# An Improved Method for Evaluating Image Sharpness Based on Edge Information
## 3 Experimental Results and Analysis
### Subjective and Objective Consistency Experiment  
The above experiments fully proved that the sharpness evaluation method proposed in this paper can well determine the blurring degrees of images with different contents. However, the consistency between the evaluation method in this paper and the subjective evaluation has not been verified. Therefore, we verified the subjective and objective consistency of the proposed method by evaluating the sharpness of all 145 Gaussian blurred images in the LIVE database. In addition, it is important to note that all 145 images above have subjective evaluation DMOS values.  
The sharpness evaluation values and DMOS values of these 145 measured images were fitted using Equation (7) [18] where \(\text{Value}_{i}\) is the sharpness evaluation value, \(\text{DMOS}_{i}\) is the corresponding subjective evaluation value, and \(\beta_{1}\)-\(\beta_{4}\) are the model parameters that need to be fitted.  
\[\text{DMOS}_{i}=\beta_{2}+\frac{\beta_{1}-\beta_{2}}{1+e^{-(\text{Value}_{i}- \frac{\beta_{3}}{\beta_{4}})}} \tag{7}\]  
Figure 21 shows the fitting curves between the evaluation values of the three evaluation methods and DMOS values. The model parameters of the fitting curve of the proposed method are \(\beta_{1}=73.14\), \(\beta_{2}=17.12\), \(\beta_{3}=10,150\), and \(\beta_{4}=1406\). The model parameters of the fitting curve of the reference [14] method are \(\beta_{1}=64.56\), \(\beta_{2}=-1.817\), \(\beta_{3}=1.857\), and \(\beta_{4}=-0.3279\). The model parameters of the fitting curve of the Tenegrad method are \(\beta_{1}=29.22\), \(\beta_{2}=227.7\), \(\beta_{3}=-1716\), and \(\beta_{4}=-1811\).  
After obtaining the fitted model parameters of the above three methods, the subjective evaluation DMOS values of the Gaussian blurred images in the LIVE database could be  
Figure 21: Fitting curves of three methods: (**a**) the fitting curve of proposed method; (**b**) the fitting curve of reference [14] method; (**c**) the fitting curve of Tenegrad method.  
predicted by Equation (7). The relationship between the predicted subjective evaluation value \(\text{DMOS}_{pred}\) and the subjective evaluation value \(\text{DMOS}\) is shown in Figure 22.  
As can be seen in Figure 22, the method of this paper was in better agreement with the subjective evaluation. To illustrate this point more fully, five additional technical indicators, which are widely used to measure the performance of the evaluation methods, were calculated in this paper. These five indicators are the root mean square error (RMSE), Pearson linear correlation coefficient (CC), mean absolute error (MAE), Spearman rank-order correlation coefficient (ROCC), and outlier ratio (OR). The higher the ROCC values, the more obvious is the trend that the predicted evaluation value of the model increases with the increase in the subjective evaluation value. Thus, the ROCC value is used to show the predictive monotonicity of the model; the larger the value is, the better the model is. A smaller OR value means that the model has better prediction ability for images with different contents, which is used to show the predictive consistency of the model; the smaller the value is, the better the model is. The performance evaluation of the three methods is shown in Table 3. It is obvious from the table that the evaluation method proposed in this paper is better than the other two methods in the above technical indicators. This proves that the evaluation method proposed in this paper can well satisfy the requirement that image sharpness evaluation should be independent of image content and has high consistency with subjective evaluation.  
Figure 22: The relationship between predicted subjective evaluation values and subjective evaluation values: (**a**) proposed method; (**b**) reference [14] method; (**c**) tenegrad method.