line is further outward, and the green line is the outermost, which correspond to the fact that the two rows of images in Figure 9  
Figure 8: Parrots’ grayscale value change curve.  
Figure 9: Gaussian blurred images.  
left to right, indicating that the edge width calculation method proposed in this paper can adequately reflect the blurring degree of images.