# Analysis of Blur Measure Operators for Single Image Blur Segmentation
## 4 Results and Discussion  
In this section, we describe a number of experiments that have been conducted aiming to analyze the comparative performance of blur measure operators. First of all, we intend to demonstrate that blurred and sharp regions of an image produce clearly distinct responses when a suitable blur measure operator is applied to the image. The essence of a well crafted blur measure operator is that it can help clearly differentiate between blurred and sharp regions. For this objective, two neighborhood windows each of size 30 \(\times\) 30 have been selected as shown in Figure 4a for the third image of Figure 1. The red colored window patch (A) is on the defocused area while the green window patch (B) is placed on the focused region, and these areas have been selected to reveal their potential difference with respect to blur measure operators. Figure 4b displays the image responses when arbitrarily chosen five blur measure operators DER05, DER10, STA01, STA04 and MIS03 have been applied on these selected areas. It clearly indicates that pixels in the blurred area yield small values (black) of blur measures as compared to those of sharp areas. (c) and (d) give the numerical values of blur measurements for the vectorized pixels of the blur and sharp areas, and the marginal gap between them can be clearly identified. More specifically, the blur measures for the pixels in the blurred (defocused) area are less than 0.1 while they all are greater than 0.2 in the case of sharp (focused) area. Moreover, blur measures in the sharp area manifest a lot of fluctuations depicting the high frequency content there.  
Regarding the blur detection and segmentation, all of the 32 blur measure operators described in Table 1 have been applied on the randomly selected images of the data set mentioned in Section 3.1. To test each of the blur measure operator under the same framework, the same blur segmentation methodology of Section 3.2 has been followed for all. Even then, the difference in image quality, degree of blur, content and nature of the image can favor some operators. Therefore, the results for images from defocus and motion blur are presented separately. Both qualitative and quantitative results are drawn and shown accordingly. The three scales chosen for local neighborhood patches were \(11\times 11\), \(15\times 15\) and \(21\times 21\) pixels. The threshold \(T_{seg}\) for the binary classification of blur map at the last step of blur segmentation has been taken as the mean of the final blur map, i.e., \(T_{seg}=\frac{1}{W\times H}\sum_{i}\tilde{n}_{i}^{(3)}\), where \(W\) and \(H\) are the dimensions of the final blur map. Firstly, in the qualitative analysis, we present the blur maps obtained by applying the mentioned blur measure operators on the images. These blur  
Figure 4: Blur measure operators’ responses for the blurred and sharp areas. (**a**) One neighborhood window selected for the blurred and sharp areas each. (**b**) Imagery responses of the neighborhood windows for five blur measure operators. (**c,d**) Display the blur measures for vectorized pixels in case of blur and sharp window patches respectively.  
maps when compared with the ground-truth give a fair idea about the competency of these operators. In the second case, for quantitative analysis, the evaluation measures mentioned in Section 3.3 have been used to evaluate the relative performance of blur measure operators. A number of experiments have been conducted for this and their results have been presented accordingly. The rankings of the performance of blur measure operators, as learnt through the experiments, are also mentioned for comparative analysis.