# Analysis of Blur Measure Operators for Single Image Blur Segmentation
## 1 Introduction  
Blur in images is considered as an undesirable effect because it leads to the loss of the necessary details required for the scene interpretation. Automatic detection of blurred and sharp pixels in an image and their classification into respective regions are very important for different image processing and computer vision applications [1]. The benefits of blur segmentation are exhibited in many applications including but not limited to object detection [2], scene classification [3], image segmentation [4], background blur magnification [5], depth of field extension [6] and depth estimation [7; 8]. Blur detection and segmentation for a single image without any prior information is a challenging task.  
For blur detection and segmentation, a large number of techniques have been proposed in the literature [9; 10; 11; 12; 13; 14; 15; 16; 17]. The blur segmentation techniques comprise of a number of key steps. The first and the fundamental step is to employ a blur measure (BM) operator which measures the level of blurriness associated with the pixels or regions of the image and realizes discrimination between sharp and blurred pixels or regions of the image is realized by applying an operator, known as blur measure (BM) operator. In the second step, the features computed through the BM operator(s) are provided to a classifier for segmentation of the blurred and sharp regions. Finally, various postprocessing techniques are deployed for improve the initial segmentation results. In each of the techniques, the quality of the underlying blur measure operator plays a distinguishing role. Recently, [PERSON] et al. [18]reported that the existing techniques perform well on images with certain properties however, their performance is deteriorated in real images. As different blur measure operators recognize and exploit different features of the input blurred image, it is difficult to determine which operator has the best performance under which conditions. Additionally, due to the diversity in the subsequent steps of segmentation process, it becomes unjustifiable to compare the output of one BM operator with that of another one.  
In this paper, we aim for a comprehensive study to analyze the performance of the state-of-the-art blur measure operators used to detect and segment blurred and sharp regions of the image. In our study, the performance of recently suggested BM's is investigated. In addition, a number of operators which have also been studied in this work were originally developed for autofocus and shape from focus (SFF) techniques [19]. They have been brought into this study because their working principle is similar to that of blur measure operators i.e., each of them can distinguish between sharp and blurred regions of the image by manifesting different responses for these different regions. For experiments, we have considered a dataset of real-world blurred images with the diverse levels and types of blur. A number of experiments have been conducted on the sample images for qualitative and quantitative results which have been presented accordingly. The statistical evaluation of different blur measure operators helps to understand their prospective performance attributes.  
The rest of the paper is organized as follows. The Section 2 sheds light on the related work done in the past. Section 3 explains the methodology for the blur segmentation, including image data sets, blur measure operators and the evaluation measures. Experimental results and analysis are presented in Section 4. Finally, the work is concluded by Section 5.